ACCRETION PROCESSES in ASTROPHYSICS Xxist RENCONTRE DE MORIOND MORIOND ASTROPHYSICS MEETING Les Arcs - Savoie - France, March 9-16, 1986

ACCRETION PROCESSES IN ASTROPHYSICS XXIst RENCONTRE DE MORIOND MORIOND ASTROPHYSICS MEETING Les Arcs - Savoie - France, March 9-16, 1986

ACCRETION PROCESSES ASTROPHYSICS IN

ISBN 2-86332-043-2

EDITIONS FRONTIERES B. P. 44 91190 GIF SUR YVETTE - France

Printed in Singapore by Kim Hup Lee Printing Co. Pte. Ltd. PROCEEDINGS OF TIIE

TWEN TY-FIRS1W CONTRE DE MORIOND ASTRO i1"SICSMEETING

Les Arcs - Savoie - France, March 9-16, 1986

N\; I "-··I , l �) . ., ACCRETION PROCESSES IN ASTROPHYSICS

Edited by J. AUDOUZE J. TRAN THANH VAN

EDITIONS FRONTIERES ,. ! .. The Astrophysics Meeting of the XXIst Rencontre de Moriond :

"ACCRETION PROCESSES INASTROPHYSICS"

was organized by

J. Audouze J. Tran Thanh Van

with the active collaboration of

C. Cesarsky P. Crane T. Gaisser D. Hegyi C. Norman and J. Truran

All rights reserved. This book, or parts thereof, may not be produced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. v

AVANT-PROPO S

La sixieme Rencontre de Moriond en Astrophysique s'est deroulee aux Arcs du 9 au 16 Mars 1986 et a porte sur les processus d'accretion en Astrophysique. Ces processus constituent indeniablement l'une des sources d'energie les plus puissantes puisqu'ils doivent etre a l'origine de phenomenes energetiques aussi differents que la forte luminosite des quasars,

!'emission des sources X, !'explosion des novae et des supernovae de type I, les sursauts X et gamma.... Ces manifestations energetiques sont etudiees dans ce livre d'un point de vue theorique et observationnel. On lira en particulier les nouveaux developpements du detecteur gamma "oeil de mouche" ainsi que la remise en cause de la detection de Cygnus X 3. Cette sixieme rencontre a connu le succes des sessions precedentes grace a l'organisation irrempla�able de J. Tran Thanh Van, les conseils judicieux du comite d'organisation scientifique en particulier de C. J. Cesarsky et de T. Gaisser. Je tiens a exprimer ma reconnaissance a Mesdames Monique Furgolle et Marie-Claude Pantalacci qui ont assure la preparation materielle

(MCP) et l'organisation sur place de cette rencontre (MF).

Jean AUDOUZE lnstitut d'Astrophysique de Paris (CNRS) et Laboratoire Rene Bernas - France

vii

FOREWORD

The sixth Moriond Rencontre in Astrophysics has taken place at Les Arcs from 9 to 16 March 1986 and has been devoted to the accretion processus in Astrophysics. These processes are indeeoi one fo the most powerful energy sources since they trigger different energetic phenomena like the huge luminosity of QSOs, the X ray source emissivity, the nova and the type I supernova explosions, the gamma and X ray outbursts.... The energetic processes are studied in this book both theoretically and observationnally. The reader will consult in particular the papers dealing with the recent developments of the "fly's eye" detector such as the discussion of the relevance of the observational data concerning Cygnus X 3. This sixth Moriond Astrophysics Rencontre has been most

successfull as the previous meetings of that sort thanks especially to the superb organization led by J. Tran Thanh Van, the wisdom of the scientific organization committee especially that of C. J.

Cesarsky and T. Gaisser. Finally, I would like to express my recognition to Mrs Monique Furgolle and Marie-Claude Pantalacci

who undertook the material preparation of this meeting (MCP)

and the local organization of it (MF).

Jean AUOOUZE Institut d'Astrophysiquede Paris (CNRS) et Laboratoire Rene Bernas- France

CONTENTS

ELBERT J. W. "Ultra-high-energy gamma rays observed

by the fly's eye" 1

SVOBODA R. "Recent results from the IMB detector and

prospectus for the future" 17

EICHLER D. "Theoretical implications of reported

ultrahigh energy detections of binary

X-ray sources" 27

WEEKES T. C. "Cygnus-X-3: source of very high energy

gamma rays" 37

WEEKEST. C. "Very high energy gamma-ray observations" 57

CHARDING. "Cygnus X-3 at high energies : a critical

review" 63

GAISSER T. K. "High energy neutrinos in close binary stars" 77

DERMER Ch D. "Neutron and antineutron production in

&RAMATY R. accretion onto compact objects" 85 x

FRIEDJUNG M. "Effects of a supercritical wind on nova

observations" 99

CANAL R. "Mass-accretion effects on white dwarf

interiors" 109

HILLEBRANDT W. "Nucleosynthesis in he-flashes on accreting

white dwarfs" 125

NOMOTO K. I. "Collapse of accreting carbon-oxygen white

dwarfs induced by carbon deflagration

at high density" 137

CHAKRABARTI S. "Nucleosynthesis in the neighborhood

of a black hole" 155

HEGYI D. J. "Black holes and disk dark matter" 169

ATTEIA J. -L. "Cosmic gamma-ray burst observations" 177

HAMEURY J.M. "A model for soft X-ray transients" 195 ULTRA-HIGH-ENERGY GAMMA RAYS OBSERVED BY THE FLY'S EYE

J.W. Elbert, R.M. Baltrusaitis, J. Boone, R. Cady, G.L. Cassiday, R. Cooper, B. Dawson, B.E. Fick, P.R. Gerhardy, K.D. Green, C.P. Lingle, E.G. Loh, Y. Mizumoto, P. Sokolsky, P. Sommers, D. Steck, and S. Wasserbaech. Physics Department, University of Utah, Salt Lake City, UT

ABSTRACT

Besides observing tracks of distant 1017 to l020ev air showers, the Fly's Eye can observe Cherenkov flashes from nearby 1013 to 1016eV showers. These have been used to search for ultra-high-energy point sources. Weak evidence of a signal has been observed from the vicinity of the Crab pulsar. Signals from Cygnus X-3 and Hercules X-1 have been detected by observing periodicity in the data. In the case of Cygnus X-3, spectral information has also been obtained. Evidence was obtained for sporadic emission from Cygnus X-3 including emission near phase 0 of the hour period. Hercules X-1 was observed at a time when the X-ray beam 4.8was inferred to be absorbed by obscuring matter. The Hercules X-1 signal requires the acceleration to occur near the pulsar in the binary system. The production of such energetic �-rays from Hercules X-1 is a challenge for acceleration models. 2

I. INTRODUCTION

The observations to be described below involve primarily Cherenkov light

produced by cosmic ray air showers. This light is intense, but produced only at small angles with respect to the direction of motion of the shower.

Consequently, the showers observed by Cherenkov light are relatively near the detector, but are also near the lower end of the energy scale of the Fly's

Eye. In contrast, scintillation light is emitted less intensely, but isotropically.Very large showers can be seen at large impact parameters, R p, from the detector by means of scintillation light.

The Fly's Eye has been described previously in l] the published Moriond proceedings , so only a brief description of it will be given here. The concept of a Fly's Eye detector was originally 2l developed by Greisen's group at Corne11 . The ' Utah Fly's Eye consists of two units, Fly's Eye I \ and Fly's Eye II. Fly's Eye II is not involved in the observations reported here and will not be

discussed further. Fly's Eye I (simply called called the Fly's Eye in the following) consists of mirror units located on 67 top of a small mountain at Dugway, Utah, U.S.A. Each mirror unit has a 1.5 m diameter f/l. mirror reflecting light onto a cluster of 12 or 14 photo multiplier tubes (PMT's). The PMT's have hexagonal light collectors, with an aperture of almost degrees. Each mirror faces a separate part of the sky 6 and the assemblage of 870 PMT's images nearly the entire sky. If one imagines a planetarium showing the field of view of all the mirror units, the display would be like that shown in the drawing. The view is shown in the direction of the north celestial pole. A dashed line shows the horizon. The dotted line shows the trajectory of Cygnus X-3 through the apparatus.

For the 1-ray studies reported here, the trigger for storing data was one or more PMT's passing over an amplitude threshold. Triggering coincidence requirements ranged from 1 to PMT's. When an event triggered the apparatus, 6 the identities of all PMT's which passed over threshold were recorded, along with the relative times (SO ns accuracy) and the values of the amplified PMT pulse integral. Until 1983, the mode of operation in which data were taken from small showers for �-ray studies was inconsistent with the normal operation of the

Fly's Eye in which tracks from distant air showers were recorded. Before 1984, only small periods of time were devoted to the collection of Cherenkov flash data. After August 1984, a PMT trigger for Cherenkov flashes was used 6 3

routinely with the normal operation of the Fly's Eye until the summer of 1985.

(See Table 1.) During a period of modification of the Fly's Eye in the summer

Table 1 Summary of Fly's Eye 1-Ray Observations Month Year Hours Trigger Signals Dec. 1980 7.9 3 tubes Crab, maybe Feb. 1981 26. 7 2 tubes No Crab signal

July 1983 25.3 6 tubes Her X-1, Cyg X-3 (both periodic) Aug. 1984 20. 1 6 tubes Cyg X-3 not seen Sept. 1984 42. 4 6 tubes Cyg X-3 not seen Oct. 1984 44.7 6 tubes Mostly unanalyzed Nov. 1984 16.5 6 tubes Dec. 1984 31. 8 6 tubes Jan. 1985 58.0 6 tubes Feb. 1985 42. 4 6 tubes March 1985 56. 0 6 tubes April 1985 16.3 6 tubes May 1985 tubes 6

June 1985 56. 2 1 tube Cyg X-3 (per., sporadic) July 1985 9. 4 1 tube Cyg X-3 (periodic) Aug. 1985 62. 8 1 tube Cyg X-3 (periodic)

Oct. 1985 14.3 tubes Cyg X-3 not seen 2

of 1985, high rate Cherenkov flash data runs were carried out with only 9 or 10 mirrors in operation. These mirrors were chosen along the path of Cygnus X- 3. In October, 1985, following the report of a very large radio outburst in

Cygnus X-3, a short Cherenkov flash run was performed to search for very high fluxes from that system. Since that time Cherenkov data runs have not been

performed.

The table summarizes the results of the different data runs. The studies

of the Crab vicinity are covered in section III. The results of a PeV 1-ray

sky survey are given in section IV. The observations of Cygnus X-3 and

Hercules X-1 are given in section V and VI, respectively.

II. PROCEDURES USED IN THE 1-RAY OBSERVATIONS

Before proceeding to the discussion of specific studies, some discussion of the analysis procedures of all the data is desirable. The direction of a

Cherenkov flash is given by the center of the field of view of the PMT with

the largest signal. The total number of photoelectrons produced in a shower is

obtained by adding the responses of PMT's which triggered within a shower.

This quantity will be used in the spectral analysis described in section V,

below. 4

The assignment of energies to individual showers is not precise in the results presented here because the conversion from detected light to shower energy depends on the impact parameter of the shower. The presence of a ?-ray signal is observed as an excess in the number of showers above the number of showers expected from the nearly isotropic cosmic ray background. The expected number of cosmic ray showers is obtained using the data rates obtained by PMT's when they viewed regions outside the target region. The expected number of events from a PMT when it is in the target region is the product of the length of time the PMT was in the target region times the rate of events obtained when the PMT was outside the target region.

The data used in the ?-ray studies were taken on clear, moonless nights. The rate of events in the entire detector has been observed for each night of observation. The rates were stable, typically varying by less than 2% per hour. A small correction is made to the expected number of events in a PMT to adjust for the rate of events in the entire apparatus. This is done in order to take into account slow variations in atmospheric transparency.

For the Crab Pulsar, Hercules X-1, and Cygnus X-3, the standard directions obtained from radio and X-ray observations were used. In all these studies, the bin size was fixed as a 7 degree square which was based on the estimated angular resolution of the system. For Hercules X-1 and Cygnus X-3, the "standard" ephemerides were used for the 1.7 day and 4.8 hour periods. For Her X-1, the X-ray period from the most nearly simultaneous observations was used to test the statistical significance of the -1.24 second periodic signal. Where arbitrary cuts were made in selecting data, the number of tries needed to select the data subset was used in evaluating the statistical significance of the result. Consequently, the quoted confidence levels for the results are thought to be quite realistic.

III. CRAB PULSAR VICINITY RESULTS 31 A report by Dzikowski et al. , presented at a meeting in Bologna in June

1980, described a large flux of PeV (1 PeV-10 15 eV) ?-rays from the direction of the Crab Pulsar. Our own rough estimates showed that the Fly's Eye might be able to detect such a flux in a relatively short running time.

A special Fly's Eye run was done on 1980 December 10 (UT) to search for a possible signal in the vicinity of the Crab Pulsar. As can be seen in Figure 1, this first attempt yielded a 3.lo excess of events in the direction of the Crab Pulsar. Plans to continue these studies in 1981 January failed because of a very unusual long period of foggy weather. In 1981 February, data were collected in three nights of good weather. As can be seen from the figure, no signal was detected in this data. 5

Figure 1. Excess showers in the Crab Pulsar vicinity. Although in dicated on Dec. 9,19 80 (local time), no signal was observed in February, 1981.

11980 DECEMBER 9 DATA) 00

�__:..:.::...:.:___.=..::..:..:==-=------, ICOMBINEO 1981 FEBRUARY DATA) 50 • m • • 0 " � 4 r·� 40 0 x m 00 � 0 --- '� 0 L 30 - f • __ _ WIr: -I "• • l20 l �------=-= , , I I I ' ' � 20 z z 4.15 15.0 15. 5 e.o e.s "''<3HT ABCEN810N I 10 15.0 15.15 hours) L--'---'----'---'---�-�4.5 e.o e.s RIGHT ASCENSION I hour al

The integral flux above 1015 eV was 2.1 0.7 x 10 12 cm s for the ± December data. The confidence level that a signal was present in that data was 97%, considering the number of tries in analyzing the December and February data. The lo upper limit of the flux from the February data was 5.3 x 10 _13 cm _2 s _1 Taken together, the two results give weak evidence for a variable PeV 7-ray flux from the Crab Pulsar. The accuracy of the clock used in taking this data was only about 1 second and no periodicity studies of the Crab were possible.

The spectrum of TeV-PeV fluxes of the Crab is shown in the drawing

displayed below. (The sources of the data are identified in Ref. 4. ) Some of

the data were quoted as both short

term peak fluxes and longer term Crab Vicinity Y-Roy Spectrum average fluxes, and the levels are

connected by dashed lines. The Fly's Eye fluxes from 19 80 December are represented at three energies by filled-in triangles. These are connected to upper limits from the 1981 February data by dashed lines. The February data also yielded an

upper limit at 10 16 eV of

10-15 :-:--11 -�:-��-12 13 -'--14--'-- 15 -'--16-_J 17 _14 2 1 10 10 10 10 10 10 10 4.5 x 10 cm s , which nearly overlaps a value obtained by the Ey CeV) 5 J 16 Akeno Group • The 10 eV observation by the Lodz group is

represented by a small circle. 6

The data suggest that a rather flat spectrum may exist in the TeV to PeV energy range . The situation is far from settled because of the rather poor statistical significance of the PeV data and the difficulty of dealing with apparently sporadic fluxes. Since the Crab Pulsar's period was not detected in the PeV observations, the possible signal is not necessarily produced by the Crab Pulsar. More details of the Crab Pulsar observation by the Fly's Eye are given in Ref.4.

IV. NORTHERN HEMISPHERE SKY SURVEY Data from 1980-1984 were combined to perform a search for point sources and to set upper limits for fluxes of PeV �-ray so urces throughout most of the northern hemi sp here sk y. The data were taken in 122 hours of operation between 1980 December and 19 84 September. A total of 82,898 showers of amplitudes corresponding to more than 20,000 photoelectrons were studied. The energy threshold was near 1 PeV. The data were binned in 7.2 degree square overlapping bins with bin centers located on a degree square grid. All 3.6 right ascension values and most bins between declinations 0 and 72 degrees were included in the survey. In each bin the observed number of showers was compared with the expected number using the method described in Section II. The results of the survey were not dramatic. The distribution of probabilities of the observed numbers occurring by chance, given the expected numbers, was approximately as expected from a Poisson distribution. None of the bins had a probability as small as would happen less than 10% of the time in a sample of over 2000 bins. No point sources were detected by the survey. Flux upper limits were obtained at the 95% confidence level for all the bins. Most of these limits fall in the range 10 _13 to 10 12 cm 2 s More details and a map of the limits obtained in different angular regions are given in Ref. The survey demonstrates that, for the current sensitivity of 6. the Fly's Eye, searches for periodicity in the data are usually needed in order to detect signals. The survey was also reassuring in that no systematic problems showed up which would produce significant disagreements between the observed and expected numbers in any of the bins. This supports the statistical assumptions used in determining the confidence level of signals detected in the data set.

V. CYGNUS OBSERVATIONS X-3 Searches for a periodic signal from Cygnus have been done in three X-3 major data sets. The triggering conditions were different in the three data sets and they will be treated separately. 7

A. THE 1983-1984 DATA Cherenkov flash data from 1983 consisted of 25 hours during 5 nights of July. During 19 84,Cygnus X-3 was observed fo r 20 hours during 3 nights of August and fo r 42 hours during 5 nights of September. The amount of Cygnus X-3 data in later months of 1984 was very small. As in the sk y survey data reported in the previous section, showers were accepted with signals of at least 20,000 photoelectrons. The trigger re quirement fo r this data was 6 PMT's. Since the results fo r 1984 differed from those of 1983, th ey will be discussed separately. There were 256 events in the Cygnus X-3 direction in the 1983 data. The expected number was 220.5 5. 4. The uncertainty results from the ± effect of fluctuations in (ol (1983 Data) determining the expected number. The • 40 � excess amounts to 2.2a. In Figure • � 30 2a, th e data are plotted in

0 20 different phase bins of the 4.8 hour � period of Cygnus X-3. The van der � 10 z Klis and Bonnet-Bidaud epheme ris is 0 7 1 0.0 0.2 0.4 0.6 08 10 used , including the time

(bl derivative term. In each bin, the histo gram shows the observed number of events and the expected number is shown by the diffuse line. Because the exposure is not the same fo r different phase bins and because of variations of PMT rates due to

0.2 0.4 0.6 0.8 LO zenith angle effects, etc., the

(c) (1984 Do ta) expected numbers are not the same in 30 . each bin. There is a significant � • discrepancy between the expected and � 20 observed number in the th ird bin. 0 � " 10 There are 32 observed events and r; z 16.9 expected. Including the effect 0 0.0 0.2 0.4 0.6 0.8 10 of the uncertainty in the evaluation

PHASE of the expected number, this amounts Figure 2. Cygnus X-3 data from 1983 to a 3.Sa excess. (a and b) and 1984 (c) , as a function In Figure 2b , the excess is plotted of the 4. 8 hour phase . Solid line- data, dashed line-expectation. as a number of standard deviations as a function of phase. The excess 8

8 occurs in the same phase bin as that observed by Lloyd-Evans et a1. . When l 9 Samorski and Stamm use the van der Klis and Bonnet-Bidaud ephemeris, their l data are also peaked near phase 0.2. The flux implied by the 1983 Fly's Eye

- - data, averaged over the entire phase interval, is 3.2 1.2 x 10 13 cm 2 s l ± The confidence level that a si gnal from Cygnus X-3 was present in the 1983 data was estimated to be 99.6%. The 1984 results are shown in Figure 2c. No significant excess is present in any phase bin. In the phase interval 0.2-0.3, the 95% confidence level flux upper limit is 2.0 x 10 13 cm_2 s _1 This is not inconsistent with the result from 1983. The 1983 and 1984 Cygnus X-3 ob servation, together with the northern hemisphere sky survey, are discussed in more detail in Ref. 6. B. THE SUMMER 1985 DATA During June, July, and August 1985, a sp ecial data run was done to observe Cygnus X-3. A group of 10 mirrors observed Cherenkov flashes from sm all air showers exclusively. The mirrors to be used were selected along the path of Cygnus X-3. They collected showers at a rate of about 4 Hz. This higher rate was obtained by allowing a single tube to provide a trigger. The threshold was left fixed at a higher than normal value to control the data rate so that the dead time was not large and to keep the data storage re quirements reaso nab le. The relaxed trigger re quirements allowed showe rs to be accepted at energies above about 10 13 eV. During the run, about 1.8 million events were accepted during 128 hours. The running time totals were 56.2, 9.4, and 62.8 hours in June, July, and August, re spectively. The relatively low threshold energy resulted in a greater dynamic range of the number of photoelectrons in sto re d showers. Consequently, a significant amount of sp ectral information was available in this data set. As mentioned earlier, the observed number of photoelectrons can be translated into a shower energy if the zenith angle and the impact parame ter of the shower are known. The Fly's Eye shower info rmation includes the zenith angle,but not the impact paramete r. As a rough shower energy estimate, the energy is evaluated at the known zenith angle assum ing that the impact parameter is 50 meters. Since this only gives an approximate energy value, showers are grouped together in decade-wide energy intervals. To avoid missing signals because of arbitrary energy interval boundaries, interval centers are taken in half-decade steps. With this choice, four energy intervals cover the range from 10 13 to 10 15. 5eV, as shown in Table 2. 9

Table 2. Summer 1985 Cygnus X-3 Spectral Data E Range Observed Expected #a Excess eV in %

1013-1014 28,184 28,257 .2 -0.4 -0.3 1013 ·5-1014 . 5 15,376 15,144.5 1. 8 1. 5 1014-1015 4,970 4,7 84.3 2.6 3.9 1014. 5-1015.5 868 785. 8 2.8 10.4

13 14 The table shows that, in the interval from 10 to 10 eV, there is agreement within 0.3% between the expected and observed number of events. In ,6 the bins above 10 13 eV, there is an excess of observed over expected numbers, with the excess increasing to 2.9a in the highest energy bin. The excess, therefore, appears as a flatter pulse he ight distribution than expected.

200 .--�� (a) 10'3

(bJ 1013·$<£< 101""eV 200 150 150 100 100 50 50 ...� Of-,f-���-+�-+--��-¥-�.)_ ...� ·50 z ·50 z ::> ::> 8 -100 8 -100 � � � 150 � 150 w w u 100 u x x 100 w 50 50 01-�-+��.__,,�_,_��-l----" ' +� ·50 Oh--lr-?c-l>--"._--4'�� "--�-+��./,9- ?-- -

50 40 40 30 20 m t 10 t Oh--'-±-'L"f'---'---'-+-'--"'--<>...Q.� .'l--9.---�-+_j_j? '---I ��01-1 '-----l'-�+-� �--4�+-��--+�� -10 t -10 �-'-..L-�--'��"-��-'-��__J -20 �-'-��--'��"-��--'--��__J 0.0 0.2 0.4 0.6 0.8 1.0 00 0.2 0.4 0.6 0.8 10

4.8 HOUR PHASE 4.8 HOUR PHASE

Figure 3. Summer of 1985 Figure Like Figure 3, 4. data from Cygnus X-3. but with 20 phase bins. 10

In Figures 3 and 4, the excess of ob served (a) 10135 < E < 101.i5eV over expected counts is plotted in 10 and 20 inte rvals of th e Cygnus X-3 4.8 hour period for the four energy intervals. In the higher

Of---+------+--+--1----1 energy bins (parts b-d) some excesses are -1 indicated near phase inte rvals 0.2-0.3 and -2 0.65-0.7. 5, w - 3 - __L _ In Figure th e excesses are 1- ---'----'----L_ ___, 1014 < E < 1015 eV replotted in units of a for Figures 3b and � (b) 4c. This emphasizes a 3.7a peak in the phase interval 0.2-0.3 (p art a) and a 3.4a peak in the phase interval 0.65-0.70 (part b) . There

-1 is evidence for periodic emission in th is

-2 preliminary data. Besides the statistical -3'-----'----'------"L_---'------l 0.0 0 2 0 4 0.6 0.8 1.0 significance of th e peaks, the fact th at the 4.8 HOUR PHASE only excesses above 2.5a fall in th e phase

Fig. 5. Excess (in units of regions where excesse s have be en observed in for Fig. 3b and 4c. cr) other experiments supports the reality of these effects. Integral fluxes have been

1 ,000 �------calculated for the two phase

(a) regions. For phase 0.2-0.3, the

100 preliminary result is 2.8 ± 0.8 x

10 _12 cm 2 s above 10 13,5 eV. For 10 phase 0. 65-0.70, the result is 1.5 ± 0. 5 x 10 12 cm -s 2 - 1 Above 10 14,5 eV, th e results are an upper limit of (bl z 100 3.3 x 10 13cm s2 for phase 0.2-0.3

� w and a fl ux of 1.4 ± 0.5 x � 10

� _ l 3 - 2 - 1 >- 10 cm s for phase 0.65-0.7. z :0 0 u ~ 0.1 Figure 6. Pulse spectrum from the (c) Cygnus X-3 vicinity for 1985 (a) 100 June 16, (b) June 17, and (c) June 18 (UT) . An excess occurs in part b 10 (\ above 250 TeV. A 3.8o excess of ob served over-expected counts occurs 1 1 10 100 1,000 lO.ooo on June 17. ENERGY PARAMETER

A search was also done for excess fluxes from Cygnus X-3 during single

nights. There is one outstanding night in this data set. It is 1985 June 17

(UT). With no energy cut, 1080 events were observed, with 959.5 ± 7.7 expected. This is a 3.8a excess. In addition, the pulse spectrum is flatter

for this night than expected. Figure 6 shows the observed and expected spectra

for the preceding night, the night itself, and the following night. Although

the other nights show good agreement with the expected spectra, June 17 shows

a clear excess of events above 2.5 x 1014 eV. In Figure 7, the distribution of

observed and expected numbers of events is plotted as a function of the 4. 8

hour phase. Unlike the total data set, no major peaks are observed near

phases 0.25 or 0.65. The distribution

200 above 2.5 x 1014 eV is especially

150 interesting since it shows 16 events

z 100 above an expected number of 4.4 in the

50 bin at phase 0. The preliminary w �

"' 0 conclusion is that no eclipsing occurs 101" eV >- (b) E >2.5X in this energy region. z 15 :::> 0 The detection of this excess in a u 10 single night implies a sporadic, high

flux. This may be related to the

sporadic component reported by lO] 4.8 HOUR PHASE Stepanian's group . The flux value

during June 17 (called the peak flux Fig. 7. The 4-8 hour phase plot for observed (narrow line histogram) below) above 10 13.5 eV is 3.7 ± 1.3 x and expected (broad line) data from 10 11cm 2 s The average of this 1985 June 17. Above 250 TeV, where the excess is apparent in Fig. 6b, flux over the 1985 summer's data is a signal appears near phase O. � - 1.1 ± 0.4 x 10 - 12 cm 2 s l Values of the June 17 and average flux above

10 14.5 eV are 8.5 ± 2.1 x 10 12 cm 2 s

and 2.6 ± 0.6 x 10 13cm 2 s These are included in the plot in Figure 8. A more final and detailed description of the 1985 Cygnus X-3 results from the Fly's Eye will be published. C. THE OCTOBER 1985 DATA

Following the 1985 Cygnus X-3 radio outburst, a special Fly's Eye run was

performed with a 2 PMT trigger during the nights October 17,18 and 19 (UT). A

total of 14.3 hours of operation allowed upper limits to be placed on the

Cygnus X-3 flux during that time period. With no energy cut on that data,

2871 showers were observed, with 2883.1 expected. Above 10 14eV there were 451 showers observed, with 454.4 expected. In both cases the agreement is better 12

than expected by chance. The nights were observed separately and no excess

was present. The figure below shows the phase distributions with no energy cut

and for E > 10 14 eV. No excess is observed at any phase. The 95% confidence

- level upper limit of the Cygnus X-3 flux above 10 14eV is 6.3 x 10 12 cm - 2 1

500 (a) No E Cut 400 D. SPECTRUM OF FLY'S EYE CYGNUS

300 X-3 RESULTS 200 Figure 8 displays the Cygnus X-3 z 100 flux measurements by the Fly's Eye. All w 0.

"' of the results were described in the >- (bJ E> 1014eV 5 100 previous subsections. The symbols Land H 80 0 stand for the low (0.2-0.3) and high u 60 (0. 65-0.7) phase region fluxes from the 40 1985 summer data. The symbols P and A 20 stand for the peak (June 17) and average 0.5 lO (over the summer) sporadic fluxes. The 0 4.8 HOUR PHASE labels the upper limit of the 1985 October 10-10 .------� run. The two Cygnus X-3 spectra given by ll] Samorski and Starnrn are shown by dashed

lines. 10-11 All of the data except the peak sporadic fluxes agree quite well with the Samorski and Stamm spectra. The peak fluxes are very high, -12 E 10 but they would Gnly influence the spectra by ;::: wA their average (A) values. The possibility of

observing such individual sporadic effects is 10-13 only present in experiments with very large

collection areas. The 1985 summer data (L, H, and A) are consistent with the spectral slope 10-14 �-�--'--�--.1--...J13 14 15 10 10 10 and normalization of the Kiel observations. No

ECeVl strong long term decrease is apparent in the Figure 8. Spectrum of Fly's Cygnus X-3 flux. The 1985 October result shows Eye Observations of Cygnus C-3. (Symbols defined in text .) that a large outburst of the 1-ray flux did not occur during our observations, which were

shortly after the radio outburst. 13

VI. A PEV OBSERVATION OF HERCULES X-1

12l Hercules X-1 was detected by Dowthwaite et a1. during a 3 minute

outburst of TeV ?-rays. With this as motivation, the Fly's Eye data from 1983

July 10-14 (UT) were tested for a signal from Hercules X-1. The data from

each night were searched separately for a 1.24 second periodic signal. The

precise period used in the search was taken from the X-ray results from two

13l months earlier by Nagase et a1. . Of the five nights, only the night of 11 July displayed evidence of periodicity. Then, the first half of the data from

this night was found to have significant periodicity. The figure shows the

observed (histogram) and expected (dashed

line) number of counts in 10 bins of the

1.24 second period. The excess in the � 15 � (arbitrary) phase 0.7-0.8 implied a signal � 10 was present at the 99.98% confidence level 0 A more detailed description of this result " " 14] z i-r- is given in Ref. . 0 00 02 0 4 0 6 08 l 0 Part a of the figure below shows the PHASE (124 s per rod) result of allowing the period to be varied

between 1.23 and 1.24 seconds. This

demonstrates how the chisquared function for the observed and expected data depends on the period. In parts a and b, the

arrow points to the period based on the X-ray data. In part b, the period is

varied between 1.2375 and 1. 238 seconds.

The chisquared function peaks at the X 60 ray period.

40 Since the event times had to be 2 x corrected for the position of the p·1lsar

20 within the Her X-1 binary system, it was possible to test the effect of shifting

0 the assumed source position from the l 23 l 24 125 PERIOD (s) pulsar to other positions within the binary system. The figure below shows the 60 b. binary system. The source of the ?-rays 50 was required by the periodic data to be x2 40 within the range of positions indicated 30 by the error bars near the pulsar. 20 The orbital phase of the center of 10 500 600 700 800 900 1000 the 40 minute observation time is 0.66. t. P (fL• I as seen in the diagram, the line 14

of sight from the source position to the earth did not pass near the edge of

HZ Herculis, the companion star. If accelerated nuclei produce the observed

1-rays in collisions with matter, the target material must not be the

atmosphere at the edge of the companion star. The target may be part of the

15l 16l accretion disk. Optica1 , and X-ray observers had concluded that during 1983 June-August an unusual obscuration of X

rays from Hercules X-1 occurred. The heating of the

companion star due to X-ray bombardment continued

during this time. The material which obscured the X ""To Earth rays may also have been the target material which

<.m produced the 1-rays. This model would imply that the 0 sporadic outburst seen with the Fly's Eye may have \ been a very rare event. The average flux during the 40 minute outburst HZ Her was 3.3 1.0 x 10 12 cm 2 s Averaged over all the ± observing time during 1983 July, the average flux is

8. 7 2. 6 x 10 14 cm s These fluxes are for 10 Light Seconds ± 1- rays above a threshold energy

of about 200 TeV, with mean energies near 500 TeV. The figure below shows the Hercules X-1 1-ray fluxes observed by the Mt.

17l lZ] Hopkins group , the Durham group , and the Fly's Eye group. For the Durham 10-B and Fly's Eye observations, peak and average fluxes are connected by dashed w-9 Mt. Hopkins ? D.. D Durham I spectrum is only meant i C)f/y's EytJ lines. The E 0 i " 10-1 to show the trend of the data.

E 1 E-

w A 10-11 VII. ACKNOWLEDGMENTS � The data described here were

-12 I obtained by the entire Utah Fly's Eye 10 I �I I I Group. I am especially grateful for the 3 encouragement and assistance of George 10-1 6 Cassiday, Paul Sommers, and Steve 12 14 15 10 10 10 Wasserbaech. This work was supported by E (eV) the U.S. National Science Foundation

grants PHY-8201089 and PHY-8515265. 15

REFERENCES

1. Elbert, J. W., in "Cosmology and Particles" ed. J. Audouze et al.

(Editiones Frontieres, Gif-Sur-Yvette, France) 69 (1981) and

Cassiday. G. L. et al., In "The Birth of the Universe" ed. J. Audouze

and J. Tran Thanh Van (Editiones Frontieres, Gif-Sur-Yvette,

France) 331 (1982).

2. Greisen, K., Proc. Ninth Int. Cosmic Ray Conf. (London)£, 609 (1965).

3. Dzikowski, T. et al., preprint (1980) and Dzikowski, T. et al. ,Proc. 18th Int. Cosmic Ray Conf. (Bangalore)£, 132 (1983). 4. Boone, J. et al., Astrophys. J. 285, 264 (1984).

5. Hayashida, N. et al., Proc. 17th Int. Cosmic Ray Conf. (Paris) 2, 9 (1981). 6. Baltrusaitis, R. M. et al., Astrophys. J. 297, 145 (1985). 7. van der Klis, M., and Bonnet-Bidaud, J. M., Astronomy Astrop�ysics 95, LS (1981). & 8. Lloyd-Evans, J., et al., Nature 305, 784 (1983). 9. Samor�ki, M. and Stamm, W. in "Techniques in Ultra High Energy Gamma Ray Astronomy", ed. R. J. Protheroe and S. A. Stephens (U. of Adelaide Dept. of Physics, Adelaide) 85 (1985). 10. Fomin, V. P., et al., Proc. 17th Int. Cosmic Ray Conf. (Paris) 1, 28 (1981). 11. Samorski, M. and Stamm, W. , Astrophys. J. (Letters) 268, Ll7 (1983). 12. Dowthwaite, J. et al., Nature 309, 691 (1984).

13. Nagase, F. et al. , Proc. Workshop on High Energy Transients, Santa Cruz (AIP, New York) 131 (1984). 14. Baltrusaitis, R. M., et al. , Astrophys. J. (Letters) 293, L69 (1985).

15. Delgado, A. J., Schmidt, H. U., and Thomas, H.-G., Astronomy Astrophys. & 127, Ll5 (1983). 16. Parmar. A. N., et al., Nature 313, 119 (1985).

17. Gorham, P. W. et al., Astrophys. J. and Astrophys. J. (Letters) in press

(1986).

RECENT RESULTS FR OM THE IMB DETECTOR AND PROSPECTS FOR THE FUTURE

The IMB Collaboration

R.M. Bionta, G. Blewitt, C.B. Bratton, D. Casper, P. Chrysicopoulou, A. Ciocio, R. Claus, B. Cortez, S.T. Dye, S. Errede, G.W. Foster, W. Ga ewski, j K.S. Ganezer, M. Goldhaber, T.J. Haines, T.W. Jones, D. Kielczewska, W.R. Kropp, J.G. Learned, J.M. Losecco, J. Matthews, H.S. Park, F. Reines, J. Schultz, S. Seidel, E. Shumard, D. Sinclair, H.W. Sobel, J.L. Stone, L. Sulak, R. Svoboda , G. Thornton, J.C. Van der Velde, and C. Wuest.

Presented by Robert Svoboda University of California, Irvine Irvine, CA 92717

ABSTRACT

The flux of upward-going muons with energy GeV is measured to be > 2 consistent with that expected from atmospheric neutrino interactions. Using a list of known strong astrophysical x-ray and gamma ray sources, the number of upward-going muon tracks arriving within an angular ci rcle about each source is compared with the number of tracks expected. No evidence for a significant excess is found. In addition, the upgraded IMB detector is discussed and a preliminary description is given of recent progress made in calculating the background to nucleon decay detection from atmospheric neutrino interactions. 18

Introduct ion The Irvine Michigan Brookhaven (UlB) detector is 8 kilotonne - - an (3 .3 kilotonne fiducial vo lume) underground water Cherenkov detector

located at a depth of 600 m (1570 meters wat er equivalent) in the Morton Thiokol salt mine in Fairport, Oh io, (lat. 41 . 72° N, long. - U.S.A. 81 .27° W). It consists of a 18m x 17m x 22 .5m tank of wat er surrounded on all six faces by 2048 photomult iplier tubes (PMT's) facing inward. The PMT's record the intens ity and relative time of arrival of the Cherenkov light produced by charged particles above the Cherenkov threshold traversing the water in the tank. This informat ion is stored on magnetic tape and is later used to reconstruct the part icle track. The INB detector is the largest of several underground detectors built ch iefly to search for nucleon decay. Detailed information on the design, construction , and cal ibration of the detector has been described elsewhe re. [l] In the phase one configuration (5 inch hemispherical PMT's) 1.2 years of data were collected and analyzed . [Z) No ev idence was found for nucleon decay. Waveshifter plates were then mounted on the PMT's in order to increase their light collection capab ility by a factor of 2 (phase two) . Only 0.2 yea rs of data were col lected in this intermediate configuration. These data are still being analyzed and will not be reported on here. Recent ly, the detector has been shut down for a year while new inch PMT's and electronics were being install ed. The new 8 configuration will be completed by Nay 1986 . brief report will be A given on the characterist ics of the new detector. Given the results of the first detector run , it is clear that if nuc leons decay, then they must do so at a rate on the order of (or less than) the rat e of atmospheric neutrino interactions ins ide the detector. If a signal for nucleon decay is to be extracted from background events , then it is important to have a good idea of the expected background rate for a given decay mode. The progress made in calculating these background rates will be described in a pre l iminary form, with quantitative results to be forthcoming within a few months. Finally, analysis of the phase one data to extract upward-going muons traversing the detector has been completed and will be reported on here. These data , wh ile interesting in their own right , serve to provide a check of the various computer simulat ion routines used to 19

model neutrino interactions and nuc leon decays inside the detector in an energy region GeV muon energy) where the neutrino flux is known to (> 2 higher precision and the kinematics simpler. Phase Three IMB Detector In order to increase the light collection of the detector by another factor of 2 above the phase two configuration, the inch 2048 � EMI PMT'S have been replaced with 8 inch hemispherical Hamamatsu PMT's. This program has taken approximately one year to complete (finished in May 1986) since it involved completely removing the old phototubes, re-drilling the waveshifter plates, building new assemblies to house the larger tubes, and replacing the tube support beams with stronger ones to carry the additional weight. In addition to replacing the PMT's , much of the trigger electronics has been replaced with newer modules due to the wear on the old modules caused by years of operation in the salt mine environment . The atmosphere of the mine is ve ry dry and contains small amounts of hydrogen sulfide which, over time , causes silver pins and connectors to corrode. The installation of filters to remove the hydrogen sulfide will help to alleviate this problem. In order to better monitor detector performance in real time, a VAX

11/750 computer has been installed to replace the older PDP 11/34 and LSI 11 processors . This allows for continuous monitoring of trigger rate and voltages and automatic computer action to be initiated should a problem be detected . Preliminary tests on cosmic ray muons indicate that the goal of a factor of 2 increase in light collection will be achieved . This will make identification and reconstruction of low energy tracks much easier. The efficiency for detecting muon decays in an event should also increase , though this has yet to be tested . Work is currently in progress to determine if more sophisticated cuts on the data can be made (such as an inv ariant mass analysis) than was previously possible in order to reduce background . Calculation of Atmospheric Neutrino Background Previous detector limits on nucleon decay were calculated without making a subtraction in the number of observed candidate events in a given decay mode for the expected rate of atmospheric neutrino interactions. This is because the rate of such interactions was known 20

only to within a factor of two due to a lack of knowledge of the cross section ratios between the various final states, especially those containing 1,2, or 3 charged pions . Previous estimates[3] were made

empirically by using bubble chamber data from Gargamelle.L4l This method requires weighting of the events to reflect the difference between the Gargamelle beam in particle make up and in energy spectrum and ignores possible scanning bias and other detector systematic errors . effort is now underway to improve on the accuracy of these An neutrino background estimates via direct calculation of the interaction final states and kinematics. Though this work is still preliminary and subject to revision, the initial results seem promising in that they fit the available accelerator data on the production of single- and multi pion final states . The following is an example of one such method:

1) use standard quasi-elastic Feynman graphs for calculating the charged and neutral current interaction cross sections for final states containing only an outgoing lepton and nucleon . 2) calculate cross sections for single pion final states from resonant production of deltas and the three low lying I=l/2 baryon

states P 11(1434), s11(1505 ), and D13 (1514). Include also the graphs for non-resonant production in which an exited baryon emi ts a pion . 3) for double pion final states, assume scaling to be valid (since this process is only important as a nucleon decay background process at energies 2 GeV) and use the proper x and y > distributions for charges or neutral current, depending upon the reaction type . This determines the kinematics for the outgoing lepton and hence also for the final state hadronic system. Choose the hadronic system kinematics randomly from the allowed momentum phase space . For completeness, the above method can be extended to triple pion production, though the neutrino energy threshold required begins to move out of the range in which the final state charged particle momenta can be low enough to resemble nucleon decay. Preliminary calculations indicate that perhaps a factor of two increase in experimental sensitivity can be achieved in detecting nucleon decay by sub tracting off the neutrino-induced background rates. 21

The Upward-Going Mu on Flux Between 1982 Sep tember 10 and 1984 Ju ly 4, 396 observational days were logged and approximately lU� particle tracks were registered. The vast majority of these tracks are due to one or more particles entering the detector from above and exi ting near the bottom . The rate (2.7 sec-1 ) and arrival direction distribution (proportional to the cosine of the zenith angle cubed) are consistent with that expected from secondary cosmic ray muons . Ap proximately once every two days a track image is recorded which enters the detector from below the horizon line, i.e., from a zenith angle greater than 90 degrees . A total of 187 events of this type were detected over the observation period. Details on the data sample search [ ) and track reconstruction of these events may be found elsewhere . 5

The majority of the 187 upward-going muon events found are due to atmospheric neutrino interactions . This conclusion is based on a comparison of the observed upward-going muon flux with a computer calculation of that expected from atmospherically produced neutrinos . The calsulation is done using a Monte Carlo comp uter program which is l based upon the high energy neutrino flux estimates of Volkova 6l , a standard scaling model of muon neutrino interactions, and a compu ter algorithm which simulates the propagation of mu ons through the detector and surrounding rock . The output of the program consists of simulated data events representing 1000 live days of detector op eration . Passing these compu ter-generated events through the same reduction and reconstruction used on the actual data provides estimates of the mu on energy threshold (2 GeV), efficiency (83%), resolution (mean error 3.5°), and effective area (390 m2 ). Thirteen of the 187 events were not found by the data reduction algorithms used on the actual and comp uter simulated data but were recovered by other routines used to study upward-going muon events in a l l search for evidence of neutrino instability. 7 These events must be subtracted from the data sample when calculating the observed absolute upward-going muon flux using the area and efficiency from the simulation results. Figure l shows the measured flux based on the original 174 events as well as the flux predicted by the simulation as a function of zenith angle. They are seen to be in reasonably good agreement. The total flux integrated over the detector aperture is 2.50± .19xl0-13cm 22

1 -2sec- sr-l compared to the expected value of 2.36± .11 (statistical) ±.35 (systematic) xlo-13cm-2sec-1sr-1• Thus the total flux is consistent with being due entirely to atmospheric neutrinos . Using the ] method of Protheroe,[8 a 90% confidence level (c.l.) upper limit of 4.0xlo-14cm-2sec-1sr-l is placed on the total contriubtion to the

observed muon flux from non-atmospheric sources . A Search for As trophysical Neutrino Sources Since muon neutrinos arriving from an astrophysical source below the detector horizon line can easily penetrate kilome ters of rock before they int eract to produce muons, the signature of such a source would be a significant number of upward-going tracks which point within a few degrees of the source position . The arrival directions of these 187 events are shown in figure 2 in equatorial coordinates. In order to determine if the track arrival directions are correlated with some source it is first necessary to know what the angular distribution of tracks about a neutrino point source would look like in the IMB detector . The muons would not be expected to point directly to the source due to the detector's angular resolution and the angle between the parent neutrino and daughter muon . To this

end, the coordinates of the objects LMC X-4, Cen A (NGC 5128), PSR0531+21 (Crab), Her X-1, and were generated and passed through the interaction and muon propagation Monte Carlo and data reduction algorithms . Two separate neutrino source spectral indices (y) were assumed, one for high energy spectrum (y=2 .3) and one for a low energy spec trum (y=3 .0) . The former value was chosen under the assumption that neutrino source spectra should be similar to that measured from such

objects by x- and gamma ray observations, while the latter value was selected because it is similar to that produced by cosmic ray nucleons striking our own atmosphere. These specific sources were selected because: 1) they are likely_!!. priori candidates for st rong ne utrino sources, and 2) their position in declination spans the aperture of the de tector, allowing a calculation of the efficiency of recovering upward going muon tracks as a function of source position. The simulations showed that in order to enclose 90% of the muon

events from a y=2 .3 source it is necessary to accept tracks within 7.0 degrees from the source . For y=3.0 sources it is necessary to extend

the cutoff to 9.5 degrees . Due to the poor absolute timing available 23

during this detector run (i .e., the on-sit e computer cl ock) , the cutoffs were extended to 9.0 and 11.0 degrees, respectively, to account for possible errors in the calculation of right ascension . Table l gives the number of events located within the angular cutoffs from the above mentioned objects , plus a number of other celestial objects detemined priori to be possible sources of neutrinos . .!. Of course , in order to decide whether a given source candidate has a significant number of upward-going muon tracks near it, an estimate must be made of the number of background events expected from atmospheric neutrino interactions. This was done by drawing a number of 11equivalent11 cutoff circles at the same declination as the source candidate but offset in right ascension enough to preclude overlap . Assuming the distribution of detector live time to be flat in local sidereal time (a good assump tion to within 7.5%), these equivalent circles should have the same acceptance ap erture and collection efficiency as the circle around the actual source candidate. The expected background was then deter.mined by simply totaling the number of events occurring inside the equivalent circles and dividing by the number of circles . Table 1 gives the results of this background determination for each source candidate. can be seen, no source in As the list has a significant excess of ev ents arriving from its direction . Using the Protheroe technique, 90% c.l. upper limits for the upward-going muon flux from each source are also given in Table 1, along with the corresponding neutrino and luminosity upper limits. These limits take into account the fraction of the live time the source was observable. Through continued operation over the next few years , the IMB �etector will be able to achieve flux sensitivi ty limits of possibly a factor of two or three better than those reported here . A significant improvement in sensitivity awaits the construction of a new generation of underground or undersea detectors . 24

This work is supported in part by the U.S. Department of Energy

REFERENCES

l. R.M. Bionta et al ., Proceedings of the Fermilab Workshop on Calorimeter Cal ibrat ion (1983) .

2. H.S. Park ��., Phys . Rev . Lett . 18 (1985) . 54, 3. B.G. Cortez ��., Phys . Rev . Lett . 52 , 1092 (1984) .

4. H. Deden ��., Nucl . Phys . B85 , 269 (1975) .

5. R. Svoboda, Ph .D. thesis, University of Hawaii at Manoa, 1985 (unpub lished) .

6. L.V. Volkova, Sov . Journal of Nucl. Phys . 3 (6), 784 (1980) . 1 7. R.M. Bionta et al ., presented by D. Casper, Proceedings of the Santa Fe Meeting:- Div . Part . and Fields A.P.S. , 255 (1984).

8. R.F. Protheroe , Astron . Express 33 (1984). 11, 25

.., 5 0 ..

I 4 .... "'

I \ 0 ' Fig. The measured flux of CD \ ' 1 · "' 3 !' upward-going muons as a func ' N , tion of zenith angle . The I ' .... solid line indicates the E .... 0 expected flux due to atmos 2' pheric neutrino interactions . .. ::> The dashed lines indicate the u.. error associated with the flux estimate . c 0 ::> �

0 0 -0.2 -0.4 -0.6 -0.8 -1.0 Cosine Zenith Angle

50 ,....,_....,...... ,....,...,...... ,...... ,...,..,...... ,'17'"..,....,..:""1 ':CyQ X-3 I • Her X-1 I . · / I · ·· . Cr�b • 25 I . . /•.• I. ., - m en ! •Ge· CD CD l. .; a. . . . Fig. 2 The arrival directions 0 ' . s�433\ c2n · . f of the 187 upward-going muon CD " · 3 . . "C . , events shown in equatorial I .. . \ .,. coordinates . The dashed c line indicates the plane of 0 -25 ) / . - • ':G.C. our galaxy . .1 0 I • c 1. • jva1I x-1 1\ Can ·: . � A ·: i -50 \ · · . 0 . ;� . . . · . � LMC X-4 - -... " . -75

20 15 10 5 0 Right Ascension (hours l 26

TMU I llUUl.TS o� SOURCE SEAllCH --- e.1. ea• IOTac.L ...... IO"lo c. I . &A. - •lo ._ ... 01steMe • L.111111ft0Sif)' -· (;.�a';,�:::!, ,:.��:�.L.i:!l 1 1-.1 1-.1 Ii• ,- , ._..,._.. (llpc) c.,,. 1•4 ·II.SI oo LMC .... 1 y Z.J 1.4 O.SI Z.!511 04 • •.o y.3.0 . . 13 2.3 11041 . . . . Cett. 11.41 -42.H A 0000 y . 2.5 1.0 0.4 0.77 2.5 11046

y.J.Q z.o ..• 10 l.91 1046 V.l• •- 1 9.0J 40.4 1.4 - 8 y Z.5 I.I 0.!51 1.9 r. 1031 • 3.0 y • 3.0 1.4 4.1 2.0 11 1039 ,. Cra• +22.01 O.H y. 2.3 I 1.3 1.0 1 1039 .• ..• z.o 12 1.Z 1040 y J.O a • .. 1•1 +:.5.H Hit l•.H Z.3 o.s . 4.9 . 1031 y • . . O.H 1 y.s.o I.I 3 1.31104 lO 1 CH 1-J ZO.SJ +40,ll IZ

y . 2.3 o 21 3. 1 l!J.!S.. 1040 .o 1 y . 3.0 .1 17 10 6.!511 04 0 I.SI +17.1 1 G... i._.. y . 2.3 l.Z 1.0 1.0

y.3.0 I.I ... " 55433 19.11 4.91 +

y.2.3 1.0 O.IZ 1.4 111039 0.1 y.3.0 1.1 2.0 .1040 9.0 .. IZ.47 •Z.14 :sczn y l.J l.Z 3.1 0.55 • y . 3.0 2. 1 3.1 14

Canter 17.71 -21.•0 10 Gel. 2.3 0.1 0.55 11040 I.I 7. ... y .0 I.I 3.0 12 9.0 11 1040 • 3 27

THEORETICAL IMPLICATIONS OF REPORTED ULTRAHIGH ENERGY DETECTIONS OF BINARY X-RAY SOURCES

David Eichler Astronomy Program University of Maryland and Department of Physics Ben Gurion University

The question is addressed as to whether standard views of binary X-ray sources and particle acceleration can accommodate all of the reported URE detections of such obj ects. It is is concluded that the correlation be tween URE emission and X-ray partial eclipse or eclipse transitions make good sense in the concept of a beam dump model for URE emission. However, the extremely energetic photons reported by air shower experimental groups strains the simple application of particle acceleration theories to the accreting neutron stars and accretion disks . 28

I. Introduction

To make ultrahigh energy (UHE) neutral quanta, a system first has to accelerate charged particles to ultrahigh energies . The charged particles then have to radiate the neutral quanta. Each of these stages poses a separate question to theorists trying to understand UHE emission. Both questions will be discussed in this paper. In section II , models for the radiation will be discussed assuming that the particles are somehow accel erated to the required energies . In section III, the question of acceler ation will be discussed. Because the two issues are quite distinct, more elaborate introduction of each will be included within their respective sections .

II. Beam Dump Geometry

Ultrahigh energy gamma ray astronomy is much older than the theories of ultrahigh energy photon emission. The latter was spurred in the late seventies by consideration of whether deep underwater neutrino detection has a chance of detecting astrophysical sources . One potential source of UHE neutrinos , among many that were proposed around that period , is a com pact source of UHE particles in a binary system. 11 The companion star, or a wind or accreting mat ter deriving from it, could serve as a beam dump to convert the UHE particles to pion decay products, and several scenarios along these lines were outlined ,

One of these scenarios , in which the base of a wind from the companion star acts as the beam dump , gained credence with the realization that Stepanian and coworkers at the Crimean Observatory had been reportedly detecting Cyg X-3 for several years at about the orbital phases 0.2 and O.s.2 1 Assuming that X-ray minimum is due to eclipse by the companion star, the orbital phases 0.2 and 0.8 are significant in that at these phases , our line of sight might be expected to pass very close to the com panion star, and hence through the deepest part of a wind coming off its surface . Such a wind had already been hypothesized to exist . 3,4] The significance of the orbital phases, and the extremely high efficiency implied by the observations for UHE particle production were noted by Vestrand and Eichler. 51 Detailed computation was completed somewhat later6l that showed that inverse Compton scattering of photons emitted by the companion star could produce broader peaks than seemed to be observed, 29

supporting the idea that the converting material is indeed non-relativistic , material from the companion star, and that the emission mechanism was either bremsstrahlung from electrons or the decay of pions from p-p colli sions . Following the reported discovery of Pev gamma rays?,8 ] it was noted9] that the primaries mu st be ions rather than electrons , because no known mechanism could accelerate electrons to such high energies . This has resulted in widespread speculation that Cyg X-3 might actually be a URE neutrino source after all .

The particular scenario developed by Vestrand and Eichler fit the data that existed then quite nicely, but apart from this motivation, there is no priori reason to favor it over the other variations discussed in � reference 1 , or by other ·authors . Indeed, other variations are suggested by the reported observations of other binary X-ray sources (as well as Cyg X-3 itself, which seems to have come to favor a phase of 0.6), and many aspects of the problem remain open. In particular, the observations of Her ,ll] X-1 suggest that the accretion disk may be acting as the beam dump . lO The discovery that Cyg X-3, Vela X- 1 and Gen X-3 emit at an orbital phase of 0.6, suggest that the beam dump is the "double dip" accretion cone , which is parallel to the line of sight at about this phase and causes double dips in the X-ray emission from such sources.121

The Pev emission also would confirm, in a sense , that the gamma ray emission is occuring far from the acceleration site, which is a basic premise of any beam dump model. The argument is that just about any acceleration mechanism would accelerate particles to at most an energy of order eBR (u/c) where B is the characteristic magnetic field, u is the characteristic velocity, and R is the characteristic spatial dimension of 6 the acceleration site. If primaries are to be accelerated to 101 eV within a region as compact as say, 108 cm, then B must be much larger than 4 10 gauss , the field strength in wh ich a Pev photon would pair produce . It follows that the gamma rays could not escape the region in which the pri maries needed to produce them are accelerated; these gamma rays must originate somewhere else.

Although the beam dump scenario seems to work on a general level, it is difficult to make detailed predictions . For efficient conversion into neutral quanta that escape the beam dump , one needs a well prescribed thickness: thick enough for reasonable thorough conversion, but thin 30

enough to allow the gamma rays to escape . How long this condition is satisfied during any transition into or out of eclipse depends on various obscure factors . For example , there may be better conversion when the compact object is going into eclipse because the converting side of the target material (e.g. the companion star) has just been heated by the passage of the compact object, so that its atmosphere is more extended and/or any wind from it is enhanced . On the other hand , there may be less converter material when the compact object is going into eclipse because its passage clears away diffuse material on its side of the companion star. Such an effect would account , for example, for the asymmetry in the X-ray light curve that is sometimes observed for Cyg X-3 where X-ray maxi mum is at a phase of 0.6. Finally, the relative importance of different parts of the flow ambient diffuse material in the binary system (e.g. the base of the wind vs . the accretion wake) could in principle depend on the wind strength of the companion star, which can vary. One of the few things

that can be predicted is that the UHE emission should be unpredictable. This much is confirmed by observations , but has proved to be a source of frustration to the field.

It should also be mentioned that the basic model for the X-ray emis sion on which nearly all discussions of UHE emission are based, which assumes that the system contains an eclipsing X-ray source and is sur l3,l4,l5] rounded by scattering material in the form of a wind or cocoon , has been contested by several authors mo re recently. 16,171 They propose that the compact object in Cyg X-3 is not eclipsed but rather that its accretion disk corona scatters the X-rays like a lampshade , giving the X ray source an extended appearance. The corona, in their model, is only partially eclipsed , so that the X-rays are modulated but not completely eclipsed at X-ray minimum. No scattering outside the binary orbit is needed to smooth the X-ray eclipse into the observed pattern, as in the earlier models. Because the screen of scattering material is carried around by the compact obj ect according to this mo del , the sharp orbital dependence of URE emission would be difficult to understand.

III. Particle Acceleration

What accel.erates the primaries in UHE emitting binaries to such high energies? This is of course a version of the general question of cosmic 31

ray origin, and the models that have been suggested for particular UHE source have all been developed in the more general context . Of these theories , several are actually motivated directly by observation. The direct association of interplanetary shocks and supernova remnant blasts in the interstellar medium, have (in addition to a highly developed theory) led to an almost universal acceptance that shocks accelerate particles in some capacity. The theory of diffusive shock acceleration can account for the universal features of cosmic rays as well as many particular observa tions reported for the earth's bow shock . Although one could argue that some other mechanism, as yet unspecified, accounts for all the observations as we ll, one should recall that highly successful theories (e.g. cosmo logical quasar redshifts and evolution) will always be subj ect to vague skepticism.

Another instance in which observations directly indicate particle acceleration of a specific type is the UHE pulsations from isolated pulsars such as the Crab and Ve la. These observations imply that the pulsar can accelerate particles up to at least 1012 eV. This is generally thought that these are e+-e- pairs which reproduce via curvature radiation, which then produces pairs in the pulsar's strong magnetic field, and thus short out significantly higher potential drops . l8,l9] However , some pulsar theorists maintain that ion acceleration to higher energy remains a possi bility (Ruderman, private communication) .

Finally, planetary magnetosphere display the ability to accelerate particles to energies that correspond roughly to the voltage imposed across them by the flow of the solar wind . There is extensive discussion on the subject in the geophysical literature.

With the reported discovery of gamma radiation by SAS 2 , Bignami , Maraschi and Treves20] proposed that high energy particles are accelerated by the shock in a wind from a pulsar striking the companion star. Milgrom and Pines211 suggested that Cyg X-3 contained a young pulsar which directly produces the gamma rays , as do other young pulsars (e.g. Crab and Vela). Their paper is probably the first western theoretical reference to the UHE observations of Stepanian and co-workers of Cyg X-3. The motivation for supposing Cyg X-3 to be a pulsar remained , until recently, quite strong and still exists to some degree. The only other galactic UHE sources , until the reported discovery of UHE emission from Her X-1 were young , rapidly 32

rotating pulsars . Moreover, Cyg X-3 is very unusual among binary X-ray sources in other regards : its X-ray spectrum extends up to several hundred Kev - not a typical spectrum for a binary X-ray source . (Cyg X-1 is the other binary X-ray source which displays hard spectra, though not as hard as Cyg X-3 , and it too is atypical .) Also, the X-ray luminosity of Cyg X-3 is mich higher than most other galactic binary X-ray sources . The X-ray luminosity alone is marginally supercritical , and if all the UHE emission is included, the inferred source luminosity is of the order of 1039 erg/s . A natural argument made by Milgrom and Pines was that the energy source is not accretion, but rather the rotation of the young pulsar . This would also explain why the binary system was enshrouded by so much diffuse ma tter: rather than being captured by the neutron star, it is blown around .

Vestrand and Eichler6l noted that their geometric model for the gamma ray production presupposed that the particles traveled from the vicinity of the neutron star to the companion star in a more or less straight line . This favored the acceleration site of Milgrom and Pines over the view of Bignami et al ., in wh ich the acceleration was likely to take place closer to the companion star and in which the magnetic field was strong enough to bend the trajectories of the energetic particles . We noted that accelera tion by an accretion shock would also fit within our assumptions, (because of the implied proximity of the shock to the neutron star) , but expressed a preference for the pulsar model, which seemed to tie together many of the unusual features of Cyg X-3.

The recently reported 12 ms periodicity in the URE emission from Cyg X-3221 supports the view that it is a young pulsar, but ironicaly, the discovery of slowly rotating URE sources l0,23,241 is evidence that there is some other mechanism at work near the neutron star that draws energy from accretion, not rotation. Thus , before the hypothesis received the strong support it did, much of the motivation for it disappeared .

To account for the reported UHE emission from slow binary X-ray sources with slow rotators, several scenarios have been proposed that invoke accretion as the ultimate power source . Chanmugham and Brecher25l invoke a pulsar mechanism, but using the accretion disk instead of the neutron star. Wang26l invokes magnetic field line annihilation in the accretion disk. Eichler and Vestrand1 11 and Ellison and Kazanas27] have 33

developed an accretion shock model, though mindful of its limitations (see below) .

An obvious difficulty with models in wh ich the accretion disk is responsible for the acceleration is that the UHE emission bears the spin periodicity of the neutron star. The accretion disk is certainly not rotating with that period, and even a beating between the spins of the disk and the neutron star would give the wrong period. In the opinion of this author, proponents of accretion disk models have not addressed this question adequately .

A second problem with the disk model of Brecher and Chanmugham is that the required efficiency for particle acceleration in these sources is typically of order unity.5 • 111 According to equation (2) in Chanmugham and Brecher, the inner edge of the accretion disk for Her X-1 is of the order of 103 neutron star radii. The disk thus seems unlikely to account for more than 10-3 or so of the energy budget .

This second difficulty, however, afflicts all models to some degree if the io12 gauss surface field is mainly in a dipole component. For then matter is greatly impeded by the magnetic field on its way to the surface , and, to minimize the distortions of the field, arrives there as an incoherent ensemble of many small rivulets .

Finally, these models fail to account for the primary energies needed to account for some of the observations; or, at best, barely account for them under the most generous , finely tuned set of assumptions . The maximum attainable energy, for all mechanisms that have been proposed , is

(u/c)(eBR) ( 1 ) where u, B, and R are , respectively, the characteristic velocity, magnetic field strengtyh, and containment radius at the acceleration site. 25l Chanmugham and Brecher multiply this by a factor ln(�axl�in), which is based on the presumption that (u/c)eBR is constant over many scales (�in through �ax) and that a particle gains this much energy for each e-fold increase in radius on its way out of the system. This seems inconsistent , given the high acceleration efficiency one must assume , because it implies that the flow puts as much power at �ax as at �in' whereas at the larger 34

radii the flow must in fact 'command a much smaller share of the energy budget .

In addition to the above constraint , there is the one that the acceleration time be less than the synchrotron loss time , which basically limits B. Similarly , invoking an accretion shock that taps much of the total power limits R. Combining the first two constraints, one obtains a 11l limit on Emax of

(2)

For shock accelerated protons , equality is otained only for a particular

field strength though �ax is weakly dependent on B. Losses due to p-p collisions can also be important in a dense accretion flow28l , and can only

lower �ax further . For other acceleration mechanisms , �ax can be higher by a fractional power of u/c, but this does not help much when u is in any case close to c. For an accretion shock, u/c is roughly (R/105cm)-l/2, so 16 that Emax cannot be much higher than io ev. Perhaps the most formidable fine tuning requirement is that just the right number of particles are picked up by the acceleration mechanism so

that , in accelerating them to �ax • it spends a large fraction of its energy budget. Too many injected particles would overload the mechanism,

so that there would not be enough power to accelerate them to �ax ; too few would leave the mechanism underloaded so that it does not operated effi ciently. The shock acceleration mechanism controls the inj ection via non linear feedback , so that optimal loading is automatic29•30l making it extremely attractive . Other mechanisms must still confront this fine tuning problem.

IV. Discussion

The association of UHE emission with partial X-ray eclipse or eclipse transition makes the reported observations highly believable. the other On hand , the extremely high energies and high efficiencies required by the observations are, in this author's opinion, marginally possible at best . The above considerations suggest that the best way for an accreting neutron star to accelerate to very high energies at high efficiency is to use the energy liberated by the accretion to drive , say , a very fast wind that is 35

tapped for particle acceleration far from the neutron star (but still close to it on the scale of the binary) so that R, as it appears in equation (2), is mu ch larger than 106 cm, wh ile u remains close to c. The fact that SS433 appears to be doing just this lends plausibility to this idea. If the spin periodicity � of the neutron star is to show up in the particle acceleration, the acceleration must probably occur well within -c� of the star. (It is important to note that air shower arrays have not yet detected spin periodicities at energies above 1015 eV.)

If , alternatively, there is a new acceleration mechanism working very close to the neutron star, it must do so in spite of a very strong surface field.

Either way , our view of accreting neutron stars mu st be dramatically amended if it is to accommodate all of the reported UHE observations . The TeV observations are easier to explain, but the PeV observations are curi ously consistent with those at lower energies and are difficult to ignore .

I thank many colleagues for useful discussions . This research was supported in part by NSF grant AST 83 17755. I acknowledge the hospitality of Dr . A. Cheng and the Applied Physics Laboratory.

References 1. Eichler, D. 1978, Nature, l:J..2., 725. 2. Neshpor, Yu . I., et al . 1979, Ap . Space Sci. , ..§..!_, 349 . 3. Davidsen, A. , and Ostriker, J. P. 1974, Ap . J., �. 331. 4. Milgrom, M. 1976, As tr. Ap ., 2!_, 215. 5. Vestrand, W. T., and Eichler, D. 1979 Proc. Workshop on Particle Acceleration in Astrophysics , Jolla (ed. Arons , Max , McKee ). La 6. Vestrand , W. T., and Eichler, D. 1982, Ap. J., �. 251. 7. Samorski , M. , and Stamm, W. 1983, Astrophys . J. Lett., 268, L17-L21. 8. Lloyd-Evans , J., et al. 1983, Nature, 1.Q2, 784. 9. Eichler, D., and Vestrand , W. T. 1984, Nature , lQZ_, 613. 10. Baltrusaitis, R. M. , et al . 1985, Astrophys . J. Lett., 293, L69. 11. Eichler , D. , and Vestrand , T. 1985 , Proc . 19th Int. Cosmic Ray w. Conf ., La Jolla, .!_, 115. 12. Hillas , A. M. 1985 , Proc . 19th Int. Cosmic Ray Conference , La Jolla (highlight talk). 13. Milgrom, M. 1976, Astr. Ap ., 2!_, 215. 36

14. He rtz , P., Joss , P. C., and Rappaport, S. 1978, Ap . J., �. 614. 15. Ghosh, P., Elsner, R. F., Weisskopf , M. C., and Sutherland, P. G. 1981, Ap . J., �, 230. 16. White, N. E., and Holt , S. 1982, Ap . J., ]J]_, 318. s. 17. Molnar , L. A. 1985, Ph .D. Thesis , Harvard U. 18. Cheng, A., and Ruderman, M. L. 1980, Ap. J. �. 516. 19. Arons , J. 1983 , Ap . J. , �, 215. 20. Bignami , G. F., Maraschi , L., and Treves, A. 1977, Astron. and Ap ., �. 155. 21. Milgrom, M. , and Pines , D. 1978, Ap . J. 3lQ., 272. 22. Chadwick , P. M. , et al. 1986, Nature (submitted). 23. Dowthwaite , et al . 1984 , Nature , 222_, 691. 24. Protheroe, R. J., and Clay, R. W. 1985, Nature , l..!2_, 205. 25. Chanmugam, G., and Brecher, K. 1985, Nature ,�. 767. 26. Wang , Y. M. preprint . 27. Kazanas , D., and Ellison, D. 1986, Nature , 1.!2_, 30. c. 28. Eichler, D. 1980, Proc. 1980 International DUMAND Symposium, Honolulu (ed. Stenger) . 29. Eichler, D. 1979, Ap . J. �. 419. 30. Ellison, D. C., and Eichler, D. 1985 , Phys . Rev . Lett., �. 2735. 37

CYGNUS X-3 : SOURCE OF VERY HIGH ENERGY GAMMA RAYS

Tr evor Weekes Whippl e Observatoryc. Harvard-Smithsonian Center for Astrophysics P. Box 97 Ama do , AZo. 85645-0097 U. S. A.

Abstract

Obse rva tion s of TeV-PeV gamma rays from Cy gnus X-3 using above ground air shower arrays and atmospheric Cherenkov de tector s are summarized. The impl ications for the ories of cosmic ray origins are discussed. 38

"There are more th ings in heaven and earth, Horatio, 'Ihan are dreamt of in your ph ilosophy " Hamlet, Shakespeare. w.

Introduction

At all wavelengths Cygnus X-3 is an extraordinary obj ect. Although it was one of the earliest x-ray sources discovered (Giacconi et al. 1967) , it is still, after 20 yea rs of research, one of the few strong x-ray sources about whose nature there is a maj or uncertainly. Conserva tive estimates of its di stance place it on the edge of the galaxy and give it an x-ray luminosity that make it one of the strongest x-ray sources in the galaxy in the kev region. As such , it sh ould be easy to identify with a class of obj ects which dupl icate its properties. No other obj ect quite matches Cygnus X-3 in its wide range of bizarre behavior ; it is signif icant that it has been comP"lred with such diverse obj ects as SS433, Circinus X-1 and Scorpius X-1 . Its unusual properties are aPP"lrent at all wavelengths. It is extremely frustrating that one of the most interesting and p

E u

Vl c Figure 1. The radio flux fran Cyg X-3 at (]) +-' 11 .1 fran Oct. ,1982 to Mar. ,1985 (Johnston c cm � et al. 1985) shaving the large variations in intensity.

10/82 EPOCH 3/85 39

3 its radio output dur ing which its radio flux increases to 10 times its quiescent level. For a period of days at sane wavelengths it is then one of the brightest radio sources in the sky. other x-ray binaries have been observed to emit radio waves but none with the intensity of Q{gnus X-3 . It is one of the fe.v sources that sh

Growd:based detection techniaues. set the very high energy gamma rey observations of Qy'gnus X-3 in To perspective, it is necessary to have sare wderstanding of the detection techniques involved. 'Ihese techniques are not new but they are relatively wderdeveloped. At Jiioton energies above 1 kev the earth's atmosJiiere is equivalent in its absorbing paver to a lead shield almost 1 m in thickness. Direct detection of very high energy gamma reys fran the earth's surface, even at mowtain altitudes, is therefore impossible. Satellite detectors are limited in size and hence in flux sensitivity ; the high energy cutoff of the experiment on the EX>REI' Gamma-Ray Observatory (originally scheduled for lawch in 1988) is 30 GeV and represents the effective high energy limit for the direct detection of gamma rays using current sr:ace technology. '!he indirect detection of very high energy gamma reys fran the earth's surface is possible if use ismade of the products of the interaction of the gamma rey with the air molecules. For a primary energy of 1 PeV (=1015evl , the resulting air shcwer at sea level consist of 100,000 i::articles in a disk 1 m can thick and 100 m in diameter. arrey of p;.rticle detectors can determine the An arrival direction of the shCMer by measuring the time of arrival of the shcwer front at each detector. Air sh

Cllerenkov light) . Al though the earth's atmosrtiere has many advantages as a detector medium (thickness, scale-height, transp:1rency, cost) it does suffer the disadvantage that it is not under the control of the experimenter who is limited by changes in pressure, tanperature and transp:1rency. After 30 years of experience these p:1rameters are well-understood. By the standards of high energy physics and sr:ace-borne astrophysics experiments, ground-based gamma-ray experiments are lcw budget and relatively unsophisticated. Being field experiments, they lack the control and calibration of laboratory experiments. 'Ibey operate at energies that generally exceed those ava ilable in p:1rticle accelerators. Many of the r:article array experiments were not purpose-built for gamma-ray astron(Jey'. It is not surprising, th erefore, tha t measurements of absolute fluxes shew rather large deviations ; there is no strong steady source of p:1rticles or photons that can be seen at all energies and that can be used as a standard candle to canp:1re estimated sensiti vi ties. 'Ihat these simpl e experiments sh ould have succeeded in the detection of very high energy gamma rays fran Qygnus X-3 is a ranarkable example of cost effectiveness in a field where cost is often assl.Illed to be p:tramount to importance.

TeV to PeV Gamma-RayQbservations. 'Ihe observation of 0.3 TeV to 10 PeV gamma rays fran Qygnus X-3 has been reported by at least twelve different groups between 1972 and 1985. All of these groups made their observations using the atmosrtieric O:terenkov technique (ACT) or air shcwer arrays Almo st all of the groups reported one or more (/IRA) . positive detections which were considered by the authors to be statistically significant in their cwn right i.e. had a significance equivalent to that of a 3 sigma effect or greater. While on= may quibble with one or two of the publ ished results on the grounds that the statistical significance is overstated, this does not effect the overall conclusion fran the gen=ral body of observations tha t the emi ssion of gamma rays fran the direction of Qygnus X-3 has been observed. Most of the photons are modulated with the 4.8 hour period of Qygnus X-3 but with a light-<:urve unlike that seen at lcwer energies and which varies in ampl itude and shape. A synthesis of the observations, listed in Table 1, either in terms of light-<:urve or energy spectrl.Ill is difficult for a variety of reasons: (i) energy thresholds, collection areas, flux sensitivities, etc. , are not well determined as outlined in the previous section ; (ii) many of the observations are at different epochs; because of the snall duty-<:ycle of the ACT and the limited nl.Illber of experiments this is p:1rticularly true at TeV energies; (iii) sane of the results are of limited statistical significance ; (iv) the publ ished light- 42

curves, i;:articularly prior to 1981 , have often been folded using different val ues of P and P, Since 1981, most garmna-ray observers have used the quadratic val ues given in van der Kl is and Bonnet-Bidaud (1981) (hereaf ter vdK-BB). It is possible that the actual variation is more canpl icated than that given since individual measures of the x-ray ephemeris of ten deviate widely. Several longer term periodicities have been suggested, including a 4.95 hour variation in the radio band (Molner et al. 1984) , In general the publ ished detections indicate emission around phase 0.2 (when the x-ray source emerges fran its i;:artial eclipse) and around '[iiase 0.6 (the time of x-ray maximun) . In sane cases, emission is seen at both phases. Because the 4,8 hour period of Cygnus X-3 is almost one-f ifth of a day, care must be taken to ensure that solar modulations do not introduce pseudo.. periodicities into the data base. In the case of air shCMer arrays this can be checked by searching at other periods that are fractions of a day e. g. 4, 6, or 8 hours, 'Ihe two minute advance in '[iiase per sidereal day means that in two weeks of observation, the observations taken in a given phase bin that is only 0.1 wide will include the same zenith angle. Air shCMer threshol ds change with zenith angle and hence background measurements must always be made at the same zenith angle to measure the real background. 'Ibis is almost invariably done so that it is very difficult to see hCM a systematic effect could introduce the narrCM phase effects reported, In Table 1, the various observations are summarized by group, the epoch of the observations, the energy threshold, the '[iiase of maximun emission and reference. 'Ihe observations are clustered by energy : (a) 0.1 to 10 TeV (b) 10 to 500 TeV (c) 100 TeV to 10 J?eV. Broadly speaking the observations in Cal which all used the ACT have the greatest reliabil ity ; those in Cb) where the techniques are mixed are the least reliable. 'Ihe most important results are discussed belCM: Cal TeV observations in the USSR; 1972-80. 'l'nese observations were made with simple atmos'[iieric Cherenkov detectors consisting of two or three 1,5 m aperture mirrors on a single mount. 'Ihe observations were taken in the drift-scan mode i.e. the earth's rotation swept the field of view of the detectors through the position of the source which was api;:arent as an increase in counting rate comi;:a red with the rate before and after the source was in the field of view. In th is way, the observations were taken at the same zenith angle and systematic changes were monitored by comi;:a ring the rates before and after transit of the source, 'Ihese experiments were carried out at the Crimean Astrophysical Observatory and at Tien Shan in eastern (CPD) Russia. 'Ihe first detection of TeV gamma rays came a few days after the 43

announcement of the giant radio outburst of September 2, 1972 as r:art of the world-wide campaign to observe Qygnus X-3 in this unusual high sta te, 'lhe results of these first few month s of observations were reported in the Proceedings of the 13th International Cosmic Ray Conference at I:enver, USA in

1973 (Vladimirsky, Ster:anian and Fanin (1973) l • HCMever, since the raper was not presented orally at the conference and since the results were not included in the special 1973 edition of Nature Physical Science that was devoted to results obtained during the outburst, the TeV garmna-ray results were largely ignored, at least in the Western Hemis{ilere. Unfortunately, this initial lack of interest in the observations which CPO were statistically significant, was to extend to the subsequent CNJ and Tien Shan observations for the rest of the decade. 'lhese USSR observations, taken with detectors whose sensitivity did not change wer eight seasons of observations, constitute the largest and most impressive data base of TeV observations of Qygnus X-3 . Unf ortunately there is no single publ ication which presents the details of all the observations although they have been summarized (Ster:anian 19821 Ster:anian 1983) and reviewed (Weekes 1985al , Fig. 2 shCMs the canposite light-curve over the eight years fran the CNJ

QJ 5 Vl "' _<:: a...... _ Vl 4 c:: 0 +-' "' 3 > QJ -0 -0 2 ,_ "' -0 c:: "' +-' Vl 1 4- 0 go CL______

.o ,1 .2 .3 .4 .s .7 ,8 1.

Figure 2, 'lhe 4,8 hour light-curve of Qygnus X-3 at TeV energies in which the excess fran source direction is plotted as standad deviations per 1/12 {ilase bin. 'lhe netthe excess is at the 3.9 sigma level based on observations fran 1972-80 (Ster:anain et al. 1982) . 44

Table 1

Publ ished I:etections of Qrgnus X-3

Group Location Ep:ich Ene rgy Phase of Reference (TeV) Max. Emission (a)Q,l l;o lO Tev

Crimean Crimea 1972 2 0.2 0.7 Vladim. et al. (1973) Astropqysical 1973 2 0.2 0.7 Observatory 1974 2 0.2 (1975) 1975 2 0.2 Step:inian et al (l977) 1979 2 0.5 Neshpor et al (1980) 1980 2 T Fanin et al (1981)

Lebedev Tian Shan 1977-78 5 0.2 0.8 Mukanov (1981) Pqys. Inst.

Whipple Whipple Obs. 1980 1 0.6 Weekes et al. (1981) Observatory Arizona 1981 0.3 T Weekes et al. (1982) Coll. 1983 0.6 0.6 caw1ey et al. (1985)

ISU-JPL Ecwards AFB 1982 0.5 0.6 Lamb et al. (1982) -UC california

CT. Durham Dugway , 1982-83 1 0.6 Gibson et al. (1982) Utah 1984 1 0.6 Chacwick et al. (1985)

(b)lQ tQ 2QQ Tey

Nuclear Gulmarg, 1976-77 500 0.6 Bhat et al. (1985) Res. Lab. India

U. Utah Dugway, UT 1983 500 0.2 Baltrus. et al ( l985bl 1985 500 T Elbert (this workshop) 'Ibr ino Platau Rosa, 1982 30 0.2 0.6 Morello et al. (1983) Italy

Institute Baksan, 1984 100 0.6 Alexeenko et al (l985) of Nuclear Research u. s. s.R.

(cl Q,l J;;Q lQ :Ee'll

Univ. of Kiel 1976-80 1000 0.2 Samorski and Kiel Germany Stamm (1983) w. Univ. of Havarah 1978-82 1000 0.25 Lloyd-E. et al (l983) Leeds Park, U. K. 1984 1000 0.6 Lambert et al (l985)

Univ. of Akeno Ranch, 1981-84 1000 0.6 Kifune et al (1986) Tokyo Jap:in 45

obsevations. 'lhree features of this result sh ould be emphasized Cll '!here is a net excess (3.9 sigrral fran the direction of the source irrespective of phase. (2) The cata is foldedwith the 4.8 period that was derived fran the gamma-ray observations by aligrnnent of the peak around phase 0.2. '!his independent measuranent of the 4.8 period (and period derivative) is in agreement with that derived fran the x-ray observations. (3) During the course of the observations the ligh t-curve was not constant i.e. there were times when emission at the later phases was more significant than that around phase 0.2. '!hegeneral features of this result were verified by a quasi-independent exi;:eriment at Tien Shan which was operated from 1977-79. '!he princip:i.l results fran these exi;:eriments are summarized belcw: (1) a periodic component of TeV gamma rays is detected fran Cygnus X-3 with an -11 -2 -1 average intensity of l.6xlo photons-cm -s • ( 2) the anission is concentrated in narrcw phase intervals corresponding to the emergence fran x-ray eclipse, the x-ray maximum and the entrance of x-ray eclipse . (3) there is also a sporadic component which is unrelated to the 4.8 hour period and which persists for some day s. (4) the gamma-ray emission may correlate with the radio outbursts. Since 1980, there have been no atmospheric Oierenkov observations of Cygnus X-3 in the USSR as the CNJ and Tien Shan groups are building new, and more sensitive, detectors. (b) TeV Observations in the USA. , 1980-83. 'lhree independent exi;:eriments ob served Cygnus X-3 in the TeV energy range using different versions of the atmosi:tJeric Cherenkov technique between 1980 and 1983. 'lhese exi;:eriments lacked the coverage of the USSR results, but they produced results that were ranarkably similar although individually they did not have the sta tistical significance of the USSR results. '!he first completely independent conf irmation of the USSR result came fran a joint Smithsonian Astroptrysical Observatory-University College, l)Jbl in exi;:eriment at the Whipple Observatory in southern Arizona in 1980. Using two 1.5 m reflectors in coincidence, an excess was seen at phase 0.6-0.7 using the vd<-BB ephaneris (Weekes et al. 1981) . l)Jring this period of observations (April-\June 1980) Cygnus X-3 underwent a maj or change .in x-ray activity ; the gamma-ray light curve was taken when Cygnus X-3 was near the peak of its x-ray activity ( fig. 3 (a) ). 'lhese observations, as well as subsequent observations at the same site, provide evidence for variability in the light-curve on time scales of months

'lWo 11 m Solar Concentrators were used as atmosrtieric Cherenkov detectors by a joint Jet Propul sion Laboratory--Oniversity of Ca lifornia at Riverside-lava State University collaboration to detect cygnus X-3 at energies of 0.5 TeV and above in August-September 1981 (Lamb et al. 1982) . 'Ihe drift-scan technique was

.o .1 .2 .3 ·." .s .s .1 .a _g 1 .

Figure 3. 'Ihe 4,8 hour ligh t-curves of cygnus X-3 in TeV gamma rays as seen in three experiments in 1980-83 . 'Ihe ordinate is in standard deviations per hase bin. (a) Whippl e Observatory (Weekes et al . 1981) ; (b) Ed.;rards A. F. B. (Lamb et al. 1983) ; (c) Dugway (1Jc111thwaite et al.1983) . 'Ihe def icits could be caused by excess emission f ran the galactic plane around cygnus X-3 (DowttMaite et al.1985) .

4.8 PERIOD

used but fast timing between the two separated detectors was used to pr eferentially select shavers caning fran the center of the field of view (and hence fran the direction of the source during transi t) . enhancement was seen An when cygnus X-3 was at the center of the field of view ; when th ese event times were folded with the vdK-BB ephemeris, the ligh t-curve sh avs a peak in the rtiase interval 0.6-0.8 at the 4.4 sigma level. 'Ihe light-curve is shavn in fig.3(b) . 'Ihe University of Durham (United Kingdom) group operated an array of four atmosrtieric Cherenkov telescopes at the Dugway Proving Ground in Utah, USA fran 1981 to 1984 . Each telescope consisted of th ree 1.5 m aperture detectors which were operated in coincidence, More than 350 hours observation of cygnus X-3 of were obtained in 1981 and 1982 in both the drift scan and tracking mode of observation. 'Ihe canbined results are shavn in fig. 3(c) ; there is evidence for substructure (as shor t as three minutes) also (Dowthwa ite et al. 1983) . Subsequent observations the general distribution emission in the galactic of of plane near cygnus X-3 suggest that the distribution may be non-uniform and that Cygnus X-3 may lie in a hollav in the plane (DowttMaite et al. 1985) , 'Ihis 47

would have the effect of increasing the significance of all drift-scan or ON/OFF observations (Qiacwick et al. 1985) but as the effect has not been confirmed, it should be treated with caution. 'Ihese th ree experiments provide evidence for an active fhase in the TeV gamma-ray emission centered on fhase 0.6 to 0.7. Hooever, it is clearly not steady emission and the D..!rham group have suggested a 19. 2 day modulation. At the peak of this modulation they see evidence for a statistically significant 12.59 periodicity. If conf irmed this result would be extremely important as ms it would provide the first direct evidence for the presence of a fast pulsar within the system and hence provide a vital clue to the acceleration processes involved. Hooever atmosfheric Olerenkov detectors are liable to various sources (man-made and natural) sources of optical contamination so that it is important that the periodicity be seen el sewhere, preferably with a non-optical technique. In these simple atmosf.heric Cherenkov experiments there is no evidence obtained about the nature of the primaries which have been assumed to be (and are consistent with) gamma rays. More sofhisticated atmosf.heric Cherenkov telescopes (Weekes 1985b; Hillas 1985) will be able to make this distinction. Cc) PeV observations: 1976-1984. 'Ihree air sh ooer experiments have reported evidence for the em ission of gamma rays with energies of 1 PeV or above fran Q{gnus X-3 . Ai r shower arrays, like atmosf.heric Cherenkov telescopes, are limited by the cosnic ray backgrcund; detection at high energies impl ies that the source spectrum is not steeper than the background spectrum. It is generally assumed that most source emission spectra will steepen with increasing energy. 'Ihese experiments were not originally designed to do gamma-ray astronany ; all are close to sea level and hence are sensitive only to primaries above 1 PeV. Taken together, the three experiments are consistent with the detection of PeV gamma rays fran Qrgnus X-3 but there are sane apparent iRconsistencies that point to source variability, and shower or detector p:irameters that are not completely understood. 'Ihe first report of the detection of PeV gamma-ray emission fran any source came fran the University of Kiel group (Samorski and Stamm, 1983) who had operated an air shooer array at Kiel from 1976-80. 'Ihe shooer arrival direction was determined in this array with unusually high accuracy (+/- 1.5°). 'Ihe data base was first culled to select only those shooers with a<}'! p:irameter, s > 1.1; these shooers corresponded to older and hence early developing, shooers such as those initiated by an electron or gamma ray. 'Ihe arrival direction of each shooer was sorted into bins of right ascension and declination. A band of right ascension (in 4° bins) centered on declination 40.9° (the declination of Qrgnus X-3) was plotted as in fig. 4; the bin centered Q{gnus X-3 , the on 48

C'fG lM I

Figure 4. Number of events per bin in oocl ination band tha t incluoos Qygnus X-3 (Samorski and Stamm, 1983) .

. '" lllGK'T •SCl!NSION c.(DEGltUSj

60 > Figure 5. r:ata fran Haverah Park foloodwith the 4.8 hour !� 11 period. 'Ihe ordinate is events per 1/40 piase bin CLl.oyd ··�· Evans et al. 1983) • ..c: "'·

� 20 Q. "' .µ i:: OJ > LU .25 .5 ,75 1.0 4.8 PERIOD

primary target of the search, sh

Stamm 1985) • Consiooring the snall number of events, these light-curves sh ould not be over analyzed. The controversy about the Kiel result does not stem fran its statistical significance but rather fran the nature of the i;:e.rticles ootected. When the data in the Q{gnus X-3 bin is examined in terms of its muon-to-electron ratio, it is found to be only slightly less than that obtained fran a typical proton sh

results (IJ.oyd-Evans et al. 1983) . A subset of the Haverah Park array was operated between 1978 and 1982 with an energy threshold of 1 PeV, 'lbe muon-to electron ratio was not measured in this experiment and the angular resolution ° was - +/- 3 . When all events were sorted by arrival direction, there was a 1.7 si� excess in the bin centered on Q{gnus X-3 . When these events were subj ected to a periodicity analysis with the vdK-BB epherneris, the light-curve sho.-m in fig. 5 was obtained. 'lbe peak at p-iase 0.225-0,25 is at the 5 sigma level i it is the narrGlest feature seen at any gamma-ray energy. It is difficult to see hGI such a sharp feature could be an artifact in d:ita spread over four years. 'lbe Haverah Park data shGI a cut-off at energies above 10 PeV. Mor e recent observations fran Haverah Park with a new array with impr oved sensitivity shGI a snall signal at phase 0.63 (Lambert et al. 1985) . Since neither the age parameter nor the muon-to-electron ratio was measured in the Haverah Park results, the signals do not bear directly on the nature of the primaries, 'lbe Akeno Ranch Air ShG1er Experiment is operated by the University of Tokyo and employs a wide variety of detectors so that many shG1er parameters are measured. r:ata taken between 1981 and 1984 have been searched for evidence of a signal fran Q{gnus X-3 . Only weak evidence for emission is found but that is in data selected to have a very small muon-to-electron ratio. A peak in the light curve (folded with the vdK-BB e?ierneris) is seen near p-iase 0.51 the significance of the detection is estimated as 2xlo-3 , considerably 1G1er than that of the Kiel and Haverah Park results. 'lbe chief interest in this result is that, if real, it points to gamma rays as the shG1er progenitors and hence counteracts the conclusion introduced by the Kiel result. New, and more sensitive, air shG1er experiments, which include large muon detectors, are nGI on-line in a number of countries so that definitive results on PeV gamma rays fran Q{gnus X-3 should shortly be available.

Ener'l{ SJ;lectrnn. Given that there is strong evidence for variability and that emission at different portions of the light-curve may have different spectra, it is not easy to plot a meaningful energy spectrum. Fig. 6 shGIS an integral energy spectrum with d:ita taken over many different epochs and averaged over many different periods of observation. It is obvious that the spectrum is very flat (cornpired with the observed cosmic ray spectrum) and can be fitted by a PG/er law exponent of -1 .1. Chardin and Gerbier (1986) have argued that a spectrum of this sort is just what would be expected if the signal arose fran sta tistical fluctrations at all energies, HG/ever, put another

I I I 100 � -

'TVI 3 N 10 g 'E I u l -6 T .!::: IT - I x ::l 10 '" u::: Roppin et al l1979 Meegan et all1979ll \ Galper et all1976l C5 c Lamb et al l1977l Figure 6. Ccrnposite of r....O'l � 109 t Hormsen et al 119831 o T gamma-ray measurements QJ T Weekes et al.11977) T ..._ v.. fran Q{gnus X-3 fran 1972 To Lamb et al. (1981 c: - -12 Oowthawaite etall19831I r I to 1984, derived fran 10 Q Neshporet aU 19791 0 Bhat et al. 1985, QJ D Danaher et nl.11981 1 v Mukanov et nl. 11980 A I I� QJ Morello Nnvarn (19831 t e - I & .� � 15 T Fegan et ai. (1981 1 10 Hnybshida et nl. 11981 T I I Lloyd- Evans etal. (19831 Samorskii Stamm 11983gJ & 2 11976-77 ). (19841 -18 Bhat , Bhat 12 a15 18 0 6 10 1 10 1 03 10 109 1 Photon Energy leY) expected if small, but statistically significant, signals were detected with current techniques in the TeV-f'eV energy range, If the signals were significantly larger than this, then they would have been apparent in previous general all-sky surveys of the Northern Hemisi;tiere. 'lbe fact, that they were not, limits the luminosity that might be expected. If they were any smaller than the measured values, then obviously they would not be detected and there would be no energy spectrum to dispute ! Hence, given tha t the detected signal is most likely to be close to noise, there is only a snall range of spectral indices that are expected. It is exactly this reasoning that led to 10\\1 expectations of the detection of a signal at f'eV energies and hence the absence of experiments specially designed to do gamma-ray astronO!l!{ at f'eV energies, 'lbe energy spectrum of Q{gnus X-3 is of more than academic interest, At energies close to 1 f'eV it is expected that ];hoton-];hoton pair producticn Con the micrCJl\'ave i;:hotons fran the 3° black body background) will cause an absorption dip, which, if measured, would have a number of interesting impl ications. It would be the first direct verification of the ];hoton-i;:hoton interaction, it would verify that the 3°K field extends to the source, it would give a measure distance to source and perhaps nost important at this of the the 51

instant, it would verify that the primary quanta were indeed gamma rays,

Time Variability. For many phy sicists the most disturbing aspo!ct of the detection of very high energy garrma rays fran Qygnus X-3 is the clear indication that the signal is variable with time. 'lhis illustrates the fundamental difference between high energy pJwsics and high energy astropJwsics. In physics the fundamental µirameters are constants which are always verifiable. In astrophy sics the only constant is that most of the observed phenanena are not constant ! Verification is still necessary but is often difficult because it must come at a later epoch and po!rhaps fran another analogous source. 'lhat the observed emission fran an x-ray binary should vary in ampl itude, in phase or even in frequency, is not unique to the se wavelengths or to this source. 'lhe sources that populate the universe of the high energy astropJwsicist are anything but constant. 'lhe degree of variability often increases with the energy of photon observed, In x-ray astronany sources vary by factor s of 104 in amplitude i their time variations may range fran milliseconds to years and the form of the variation can be po!riodic, quasi po!riodic, transient or completely irregular. It would be naive to think that this kind of variability would not also be seen at garrma-ray energies i in fact, there are a number of reasons to bel ieve that it would be more pronounced at the highest energies. Very high energy gamma rays are inevitably the by-product of the interaction of very high energy µirticles (ions or electrons) within the sources. It is notoriously difficult to accelerate µirticles to energies in excess of 1 TeV in man-made accelerators. Even using our most sophisticated 20th century technology, it is difficult to maintain the conditions necessary for efficient µirticle acceleration. It is hard to conceive of a natural µirticle accelerator which would act like a standard candle, 'lhe target material (the beam dump) is also a variable which must increase the fluctuations in the gamma-ray beam. In the chaotic conditions of cosnic sources (µirticularly those in which accretion is the driving energy source) a steady flux of gamma rays must be the exception rather than the rule. 'lhe only cosnic source where we can directly monitor the production of high energy µirticles is the sun. Nobody could eXpo!ct the flux of gamma rays produced in solar flares to be a standard candle. It could be that cosnic µirticle production takes place as a series of flare-like outbursts. Qygnus X-3 is knam to be variable at every wavelength at which it can be monitored. 'lhe radio outbursts, which only last for days, are seµirated by years of inactivity and represent increases of intensity of factors of 103 to 52

io4• Flaring activity is also seen in the infrared. 'Ihe long term x-ray behavior is shwn in fig. 7 as 10-day averages observed by a Vela satellite. If the x-ray detectors were less sensitive or if the source was further

Cyg X-3 Figure 7. X-ray measurements (3- 12kevl fran Q{gnus X-3 plotted as 10-day averages fran 1969-76 as seen by the Vela 5B satellite (Priedhorsky and Terrell,1986) •

As we shall see belw, the gamma-ray observations sugge st that Q{gnus X-3 is an extremely pwerful source of cosmic rays. A source of th is luminosity would not be expected to persist for long ; Hillas (1985) has suggested a lifetime of 100 years meaning that the source is evolving rapidly. Bhat et al. (1985) have suggested that there may be evidence for a secular decrease in gamma-ray intensity. 'Ihe evidence for th is decrease is still rather sketchy and the conclusion does not seem justif ied. A secular decrease should also be seen in x-rays.

Other sources. 'Ihere is increasing evidence that Q{gnus X-3 is not alone as an x-ray binary producing very high energy gamma rays. A recent catalog of observed TeV or T'eV sources (Ramana Murthy 1985) lists twelve sources including the Crab and Vela pul sars, the Crab Nebula and Centaurus Since not all of these have been A. independently verified, the list must be treated with sane caution. 'Ihe binary x-ray sources that have been seen at TeV or PeV energies are listed in Table 2. While those at the top of the list can be considered as well established, having been seen by one or more groups, the others

'!able 2

TeV-PeV Observa tions of X-ray Binaries (excluding Cygnus X-3) source Energy Technique Group Epoch Reference

Her X-1 TeV AC Univ. of 1983 Cllacl'1ick et al. (1985) Durham

TeV AC Whipple 1984 Gorham et al. (1986) Obs.Coll.

PeV AC U. of Utah 1983 Baltrus. et al .(1985a)

4U0ll5 TeV AC Crimean 1971-73 Stepmian et al. (1975) +63 Ast. Obs.

TeV AC Univ. of 1984 Cllacl'1ick et al. (1985) Durham

TeV AC Whipple 1985 I.amb et al. (1986) Obs. Coll.

Vela PeV PA Cllacaltaya 1964-66 Suga et al. (1985) X-1 Mt.Coll.

PeV PA Univ. of 1982-83 Protheroe et al. (1984) Adelaide

LMC X-4 PeV PA Univ. of 1982-83 Protheroe and Clay (1985) Adelaide

Cen X-3 PeV PA Cllacaltaya 1964-66 Suga et al. (1985) ColMt. l.

LLJDinosity. Cosmic Rav Ap:trt fran the impl ication of hitherto unsuspected modes of p:i.rticle acceleration in binary x-ray sources, the astrophysical importance of the detection of very high energy gamma rays fran Cygnus X-3 arises fran the impl ied total luminosity in high energy p:i.rticles. '!be flat energy spectrum (figure 6) means that at the highest detected energies (1-10 PeV) the gamma-ray luminosity is canp:i.rable with the x-ray luminosity in the keV region. '!be p:i.rticle 11.111inosity must be even greater. '!be gamma ray lLJDinosity Lg is obtained fran the expression: 2 Lg = 4M d • e. Fg 54

where F the observed gamma-ray luminosity between g = -2 -1 1 and 10 F'eV in ergs -cm -s d distance to the source in cm e absorption correction -lO -2 -1 Fran the air shCMer experiments F 10 erg-cm -s • '.Ihe distance is not g = easy to measure. '.Ihe best distance estimates rely on optical measurements which are not possible for cygnus X-3. D.Jring the large radio flares, the 21 cm absorption feature can be measured with high accuracy and the presence of intervening hy dJ;ogen clouds (HI regions) can be 6x10 x 10 x 10 - 6x1038 erg-cm-2-s-l . Hillas (1984) has estimated the flux of particles required to keep the -2 -1 observed cosnic ray flux in equilibrium as 2 x 1037 ergs-cm -s • cygnus X-3 55

is thus more than sufficient to supply the entire galaxy. Since it is unlikely that this is a unique source, the implication is that it must evolve rapidly. 'Ihe pi.rticle production can be significantly reduced if the p:irticle production is beamed. 'Ihere are as yet no canpletely satisfactory model s of (¥gnus X-3 and the full significance of the discovery of the gamna-ray em ission for theories of cosmic ray origin must await such models. HCMever, it seems likely that there is a direct link bebl'een the production of high energy p:irticles in x-ray binaries and the observed cosmic radiation.

Discussion Reports of a phenanena such as the emission of high energy quanta fran new (¥gnus X-3 deserve critical scrutiny. O!ardin and Gerlier (1986) and Molner (1986) have recently expressed sane reservations about the val idity of sane of the claimed detections of (¥gnus X-3. Sane th eir criticisms may be valid but of because a small nll!lber of the reported observations are doubtful, it does not foll CM that the phenanena is not real. 'Ihe sheer number of "non-sta tistical " observations reported fran the di rection of (¥gnus X-3 is difficult to explain in arw other way than in the detection high energy photons. Short of an of international conspi racy, an unconscious boot-strapping or a most unl ikely series of coincidences this seems the most likely hypothesis. More and better observations are urgently needed and fortunately these should soon be forthcaning. improvement in sensitivity by even a factor of 2 An or 3 should settle the issue. 'Ihe above ground experiments say little about the nature of the detected p:irticle, p:irticularly at lCMer energies. 'Ihere is thus little that can be said about the underground detections except to note that the bl'o reported detections are not consistent with the gamma-ray flux measurements. I am grateful to Drs. Cllardin and Molner for preprints of their work and to several colleagues for critical discussions p:irticularly Drs. M. F. cawley and R. C. Iamb. 'Ihe work is supported by the u. s. n. o. E. References

Al.exeenko, et al. : 19th I. C.R. IaJolla, 91 (1985) . Baltrusaitis,v. v. R. M. et al. : Ap. J. Lett.c. , , 169L (1985a) . Bal trusaitis, R. M. et al. : 19th I.C.R. C. , 223_, La.Jolla, 234 Cl985b) . Bhat, C. L. et al. , 19th I.C.R.C. , IaJolla, 83 (198L 5) . G:twley, M.F. et al. : Astroi;t'lys. J. , �. 184L (1985) . Q:iw ley, M.F. and Weekes, T. C. : Astron. Astrophys. , 80 (1984) . ill, Qia

Chardin, G. and Gerbier, G. i preprint (1986) . Dickey , J.M. i Astrophy s. J. , 21l, L7 1 (1983) . DcMthwaite, J. C. , et al. i Astron. Astrophys. , 1 (1983) . DcMthwaite, J. C. , et al. i Astron. Astrophys. , J.2[, 55. (1985) . Fomin, V.P. et al. i 17th I.C.R.C. , Paris 28 �.(1981) . Geldzahler, B.J. et al. i Astrophys. J. , 21lrL I.65 (1983) . Giacconi , R. et al. i Astrophy s. J. , Lll9 (1967) . liar Gibson, A. I. et al. i Proc. Ooty Workshop, 97 (1982) • Gorham, P. M. et al. i preprint (1986) . Gould, R.J. Astrophys. J. , (1983) . Hillas, A.M.l Nature, 5021lr (1984) L23. Hillas, A.M. l 19th I.Cill,.R.C., Ia.Jolla, 445 (1985) . Hj ellming, R.l M. Science 1089 (1973)J_, . Johnston, K. et i al. i preprintJ.a2, (1985) . Kifune, T. et al. i 19th I. C.R. C. I.aJolla, 67 (1986) . L van der Klis, M. and Bonnet-Bi&.ud, J. M. i Astron. Astrophys. , 2,5., (1981) • R. C. et al. i Nature 543 (1982) . L5 Lamb,lamb, R.C. et al. i preprint22[, (1986) .

Lambert, A. et al. i 19th I. C. R. c. , I.aJolla, 71 (1985) • Lloyd-Evans, J. et al. i Nature, �. 784 (1983)L . Molnar, L. A. et al. i Nature 662 (1984) . ll..Q., Molnar, L.A. et al. i preprint (1986) • Morello et al. i 18th I. C. R. C. Bangalore 127 (1983) . Mukanov, J.B. et al. i Izv. Kryrn. Ast. Ob.L 151 (1981) . 6..J., Neshpor et al. i Izv. Kryrn. Ast. Ob. 61 (1980) • PriedhorskY, W. and Terrell, J. i 6.l,886 (1986) . Protheroe, R.J. et al. i Astrophys.lQJ.., J. Lett. IA7 (1984) . Protheroe, R.J. i 19th I. C.R. C. , I.aJolla, 200.,297 (1985) . Protheroe, R.J. and Clay, R.W. i Nature L 205 (1985) . Ramana Murthy, P.V. i I. A.U. New Delhi (1985)ID, (In press) . Samorski, M. and Stamm, i Astrophys. J. , Ll7 (1983) . Samorski, M. and Stamm, w. i Techniques in 2@.,tra High Energy Gamma-Ray Astronaey", Wor kshopw. Proceedings, I.aJolla,U1 85 (1985) . Stepmian, A. A. et al. i 15th I.C.R.C. , Pl ovdiv, 135 (1977) . Stepmian, A. A. et al. i Proc. Ooty Workshop on L Gamma-Ray Astronaey", 43 (1982) . VHE Step:mian, A.A. i Advances in Sp:ice Research, 123 (1984) . J_, Suga, K. et al. i Tech. in UHE Gamma-Ray Ast. , Ia.Jolla 48 (1985) • Vestrand, W.T. and Eichler, D. i Astrophys. J. , 251 (1982) . VladimirskY, B.M. et al. i 13th r. c.R.C. 456 22,l,(1973) . VladimirskY, B.M. et al. i 14th I. C.R. C. MunichL 118 (1975) . Weekes, T.C. i Astron. Astrophys. l2l.r 23 2 (1982)L. Weekes, T.C. i Proc. of Conf. New Particles '85, Madison CJ,985a)

Very High Energy Gamma-Ray Observations of Hercules X-1 and 4U0115+63

Trevor Weekes Whipple c.Observatory Harvard-Smithsonian Center for Astrophysics P.O. Box 97, Amado, 85645-0097 NZ,U. S. A.

Abstract

'lhe canµiratively well-imderstood x-ray binary, Hercules X-1 , has been detected by two groups at TeV energies and one at PeV energies, all using the at:rocispheric Clierenkov technique. '!he x-ray binary, 4U0115+63 is aPEBrently the same source as casGamma -I, detected by the Crimean Astroptwsical Observatory as a TeV gamma-ray source in 1971. It has been seen as a pul sed TeV source by two groups in recent years. Because these sources have optical coimterµirts, they are better candidates for investigating the mechanisns cosnic ray µirticle acceleration than Q,rgnus X-3 . of 58

Introduction Because Qygnus X-3 is optically obscured, it is unlikely that a complete understanding of the system will be obtained ; for th is reason a considerable effort has been made by very high eI"Ergy gamma-ray astronaners to find similar obj ects (albeit weaker) which are sources of very high energy psrticles. 'lhe two best candidates are Hercules X-1 and 4U0115+63, each of which has been detected at energies greater than 0.5 TeV by three indei:enrent groups. 'lhey are also unique in that they are the only two x-ray binaries that have been observed to have cyclotron features in the tens of kev energy range.

Hercules X-1 'lhis was first retected at TeV energies by the University of Durham group in a three minute outburst which was believed to coincide with the onset of the 35-day cycle (DoNthwaite et al. 1984) . 'lhe flux, which was all pulsed at the -9 -2 -1 1.24 pul sar i;:eriod, was l.2xl0 photons-cm -s ; the energy th reshold was 1 TeV. For a distance of 5 kpc this corresponds to a total gamma emission of 36 -1 8x10 erg-s • Subsequent observations by the same group later that year did not retect any signal above the 2 sigma level. TeV emission fran the pul sar in the Hercules X-1 system was conf irmed by the Whipple Observatory llaborationco in 1984 and 1985 Ccawley et al. 1985, Gorham et al. 1986) • Pulsed emission is retectable about 8% of the total obse rving time. 'lhe retails of the observations are given in Table 1. Fran this limited data set it api:ears (a) that the em ission is predominantly during the Main On state of the 35-day cycle (b) that there is no clear correlation with the 1. 7 day-cycle (c) that the em ission is all pul sed at the 1.24 s pulsar frequency and (d) that the gamma-ray emission frequency may be slightly different fran the x ray frequency but within the range of IX>ppler sh ifts of the Hercules X-1 system. Observations in June, 1985, sh

Summary of Hercules X-1 Observator ies

Il9.te of Group/Site 'lbreshold Phase D.lration Emitted Energy Orb Pree (Minutes) Energy Observation 1 (TeV) (erg-s l

36 17 Apr il D.Jrham 1 0.76 3 8xl0 1983 u.IX!gway, UT o.o 37 ll July U. Utah 500 0.66 0.63 >40 10 1983 D.Jgway , UT 35 4 Apr il Whipple Obs. 0.25 0.42 0.12 >28 2x10 1984 Coll. N1.. 35 5 May Whipple Obs. 0.25 0.58 0.98 >90 2x10 1984 Coll. N1.. 35 23 May Whippl e Obs. 0.25 0.18 0.50 >25 2xl0 1984 Col l. N1.. 3 16 June Whipple Obs. 0.6 0.95 0.7 ? >100 2x10 1985 Coll. N1..

Because Hercules X-1 is aPEBrently active a large fraction of the time and because of the increased sensitivity that the pulsed canponent gives, it is potentially the best candidate for understanding mechanisms of high energy p:irticle acceleration in binary systems.

400115+63 '!his is a transient X-ray source which is only detectable for a small fraction of the time. When it flares in x-rays it increases in intensity by a factor 104• '!his emission may last for weeks and during this time a pul sar of period of 3.616 s is detected together with a 24-day orbital period. A chronology of observations is given in Table 2. In 1971-72 the Crimean Astrophysical Observatory group (Step:inian et al. 197 2) discovered a transient source close to the position of 4U0115+63 at energies of 1 TeV. 'lbe source was seen twice for periods of about 30 days. '!here were no coincident x-ray observations. '!he source, cas Gamma-I , was not identified with any known object but later the app:irent coincidence with a 100 M;!V source was noted (Step:inian et al. 1979) • '!he University Durham group observed 4UOll5+63 in September, 1984 because of 60

it resembled Hercules X-1 in sane ways (Chacwick et al, 1985) . In nine nights observations they detected a signal at the predicted pulsar period. '!here of -ll was no evidence variability and the signal level was 7 x 10 -2 -1of photons-cm -s • For a distance 5 kpc this corresponds to a total energy 35 -l of emission of 10 erg-s Because the positional coincidence and the of transient behavior Cas Garrana-1 has been identified with 4U0115+63 (Lamb and Weekes (1986) ), TeV emission was again detected in October, 1985 , by the Whipple Observatory Collaboration as a three day outburst (Lewis et al. 1986) . 'lhe flux level was similar to that seen in the earlier observations and the signal was pul sed with a slightly longer period, During its periods x-ray emission the source is

. of observed to have a larger P term so that the observed signal is consistent with earlier observations,

Discussion UHE gamma-ray emission has been reported at PeV ergiesen fran Vela X-1 (Protheroe et al, 1984 1 Suga et al. 1985) , U1C X-1 (Protheroe et al. 1985) and Cen X-3 (Suga et al. 1985) but only Cygnus X-3 , Hercules X-1 and 4U0115+63 have been seen by at least three independent experirrents. Sare the properties of of these three sources are listed in Table 3. Although the three systems have sane very obvious differences (only Cygnus X-3 is a strong radio source, 4U0115+63 is transient x-ray source, Hercules X-1 has lCM mass and circular orbit, 4U0115+63 has high mass and a highly eccentric orbit) , they do have one outstanding property in common -- evidence for a cyclotron emission feature. Hercules X-1 and 4U0115+63 are the only x-ray binaries kn<:Mn to have a cyclotron feature. A cyclotron feature is seen in the direction of Cygnus X-3 but it cannot be positively identified with the source because the wide angle the detector. of of '!here is as yet no satisfactory model to explain all the features of the observed very high energy emission fran these sources. 'lhe nstruction co of detailed models is probably premature until further observations at greater sensitivity allCM the detailed time history the very high energy ganrna-ray of emission to be determined. I am pleased to acknCMledge the assistance the other members of the of Whipple Observatory Collaboration, M.F. cawley, D, F, Fegan, K,G, Gibbs, P.W. Gorham, R. C. D. A. Iai'is, N.A. Porter, and V,J, Stenger. Iamb, '!his work was supported by the D. u. s. o. E, 61

Summary of Outbursts of 4U0115+63 rate Wavel ength Instrument Duration Reference (D:!ys)

�c. 1970 X-Ray UHURU 90 Forman et al. (1976)

Sep. 1971 VHE Gamma Ray C. A. O. 30 Stepi.nian et al. A. C. T. (1972)

�c. 1972 VHE Gamma Ray C. A. O. 30 Stepi.nian et al. A. C. T. (1975)

Mar. 1973 X-Ray OS0-7 2 f.brkert (1985)

Mar. 1973 HE Gamma Ray Sl\S-2 7 Houston and Wolfend3.le (1983)

�c. 1977 X-Ray Sl\S-3/ 30 Rose et al. (1979) Ariel 5

Sep. 1980 Optical l.3m McGraw 90 Kriss et al. (1980) Tel.

�c. 1980 X-Ray Hakucha/ 30 Ricketts et al. (1981) Ariel 6

Sep. 1984 VHE Gamma Ray Durham 9 Cl:tac:Mick et al. (1985) u.A. C.T.

Oct. 1985 VHE Gamma Ray Whiwle Obs. 3 lewis et al. (1986) A. C. T.

Compi.rison of TeV binary sources.

Source Time scale cyclotron Luminosity Spin Orbit Precession lire (kev) X-Ray VHE Gamna Rays erg-s-1 erg-s-1

<:yg X-3 12.59ms 4.8h 19.2d ? 85 (?) (?) 34d?

Her X-1 l.25s l.7d 35d 30-50

4U0115+63 3.6ls 24d Transient 11.5,23 62

References

Baltrusaitis, R. M. et al. ; Ap. J. Lett. , ...223_,I.69 (1985) G:iwley , M.F. et al. ; 19th I. C.R.C., IaJolla, 119 (1985) . Chadvick, P. M. et al. ; Astron. Astroi:tJys. 2., (1985) . D:Mthwaite, J. et al. ; Nature 691 (1l.2l_,984) IJ.. Forman, et al.c. ; Ap. J. Lett. J..Ql!, L29 (1976) . Gorham, w.P.W . et al. ; preprint (1986)2Q.6.,. Gorham, P.W. and Learned, J. ; preprint (1986) . Houston, B. P. and Wolfendale, ; Astron. Astroi:tiys. l.22., 22. Kriss, G. et al. ; Ap. J. 806A.w. (1983) . 2Qli, Lewis, D. et al. ; B. (in press) (1986) • Markert, T.A.H. ; private A.canmunicatio A.s. n (1985) . Protheroe, R.J. et al. ; Ap. J. Lett. IA7 (1984) . Protheroe, R.J. and Clay, R.W. ; Nature2llQ, 205 (1985) . Ricketts, M.J. et al. ; Sp. Sci. Rev. ill,399 (1981) . Rose, L. et al. ; Ap. J. 919 (1979);lil,. ZiJ., Step:mian, et al. ; Nature Phy s. Sci. 40 (1972) • Stei;:anian, A. A. et al. ; Astroi:tiys. Sp. Sc23..2_,i. , 267 <1975) . Stei;:anian, A. A. et al. ; Bull. Crim.& Ast. Obs. QQ,JJl., 80 <1979) . Suga, K. etA. al. A. ; Proc. Workshop on Techniques in Garnna-Ray Astronomy, UHE IaJolla. 48 (1985) • 63

CYGNUS X-3 AT HIGH ENERGIES: A CRITICAL REVIEW

G. Chardin

DPHPE, SEPh, CEN Saclay

ABSTRACT: The standard model would be endangered if deep-underground observations of muons coming from Cygnus X-3 were confirmed. The detection of cosmic radiation at high energies from Cygnus X-3 would also have far reaching implications in astrophysics. We review the underground and surface experiments and question the consistency of the reported observations. We propose some experimental and statistical tests to settle this important question. 64

I. INTRODUCTION

the last few years, many groups have reported evidence for the gamma ray emission In of Cygnus X-3 at higher and higher energies (see review by Watson Recently, two 1l). underground experiments claimed observation of an excess of muons pointing towards Cygnus X-3 Although the combined evidence from all results seems impressive, we will 2-3l. show that no measurement is convincing by itself; in addition, a large number of questions threaten the consistency of all these data. We would like to present some arguments explaining our reservations. We will first discuss the gamma ray observations per energy range and then the data from deep underground experiments. We will then propose some experimental and statistical tests to settle this importantquestion.

GAMMA-RAY OBSERVATIONS II.

In the 30 MeV- 1 GeV range, the SAS-2 satellite experiment reported an excess of 4l gamma-rays (data taken in March 1973) pointing in the direction of Cygnus X-3, together with a modulation in time along its period. The COS-B satellite collaboration (data taken betwen 1975 5l and 1982) found a spatial distribution of the emission which is compatible with that observed by SAS-2. However, taking advantage of a much larger statistics ( = 2 orders of magnitude), they also showed that this distribution is entirely compatible with that of the diffuse emission of the * interstellar gas in the Cygnus X-3 direction (Fig 1). Moreover, the phase distribution( ) for their events appears completely flat. When the SAS2 data is re-analyzed using this new value for the background, the chi-squared probability appears marginally significant (=2.5 s.d.), but one must take into account the fact that the binning has been chosen to optimize the signal (dataare grouped in five bins [0.9, 1.1], [1.1, 1.3], ... ) and that the negative part of the phase plot now contributes significantly to the chi-squared value.

Above 500 GeV, measurements have been reported by 14 independent groups (see review by Watson . The various detectors fall mainly into two categories: air Cerenkov 1l) telescopes with a threshold energy between 500 and 2000 GeV and air shower arrays sensitive to energies above 300 Te V. It should be noted that, except for one case 6), the reported signals never result from the direct observation of a clear excess of events in the direction of Cygnus X-3, but from a "peak" in the phase distribution. ** In the TeV range (mainly the air Cerenkov telescopes< l), some of the experiments have a fairly good statistical accuracy, but there are some details which cast a shadow of doubt on its significance: - since the period of emission of Cygnus X-3 is very close to l/5th of a sidereal day, there is a correlation between the phase and the period of observation. Unexpected harmonics can resultfrom this coincidence. The Cerenkov experiments operating in the tracking mode are very sensitive to an error in the background estimate since the energy threshold varies rapidly with the 65

zenith angle and the conditions of observation ; a small error on the estimator of the background 7bJ can then simulate a signal. The high optical activity in the Cygnus region (Gamma Cygni, the crossing of the galactic plane) tends also to increase the background level in this region. - the Cerenkov experiments operating in the transit mode have a safer background estimate but are severely limited by low statistics. Moreover, when using the transit mode, some data are rejected when the OFF-source regions do not fulfill homogeneity or compatibility criteria 8·9l; however, this does not guarantee that some background problem, which could simulate a signal, does not occur in the ON-source regions. As a general comment which also applies to the experiments discussed below, one can question the published level of significance for signals which are maximized with respect to the period or the binning of the phase plot or the size and position of the angular window used lOJ, 7l, to select the events 2·3l. Moreover in the last thirteen years, gamma-ray observations from Cygnus X-3 have been reported virtually everywhere in the phase histogram. The signals appear to have a sharply peaked structure(Samorsky and Stamm, Lloyd-Evans et al., Bhat et al.) or a rather broad distribution (Marshak et al., Samorsky and Stamm when their data is analyzed using the more recent ephemeris from Van der Klis and Bonnet-Bidaud, Kifune et al.) so that no independent constraint can be used either from the location of the peak or from its structure a priori. The observation of a pulsar associated with Cygnus X-3, with period 12.5908 ms, has been claimed by the Durham group 11l. Starting with a sample of 450 events distributed over a 7 observation period, this result has been obtained by scanning the period between 10 ms and 50s mn and selecting the one which gives the smallest probability to the Rayleigh test. The probability of occuring by chance is stated to be 4.8 10-8; this probability becomes 3 10-3 when corrected for the number of trials. In addition, they found that the most populated 1 mn sub-intervals show a clear modulation. A conservative probability of their observation is then stated to be less than 3 10-7 when combined with period scanning on other samples. Even on the 7 sample, the Doppler mn shift should prevent the folding of the data. Moreover, this observation has not been confirmed by other experiments operating during the same periods. Evidence for the variability in the emission of Cygnus X-3 has been reported but 7•-bl, the data samples exhibit negative fluctuations which are too large to originate from a Poisson distribution (see in particular the samples 4 and 8 on figure 1 of ref. 7a). If one assumes that the negative fluctuations in these samples originate froma distribution which still has a variance (i.e. if one renormalizes the fluctuations), the evidence for the emission and variability of Cygnus X-3 becomes only marginally significant (less than 2 sigmas). At very high energies (1015-1016 eV), the Kiel experiment (data taken between March 1976 and January 1980 6l ) is probably the only one reporting a clear and steady excess of events in the direction of Cygnus X-3, fromthe spatial distribution of the events (at a level of 4.4 sigmas). In addition, the phase distribution shows an impressive peak with a very fine structure and with a probability of occuring by chance of 10·8; several comments can be made concerning this well-known experiment: 66

- the ephemeris used was that from Parsignault et al. since the publication of the 12>; result, more precise ephemeris have been computed by Van der Klis and Bonnet-Bidaud13) . When the Kiel group use this new ephemeris and apply the heliocentric correction (which was not done previously) "the peak broadens and shifts the signal in the phase diagram to the interval 0.1 to 0.3" The statistical significance of the signal is then greatly reduced, which is quite surprising 1>. since this treatment of the data is supposed to be more correct. - generally, the particles detected in these experiments are assumed to be gamma-rays, which represent only 10-3 of the cosmic-rays, since this is the only known particle which meets the requirements of being neutral, stable and light (to keep both the spatial and temporal information from Cygnus X-3). However, using the flash tube array which complements their scintillator array, this group foundthat the muon content is approximately 80% that of normal nucleon-like showers. This is in contradiction with the expected muon content forgamma-ray induced showers (less than 10% of the muon content of normal events 14l) and also with the Akeno result for which the 15> selected events have a ratio N iN less than 3 % of the ratio for normal events. µ e - to increase the proportion of gamma-ray induced showers, the Kiel group has made a selection on the shower age parameter. However, "the justification for this approach is not clear and indeed the Ooty group find their most significant signal (1.5 sigma at phase = 0.675) when showers of all ages are used" l). In the energy range considered, the various flux estimates from Cygnus X-3 appear rather inconsistent, and it has been suggested 16-17) that the emission of Cygnus X-3 was decreasing with time with a characteristic decay time of the order of a few years (Fig. There 2). could be another interpretation: taking into account the luminosity(***) of the detectors (Table!), a strong correlation appears between the decrease of the observed flux and the increase of the luminosity of the detectors. This is indeed what would be expected if all the signals reported were statistical fluctuations. In particular, the Gulmarg group who reports a signal two orders of 16>, magnitude higher than the other groups, at a 6 sigma level, uses as a detector two uncollimated photomultipliers. (A somewhat similar argument has been used by J. van der Velde: he proposed to plot the energy output of high-energy gamma-ray sources as a function of the square of their distance from the Earth.) All these flux measurements seem to fit a power-law spectrum with an index = for -I.I the integrated flux (Fig. 3). We have tried to estimate the index which would be obtained if the "signals" were produced by statistical fluctuations. For a given experiment with a threshold energy

E, the number of events N (E) observed in a portion of solid angle (E) is equal to : e

N (E) L (E) * (E) * e (E) =

where (E) is the integrated flux above the energy E and L(E) the luminosity. A statistical

fluctuation on N (E) will be roughly proportionnal to /N(E) so that the "measured flux" 67

corresponding this fluctuation is : to (E) (E) /L(E) = µ(E) * /8(E) JL(E).

DEEP-UNDERGOUND EXPERIMENTS III.

In the domain of deep underground experiments, the Soudanl and NUSEX 3•-b) 2•-b) experiments have quasi-simultaneously claimed evidence for a time-modulated emission from Cygnus X-3. In the first publication of the Soudanl group the maximum signal in the phase 3•l, histogram was obtained with muons selected in an angular window (6° in diameter) centered on a direction 2.7 ' away from the direction of Cygnus X-3; the signal consists of 84±20 events ; but, fromthe variation of the chi-squared value when the center of the window is varied, it appears that, when centered on Cygnus X-3, the chi-squared probability becomes of the order of 10%. However, in the second publication with the same data and for anangular window centered on 3bl, Cygnus X-3, the background estimate is now uniform along the phase and the signal becomes (60±17) events; this corresponds to a probability of occuring by chance of 2 104. These two results seem hardly compatible. In the same publication, the authors analyze the pairs of events occuring within a short period of time (0.5 h). They observe a signal in the phase distribution which amounts to 29 muon pairs. The background level used to compute the signal in that distribution (8 events/bin) is said to be calculated from two nearby off-sourcereg ions; we have done this calculation and found a mean background level of 8.8 events per bin. Their background calculation assumes the flatness of the phase distribution; a crucial point which should be tested. Moreover, since they have used only 2 windows out of the 59 similar windows on the Cygnus X-3 path for the background calculation, the uncertainty in the background level limits the significance of the signal to less than 3.5 sigmas. We can then ask what is the probability to find a 3.5 sigma (positive) signal in a plot of 20 bins in any group of 1 to 5 adjacent bins (the maximal evidence is found in a group of 5 bins) with a Poissonian distribution having a mean of 8 for each bin: the answer is � 3%... These 29 event pairs (corresponding to 58 single muons) are to be compared to the 6o± l 7 events of the first analysis: this would mean that the observed signal consists almost exclusively of bunches of muons; such a peculiar behaviour should be observed by the other experiments. 68

The NUSEX group has also reported a signal of 19 events above a background of 2aJ 13 in the phase histogram. Here also, the background phase distribution is assumed flat. Moreover,

it should be noticed that the size of the angular window (10'* 10') has been chosen to optimize the

signal. In fact, the quoted angular resolution ( = 1 ') and the dispersion due to multiple scattering and the geomagnetic field 0.5 ') leads to an appropriate size of the order of 3'*3' ; the 19 events ( = of signal would then be expected to lie in that window: only 2 are observed. As the nature of the

parent particle is unknown, one could invoke a specific production mechanism that would give a very high transverse momentum to the muon and explain the large angular spread; however, Pt

even a of 5 Gev/c would induce only a 0.1 angular deviation relative to the parent particle for a Pt ' muon of 5 Tev (threshold energy for the NUSEX experiment). In any case, if such a large spread

is a true effect, the SOUDAN experiment, with a lower muon energy threshold, should not have

seen any signal in their smaller window. As a test of the authenticity of its signal, the NUSEX

group has studied the variation of the statistical significance of their signal with the period of 2bl Cygnus X-3 (Fig. 4a). They found that indeed the maximum of significance occured at the nominal

value. We would like to point out that this does not prove that the signal is truly authentic. This

could also occur in the case of a rather large statistical fluctuation and is strictly analog to the

behaviour of the Boltzmann function in statistical mechanics; we have done a computer simulation

of the NUSEX data and found a shape of the variation of the probability with the period quite similar to the NUSEX one (Fig. 4b).

Molnar has made similar comments on the statistical significance of the NUSEX 21•22l and SOUDAN observations. He stresses the point that these authors do not take into account the

non-uniform structure of their background. The two methods used to estimate the background

distribution in the two publications of the SOUDAN group give a priori biased estimates of the

expected phase distribution, and cannot test the hypothesis that this expected phase distribution is

not uniform. Moreover, Molnar calculates the chi-squared probability for the hypothesis of a flat

background in the control samples used by these experiments, namely 0.09 for the NUSEX

experiment and 0.08 forthe SOUDAN experiment, indicating that the background is probably not

expected to be uniform. Assuming that both their test and control samples derive from distributions

with the same variance, he finds, using the F-test, a confidence level for the compatibility

hypothesis between the signal and background samples which is 0.11 for the SOUDAN data, and

0. 17 for the NUSEX data. This means that even without taking into account the optimization of the

signal with the size of the angular window, the signal samples do not appear very different from the

control data samples.

With larger detectors and statistics, the Frejus and Karnioka 19l experiments could 18l not confirm the observations of the NUSEX and Soudan groups.

Recently, the Soudan group has reported evidence for a correlation between the radio

outburst which occured during September-October 85 and the rate of the detected muons in its

detector I propose here a simple (and testable) interpretation of this effect. First, the events 23l. 69

have been selected in a very particular phase window [0.725, 0.745] just because they seemed to accumulate in this region 23bl, and we have seen that there is no theoretical or experimental justification of this procedure. This corresponds to approximately 103 trials. Second, the size (5') of the selected angular window around Cygnus X-3 does not correspond to the angular resolution ' of the detector, stated to be 1.4 . This again corresponds to a factor of approximately 5 in the number of equivalent trials. Third, and this is the crucial point, the background is assumed to be flat, which is a priori not the case over a period of observation which is small compared to the precession period of the phase (about 170 days). This is illustrated by the fact that the background phase histogram during the same period in the Frejus experiment varies from bin to bin by as much as a factor 1.9 18>. The argument that a flat overburden gives a flat background phase histogram is obviously irrelevant, and a simple counter-example is given by the IMB experiment, which has an essentially flat overburden and a non-uniform expected phase distribution. The phase at which

Cygnus X-3 passes at the zenith in the Soudan 1 detector on October 10th 85 (the middle of the radio burst period) is approximately 0. 73. (The phase at the zenith position precess from 0.65 to

0.81 between the beginning and the end of the radio burst). Obviously, the expected muon rate is maximum when one looks at the zenith in an underground experiment with a flat overburden, and this is indeed the phase region chosen by Marshak et al. An unbiased background estimate, taking into account the modulation along the sidereal day, is necessary to confirm this observation (or to confirm the validity of this last argument). This example illustrates the pitfalls involved in the

temporal analysis of Cygnus X-3, especially over short periods.

I would like end with some suggestions, both statistical and experimental, in order to to clarify the rather confused situation of Cygnus X-3 above 1 MeV. Clearly, at all energies, a considerable increase in sensitivity is a crucial point.However, this seems rather difficult forlarge

shower arrays already operating almost continuously over several years. There may be a better chance for the Cerenkov telescopes, especially if their operation becomes possible during the

periods of full moon 7•>.A precise monitoring of the background is also essential for all these experiments. For underground experiments, the background can be safely estimated using the

methods which have been proposed in the Frejus18>, IMB or Karnioka19> analysis. particular, it In should never be assumed that the background in the phase histogram has a flat distribution. This is especially true in the case of observations over short periods. Whenever possible, the experiments

should provide the structure of their data in the region of Cygnus X-3 in order to obtain a calibration of the background fluctuations (which sometimes not just given by the square root of are the number of events, as it has been illustrated by some examples in the Cerenkov experiments).

A rather high degree of redundancy is now necessary to assess or contradict the observations of gamma-ray point sources. Clearly, in the TeV range, the correlation between at least three similar experiments, operating at a few tens or hundreds kilometers apart at the same of latitude, in order to avoid local pick-up fake signals and record Cygnus X-3 simultaneously with to similar systematics would provide a much safer monitoring of Cygnus X-3 activity. There is no 70

clear evidence that the selected showers, either in the TeV or the PeV range, are induced by

gamma-rays. At the very high energies, the ratio gammas/(everything hadronic) is expected to be of

the order of It is then crucial to to find some bias against the hadronic background. 10-3. try Lowering the threshold energy to 100-200GeV would probably result in a better signal/noise ratio

as one expects that at lower energies, the hadronic background would decrease more rapidly than

the gamma-ray contribution20>. However, this argument is not entirely clear since the Cygnus X-3

energy spectrum is assumed to be flatter than the hadronic background, and there would be a

competition between these two effects. Using new fast acquisition techniques in order to control the

structure of the detected pulses, to bias against spurious signals and to detect more precisely the

front edge of the Cerenkov signal, and sampling the whole Cerenkov ring with several mirrors

could also increase the angular resolution and allow a more precise mapping around the source, and therefore a better rejection against the background. In the PeV range, and probably starting from 0.1 PeV, one could use the measurement of the µ/e ratio, combined with the knowledge of an estimate of the total energy of the shower to separate electromagnetic and hadronic showers 24l. This is done assuming conventional muon production in gamma-induced showers27l, and would provide a crucial test for the unconventional observations by the Kiel group or in underground experiments .

CONCLUSION

Cyg X-3 has been observed many times by gamma-ray telescopes at TeV energies and

more recently by cosmic-ray detectors at PeV energies. There is a consensus that the TeV emission is confined to two short periods in the 4.8-h X-ray modulation cycle, with the stronger period occuring about X-ray phase 0.625". The reader who has not fallen asleep during the last two pages

should probably have realized that this does not reproduce my personal opinion but the fi rst two sentences of ref. 11. Is there really something behind the rather strong inconsistencies which plague the gamma-ray observations of Cygnus X-3 at high energies Underground observations ? are obviously in danger and the larger experiments have not confirmed the effect. From a different 25 27 point of view, some authors - l have shown in considerable detail how difficult it is to build a coherent picture of Cygnus X-3, even if one takes into account the possibility of a new neutral

particle. The situation is probably even worse for other high energy gamma-ray sources. However,

the impressive number of planned experiments to observe Cygnus X-3 at high energies which were

presented at this conference, in the Te V range and above, should settle this important question

within the next few years.

Much of this is based on work done with G. Gerbier 28l(now at L.B.L, CA, USA). talk 71

(*) Phase distribution: arrival times of events analyzed modulo the period of the source (**)The Cerenkov experiments operate essentially under two different modes: a tracking mode, where the detector follows the scanned region to correct for the apparent motion due to the rotation of the earth, and the transit mode, where the detector keeps a fixed orientation relative to the earth and the celestial object crosses its field of view, usually during a few minutes. (***) luminosity= area x detector-on time

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Experiment Gul marg Kiel Haver. A keno Baksan P. (1 1) (12) Ref. (9) (14) (13)

1· 3. 1.2· Ang. resol. ::::::: 50 Radius Ang. windov. 3°X 4° 2o•x 20• g•x5• 2.5° s) (<>< x Sensitive 2 uncol. 2 area 2 4x 14 m2 ri PM 28 x lm 200 x Im sosxo.s

Luminosity 12 2 2.6 160 2300 630 1900 10 cm s

Table 1

Vari ous characteristics of 5 experi ments sensitive 5 to energies above 3 10 Gev. The l umi nosi ty has been obtained from the published values of the flux and absolute intensity of the signal.

-s·

go• ao• 70°

Figure 1

Gamma-ray intensity distribution the C gnus X-3 region (E>500 Mev). in r 2 Contour levels are 4, 6, .. ., 12, 14 * 10- gamma/cm /s/sr. First step in grey scales at 2*10-5 2 gamma/cm /s/sr. The cross indicates Cygnus X-3 position. 74

Gulmarg

ObservationPeriod

Figure 2

Corrected photon flux as a function of the data taking period for 5 experiments.

SAS I I Il

------r\ - - �- (cm·2.-1 evl log IE � B ( -� ) � \ ·1 Satellite Air-C EAS 1HeV l 1GeV 1TeV 1PeV ' 6 0 2 0 0 08 1 1 4 1 4 1 1 10 10 1J leV J E

Figure 3

The integral spectrum of gamma rays from Cygnus X-3 above Mev. The points near 12 eV represent the Cerenkov experiments. C is Baksan and H is Haverah1 Park. 10 75

4· -4 10- 10 al

3. 10_

. 10. 2

1 . 1 0-

-7 400 200 0 -200 -400 x10 PERIOD VARIATION dp (days)

Figure 4

Variation of the probability of occuring by chance of the phase distribution with the tested period: a, Data from NUSEX (ref2b ). b, Simulation described in the text.

HIGH ENERGY NEUTRINOS IN CLOSE BINARY STARS

T.K. Gaisser Bartol Research Foundation of the Franklin Institute ** University of Delaware Newark DE USA 19716 Department of Nuclear Physics Oxford Univers ity, UK and

INFN Laboratori Nazionali di Frascati ITALY

ABSTRACT A compact partner in a binary star in wh ich high energy protons are accelerated will lead to cascading and hence to production of both photons and neutrinos . This talk is about the high energy neutrinos-- whether their signal is vi sible at Earth and how they affect the system in which they are produced.

Permanent address . ** 78

The question I discuss in this talk is, "What happens when you have an accelerator in orbit with a star?" Fig . 1 shows the general scenario. The situation is essentially a beam dump , and the end products will include protons , anti protons , photons , neutrinos and any other stable particle that is above threshold for production by the beam. Here I want to focus on high energy neutrinos .

Fig . I.Schematic view of a close binary with a com pact accelerator . The dots indicate matter blown off the surface by the cascade of particles at the com panion star .

There are three principal questions to answer , and these form the outline of the talk: 1. How many neutrinos are produced and with what energy spec trum?

2. How many neutrinos get out of the source and is it enough to produce a detectable signal? How many neutrinos are absorbed deep in the companion star 3. and is it enough to disrupt the system or produce variabi lity?

The details of 1 and 2 have been presented in Refs. and 2; 1 the third question is the subject of Ref . In this talk I 3. will give a brief overview with emphasis on a discussion of

stability of a close binary system when one of the partners 79

is an intense source of high energy particles .

1. Neutrino production . 2 The calculation of the cascade indicated in Fig . 1 is essentially a higher energy version of the calculation of atmospheric neutrinos1 except that the atmosphere is that of the stellar companion and the surrounding debris. The cascade occurs in the first few interaction lengths of material 2 ( rv 100 g/cm ) i.e. in the outermost skin of the companion , -7 3 where the density is low, of order several times l0 g/cm • Neutrinos are produced largely via decay of charged pions and kaons . The critical energy is that at which the interaction length equals the decay length, ¥c1:", where here is the iS Lorentz factor of the decaying particle.

( 1)

-7 3 gives E 30 TeV for 2xl0 g cm • In fact the me- critical � p = / dium in which the cascade energy is dumped is likely to expand , in which case the critical energy would be even higher. Whereas neutrinos are produced in the outer layers of the companion , they will be absorbed (if their energy is 2 high enough ) deep inside at depths X(g/cm )-:> , where .A .,, l/N is the neutrino interaction length. Typical stel- Av = A 2 11- M2 2 lar thicknesses are given by 2M/�R 2.6xl0 M/R g cm � / where the tildas indicate that the quantity is expressed in solar units . The pion cross section increases with energy and -36 2 reaches 6xlo cm around 1 TeV . Neutrinos above this ener gy will be absorbed if their trajectories intersect the main body of the companion star . I will discuss neutrino absorb tion further in Section 3 below, but it is clear tha� it will be important for close binaries be cause E TeV , critical >> 1 i.e. the energy below wh ich the neutrinos are readily produced is well above the minimum energy for absorption. 2. Neutrino-induced signal .

The first step is to normalized the calculation by estimating the power in the cosmic ray beam. This has been done 5 6 by Hillas starting from the observed TeV and PeV photon fluxes 80

that have been so much discussed at this conference, then calculating photon production in the cascade of Fig . 1. The relation for the cosmic ray luminosity at the source is

observed 2 R/-R ( ) ( 4rrR ) (e y) ( 2) flux (l) (l) Dy €'If -lO erg 46 2 39 erg "-'(10 2)(10 cm )(50) (3) (10) "' 10 �- · cm s

(The numbers in Eq . 2 are specifically for Cygnus X-3. ) The observed surface signal is assumed to be photon-induced . The second factor in Eq . 2 assumes particles to be emit ted isotropically from the acceleration region . is the frac Dt tion of the binary orbit during wh ich photons are produced and escape from the source region . Th is factor is the most uncertain and model-dependent because there is only a small 2 range of column thicknesses (about 20 to 200 g/cm ) for wh ich photons are copiously produced without being reabsorbed. The fourth factor compensates for the absorption of photons by the intervening universal microwave photons and the last factor reflects the fraction of particle energy that goes into pro duction of high energy photons . 2 Fig. 2 shows the expected fluxes of muon-type neutrinos and antineutrinos , 10� averaged over the 4 .8 hour period of Cygnus X-3 , for two assumptions about the beam of accelerated particles .

Fig . 2.Dash7d curve for � monoenergetic beam of 10 GeV protons from the acce- 1 era tor ; solid curve for a beam with a differential energy spectrum proportional id" to l/E2 from 1 TeV to 105 TeV . In both cases the power in the accelerated beam is given by Eq. 2.

10 81

Neutrinos are detected in large, deep detectors by the muon tracks produced in material surrounding the detector by the charged current reaction,

N anything '). + - f' + 1 ( 3) with signal  P ( E-y ) dE7 , = J .,, (4) where P is the probabi lity that a neutrino aimed at the detec .,, tor produces a muon through the detector (or above the detector

threshold ). Essentially

P x(muon range ) x N . ( 5) '1" "--' V-y A

1 7 Detailed ' calculations of P are shown in Fig . The signal -y 3. 2 8 9 2 calculated 1 1 from Eq . is of order one event per l OOOm per 4 year with the normalization of Eq . 2. To within a factor of two , it is independent of the detailed shape of the neutrino / spectrum. The important range of neutrino energies for pro ducing the signal is 1-100 TeV, so the result is also indepen 1(/ 7 dent of how the structure 16' functions are extrapolated to � ultra-high energy to obtain the � neutrino cross section and hence P in Fig . Because y 3. one event per year is tan talizingly close to detectability in large deep detectors , it is

interesting to ask, how much 102 103 10"' Jr/' 1<:1 rrl E., (GeV) stronger the source can be with

out blowing itself away . This Fig. Probability that a neutrin3.o directed at is one motivation for the next (E-y) a detector produces a muon section . (E > GeV) at the detector . l:' 2 Solid line : Ref. 1. Dashed line : Ref. 7. 82

3. Neutrino absorption in the companion . In Re f. 3 we calculated neutrino absorption for four examples for wh ich PeV signals have been reported . The relevant properties are shown in the Table. The crucial geometric fac tor is the ratio of separation, a to radius of the companion, R . This is estimated from c

a3 period 21/ (6) = ��-_�� V-G(M + M ) � ns c assuming the compact object to be a neutron star with M 1.4 ns = and that the companion radius is that of a main sequence star of mass . Mc

TABLE . Properties of PeV emitting binaries

binary companion System per iod mass L a/R CR C 11.-y (days ) ( ) (erg/s ) M (erg/s ) 39 37 Cyg X-3 0.19 l(?) 10 1.6-2 .0 10 < .�> 37 33 Vela X-1 8.965 23 "-'10 1 2 2xlo

4 1 38 L MC X-4 1. 408 19 10 3.5 3xlo >"" 38 3 4 Her X-1 1. 7 2.4 "'10 6 5xlo

The last column in the table gives the result of calculating 3 neutrino absorption in the companion star . For the two ex amples with the shortest periods the accelerator is close enough to the companion so that the energy due to neutrino deposition is significantly larger than the natural luminosity of the star due to nucleosynthesis. Roughly one per cent (or somewhat less) of L is dumped in the companion (depending CR on the parameters of the system) . An even larger fraction of L is dumped by the hadronic cascade near the surface . This CR energy will in part be radiated away and in part will drive a wind off the surface. (If there is too much wind the system will be rapidly eroded from the surface.) The neutrino energy, however , will be deposited deep inside the star , where it cannot be radiated away quickly. If 83

we assume that the excess energy goes into work done to expand the star , we can write

-(natural luminosity ) ( 7) Vl, .,

The solution is

( 8 ) where R is the initial radius and t The time for 0 0 total disruption (A R/R 1) is 0 � 4 thus of order 10 years , depending on details of M ' R and c 0 l'"ty• On the other hand , the amount of overflow of the 10 Roche lobe needed to maintain a steady accretion flow is -4 only AR/R "-' 10 • Perhaps neutrino pumping can lead to O l sufficient inflation on a short (lO � year ) time scale to give periodic catastrophic overflows which lead to radio out bursts, jets and switching off of the accelerator until the sys- tern recovers. Although this last remark is merely a speculation , it is meant to illustrate the importance of taking neu trino production and absorption into account in the case of an energetic accelerator in a close binary system.

Acknowledgements. I am grateful to the SERC and to D.H. Perkins for hospitality at Oxford where this talk was prepared and to INFN and to E.

Iarocci for hospitality at Frascati where this paper was writ ten. This talk was given both at the 1986 Moriond Astrophysics Meeting (Les Arcs ) and at the 1986 Vulcano (Sicily) Workshop, and the written version is identical. This research was supported in part by the U.S. Department of Energy under DE-78-ER-05007 . 84

REFERENCES 1. T.K. Gaisser and Todor Stanev , Phys . Rev. DJl, 2770 (1985 ).

2. T.K. Gaisser and Todor Stanev, Phys . Rev . Letters 5 4 , 2265 (1985).

3. T.K. Gaisser , F.W. Stecker , A.K. Harding and J.J. Barnard , NASA/Goddard preprint 8 6-008, to be publ ished in Ap . J.

4 . T.K. Gaisser , Todor Stanev , S.A. Bludman and H. Lee , Phys . Rev . Letters 51, 223 (1983 ).

5. A.M. Hillas , Nature 312 , 50 (1984 ) and Highlight talk, Proc . 19th International Cosmic Ray Conference (La Jolla) 1985.

6. A.A. Watson, Rapporteur Talk, Ibid.

7. T.K. Gaisser and A.F. Grillo (in preparation).

8. Berezinsky, C. Castagnoli and P. Galeotti, Nuovo v.s. Cimento 8C , 185 (1985 ).

9. E.W. Kolb, M.S. Turner and T.P. Walker , Phys . Rev . D32, 114 5 (1985 ); 33 1 859 (E) (1986).

10. J.E. Pringle in Interacting binary stars (ed. J.E. Pringle and R.A. Wade ) Cambridge University Press (1985) p. 12. 85

NEUTRON AND ANTINEUTRON PRODUCTION IN ACCRETION ONTO COMPACT OBJECTS

l Charles D. Dermer and Reuven Ramaty NASA/Goddard Space Flight Center Greenbelt , MD 2077 , U.S.A. 1

ABSTRACT Nuclear reactions in the hot accretion plasma surrounding a collapsed star are a source of neutrons , primarily through spallation and pion producing reactions , and antineutrons , principally through the reaction p+p+p+p+n+ . We calculate spectra of neutrons and antineutrons produced n by a var iety of nonthermal energetic particle distributions in which the target particles are either at rest or in motion. If only neutral particles are free to escape the interaction site, a component of the proton and antiproton fluxes in the cosmic radiation results from the neutrons and antineutrons which leave the accretion plasma and subsequently decay in the interstellar medium. This additional antiproton component could account for the enhanced flux of antiprotons in the cosmic radiation, compared to values expected from the standard "leaky-box" model of cosmic-ray propagation and confinement . Moreover , the low-energy antiproton flux measured by Buffington et al . could result from (1981 ) target-particle motion in the accretion plasma . This model for the origin of antiprotons predicts a narrow 2.223 MeV line which could be observable .

l NAS/NRC Resident Research Associate 86

INTRODUCTION

Matter accreting onto collapsed objects can attain very high ener gies

due to the conversion of gravitational energy into kinetic energy.

Because of thermal decoupling of the electrons and ions in accreting

thermal plasma, the ion component may reach temperatures in excess of 100

MeV in disk (e.g., Shapiro, Lightman and Eardley 1976 ; Eilek and Kafatos

1983) and spherical accretion models (e.g., Dahlbacka , Chapline and Weaver

1974; Kolykhalov and Sunyaev 1979 ; Meszaros and Ostriker 1983 ). Neutrons

are formed in a hot accretion plasma through nuclear breakdown reactions at temperatures > 1 MeV (Aharonian and Sunyaev 1984 ; Gould 1986) and in

association with pion-producing reactions (Dermer 1986) at temperatures

> 20 MeV. At temperatures ( 200 MeV , a channel of neutron and antineutron

production is opened through the reaction p + p � p + p + n + n which , moreover , produces a spectrum of antineutrons extending to low energies

(Dermer and Ramaty 1986) , in contrast to the spectrum of antineutrons

produced in collisions of protons with a stationary target (e.g., Stephens 1981). These neutrons and antineutrons , unconfined by the magnetic field

of the accretion plasma, can escape into the interstellar medium and,

after decaying, be detected as a low energy proton and antiproton

component of the cosmic radiation. Support for thermal accretion models of galactic X-ray sources is

provided particularly by the case of Cyg X-1 , whose X-ray spectrum is

successfully fit using either disk (Shapiro, Lightman and Eardley 1976) or

spher ical (Meszaros 1983) accretion geometries. But the existence of

1 2 galactic point sources emitting gamma radiation at energies £>1 0 eV

implies that energetic nonthermal particle spectra are common in galactic

binary X-ray sources such as Cyg X-3 and Her X-1 . Particle acceleration in confined volumes , with maximum sizes inferred from time-variability

arguments , requires intense magnetic fields (Hillas 1984a). Only charged

particles with energy E(GeV) ( 90ZB,M0 , where B , is the magnetic field at ' the interaction site in un its of 10 gauss , M0 is the mass of the collapsed obj ect in solar masses and Ze is the charge of the ion , can

directly escape from the interaction region, assuming that the gyroradius must approximately equal the Schwarzschild radius for charged-particle

escape. Neutrons and antineutrons , on the other hand , leave the

interaction region directly provided that the mass of the collapsed (i) 7 object is <10 M0 (Dermer and Ramaty 1986) , (ii) the grammage s �ouding 2 � the interaction region is 50 gm/cm , and (iii) µ·oB/dx 10 B ,/M < � = 0 87

E(GeV) , where µ is the magnet ic dipole moment of the neutron . These conditions ensure that the neutrons or antineutrons (i) do not decay before escape , (ii) do not interact strongly before escape , and (iii) do not significantly change energy when traversing the intense , turbulent magnetic field likely to be found in the accreting plasma . Condition

(iii) is easily satisfied even if the correct distance scale for magnetic field variat ion is much smaller than the Schwarzschild radius used in this estimate. The other conditions are also not difficult to satisfy in galactic sources .

In this paper , we calculate the spectra of neutrons and antineutrons produced by energetic nonthermal particle distributions located in the vicinity of a compact obj ect . We do not consider the detailed nature of the acceleration mechanism and interaction site , but for simplicity assume an isotropic, energetic particle distribution of solar (photospher ic) composition . We consider two interaction models which take into account the trapping of the charged particles in the interaction region . In the first , the particles are assumed to interact with an ambient background plasma in the thick-target model (e. g. , Ramaty, Kozlovsky and

Lingenfelter This model has been extensively developed to 1975) . interpret gamma-ray and neutron observations from solar flares (Murphy and

Ramaty and references therein) . In the second , the energetic 1985, particles interact only with each other , that is, we consider a relativistic nonthermal plasma . We employ shock-acceleration spectra with a spectral index -2 .2 appropriate to the cosmic radiation before effects of the energy-dependent escape are taken into account . This source could account for the antiprotons observed in the cosmic radiation (Golden et al. Bogomolov et al. Buffington et al. in excess of the 1979; 1979 ; 1981 ) leaky-box model prediction. narrow 2.223 MeV line due to the energetic A neutrons thermalizing and being captured by protons in the atmosphere of a binary stellar companion might also be formed.

ANALYSIS

In the thick-target model , the interacting pr imary and secondary energetic charged particles remain trapped in the interaction region and lose energy through particle collisions with the ambient plasma, while the neutral particles are free to escape . The spectrum of the antineutrons inj ected into the interstellar medium is identical to the spectrum at production under the conditions listed in the Introduction , except for a 88

possible gravitational redshifting. Neglecting this last complication, the source spectrum of antineutrons (particle 3) produced in the

reaction 1 + 2 7 3 + X is just

3 w d (E, E l l o1 + ; 2l 4�n 273+X n 3 (E,) [cm -s -GeV 1fdE2 •J2 (E2 )·��- ��-- (1) J d� in E� ( E,) where n1 is the ambient target particle density, J2(E2) is the equilibrium in flux of energetic particle species 2, including secondaries, E� (E,) is the minimum energy of a particle of type 2 necessary to produce particle 3 with energy E , , and da (E3;E 2 )/dE 2 is the differential cross 1 +273+X section for the production of particle 3 with energy E , in a collision between particle 2, with energy E 2 , and stationary particle The flux 2 1 1 1 1. [cm- -s- -sr- -GeV - ]

E'2 dE dE2 2 i c:o J 2 (E2 ) [ 4�m n 1 ] dE� ·n2

in reactions of particles of type 1 and 2 is given by

3 1 +1 - 1

(cf. Dermer In this equation , 1984).

( 4)

is the density, F ( p ) is the isotropic differential momentum spectrum , i i 89

and p =m 8 Y is the momentum variable of particles of type i. The term i i i i E* is the maximum CMS energy of particle 3 and is a function of the max ,3 relative Lorentz factor Y =(E1E2-p1p2 cos8)/m m2 only, where E1 and E, are r 1 the energies of the colliding particles and is the angle between their 8 directions of motion in the LS . The CMS differential cross section for the production of particle 3 in terms of CMS energy E* and CMS angle 2 _I B*=cos µ* is denoted by ct o*/ctE*dµ*. We employ nonthermal energetic particle spectra predicted by shock acceleration theory. The momentum spectrum resulting from diffusive shock q acceleration is given by F (p ) p - (e.g., Blandford and Ostriker i i � i 1978) . Normal izing this spectrum using equation (4) gives

n. i=1 '2' (5) 1 where K is the normalizat ion constant , n is the volume density, and i i

Pco ,i is the low-momentum cutoff in the momentum spectrum of particles of type i.

We solve equation (3) using the Monte-Carlo method , generalizing the

technique of Ramaty and Meszaros (1981 ) to secondary particles created in the collisions of particles with, in general , different masses . Introduce an array of six numbers chosen randomly between 0 and 1 , namely r1, ,r Choose values of momenta p and p from the inverted particle .•. •• 1 2 distribution functions . The shock spectrum can be analytically inverted , giving

(6)

Choose the remaining variables from un iform distributions : cos8=2r ,-1 ,

E* = m,+[E ( Y )-m,]•r,, µ*=2r s+1 and $*=2nrs, where $* is the CMS �ax ,3 r azimuthal angle of the outgoing particle of mass m , . The reaction rate (3) is then given by

N tot 28 y ( r r o* Q , -- ·[E* ( Y )-m,] ·2· ct, (7) l Y 1 Y2 ) max ,3 r -- i=l dE*ctµ* in the limit Ntot • the number of Monte-Carlo trials, goes to infinity. Differential energy spectra are determined by calculating differential reaction probabilities from the individual Monte-Carlo trials of equation

(7) and binning in energy. The energy of particle 3, E , , was determined 90

the kinemat ical relations E, from = Y0 (E1+S0p�cos6*), where 2 2 2 Y ( Y +Y2 )/s , s = m1 +m2 +2m1m2Y ' and cos 6* 0 1 Y.: r 2 2 2 2 \!·(1 \!•c os �* . where n* (E1 Et )/S p and µ*n*+(1-µ* ) -n* ) = -Y0 0Y0 f 2 2 E 2 (p m f = (s+m1-m2)/2s't• In the limit Y2 ..1, that is, F(p2 ) .. o 2- 2), equations (3) and (7) reduce to the stationary target case .

NUMERICAL RESULTS

A detailed descr iption of the cross sections and energy spectra for

the production of secondary neutrons and protons in reactions involving

protons and particles is given by Murphy, Dermer and Ramaty (1987) . A a description of secondary neutron production in collisions involving heavier nuclei wi ll be given elsewhere. A complete version of the

calculations relevant to this work is in preparation.

For calculations of neutron and antineutron production in a thick target , we assume solar compos ition (Cameron 1982) for the ambient plasma

and the energetic particles , that is, the number of particles with energy

greater than 30 MeV/nucleon is assumed proportional to the Cameron

abundance of that species . Calculations of secondary proton and neutron production at energies : 5 GeV/nucleon involve integrations over

complicated secondary energy spectra and cross sections and were evaluated

from equations (1) and (2) using a Monte Carlo simulation (cf. Murphy

1985) . At energies ( 5 GeV , the effects of particles and heavy nuclei a can be treated as a multiplicative correction to the basic proton-proton 2 '

(p-p) reactions. Taking A % 50 gm/cm and dE /dA % 4x1 0- 2 p-p l P I GeV/(gm/cm ) (Murphy 1985) in equation (2) gives a simple 1 -dimensional

integral for the thick-target equilibrium proton flux . Using this flux , we calculated the injection sources of antineutrons and ( 5 GeV neutrons

from equation (1) using the scaling representations� of Tan and Ng (1983a; see Murphy , Dermer and Ramaty 1987) .

In the calculations of neutron and antineutron production in a

' relativistic plasma , we assume that there is 1 proton per cm with

momentum greater than the low-momentum cutoff, and that the number of energetic particles above the cutoff momentum is proportional to the tends Cameron abundance of that species . If the low-momentum cutoff Pco ,i to zero, interactions of the energetic particles with particles nearly at

rest dominate secondary production because of the divergence in the

normalization of the shock spectrum in this limit [see eq. (5)]. The 91

As becomes problem therefore reduces to a thin-target calculation. Pco ,i large , the average collision energy increases , and reactions of particles

in motion with other particles in motion becomes more probable . Due to

the large antineutron production threshold , the effect of increasing Pco ,i causes the relative production of antineutrons compared to neutrons to

increase . Also, the spectrum of antineutrons now extends to low energy ,

as most n are formed with low energy in the CMS of the colliding protons ,

and the CMS can now have low velocity in the rest frame of the plasma

(Dermer and Ramaty 1986).

We consider neutron and antineutron production in a relativistic

plasma using a specific model with =500 MeV/c for all i. A Pco ,i = Pco low-momentum cutoff of 500 MeV/c corresponds to a low-energy cutoff of

-1 25 MeV for the protons . We find that for these parameters and normalizations , the integrated production rates of neutrons and

l 6 3 _ 19 3 _l antineutrons are 3.2x10 cm -s and 5.5x10 cm -s

respectively. This impl ies that -580 neutrons are produced for each

antineutron .

OBSERVABLE CONSEQUENCES

A review of the cosmic ray antiproton observations and models is

given by Golden (1984), and the measured fluxes of antiprotons in the

cosmic radiation are shown in Fig. 1. The prediction of the leaky-box

model (Tan and Ng 1983b), in which cosmic rays traverse an energy

dependent average grammage before escaping from the galaxy , is also shown

here. This model fa ils by about three to five to account for the measurements between 2 and 10 GeV. It fails by over an order-of-magnitude

to explain the low-energy measurement of Buffington et al. (1981 ), even if

the effects of the solar modulation of cosmic-ray protons and antiprotons

are taken into account (Tan and Ng 1983b).

We propose that the antiprotons in the cosmic radiat ion in excess of

the leaky box contribution have their or igin in additional discrete

galactic sources which produce antineutrons through nuclear reactions in

an accretion plasma. The production of antiprotons through secondary collisions is suggested ·by the lack of observations of A 1 antinuclei, > whose production in collisions of normal matter particles is negligible.

This argues in favor of an additional secondary source of antiprotons . Low-energy antiprotons are produced in relativistic plasmas as a direct

consequence of the kinematics of such systems , and these plasmas could be 92

Fig. 1. The observed 10·3 cosmic-ray antiproton

= fluxes , shown by the data Pco 500 MeV/c points , are designated by 10-4 Bu (Buffington, et al. 1981), Bo (Bogomolov , et > Bo al . 1979) , and G (Golden et

formed in the vicinity of a compact object . The associated production of neutrons is a necessary consequence of this· model , and suggests a

potentially observable signature , which we discuss below .

The antiproton flux resulting from the decay of antineutrons produced

in a relativistic plasma with P = MeV/c and normalized to the data co 500 is shown in Fig. 1. The ga lactic antiproton flux was evaluated from the

antineutron source spectra using the relation

) m ;,, (E- p n- n nel J (E ) 0: ) (8) n 41m --+A p p G ( esc p

- ' where nG [cm ] is the average proton density in the galaxy . The para

meters describing the average grammage traversal Aesc and the antiproton i�el inelastic cross section cr are given by Tan and Ng (1983b). The p effects of ionization energy loss and reinjection of antiprotons 'fo llowing

nonannihilation inelastic interactions are unimportant for this source

spectrum and are neglected. The constant in equation (8) was chosen to n 93

give the proper source strength to account for the observed antiproton observations . We obtain a total galactic antineutron production rate of

39 -1 .3x10 no antineutrons per second fo this model , where is the v.7 2 v.7 6 7 3 volume of the Galaxy in units of 10 cm and no 2 is the average galactic

proton density in un its of 0.2 protons per cm • From Fig. 1 we see that the combined source of antiprotons resulting from this model and the

leaky-box model gives an adequate representation of the data above 2

GeV . There is also a substantial flux of low energy antiprotons produced

in this model , which might be sufficient to account for the low-energy measurement of Buffington et al . (1983 ), depending on the uncertain degree of solar modulation occurring during this period of observation.

The value of chosen to fit the cosmic-ray antiproton observations n implies a related proton flux from neutron decay. We have evaluated this

flux from the neutron source spectrum associated with the antineutron !nel source spectrum , but now with a in equation (8) replaced by the p proton-proton inelastic cross section. The result is compared in Fig. 2

to the observed cosmic ray proton flux (data referenced in Gloeckler and

Jokipii 1967 and Tan and Ng 1983b) . As can be seen , the neutron-decay

proton flux implied by this model does not conflict with the observed

protons in the cosmic radiation. Above several GeV , these protons

comprise about 10% of the observed cosmic-ray protons . At lower energies

this source appears to contribute a larger percentage , but the effects of

solar modulation will lower the calculated flux at these energies . The

total galactic neutron production corresponding to the antineutron flux of

Fig. 1 is -7 .5x1 0 ., neutrons per second . v.7no02 Antineutrons and neutrons escaping from the interaction region either

decay in interstellar space or are captured or annihilate in a dense medium , such as the atmosphere of a star . In the first case, positrons

and electrons are formed in the decay of the antineutrons and neutrons ,

but represent negligible additions to the electron and posi tron fluxes of

the cosmic radiation due to the relatively small Lorentz factors and intensities of the neutron and antineutron source functions . An inner

bremmstrahlung (Petrosian and Ramaty 1972) X-ray emissivity from the decay

of the neutral particles is also produced at a level of - a·0.5 MeV/n

�2 33 10 n/s - 6x1 0 ergs/s , where a is the fine structure constant . This represents a weak X-ray luminosity , even if concentrated in a single source . 94

Fig. 2. The data points give the observed solar

minimum cosmic-ray proton Pco = 500 MeV/c fluxes (see Jokipii and

Gloeckler 1967 and Tan and

Ng 1983b). The solid curve ·;; Q) represents the interstellar (.'.) neutron-decay proton flux 2 Iii 10- produced in association I CJ) I with the antiproton flux 'E of Fig. 1. -':'. L:e,_,10 -3 ! + I

5 10- �-�� 1 0 2 10- 10 101 10 Ep (GeV)

The capture of the neutrons and antineutrons is possible if, for

example, the compact object is accompanied by a binary companion which

subtends a significant solid angle about the interaction region. This

companion star could also be the source of the accretion plasma that

powers the system. Neutrons impinging on the atmosphere of the star would

3 thermalize and , depending on the He content of the stellar atmosphere,

produce deuterium in the capture reaction n + p -> H + Y(2.223 MeV) , as in the case of solar flares (Wang and Ramaty 1974) . If all neutrons are captured and produce deuterium, this represents a production rate of

17 't2 59 2

--3x10 sec • 1 0 n/s - 3x10 H produced dur ing the age of the galaxy .

• 3 This can be compared to a value of -1 .2x1 0 c_s deuterons in the galaxy,

where c_ s is the relative deuterium-to-hydrogen galactic abundance in

units of 10 This source obviously does not conflict with the observed

2 galactic H abundance , but neither does it significantly contribute to it. The formation of a deuteron is accompanied by the production of a

2.223 MeV gamma ray . For solar flares , where this effect is clearly seen , 95

approximately 0.1 line photons are produced per neutron (Murphy and Ramaty

1985). Let 0. 1f_1 be a numer ical factor reflecting the probability that

for each neutron formed in the accretion plasma, a 2.223 MeV photon is

emitted into interstellar space . This factor incorporates a number of

uncertain factors including the sol id angle of the companion star and the

probability that the gamma ray is both produced and able to leave the

stellar atmosphere without being absorbed. We therefore have that -

.. , 7.5x1 0 f_ 1V.1no. 2 line photons per second are produced in the galaxy . If there are a large number of sources distributed in the galaxy , this _s 2 represents a flux observed at Earth of - 10 f_ 1V•1no . 2 photons/(cm -s- 2• rad), normalizing to the observed flux of 1.809 MeV photons from Al

2 6 6 decay (Le., 3 M0 of ·Al with a mean 1 ife 2 • - 1.1x10 yr produce t Al -� - 2 - 1 about 5x10 photons-cm -s -rad [Mahoney et al . 1984]).

If the number of discrete sources is small , then the 2.223 MeV line

flux could be observed from a single obj ect . Taking the number of sources

in the galaxy to be 10N10, the flux of 2.223 MeV photons observed at Earth

- 7 2 2 from a single source is - 6x10 f_ 1V•1no 2/(N1 or 10 ) photons/(cm -s) , where r10 is the distance of the source to the Earth in units of 10 kpc .

The detection of the line flux would be aided by the fact that the line

intensity will vary with the underlying binary period of the system. In

addition, since this estimate is based on the average source luminosity

over the age of the cosmic rays , a temporary outburst could increase the

emission expected from a single source. Likely candidates for observation

include the binary X-ray sources listed in the Introduction, whose ultra

high-energy gamma-ray flux is evidently powered by an accretion mechanism,

perhaps in association with a neutron star . A current interpretation of

the or igin of the high-energy gamma-ray flux pictures energetic hadrons emerging from the compact object and impinging upon the atmosphere of a

companion star (e.g., Berezinsky 1977 ; Vestrand and Eichler 1982 ; Hillas

1984b ; Kazanas and Ellison 1986) . The observation of a 2.223 MeV signal

in the transient event of 10 June 1974 (Jacobson et al . 1978; Ling et al .

1982 ) is perhaps an example of this type of source , although with

nonsteady accretion. 96

CONCLUSIONS

We have presented the physics of secondary neutron and antineutron production from particle collisions in a thick target and in a nonthermal

relativistic plasma. Because the neutrons and antineutrons are not

confined by the magnetic field of the accretion plasma , they can leave the interaction site and either decay in interstellar space or be captured on

a companion star . Assuming that most of the neutral particles decay in

interstellar space , we have fit the spectrum of secondary antineutrons to

the observed cosmic ray antiproton flux , using a relativistic plasma with

a low-momentum cutoff of 500 MeV/c and taking into account the leaky-box

contribution of antiprotons . This normal ization implies a production rate •2 of about 10 neutrons per second in the galaxy . This level of production does not violate the deuterium content of the galaxy and provides only a

weak X-ray source resulting from inner bremsstrahlung in neutron decay .

If about one 2.223 MeV gamma-ray photon is emitted into interstellar space

for every 10 neutrons formed , for example by neutron capture on protons in

the atmosphere of a stellar companion of the compact object , a flux of - 5 2 line photons of -1 0 photons/(cm -s-rad) could result from distributed

sources in the galaxy . A gamma-ray line flux at 2.223 MeV might be

observable from discrete sources depending on source luminosity, distance and duration of the active phase . Detection of this line could be

facilitated by the var iation of the flux with the period of the binary

system.

ACKNOWLEDGEMENTS

C.D.D. would like to acknowledge the suggestion of C. J. Cesarsky to

calculate the joint neutron and antineutron production in compact

sources . We also acknowledge useful discussions with R. J. Murphy and D. Kazanas . 97

REFERENCES

Aharonian , F. A. , and Sunyaev, R. A. 1984 , M.N. R.A.S. , 257. 210, Berezinsky , V. S. 1980, Proc . 1979 DUMAND Summer Workshop at Khabarovsk

and Lake Baikal, ed. J. G. Learned , U. Hawaii Press , p. 245.

Blandford, R. D. , and Ostriker , J. P. 1978, Ap . J. , L29. 221 , Bogomolov, E. A., Lubyananya , N. D., Romanov , V. A., Stepanov, S. V.,

Shulkova, M. S. 1979, Proc . 16th ICRC, (Kyoto) , 330. 1, Buffington, A. , Schindler , S. M. , and Pennypacker , R. 1981 , Ap . J. , c. 1179. 248, Cameron, A. G . 1982, in Essays in Nuclear Astrophysics , ed. Barnes , w. c. D. D. Clayton , and D. N. Schramm (Cambridge University Press :

Cambr idge) , p. 23.

Dahlbacka , G. H. , Chapl ine, G. F. , and Weaver , T. A. 1974, Nature, 250, 36.

Dermer , D. 1984, Ap . J. ' 328. c. 280, Dermer , D. 1986, Ap . J.' in press. c. Dermer , D. , and Ramaty, R. 1986, Nature, 205 . c. 31 9, Eilek, J. A. , and Kafatos , M. 1983, Ap . J 804 . •• 271 , Gloeckler , G. ' and Jokipii, J. R. 1967, Ap. J L41 . .• 148, Golden , R. L., Horan, S. , Mauger , B. G., Badhwar , G. M. , Lacy , J. L.,

Stephens , S. A. , Daniel, R. R. , and Zipse , J. E. 1979, Phys . Rev.

Lett ., 1196. 43, Golden , R. L. 1984, Proc . 19th Rencontre de Mor iond Ap . Meeting, p. 193. Gould, R. J. 1986, Nucl. Phys ., B266 , 737.

Hillas , A. M. 1984a , Ann. Rev . Astr. Ap ., 425. 22, Hillas , A. M. 1984b , Nature, 50. 312, Jacobson, A. S. , Ling, J. C., Mahoney , W. A. , and Willett , J. B. 1978, in Gamma Ray Spectroscopy in Astrophysics , ed. T. L. Cline and R. Ramaty (NASA TM 7961 9) , p. 228.

Kazanas , D. , and Ellison, D. 1986, Nature, 380 . c. 31 9, Kolykhalov, P. I. and Sunyaev, R. A. 1 979, Sov . As tr ., 189. 23, Ling, J. C. , Mahoney , W. A., Willett, J. B. , and Jacobson, A. S. 1983, in

Gamma Ray Transients and Related Astrophysical Phenomena , ed. R. E.

Lingenfelter , H. S. Hudson , and D. M. Worrall (AIP : New York ), p. 143. Meszaros , P. 1983, Ap . J. , L1 3. 274, Meszaros , P. , and Ostriker , J. P. 1983, Ap . J. , L59. 273, 98

Mahoney, W. A. , Ling , J. C., Wheaton, W. A. , and Jacobson, A. S. 1984, Ap . J. ' 573 . 286, Murphy, R. J. 1985, Ph . D. Thes is, Univ. of Mar yland .

Murphy, R. J. , and Ramaty , R. 1985, Adv. Space Res ., 4, 127.

Murphy , R. J., Dermer , C. D., and Ramaty , R. 1987, Ap . J. (Suppl .),

submitted.

Petrosian, V., and Ramaty , R. 1972, Ap . J. , L83 . 173, Ramaty, R. , Kozlovsky , B. , and Lingenfelter , R. E. 1975, Space Sc i. Rev.,

341 . 18, Ramaty, R. and Meszaros , P. 1981 , Ap . J. , 384 . 250, Shapiro, S. L. , Lightman , A. P. , and Eardley, D. M. 1976 , Ap . J. , 204, 187.

Stephens , S. A. 1981 , Ap . and Space Sci ., 87. 76, Tan , L. C., and Ng , L. K. 1983a , J. Phys . G, 1289. 9, Tan , L. C., and Ng , L. K. 1983b , J. Phys . G, 227. 9, Vestrand , W. T. and Eichler , D. 1982 , Ap . J., 251 . 261 , Wang , H. T. , and Ramaty, R. 1974, Solar Phys., 36, 129. 99

EFFECTS OF A SUPERCRITICAL WIND ON NOVA OBSERVATIONS

M. Friedjung Institut d'Astrophysique, Paris, France

ABSTRACT.

Continued ejection of optically thick winds of novae after optical maximum is probably driven by the radiation pressure of an object above the Eddington limit . The total luminosity of nova FH Ser was probably well above this limit for quite a long time . Conditions of and physical processes which could produce such a wind , are discussed . Collision between such a wind and material ejected before optical maximum could produce a shell which will eventually contain most of the mass of the envelope. Collisions between different parts of the wind at different veloci ties could produce other layers. 100

The development of a nova especially after optical maximum is complex , and not easy to relate directly to theories of thermonuclear runaways. I shall describe in what directions we can expect progress to be made, and some new results .

I WHAT DO OBSERVATIONS TELL US - ?

The spectrum of a nova indicates that one is observing an expanding medium with velocity stratification. Line profiles can be considered as the superposi tion of P Cygni profiles, associated with layers moving at different veloci ties. These layers can be classified as described by Mclaughlin (1943). The "premaximum system" is present before visual maximum, and tends to disappear after this maximum : the "principal system" appears soon after the same maxi mum, while the faster "diffuse enhanced" and "Orion" systems appear afterwards. The "principal" system will later at least come to contain most of the mass of the envelope; its expansion velocity is approximately that of the nebular envelope observed in later stages . What must be emphasized is, as shown by Mclaughlin (1964 ), that higher velocities occur nearer the centre of the enve lope, the velocity increases inwards on average. Observations in the ultraviolet and infrared spectral regions indicate that activity continues for a long time after optical maximum (Gallagher and Code 1974, Friedjung 1977b, Wu and Kester 1977, Stickland et al 1981 , Snijders et al 1984). The bolometric luminosity decreases much more slowly than the optical luminosity, and can be for a time nearly constant , near the Eddington limit. If one studies possible models which fit the observations, one finds that models involving a long time of continued ejection are necessary. This was already clear from groundbased observations (Friedjunq 1977a), and is supported by the more recent results especially in the space ultraviolet indicating continuing activity. A point to be emphasized is that normally one does not see signs of a stationary "photosphere" . In some cases one might expect to be able to detect unshifted absorption lines produced in such a region; a test I made for nova FH Ser (Friedjunq 1977b) did not show signs of such lines. In any case it seems that one normally sees an optically thick wind after optical maximum; the fact that the highest velocities seen appear to be nearest to the centre of the envelope indicates that one does not see the regions where the wind is accelerated. A possible exception is nova HR Del which had a very slow develop ment of half a year before its maximum in December 1967 . In this stage its spectrum showed narrow emission lines, which could have come from a wind acce leration region. An optically thick wind can be accelerated by radiation pressure if the IOI

luminosity is above the Eddington limit , and calculations I made very many years ago (Friedjung 1966), suggested acceleration of such a wind at 2 the 10- radius where the wind optical thickness � 1. This means that the ejecting star, if taken to be the white dwarf component of a binary, could have been somewhat expanded , but much less than the radius of the visible "pseudophosphere" , where the optical thickness of the wind � 2/3. The kinetic energy flux of the wind needs naturally to be added to the radiative luminosity to obtain the total luminosity of the nova, and as we shall shortly see this total luminosity is very probably above the Eddington limit.

II - IS A SUPER-EDDINGTON WIND PHYSICALLY POSSIBLE FOR A NOVA ?

Super-Eddington winds present a number of physical problems : the radiation flux must be continuously produced not far below the stellar surface, so most of the star remains stable. In addition if there is a spherically symmetric steady state, one can only make the solution go through the critical point if a substantial proportion of the radiative flux is advected (Ruggles and Bath 1979). Conditions were given by me (Friedjung 1981 ) for this to occur, resul ting in an approximate equipartition of energy flux between radiation and kinetic energy seen leaving the nova for luminosities well above the Eddington limit. The derived condition is more precisely :

B GMm B fl ( ) 1 3

where f is a factor near unity depending on the opacity, L is the radiation flux at small optical depths, Vac and rac the velocity and radius where most of the acceleration takes place, Vs the final velocity near that of the pseudophotosphere, M the mass of the star, the mass loss rate, and the gra � G vitational constant. The second term, which becomes small for luminosities far above the Eddington limit is, if V is taken as equal to 0 Vs, 4/3 the ac .5 gravitational energy flux at a radius equal to rac • while the right hand term is then B/3 the kinetic energy flux. For L far above the Eddington limit one obtains approximately :

L (2) 100 v�

It may be noted that as rs is the radius of the pseudophotosphere, one 102

can relate r /r to energy densities in the pseudophotosphere 5 a

r ac (f' x radiative energy density-0,5 gravitational energy density )

kinetic energy density f' like f is of order unity. When opacity is due to Thompson scattering

16 (3) 3 c

FH Ser, a nova well observed over a wide range of frequencies from the ultraviolet to the infrared, can be used to test these ideas. Bolometric lumi nosities and black body colour temperatures can be used to calculate pseudopho tospheric radii, and the measured velocities from optical spectra can be compa red with the theoretical prediction of eq . (2). Results are given in table 1, assuming a distance of 650 pc. The velocity predicted by eq . (2) if compared with that observed for the "high velocity" system, most probably that of the optically thick wind, is too low, and a correction of eq .(2) to :

L 3 (4) 10 v s is suggested. When the luminosities (in the form of radiation) are compared with the Eddington limit (taken as 1.6 x erg s- 1 for a 1 M0 star), lumi 1038 nosities for the first two dates of table 1 only, are above the limit; all would be below for an assumed distance slightly below 500 pc, and all above for an assumed distance slightly above Kpc . However if the sum of the radiative 1 and the kinetic energy fluxes, which should give a lower limit to the total radiative flux at the base of the optically thick wind , is considered, a such clearer result is obtained . The lower limits vary between 12.8 and 6.9 x 1038 erg s- 1 between days 15.85 and 31 .87 of table 1 and descend to 2.7 x s-1 1038 for the last date, when a distance of 650 pc is assumed. Even with a distance of pc , the value for the last date would still be close to the Eddington 500 limit . This conclusion, compatible with the present theoretical considerations of a total luminosity well above the Eddington limit , can only be avoided if the continuously ejected wind is not optically thick. In this case however , contradictions with observations would be hard to avoid, as seen above. However, what has been described leads to predicted velocities which are too small, and the assumption of spherical symmetry is probably not valid. This 103

can be seen if one notes that a very plausible way for producing a luminosity above the Eddington limit in only the outer layers, is through interaction of a bloated white dwarf with the companion star of the binary system , in which a nova outburst occurs. This interaction was already considered by MacDonald (1980) and by Mac Donald, Fujinoto and Truran (1985). However the full non spherical dynamical friction effects have not been taken into account , and

calculations still need to be made . It is nevertheless possible that rac can become as small as the stellar companion in this situation. The lack of inter action between the components of the widely separated binaries T Cor Bor and RS Oph , might be the reason for what may be an absence of optically thick winds in the cases of these recurrent novae (Friedjung 1986). A problem with the type of interpretation suggested here is that the very high velocities observed in the ultraviolet spectra of novae Aquilae 1983 and Serpent is 1983 may be hard to produce unless acceleration took place at radii smaller than that of the stellar companion (see eqs (3) and (4)), and another mechanism for a super Eddington luminosity could be necessary in such situation. In any case the way forward here is through better calculations.

III - THE FORMATION OF LAYERS WITH DIFFERENT VELOCITIES

If the interpretation described up to now is accepted, how can one explain the existence of layers with different velocities, classified by Mclaughlin (1943 )? In a model which I am developing (a preliminary version is described in Friedjung, 1985) the effects of collisions between material moving at different velocities is taken into account . The wind collides with slower moving material ejected before optical maximum , and this can produce a dense shell which could be the material of the "principal system"; the theory of colliding media of this type is similar to the Kwok , Purton and Fitzgerald (1978) theory for the origin of planetary nebulae, and also to theories for the interaction of a stellar wind with the interstellar medium (see McCray 1983). In such a theory two cases can be distinguished for the interaction, depending on the timescale for cooling of the shocked material . In the energy conservation situation the cooling timescale for the shocked continuously ejected wind of a nova is grea ter than that for the increase of radius of the nova envelope, while in the momentum conservation situation the opposite can be assumed . In the latter situation a cool shell is formed, while in the former the pressure of the hot shocked material causes this material to tend to fill the nova envelope, so the shock between the wind and the hot material occurs at small radii. If one examines the conditions for the collision of a continuously ejected nova wind with material ejected before optical maximum , one finds that the 104

momentum conservation situation occurs in early stages , and the energy conser vation situation later. Therefore a cool shell is formed , which is later acce lerated by the pressure of the hot shocked wind. The transition time between the two situations can also be stated as being the time when the cooling rate of the hot gas multiplied by the time in days since the start of the wind tc is less than the wind kinetic energy per unit volume. If cooling is by free free emission

x 1015 3.3 (5)

V the wind velocity relative to slower moving material , T is the tempera r is 1 ture, and is a mean mass loss rate. When V = 108cm s- , = 7 and = ni r 1D K � 1022 - gm s 1, transition occurs when tc • 10 days. A more rigorous expression for tc using among things the cooling rate of Raymond et al (1976) as appro ximated by Kahn (1976 ) gave a value of tc • 6 days. However all these results depend on the exactvalues of different parameters, and are liable to be modi fied . The hot shocked material should emit rays. The total flux emitted at a X time t is :

. �2 (te- t c l 2 F 1.6 x 101 5 g To s ergs s- 1 (6) v3 t 3

where te is a time for which the mass loss rate is assumed constant and very small thereafter ( te and tc are in days), while g is the Gaunt factor. When t t 101 "5 days, t 102 days, V the velocity is 108cm s-1 , and is as e- c = � before , one obtains a value of F 5 x 1035 erg s- 1 • However, ray absorption = X needs also to be taken into account . A spherical shell with a mass of 1D29gm would after 102 days of expansion at 108cm s- 1 have a column density of the order of x 1022 nucleons cm- 2• With cosmic abundances the optical thickness would be 2 at 1 Kev, but CNO overabundances could increase this value, while deviations from spherical symmetry could decrease it. In earlier stages most X rays would in any case be absorbed . The rays of nova Muscae observed by X 1983 Ogelman et al however may come from another mechanism , such as thermal ( 1984) emission from a white dwarf remnant . In principle these ideas can be used to interpret observed velocities . Outer parts of the premaximum system material should be swept up last by the 105

cool shell qivinq rize to the principal system. If Vm is the velocity of the premaximum system when last seen, VP the mean velocity of the principal system over the times when the premaximum system is still visible, tm the time since the ejection of the parts of premaximum system material seen just before the premaximum system becomes invisible, and tp the time at this staqe since the ejection of the principal systems :

(7)

One can find when the parts of the premaximum system last seen should have been ejected, and compare with observations of this system before optical maxi mum. Two novae well observed before optical maximum DQ Her and HR Del can be used for the present study. One firstly sees that the highest velocity premaxi mum system material only observed at very early stages disappears quickly; this could be due to a low density. The last seen premaximum system material in the case of DQ Her would have been ejected about 11 days before optical maximum , and could have first become visible (appeared in optically thin regions) not far from the time when the mean premaximum velocity had decreased to a value near the mean premaximum system velocity later attained just before disappea ring well after optical maximum. The test accordinq to these preliminary calcu lations may not work very well for HR Del; the last seen premaximum system material should have first appeared a month later than the date when the mean velocity before optical maximum had decreased to the relevant velocity. It is clear that the situation is probably less simple and more detailed calculations and models are required. The present results are only extremely approximate. Collisions between parts of the wind itself, with different velocities , might produce other layers. Much more work is required on this subject . To summarize, the ideas expounded here are capable of further development , and may be able to explain many observations of novae .

REFERENCES

Friedjunq , M. 1977a, in "Novae and Related Stars" , Ed. M. Friedjung , Reidel, Dordrecht, Netherlands, p.61

Friedjung , M. 1977b, in "Novae and Related Stars" , Ed. M. Friedjung , Reidel , Dordrecht , Netherlands, p.95 Friedjunq, M. 1981 , Acta. Astron. l:!_, 373 Friedjung, M. 1985, in "Recent Results on Cataclysmic Variables", ESA SP-236 , European Space Agency, Paris, France, p.181 106

Friedjung, M. 1986 , in "RS Oph (1985) and the Recurrent Nova Phenomenon" , Ed. M.F. Bode, VNU Science Press, Netherlands, in press Gallagher, J.S., Code , A.D. , 1974 , Astrophys. J 303 • .!§2_, Kahn, F.D. , 1976, Astron. Astrophys. �' 145 Kwok , S., Purton, C.R., Fitzgerald, F.M., 1978 , Astrophys.J. �' l 123 Mac Donald, J. 1980, Mon . Not. Roy. Astron. Soc 933 • .l22_, Mac Donald, Fujimoto, M.Y., Truran, J.W. , 1985 , Astrophys.J. 294 , 263 J., McCray , R., 1983, in "Highlights of Astronomy", vol .6, Ed. R .M. West , IAU and Reidel, Dordrecht, Netherlands, p.565 Mclaughlin, D.B., 1943 , Publ . Obs. Univ . Michigan, �' 149 Mclaughlin, D.B. , 1964 , Ann . d'Astrophys. '!]_, 495 Ogelman, H., Beuermann, K., Krautter, J., 1984, Astrophys. J. 287, l31 . Raymond, J.C., Cox , D.P., Smith, B.W. , 1976, Astrophys.J. 204 , 290 Ruggles, C.l.N., Bath, G.T., 1979, Astron. Astrophys. 80, 97 Snijders , M.A.J., Batt, T.J., Seaton , M.J., Blades, J.C., Morton , D.C., 1984 , Mon. Not . Roy. Astron. Soc. �' 7p Stickland, D.J., Penn, C.J., Seaton , M.J., Snijders, M.A.J., Storey , P.J., 1981 Mon. Not . Roy. Astron. Soc 107 • .!22• Wu, C.C., Kester, D. , 1977, Astron. Astrophys. �' 331 107

Table The Photosphere of FH Ser 1 :

Day from I Measured� I Colour I Measured Predicted I Mean measured L in 8 tempera- r in V in 2 high veloc. low veloc. 14.2.1970 10 s S 10 1 at ergs s- ture °K 1 0 12cm km s- 1 in 1 02 km s-1 in 2km s- 0.0 UT 1 , , 1 10 Most I hydrogen neutral 6.39 2.65 5250 22.0 8.41 2.39 5370 20 .1 15.85 1.32 7410 7.8 5.6 13.1 6.7 22.05 1 .05 9120 4.6 6.1 15.1 7 .1 27 .34 0.92 9770 3.7 6.3 16.3 7.3 29.34 1 .39: 8320: 6.3: 6.1: 16.8 7.4 31 .87 0.91 9200 4.3 6.0 17.2 7.4 49 .83 0.73: 14800: 1.5 7.9: 18.5 7.6 57.49 0.64: 18600: 0.84: 9.2: 18.7 7.7

109

MASS-ACCRETION EFFECTS ON WHITE DWARF INTERIORS

1 2 3 3 4 2 3 3 4 R.Cana1 • • , M. Hernanz • , J. Isern • , J. Labay • 5 and R. Mochkovitch 1 Departamento de Fisica Moderna , Univ. of Granada , Spain 2 Instituto de Astrofisica de Andalucia, Granada , Spain 3 Grup d'Astrofisica del I.E.C. , Barcelona , Spain 4 Departamento de Fisica de la Tierra y del Cosmos , Un iv.

of Barcelona , Spain 5 Institut d'Astrophysique de Paris . France

ABSTRACT .- There is observational evidence of the presence of young neutron stars in old binary systems . A likely explanation is that those neutron stars were produced in the collapse of old C+O white dwarfs . Old white dwarfs being cold and at least par tially solid , accretion-induced mass growth should finally lead , in a number of cases , to their collapse rather than to their explosion . We show in detail how mass accretion on initially so lid wh ite dwarfs can leave central solid cores when dynamical instability sets in. We also study the different effects of the existence of such cores on the outcome of the competition between thermonuclear explosion and gravitational collapse. 110

INTRODUCTION .- There is growing observational ev idence that yo ung neutron stars (with ages less than one hundred million ye ars ) are components of old binary systems (ages of the order or larger than five thousand million years ) . Such evidence comes from several types of obj ects :

1) a ) Wide binary radio pulsars , such as PSR0820-02 and PSR1 953 +29 . 1) b ) Wide low-mass pulsating X-ray binaries , as GX1+4 . c ) Very close pulsating X-ray binaries , such as 401626-67 and l ) 1E2259+59 . 2),3) ,4) d ) Millisecond pu lsars . 5) 7) e) Quas iperiodic oscil.l ators ' . ,5)

There are , of course, scenarios for the origin of every separate kind of those objects that do not involve recent neu tron star formation . Often , they have been inspired by the be lief that there is no way for producing a neutron star in an old binary system . Taken together , nonetheless, all the prece ding examples strongly point out that neutron star formation in already old binary systems should be no exceptional event . And we will show that such systems are precisely the best sites for neutron star formation , along with the burnt out cores of mas sive stars .

The only kind of old objects that can become unstable and collapse are old white dwarfs , recently reactivated by mass ac cretion from a close binary companion . Mass growth up to Chan drasekhar 's limit induces collapse to neutron star densities unless the star explodes first. Direct collapse of a wh ite dwarf 8 > 9) into a neutron star was first formu lated by Schatzman . Mestel l O) and Schatzman also proposed wh ite dwarf explosions as the me chanism for Type I supernovae . In recent years , the emphasis lO) ,ll) has been put on this last process . Less attention has be en paid to the first possibility . How can a white dwarf someti 1 2 ) mes collapse and sometimes explode ? Canal and Isern pointed out that solidification of the white dwarf interior plays the key role in deciding among the two opposite outcomes : fluid whi te dwarfs explode ; solid white dwarfs collapse . And old white dwarfs are expected to be solid , Solidification implies : 1 ) High 10 - 3 er ignition densities (�1x10 g cm ), since the nuclear reac- Ill

tions happen in the pycnonuclear regime . This means higher electron capture rates on the incinerated material . 2) Slower burning propagation , as conductive burning fronts replace hydrody namic burning. Contraction induced by the electron captures can compete with hydrodynamic expansion. 3) Depending on the phase diagram adopted , in the case of white dwarfs , chemical sepa c+o ration in the solid phase is possible . In this last case , the central layers of the star will be made of solid oxygen and ther 10 monuclear ignition will be further delayed (up to 2xlo g fc � - 3 cm ). Those effects of solidification on the final behaviour of C+O white dwarfs (the chemical composition expected in most . . . 13 ) 14 ) 15) 16 ) ' ' ' cases ) have been studied in a series of papers . From total collapses to completely disrupting explosions , along with partial explosions leaving bounded remnants , have been pre dicted for different assumptions concerning the size and chemi cal composition of the solid cores at ignition . It must be stres sed that effect 1) alone can already ensure collapse , unless a detonation (which means supersonic burning propagation ) is assu med to form immediately at the centre . This has been repeatedly 12 l l 5l pointed out in refs . - . 17) A different approach was adopted by Miyaji et a1 . and l B ),l g ) Nomoto . Collapse was exclus ively attributed to mass-accre ting O+Ne+Mg white dwarfs , the hypothetical descendants of s±2M 0 M 10+-2M stars . Whether such stars might explain any signifi � 0 - cant fraction of systems a) through e) still remains an open question . The now widely recognized fact that ''plain" C+O white dwarfs can easily collapse , provided that they are cool and den se enough (see Nomoto , this same volume ) makes it timely to stu dy in detail the conditions that produce the appropriate precol lapse structures .

Old white dwarfs that start accreting mass from a compa nion star must be solid through most of their interiors . Mass accretion , however , can change the physical state of those co res : compressional heating plus heat conduction from outer bur ning layers will melt the star's interiors to a variable extent , Complete melting will result for a range of combinations of ini tial mass , initial internal temperature , and accretion rate (that 112

also depending on the chemical composition of both the interior and the accreted materials ) . Here we wi ll systematically study the changes produced by mass accretion in the white dwarf inte riors . We will show how solid cores of variable size are still

left after the mass- accretion stage , when both thermonuclear and dynamical instabilities set in , and that for a rather wide range of the three aforementioned parameters (initial mass and inter nal temperature , plus accretion rate ) . This ensures the entire viability of the coll apsing models already studied by us and it wi ll allow later modelling of specific ob jec ts .

SOLID WHITE DWARFS.- White dwarf crystallization has been stu 20 ) 2 1) 22) died by Mestel and Ruderman , Shaviv and Kovetz , Van Horn , 23 ) 24) 23 ) Lamb and Van Horn , and Iben and Tutukov . From ref . , for

instance , we have that the time for a C+O wh ite dwarf of 1M to 0 cool down to the point when half of its mass has become solid is : 8 - 5xl0 yr . This is quite short , compared to the ages of 't'cool - the aforementioned systems .

As to the chemical composition of the solid cores , it de pends on two possible phase diagrams : 25 ) a ) In the phase diagram of Loumos and Hubbard , carbon and oxy gen are completely miscible in both the fluid and the solid pha

se . The melting temperature of a given C+O mixture is the weigh 12 16 ted average of the melting temperatures of pure c and pure 0. It is supported by a Monte Carlo simulation for a X =X =0 .50 mix c 0 ture . 26) b ) In the phase diagram of Stevenson , there is an eutectic (temperature minimum ) in the phase diagram for a composition 12 16 c; o � 2 (by number ) . A solid C+O alloy can only form with this fixed C/O proportion . For an oxygen excess (such as for X =X =0 .50 ) oxygen should crystallize first and fall to the cen c 0 tre ("oxygen snowflakes " ) . This would lead to complete separation 27) of oxygen from carbon (Mochkovitch ) , the innermost half of the star being made of pure oxygen . The cooling times are increased , however : complete solidification of a 1M c+o white dwarf takes 0 9 2xl0 yr if carbon and oxygen remain thoroughly mixed in the so 9 lid phase; it would take 8xl0 yr if carbon and oxygen do separa- 113

te .

The fact that phase diagram a) is based on a numerical si

mulation while phase diagram b) comes from an approximative cal culation only should not be regarded as highly significant : di rect Monte Carlo simulations are not likely to reproduce the eu tectic behaviour , however real it might be , due to relaxation problems . They should rather be used to derive analytical appro ximations to the free energies , in order to calculate the phase 26) boundaries (ref . ).

ACCRETION MELTING. - We have calculated the evolution , driven AND by mass accretion , of a number of partially solid wh ite dwarf

models , characterized by their initial total masses M�n , their O initial solid core masses M and their initial central tempe- c' 0 ratures (the three parameters are obviously not independent , T?c the Jast one being only given for the �ake of easiest visualiza 14) tion). The input physics is similar to that described in ref . . The models listed in Table 1 correspond to Loumos and Hubbard 's phase diagram . Those in Table 2, to Stevenson 's phase diagram . 12 - l The accretion rates considered are in the range l0- M yr < -6 - 1 ° " 10 M yr for both types of models . � ( 0 The final results , as to the greater or lesser extent of core melting , arise from the combined effects of compression, nuclear reactions (both in the core and in the accreted layers ), thermal conduction , and neutrino cooling .

When mass accretion starts , there is heat conduction from the outer into the cent�al layers . Its time scale can be appro ximated by :

"'[' th (1)

where , T, , and c have their usual meanings and 1 is ),.( , f a- p 28) the linear extent of the region considered (ref . ). The cen tral density increases on a time scale :

10 .08 = ( 0. )( (2) M 3 Yo where is the mass accretion rate and with � 114

TABLE 1

Solid mass fractions and central temperatures for models ba sed on Loumos and Hubbard 's phase diagram .

1.2 1. 3 1.4 ---- o o M /M T c 7c 0

A 0.00 1.53 0.00 2.18 0.00 5.41

B 0.62 0.96 0.59 1.40 0.67 3.40

1.10 0.50 1.20 0.66 1.25 1.71 c

TABLE 2

Solid mass fractions and central temperatures for models ba sed on Stevenson 's phase diagram .

1. 2 1. 3 1.4

A 0.00 0.96 0.00 1.37 0.00 3.40

B 0.20 0.61 0.22 0.87 0.24 2.12 c 0.40 0.54 0.43 0.76 0.47 1. 85

D 1. 03 0.46 1.09 0.65 1.13 57 1.

The fact that a thermal wave propagates inwards on a time scale given by (1) is due to the greater compressibility of the outer , partially degenerate layers . This "luminosity " can be ap proximated by :

( 3 )

7 T being the temperature in units of 10 K and the accretion 7 �lO 1 0 -l 3 o l rate in units of 10 g s (ref _ ) .

During the accretion process , there is competition betwe en the time for the thermal wave to reach the centre and that 115

for going over Chandrasekhar 's limit. The numerical results can be easily understood in those terms . There are three qualitati vely different behaviours : -12 -1 -10 i) For low enough accretion rates (10 M yr 10 M 0 � � � 0 -1 yr ), the thermal wave reaches the centre , but compression is so slow that surface cooling dominates . The last can be approxi mated by the classical expression :

4µ. l L/L = 4.6xl0_ ( 4) 0 � f4 (1 X) e Z + 31 ) (ref. ) .

-8 -1 -6 ii) For high enough accretion rates (5xl0 M yr 10 0 � � � -1 M yr ), the thermal wave has no time to reach the centre (this 0 happens for M 1.2 M in the cases considered ). In the central � 0 layers "( : they evolve adiabatically , their index be th >> "'Cc ing : 1 4 0.815 0.215 r 1 + ( 5) 1 4 o.945 o.646 r 1 + 27) (ref . ), where r is the plasma coupling constant (in our cal culations , solidification corresponds to 171). r > 10 -l iii) For intermediate accretion rates (lo- M yr 0 � � � -9 -1 10 M yr ), the thermal wave has enough time to reach the star 's 0 centre and to melt (often completely) the core . The final outco me depends on the phase diagram adopted .

RESULTS AND DISCUSSION . - We present , now , the results from the full numerical computations :

I) Results for the Lournes-Hubbard phase diagram . In Table 3 are displayed the central densities and solid mass fractions at ignition , for the initial models of Table 1 and several mass-ac cretion rates . As we see , there are many combinations for which a central solid core remains . The ignition densities are in the 9 -3 10 -3 range : 6xl0 g cm f l.3xlo g cm . As already sta � ign � ted in the Introduction , at those densities electron captures on the incinerated material are very fast. Thus , even for complete ly fluid layers (as in the cases with M = 0 of Table 3), where c 116

TABLE 3 -3 Ignition densities (in g cm 1 and final solid core masses for models in Table 1 ( Lournes- Hubbard phase diagram ) and seve ral mass-accretion rates .

1.2 1.3 1.4

A 7.9 0.00 9.5 0.00 11 . 0 0.00

B 10 .2 0.00 10 .8 0.00 12 .5 0.48

c 12.5 0.32 13 . 2 0.63 13 .9 1.15

A 6.1 0.00 7.9 0.00 9. 7 0.00

B 6.7 0.00 9.6 0.00 11. 2 0.48

c 7.6 0.00 11 . 7 0.18 12 .4 1.08

A 6.4 0.00 7.3 0.00 9.5 0.00

B 6.5 0.00 8.7 0.00 10 .8 0.51

c 6. 9 0.00 11 . 0 0.14 12.0 1. 09

A 9.5 0.00 9.5 0.00 9.1 0.00 -9 10 B 9.5 0.61 9.5 0.60 9. 7 0. 71

c 9.5 0.61 9.8 0. 76 10.6 1.22

------

A 10. 7 43 10 .7 1.43 10 .3 1.43 1. -10 10 B 10.7 1.43 10.7 1.43 10.4 1.43

10.7 1. 43 10.7 1. 43 10.6 1.43 c

------

A 10 .7 1.43 10 .7 1.43 10.8 1.43 ll 10- B 10 .7 1.43 10.7 43 10.8 1.43 1.

c 10.7 43 10.7 l.43 10.8 l.43 1. 117

a turbulent flame front driven by hydrodynamical instability can freely develop , slightly subsonic propagation velocities and/or any delay in the start of the fluid motions and mixing will already entail accelerated contraction instead of expansion .

That delay is to be expected , since the buoyancy is null at the 32 ) star's centre (ref . ). Low initial speeds for the burning front are indeed found in the numerical experiments of Muller and Ar 33> 34 > nett . . Bu t, through still solid layers (the cases with

M � 0 of Table 3), thermonuclear burning must propagate as a c conductively driven front : the strongly degenerate electrons , with relatively long mean free paths , do provide the thermal link between the burnt up , fluid layers , and the unburnt , solid la 35 ) yers . Characteristic velocities are given by (ref. ):

v ( 6)

2 - 1 where is the conductivity coefficient (in cm s ) and 'X 't is the characteristic time of the thermonuclear reactions . Ve locities given by (6) are always much smaller than local sound speeds in the central layers of the models in Table 3. Collapse 12 ) thus ensues , as already calculated in ref . . It might be objec ted that , the latent heat of melting being small , the solid la yers should be easily penetrated by the turbulent motions origi nated in the fluid layers and burning propagation would be hy drodynamical after all. In order to check this , solid "strength " mus t be compared to the energies involved in the "impacts " of the fluid eddies . A measure of the strength of the solid is pre cisely given by the latent heat of melting . From Monte Carlo si 36 ) mulations for a one- component plasma (ref. ), it is of the or der of kT per ion , T being the melting temperature . The kine tic energy of the fluid "blobs " impinging on the fluid/solid boundary comes from their acceleration by the buoyancy force along a "mixing length " (when the linear extent of the fluid region is smaller than , say , a pressure scale height , we can take this same extent as the mean free path of the "blobs"). We can then calculate the kinetic energy per ion and compare it to

the latent heat given above . Due to the small size of the molten

zone when thermonuclear runaway starts at the centre , the kine

tic energies always remain about one order of magnitude lower 118

than the melting energies . Thus , "penetrative convection" into the solid layers must be negligible and burning front velociti

es can be approximated by ( 6 ).

II ) Results for Stevenson 's phase diagram . They are given in

Table 4, for the models that underwent central oxygen ignition

and in Table 5 for those that ignited carbon off- centre . All 16 models that reached the point where electron captures on 0 lO 3 start the thermonuclear runaway do ignite at f 2xl0 g cm- Thus , only the remaining solid mass is specified. A label "C" means that carbon ignited off-centre . In Table 5, both central and ignition densities are also given . There , label "X" means

central oxygen ignition . The off- centre carbon ignitions always happened at the base of the carbon- rich layers , but for the com bination of the lowest initial mass (1.2 M ) with the highest 0 -6 -1 accretion rate (10 M yr ). 0 All models that experience central oxygen ignition do start collapsing . Full hydrodynamical calculations have been

performed for several of those models , up to a central densi- 11 -3 37) ty ; 5xlo g cm (one of them is reported in ref . ). � c Off-centre ignitions give partial explosions . Their bounded rem nants should be wh ite dwarfs of lower masses . Light curves for 38 ) such explosions have been calculated (ref . ). They agree with observed light curves of Type I supernova explosions and they can reproduce the Pskovskii-Branch effect : brighter maxima co rrespond to faster expansion of the ejected material and also to a broader peak in the light curve .

In all the preceding computations we have proceeded as if the accreted material were a mixture of This would only C+o . be a realistic assumption for double white dwarf scenarios as 39 ) those discussed by Iben and Tutukov in the context of models for Type I supernovae . But even in the cases where we predict collapse to nuclear matter densities and formation of a neutron star , the companion star would be disrupted and no binary sys tem would remain. In order to explain the kind of systems dis cussed in the Introduction , we must in general assume that the accreted material is hydrogen-rich , or at least helium-rich . This poses the problem of the behaviour of the accreted layers . 119

TABLE 4

Final solid masses for models based on Stevenson 's phase dia gram . Values (in M ) are only given for models that underwent e central oxygen ignition . Models that ignited carbon off-centre are labelled "C" .

0 M /M 1. 2 1. 3 1. 4 T 0

-1 (M yr ) [QI 0

A c c c B 0.20 0.24 c 0.44 0.48 c c 0.60 1. 03 D c

A c c c B 0.24 c c 0.48 c c c 0.22 0.94 D c

A c c c B 0.24 - 8 c c 5xl0 0.48 c c c 0.00 0.15 0.90 D

A c c c B - 9 c c c 10 0.40 0.44 0.54 c 0.60 0.65 1. 00 D

A c c c B c c c 1. 44 1. 44 1.22 c 1. 44 1. 44 1. 44 D

A c c c B c c c 1. 44 1.44 1.44 c 44 1. 44 1. 44 D 1. 120

TABLE 5

9 - 3 Central densities , ignition densities (both in 10 g cm ), and final solid masses , for models based on Stevenson 's phase diagram . Models that underwent central oxygen ignition are la belled "X" .

1. 2 3 1. 4 1.

f i9

A 10 .2 10 .2 0.00 10 .8 10 .8 0.00 12 .5 12 .5 0.00

B 3.2 13.8 0.21 x x x x x x

c 2.9 13.2 0.24 x x x x x x

D 2.7 10 .2 0.35 x x x x x x

A 6.7 6.7 0.00 9.6 9.6 0.00 11 .2 11 .2 0.00

B 5.8 9.9 0.00 10.6 12 .4 0.02 x x x

c 5.3 13 .1 0.00 6.5 17.3 0.16 x x x

D 4.5 17.5 0.00 x x x x x x

A 6.5 6.5 0.00 8.7 8.7 0.00 10 .8 10.8 0.00

6.3 10 .8 0.00 7.8 12 .6 0.09 x x x 5xl0 -SB C 6.0 14 .8 0.03 6.8 18 .1 0.09 x x x

D x x x x x x x x x

A 9.5 9.5 0.00 9.5 9.5 0.00 9.7 9.7 0.00

B 9.5 16 .3 0.21 9.6 17.0 0.22 10 .1 18 .8 0.24

c x x x x x x x x x

D x x x x x x x x x

A 10 .7 10 .7 1.43 10 .7 10 .7 1.43 10 .4 10 .4 0.87

B 10.4 17.9 0.21 10 .5 18.6 0.22 10 .4 19 .0 0.24 - 10 10 c x x x x x x x x x

D x x x x x x x x x

A 10.7 10.7 1.43 10 .7 10 .7 1.43 10.8 10 .8 1.43

B 10.1 17.3 0.21 10 .1 18 .0 0.22 10 .0 18.7 0.24 - ll 10 c x x x x x x x x x

D x x x x x x x x x 121

TABLE 6

Comparison of the ignition densities , with and without in clusion of an outer burning layer , for models based on the Lou mos-Hubbard phase diagram .

0 M /M 1. 2 1. 3 1. 4 T G

-1 (M yr ) ti! 8 �i9 � i9 � i9 yes no yes no

B 10 .2 10.2 10 .S 10 .S 12.5 12 .5

c 12 .5 12 .5 13 .0 13.2 13 .9 13 . 9

A 6.5 S.7 10 .S 10 .S - S 5xl0 C 6.9 6.9 11 .0 12 .0 12 .0

TABLE 7

Comparison of the final solid core masses , with and without inclusion of an outer burning layer , for models based on the Loumos- Hubbard phase diagram .

0 M /M 1. 2 1. 3 1.4 T G

- 1 (M yr ) M M M M M M ti! 8 c c c c c c yes no yes no yes no

B 0.00 0.00 0.00 0.31 0.33 o.oo c O.lS 0.22 0.42 0.44 0. 76 o.so

A 0.00 0.00 0.33 0.36 - S 5xl0 C 0.00 0.00 0.10 0.52 0. 76

We will not discuss the limitations on the allowed range of accretion rates that come from the need to avoid nova outbursts

(when accreting hydrogen- rich material ) nor those arising from the risk of helium detonations (when accreting helium-rich ma terial or after producing it in a hydrogen- burning layer ). But , as we are dealing with the ignition densities and with the so lid mass fractions left after the accretion process , we must 122

check the effects on those quantities of the presence of an ou

ter burning layer (either steady or flashing ). We have thus si mulated a helium- bu rning layer , at a constant temperature of 8 2x10 K. This is an upper limit for both steady and flashing bu rning . The comparison with accretion without burning is gi - 8 ven in Tables 6 and 7, for accretion rates in the range Sxl0 - 1 -6 - 1 M yr 10 M yr (for which neither nova outbursts nor 0 � � � 0 helium detonation are expected ) . As we see , they do not change the general picture deduced from the calculations assuming di rect accretion of C+O .

CONCLUSIONS .- We have shown that old , partially solid, rather massive white dwarfs , can remain so after mass accretion up to the point of dynamical and/or thermonuclear instability . Collap se to nuclear densities is predicted in two different cases :

1 ) Solid central layers made of a random C+O alloy . Collapse is due to the high ignition densities plus the relative slow ness of conductive burning propagation . 2) Central layers made of almost pure oxygen , due to carbon/oxygen separation in the crystallization process . The igntion density would be even high er than in the preceding case . Off- centre carbon ignition is ex pected when the size of the central oxygen core is small: those cases would give Type I supernova outbursts . It must be stressed that c+o white dwarfs can collapse to form neutron stars irres pective of which phase diagram is the correct one : Lournes and

Hubbard 's or Stevenson 's. Recent neutron star formation in old binary systems makes a consistent pictu re , since such old sys tems are the most likely to contain cold, largely solid white dwarfs .

REFERENCES . -

1 van den Heuvel , E.P.J. , and Habets , G.M.H.J. 1985 , preprint 2 Henrichs , H.F. 1983 , in Accretion- Driven Stellar X -Ray Sources ,

ed . W.H.G. Lewin and E/P/J/ van den Heuvel (Cam

bridge University Press , Cambridge ), 393 3 van den Heuvel , E.P.J. 1983 , in Accretion-Driven Stellar X-Ray

Sources , ed . W.H.G. Lewin and E.P.J. van den He

uvel (Cambridge University Press , Cambridge ),303 123

4 van den Heuvel , E.P.J. 1984 , preprint 5 van der Klis , M. , Jansen , F. , van Paradijs, J. , Lewin , W.H.G. ,

van den Heuvel , E.P.J. , Trumper , J.E. , and

Sztajno , M. 1985 , Nature , 316 , 225 6 Hasinger , G. , Langmeier , A. , Sztajno , M. , Trumper , J. , Lewin ,

W.H.G. , and White , N.E. 1986 , Nature , 319 , 469 7 Midd leditch , J. , and Priedhorsky , W. 1985 , IAU Circu lar 4060 8 schatzman , E. 1956 , in White Dwarfs (North Holland Publ . Co . ,

Amsterdam ) 9 Mestel , L. 1952 , Monthly Notices Roy . Astron . Soc. , 112 , 583 10 schatzman , E. 1963 , in Star Evolution , ed . L. Gratton (Acade

demic Press , New York ) , 389 11 wheeler , J.C. 1982 , in Supernovae : A Survey of Current Rese

arch , ed . M.J. Rees and R.J. Stoneham (Reidel ,

Dordrecht ), 167 12 canal , R. , and Isern , J. 1979 , in White Dwarfs and Variable

Degenerate Stars , ed . H.M. Van Horn and v. Wei

demann (Univ . Rochester Press , Rochester ), 52 13 canal , R. , Isern , J. , and Labay , J. 1980 , Ap_ J_ (Letters ),

241 , L33 14 rsern , J. , Laby , J. , Hernanz , M. , and Can al , R. 1983 , � .- 273 , 320 15 rsern , Labay , J. , and Canal , R. 1984 , Nature , 309 , 431 16 canal , R. , Isern , J. , Labay , J. , and Lopez , R. 1985 , in Nu

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and Particle Physics , in press 17 Miyaj i, s. , Nomoto , K. , Yokoi, K. , and Sugimoto , D. 1980 ,

Publ . Astron . Soc . Japan , 32 , 303 18 Nomoto , K. 1982 , �. 257, 780 19 Nomoto , K. 1984, � . 277, 791 20 Mestel , L. ' and Ruderman , M.A. 1967, Monthly Notices Roy . As-

tron . Soc , 136 , 271 21 shaviv , G. , and Kovetz , A. 1976 , Astron . Ap . , 51 , 383 & 22 van Horn , H.M. 1968 , 151 , 227 �. 23 Lamb , D.Q. , and Van Horn , H.M; 1975 , �. 200 , 306 24 rben , I. , and Tutukov , A.V. 1984, 282 , 615 � . 25 Loumos , G.L. , and Hubbard , W.B. 1973 , 180 , 199 � . 26 stevenson , D.J. 1980 , J. Phys . Suppl . NQ 3, 41 , C2- 61 124

27 Mochkovitch , R. 1983 , Astron . Ap. , 122 , 212 & 28 Henyey , L. , and L'Ecuyer , J. 1969 , �' 156 , 549 29 canal , R. , and Schatzman , E. 1976 , Astron . Ap ., 46, 229 & 30 Nomoto , K. 1982 , Ap . J. , 253 , 798 31 schwarzschild , M. 1965 , in Structure and Evolution of the Stars

(Dover , New York ) 32 Buchler , J.R. , Colgate , S.A. , and Mazurek , T.J. 1980 , J. Phys .

Suppl . NQ 3, 41 , C2-155 33 Mi.iller , E. , and Arnett , W.D. 1982 , Ap . J. (Letters ), 260 , L26 34 Mi.i ller , E. , and Arnett , W.D. 1985 , in Nucleosynthesis : Challen

ges and New Developments , ed W.D. Arnett and J.

W. Truran (Univ . of Chicago Press , Chicago ), 138 35 Landau , L. , and Lifchitz, E. 1970 , in Th�orie des Champs (Mir,

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J. 1985 , in Recent Results on Cataclysmic Varia

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Ap. , 155 , 1 & 39 rben , I. , and Tutukov , A.V. 1985 , Ap . J. Suppl ., 58 , 661 125

NUCLEOSYNTHESIS IN HE-FLASHES ON ACCRETING WHITE DWARFS

W. Hiiiebrandt. M. Lechle. W. Zlegert Max-Planck-lnstltut fOr Astrophyslk D-8046 Garchlng bel MOnchen . FAG

K. Nomoto Physics Department. Brookhaven National Laboratory Upton. New York 11993. USA

F. K. Thielemann Department of Astronomy. University of Illinois Urbana. Illinois 61801 . USA

ABSTRACT

We present preliminary results of Investigations of He-flashes on accretlng C-0 -8 white dwarfs. It Is shown that for accretion rates of about a few times 10 to -7 10 M0 per year which are believed to lead finally to carbon deflagratlon supernovae the nucleosynthesls products are significantly different from those of hydrostatic He-burning. In particular. we find large enhancements of C. Mg and SI. together wlth an overproduction of certain rare Isotopes of heavy elements. These results should be taken Into consideration If attempts are made to model the spectra of type I supernovae. Finally. we have also computed the yields of elements and their Isotopes beyond Iron which are modified by neutron capture reactions during the flashes. We find that the neutron flux Is not sufficient to 1 1 drive an r-process mainly because 8F has no time to decay to 80 during the short duration of the flashes. but nuclei with A are enhanced by factors up :s; 70 to 50 relative to their solar system values. 126

I. INTRODUCTION

At present C-0 white dwarfs accretlng matter at a rate of somewhere In between - -6 a few times 10 8 and 10 Mei per year from a companion star are thought to be

the progenitors of normal type I supernova explosions. Although It Is not quite

clear whether or not such high accretion rates Indeed can be obtained from

binary evolution sequences these models can explain the observed properties of type I supernovae surprisingly well Including even details of early and late time

spectra Csee . e. g .. ref. ll and 2l l. At the accretion rates under consideration

here. carbon will Ignite at the center of the C-0 white dwarf. a subsonic burning front C"deflagratlon wave"l will Incinerate the Inner 0. 5 to 0. 8 Mei mainly Into 56 Ni. whereas the outer layers of the exploding white dwarf will not be processed to Iron group nuclei leaving enough Mg. SI and Ca to explain certain absorption features In the spectra. It Is certainly of Interest. however. to check whether the composition of the ejecta depends upon the history of the accreted material. In

particular. one might expect that the He-burning conditions on the surface of accretlng white dwarfs are significantly different from those In normal stars . and they will also depend upon the accretion rates . In addition. one may speculate that neutrons being liberated by certain Ca. nl -reactions during degenerate

He-burning may also change the heavy element abundances considerably. We have therefore computed the thermal evolution of the He-layer of an accretlng

Mei C-0 white dwarf. Some of the details of these computations are given In section II. In section Ill we present the results obtained from a reaction network

Including all elements from hydrogen up to germanium. Finally. In section IV we discuss the prospects of heavy element nucleosynthesls by neutron-capture processes.

II. HELIUM SHELL FLASHES

The properties of the C-0 white dwarf model used In our computations are summarized In table The Input physics adopted was the same as In ref. 2l l. and 3l .

Initial model of the C-0 white dwarf �:

-3 MC M > eil Pc

The accretion of helium-rich material CY 98. 0. 02> onto the C-0 white = o. Z = - -1 dwarf was calculated for two cases with M 1-10 7 Me yr Cease Al7> and = - -1 4 .10 8 Me yr Cease A48) . respectively. but the model also simulates the average growth of the helium layer through many cycles of hydrogen shell flashes

and 5l >. If hydrogen-rich matter accretes onto a Me white dwarf l at the rates under consideration here. a hydrogen-shell flash Is Ignited when the accreted matter Is about 2. 10-5 Me >. The flash will be relatively mild and most of the matter will be processed Into helium Csee rel. 7> . and 8> for numerical examples> . Although the hydrogen-burning shell was not

Included In the present calculations the thermal structure near the bottom of the helium layer does not depend on It but Is determined by the balance between the compressional heating and the radiative cooling during the long accretion phases between subsequent hydrogen flashes. Therefore the approximation used here Is good enough to treat the long term evolution and the progress of a shell flash except for the mixing of hydrogen-rich and helium layers due to convection .

As the helium zone grows the material near Its bottom Is compressed and the density and temperature Increase. It should be noted that the maximum temperature does not appear at the base of the helium layer but a somewhat outer shell. This temperature Inversion arises from the fact that the timescales of both compressional heating . and radiative cooling. T0001 • are shorter near Tcomp · the surface than In the Interior and a temperature peak forms near the surface where and 9) >. Tcomp :> Trad

When a certain amount of matter has been accreted He-burning Is Ignited near the shell of maximum temperature. The mass of the white dwarf. M. the

Lagrange mass of the burning shell. M . the temperature. T • and the density. r 19 at Ignition are given In table 2. as well as the peak values of temperature Pig· and density. In figure l temperatures and densities of both models are shown from the onset of He-Ignition to the end of the first flash .

Table 2: Models at Ignition and at the peak of the first flash

Case M M M r T T ;g P;g peak Ppeak -3 -3 c Me/yr> CMe> CK> Cgcm > CK> Cgcm >

-7 7 5 Al7 10 l. 0207 1.008 0 9. 7·10 3.10 6. 4.108 3. 3.104 l. - 5 A48 4. 10 8 1. 0705 1.0445 l .108 6. 5.10 9. 108 6. 2. 104 l. 128

0. 0 ....: c.o w * (X) (X) . . 0 0

ill > • f- a 1--i ([) "'"z Ol'

(\J (\J . 0 0

0 0 . 0 0 o.o 1.0 2.0 3.0 4.0 5.0 TIME • E4 -3 Figure Density C marked by dots> In units(S) of 06gcm and temperature In l: 9 l 4 units of 10 K versus time In units of 10 s from the onset of He-burning through the first flash of model A 17 C upper dlagramme> and model A48 Clower diagram me> .

0 0 ....: c.o w * (X) . 0

ill > . l- o 1--i ([) "'"z . w o O

(\J . 0

0 . 0 0 o.o 0.2 0.4 0.6 a.a 1.0 TIME • E4 (S) 129

For the smaller accretion rate Ignition Is delayed to a stage with larger envelope

mass and higher density because cooling Is more efficient In this case. After

He-Ignition the temperature Increases due to electron degeneracy until expansion starts and adiabatic cooling sets In. For lower accretion rate M both peak temperature and density are higher because the white dwarf has accumulated

more mass C ref . lOl >.

During the flash a convective zone develops and extends almost up to the outer

edge of the accreted layer. Near the peak of the flash the temperature gradient -1 Is superadlabatlc and convective velocities. are typically around 500 km s . Vconv· The mixing timescale. Is therefore of the order of a few seconds and rconvlVconv· thus sufficiently short for a complete and uniform mixing of most freshly produced

elements throughout the outer layers of the star. The further evolution of the low

accretion rate model A48 has been computed through the second and third flash

which occur when the burning front moves Inwards In mass. This Inward

propagation Is due to radiative energy transport. At Ignition the helium envelope

has al.ready expanded to lower densities due to the first flash and. therefore. the

second and the th ird flash are both much weaker than the first one as can be

seen from table 3.

Table 3: Lagrange mass. peak temperature and peak density for the second and third flash of model A48

M r Tpeak Ppeak -3 CM0l

8 4 2nd flash 1.0384 5. 3.10 2. 0.10

8 4 3rd flash 1.0318 5. 4-10 2. l.10

During this later flashes the entropy In the outer layers Is already so high that

convection does not develop until the peak temperature Is almost reached. Mixing

Is therefore negligible and the flashes are essentially confined In a single zone.

These successive flashes will continue until the burning front reaches the surface

of the carbon-oxygen core .

We expect that from then on helium will burn quietly In a shell on top of the

C-0 white dwarf and that this burning shell moves outwards In mass. Since the

depletion of helium will proceed faster than the accretion of new fuel the mass of 130

the helium layer wlll decrease and eventually It wlll become so small that helium

burning Is quenched. Afterwards. fresh material has to be accreted untll the next

cycles of helium shell flashes can start.

In this way Inner parts of the hellum layers that have undergone nuclear

processing In flashes are brought Into the C-0 core white outer shells undergo new flahses. Of course. from our present computations we cannot make firm predictions what fraction of the accreted matter Is processed In this way.

We conclude this section with some remarks concerning the possible admixture of

protons Into the hellum-burnlng shells which may modify the nucleosynthesls yields considerably. If the C-0 white dwarf Is accretlng hydrogen-rich matter and a -5 hydrogen-rich envelope of about 10 M0 Is attached to the helium layer the

entropy at the bottom of the envelope Is much smaller than . for example. the entropy barrier In red giant stars. Therefore. during the flash the convective zone can easlly reach the hydrogen shell and protons wlll be mixed Into the hellum burning layer 111 We can estimate an upper llmlt of the proton mass fraction In . -3 """' the helium layer and find 2.10 and 4. 1 0 In models A17 and A48. respectively. On the other hand . If the companion star of the C-0 white dwarf Is a helium star transferring helium as a result of angular momentum loss due to gravitational radiation. mixing of hydrogen does not take place.

Ill. LIGHT ELEMENT NUCLEOSYNTHESIS

We have used a reaction network going from hydrogen up to germanium In order to compute the abundances during and after the hellum flashes. The reaction rates were taken from the compllatlons of Fowler. Caughlan and Zimmerman 12> 13 < 1975> and Harris et al. 983) > . or from Hauser-Feshbach calculations Cl 14> 15> by Woosley et al. < 1978) and Thielemann < 1980) when no experimental rates were avallable. Table 4 summarizes the results of a set of computations In which mixing has been neglected. was discussed In section II this assumption As Is well Justified for all flashes but the first ones . but overestimates the amount of nuclear processing during the first convective flashes. Note that the second and the subsequent flashes have slmllar peak temperatures and densities. so the nuclear abundances given In table 4 for the second flash of the tow accretion rate model A48 wlll be characteristic for the Inner 50'111 of the accreted matter. 131

Abundances of selected Isotopes relative to their solar system values .Ill.b..!.L.1:

Y/Y0

model A48 model A1 7

1st flash 1st flash 2nd flash 1st flash Isotope

12 0 38. 7 45. 0 134 131 16 0 0. 1 0. 3 2. 1 1. 0 2 0Ne 0. 3 0. 5 2. 8 2. 0 23 Na 0. 01 0. 002 3. 4 0. 005 24 Mg 31 . 7 28. 2 34. 3 183 25 Mg 7. 2 2. 2 78. 8 63. 6 2 6Mg 1. 5 1. 3 39. 4 22 .6 2 7AI 17. 4 17. 7 7. 9 7. 1 2 851 817 571 1. 3 92. 5 29 SI 151 124 7. 5 72.9 30 SI 128 138 14. 0 17. 7 31 27. 9 28. 3 11. 2 5. 6 32p 5 290 183 0. 4 1. 3 33 5 168 159 1. 9 4. 3 M 25. 7 26. 8 2. 0 2. 0 35s CI 9. 2 8. 6 4. 7 2. 8 36 Ar 5. 9 3.4 0. 3 0. 5 46 Ca 1. 1 1. 1 441 181 45 Sc 3. 0 3. 3 27. 1 17. 3 SO 1. 0 1. 0 11. 7 8. 8 54T! cr 1. 2 1. 2 16. 6 16. 0 58 Fe 1. 3 1. 4 103 117 s sco 1. 6 1. 7 110 61. 8 60 Ni 1. 0 1. 0 18. 8 0. 6 1 6 NI 1. 7 1. 8 51. 4 19. 6 62 Ni 1. 0 1. 0 7. 7 8. 8 64 Ni 1. 1 1. 1 34. 0 12. 6 63 cu 1. 0 1. 0 19. 8 16. 5 65 cu 1. 1 1. 3 58. 1 10. 0 70 zn 1. 0 1. 0 58. 6 33. 4

It Is obvious from the numbers given In table 4 that the first strong flash of model A48 mainly overproduces the elements SI and by large factors because s the peak temperature Is sufficiently high to allow for a-captures up to "" 16 Z . For the more moderate flashes. models Al7 and A48 . a-captures stop earlier at "' 14 . respectively. but In all Z Z cases the abundances are slgnlflcantly different from what one would obtain In hydrostatic helium burning. It Is also of Interest to note that In the moderate 54 58 64 flashes various neutron-rich Isotopes of heavier elements < cr. Fe . Ni. ...> are also overproduced by large factors Indicating strong neutron processing during the flashes. We wlll come back to this point In section IV. 132

~~Finally. in order to check the sensitivity of our results with respect to the assumptions made about convective mixing during the first strong shell flashes. we~~

have scaled the strongly temperature-dependent charged particle reaction rates by a factor equal to the ratio of the mass Inside the flashing shell to the mass of the overlaying non-burning material. This description mimics the fact that due to convection each nucleus spends only a certain fraction of time In the burning shell. The results are given In the second column of table 4 and should be compared with the first column. It Is obvious that. with a few exceptions. the differences caused by convective mixing are not large and that the general

~~conclusions remain the same.~~

~~IV. HEAVY ELEMENT NUCLEOSYNTHESIS~~

During the early phases of the helium flashes 14N Is converted Into 18F by a-captures as In hydrostatic burning . But unlike the latter case the rise time of the temperature In the flashes Is shorter than the 13-decay half-life of 18F Cr� "'

110 minutes> and therefore the production of the neutron source 180 Is strongly red uced . Moreover. since 18F Is mainly destroyed by the 18FCa. pl 21Ne reaction and 21Ne acts also as a neutron poison the total yield of neutrons during the flashes is further reduced . Nevertheless. the main neutron sources turned out to be 180. 21Ne and 22Ne via Ca. nl reactions . but the peak neutron concentrations

~~A 17 the neutron concentration stays rather high for a sufficiently long time after the peak temperature so that Interesting nucleosynthesls results could be expected .~~

~~We have . therefore . computed the changes In nuclear abundances due to the neutron exposure obtained from models A48 and A 17. The network applied~~

Included elements from 24 C Crl to 92 c Ul and Isotopes from the valley Z = Z = of 13-stablllty to the neutron drip lines. Neutron-capture cross sections were taken from Hauser-Feshbach calcutatlons 141 151 . Experimental results on 13-decay rates 6 and 13-delayed neutron emission probabilities whenever data were available 1 1 or from shell model calculations 171 were used . The lnltlal abundances were 8 assumed to be solar 1 1. The network code was orlglnally designed to perform r-process computations but It can treat more moderate neutron exposures as well.

~~Figure 4 shows the results obtained for model A 17 which produced a higher 133~~

~~3 1 0 - 1 w u z c:( 0 z 0 - 1 s ::J 1 OJ c:(~~

~~I 0 - 1 1~~

~~o.o 0.2 0.4 0.6 0.8 1.0 TIME *E2 Neutron concentration versus time for model(S) A 17. Note that the zero Figure 1: point of the time axis has been changed as compared to fig . l.~~

~~3 1 0 - 1 w u z c:( 0 z 0 - 1s ::J 1 CD c:(~~

~~1 0 - 11~~

~~o.o 10 .0 20 .0 30 .0 40 .0 50 .0 TIME (S) Same as fig. but for model A48. The time Is now given In Ela11r11 ;I; seconds. l. 134~~

~~I 0-4~~

~~w u z c:( 0 I 0 -5 z � rn c:( I 0-9~~

~~1 0 -10 '--�---'-��--'-��'--�----'--'---�_L_.Ll.lJllillllL-Ll..___J_..J.L___J 50 100 150 200 250 MASS NUMBER 4: Abundances versus nuclear mass for model A 17. Figure 1 0 2~~

~~. . 01 0 1 1-i l e:( a: ... . I 0 ° ------� - � ------� ---- t3z c:( 0 z � rn 0 -1 c:( I~~

1 0 -2 '-----+�-'-�-'----''------'-�-'-�...___---'-�-'-�.J..._---1.�� 50 60 70 80 90 100 110 MASS NUMBER Enhancement factors relative to solar abundances versus mass number Flgyre 5: for model A 17. 135

neutron flux than model A48. It Is obvious that the abundances do not resemble the solar system r-process distribution upper curve In fig . 4l . as was expected C from the rather low neutron flux. Also large odd-even effects and the absence of r-process abundance peaks Indicate that only a few neutrons have been captured 50 86 per seed nucleus. We still find abundance peaks at N = c Krl . N "' 82 2118

~~but no convective mixing the heavy element abundances shown In figure 4 will be characteristic for the outer layers of accretlng white dwarfs If the accretion rates are In the range considered here.~~

~~V. SOME CONCLUDING REMARKS~~

~~We have Investigated the evolution of a M0 white dwarf accretlng He-rich matter l -8 7 at a rate of 4. 1 0 M0/yr and 10- M0/yr. respectively. Under these conditions~~

helium Is burnt In a series of shell-flashes and the nucleosynthesls products were found to be significantly different from those of hydrostatic burning. In particular. certain light elements such as Mg and SI are overproduced by large factors which

~~may have Interesting Implications for the ejecta of type I supernovae. Moreover. It~~

~~has been shown that due to the strong neutron flux predominantly neutron-rich~~

~~Isotopes of elements In the Iron-group and beyond are produced and thus It Is~~

~~possible that type I supernovae. If they originate from this class of objects . may be the origin of Isotopic anomalies ccr. Tll found In certain meteorites .~~

In section II we have mentioned the possibility that during the first strong flashes protons may be mixed Into the helium-burning shell near the peak temperature If hydrogen-rich matter was accreted onto the white dwarf. A proton mass fraction of the order of wltl certainly alter the final abundances and should be taken l o-3 Into consideration.

Finally. one may speculate that overabundances of several heavier elements observed In nova ejecta 20> 2 Mg. SI and S In nova Al 82 may stem from a short high accretion rate 1 » phase followed by a long low accretion evolutlon with nova outbursts. This posslblltty certainly deserves future Investigations. 136

~~REFERENCES~~

1) 1985. Branch. D .• Doggett. J. B .. Nomoto. K .. Thielemann. F. -K. : Astrophys. J. 619 �. 2> Nomoto. K .. Thielemann. F. -K.. Yokol. K. : 1984. Astrophys. J. 644 3) 1985. 2-l!.§. Nomoto. K .• lben. I. : Astrophys . J. 1977. 765 4> Nomoto. K .• Sugimoto. D. : Publ. Astron. Soc. Japan 1980. Zi. 5> Narlarl. K .• Nomoto. K .• Sugimoto. D. : Publ. Astron. Soc. Japan �. 473 6) Nomoto. K. : 1982. Astrophys . J. 798 7> 1978�.. 604 Paczynskl. B .• Zytkow . A. N. : Astrophys . J. �. 8) Slon . E. M .. Acierno. M. J .. Tomczyk. S. : 1979. Astrophys. J. 832 Zfill . 9) Nomoto. K. : 1980. In Type I Supernovae . ed . J. C. Wheeler . p. 164 10) Sugimoto. D .. Fujimoto. M. Y .. Narlarl . K .. Nomoto. K. : 1979 . In IAU Colloq. No. 53. White Dwarfs and Degenerate Variable Stars . ed . H. M. van Horn and V. Weidemann . p. 280 Sugimoto. D .. Fujimoto. M. Y .. Narlarl . K Nomoto. K. : 1977. In IAU lll .• Symp. No. 76. Planetary Nebulae. ed . Y. Terzian CDordrecht: Reidel> p. 208 12> Fowler. W. A .. Caughlan . G. R. . Zimmerman. B. A. : 1967. Ann. Rev. Astron. Astrophys . 525 13) .Q. 1983. Harris. M .• Fowler. W. A .. Caughlan . G. R. . Zimmerman. B. A. : Ann. Rev. Astron. Astrophys. ZJ.. 165 14l Woosley. S. E .. Fowler. W. A .. Holmes. J. A .. Zimmerman. B. A. : 1978 . At. Data Nucl. Data Tables 371 2.2. 15) Thielemann. F. -K. : 1980. Ph. D. thesis. TH Darmstadt 16) 1984. Mann. F. M .. Schreiber. M .• Schenter. R. E .. England . T. R. : Nucl. Sci . Eng. fil. 418 17l Klapdor. H. V .. Metzinger. J .. Oda . T. : 1984. At. Data Nucl . Data Tables fil. 81 18) Cameron . A. G.W. : 1982 . In Essays In Nuclear Astrophysics. ed . C. A. Barnes et al. p. 23 19> Wiiiiams. R. E .• Ney. E. P .. Sparks. W. M .• Starrfleld. S. G .. Wyckoff. S .. Truran. J. W. : 1985. Mon. Not. R. Astr. Soc . 753 .2..12. 20) Wi lliams. R. E. : 1985. In Production and Distribution of CNO Elements. ed. I. J. Danziger. F. Matteucci . K. Kjlir C Garchlng: ESOl p. 225 21l Snljders. M. A. J .• Batt. T. J .. Seaton . M. J .. Blades. J.C.. Morton . D. C. : 1984. Mon. Not. R. Astr. Soc . 7P .2.J.1. 137

~~COLLAPSE OF ACCRETING CARBON-OXYGEN WHITE DWARFS INDUCED BY CARBON DEFLAGRATION AT HIGH DENSITY~~

~~Ken'ichi Nomoto 1~~

~~Department of Physics, Brookhaven National Laboratory Upton, NY 11973, U.S.A.~~

~~l ABSTRACT~~

We have obtained a critical condition for which carbon deflagration induces collapse of a accreting C+O white dwarf, not explosion. the carbon deflagration is initiated at If central density as high as 1010 g cm-3 and if the propagation of the deflagration wave is slower than is the sound speed , electron capture behind the burning front � 0.15 v8 (v. ) induces collapse to forma neutron star. This is the casefor both conductive and convective deflagrations. Such a high central density can be reached if the white dwarf is sufficiently massive and cold at the onset of accretion and if the accretion rate is in the appropriate range. Models for Type Ia and supernovae are also discussed. lb

~~1 On leave from the Department of Earth Science and Astronomy, College of Arts and Sciences, University of Tokyo, Meguro-ku, Tokyo 153, Japan. 138~~

~~1. INTRODUCTION~~

The final fate of accreting white dwarfshas attracted a lot of recent attention because it is related to the origin of Type I supernovae and low mass X-ray binaries. In fact, the exploding white dwarf model for Type I supernovae, in particular, the carbon deflagration model is in good agreement with many of the observations.1•2> Such success implies that at least some accreting white dwarfs increase their mass to the Chandrasekhar mass, though the exact evolution of the binary systems leading to the supernova stage is not yet known.

Recent observations of several interesting binary systems, low mass X-ray binaries, QPOs, and binary radio pulsars have suggested that in these systems a neutron star has formed from accretion-induced collapse of a white dwarf.3•4>

Possible models for thewhite dwarf collapse involve solid C+O white dwarfs, in which carbon and oxygen may or may not have chemically separated and O+Ne+Mg white 5,s) dwarfs.7> For a wide range of mass accretion rates and initial white dwarf masses, the O+Ne+Mg white dwarfs collapse due to electron capture on 24Mg and 2°Ne.8•9) On the other hand, depending on the conditions of the white dwarfs and binary systems in which they are formed, the C+O white dwarfs could either explode or collapse. Chemical sep aration in such objects is still hypothetical and in any case could not be complete before carbon burning starts.10> It takes a carbon fraction of only a few percent to sustain a deflagration.

Therefore,it is worth determining the critical condition forwhich a carbon deflagration induces the collapse of a C+O white dwarf rather than its explosion. Such a condition has been obtained for the carbon detonation, but not for the carbon deflagration exceptfor ll) the pulsation-driven propagation model.12) We have performed numerical simulations of conductive and convective deflagrations starting from 1010 g cm-3 and found that Pc - the C+O white dwarf collapses if the propagation velocity is slower than - 0.15 110 (111 is the sound speed). Generally, for both conductive and convective deflagrations, this is the case. 139

~~O+Ne+Mg WD Fo rmation � NS~~

~~10-6 Neutron Star Type Ia Supernovae I� t t deflag. l >- (carbon deflagration ) ( C 0 :::;:~~

~~· ::E 10-0 Type Ib "Dim" SN I / Supernovae i ( off - center Neutron Star Io-IO He detonation ) deflagrt ation l ( C 0.8 1.0 1.2 1.4~~

Mc+o ( M0l Figure 1: The final fate of accreting C+O white dwarfs expected for their initial mass and accretion rate M. For two regions in M plane indicated by Neutron Meo - Me o carbon deflagration is ignited in the center when the density is as high as 1010 gStar, cm-3• Propagation of the deflagration wave will induce collapse to form a neutronPc � star. See text for other cases.

~~10-4~~

~~/MEdd~~

~~10-6 Neutron Star Formation I � (electron t captures) >- 0 :::;:~~

~~· ::E 10-0 "Dim" Type I Supernovae . (off -center H! detonation ' l ,~~

~~10-IO~~

~~1.2 1.3 1.4 I.I~~

M (M0l O Ne M� Figure 2: Same as Fig. 1 but for O+Ne+Mg white dwarfs. For a wider range of M and the initial mass, neutron star formation triggered by electron capture on 24Mg MoNeMg, and 20Ne is expected. 140

~~2. THE EVOLUTION OF WHITE DWARFS AS A FUNCTION OF ACCRETION RATE~~

Isolated white dwarfs are simply cooling stars that eventually end up as dark matter. In binary systems they evolve differently because mass accretion from their companion provides gravitational energy that rejuvenates them. The gravitational energy released at the accretion shock near the stellar surface is radiated away and does not heat the white dwarf interior. However, the compression of the interior by the accreted matter releases additional gravitational energy. Some of this energy goes into thermal energy

(compressional heating) and the rest is transported to the surface and radiated away (radiative cooling). Therefore, the interior temperature is determined by the balance between heating and cooling and, thus, strongly depends on the mass accretion rate, .M.13,14)

Compression first heats up a layer near the surface because of the small pressure scale height there. Later, heat diffuses inward (Fig. 3). The diffusion timescale depends on M and is small for larger M's because of the large heat flux and steep temperature gradient generated by rapid accretion. For example, the time it takes the heat wave to reache the central region is about 2 05 yr for M 10-6 yr-1 Fig. 3 15) and 106 yr for x 1 � M0 ( ) 5 x M 10-5 yr-1.16) Therefore, more than 0.2 of matter has accreted fromthe � 4 x M0 M0 companion if the entropy in the center increases due to the heat inflow. In other words, if the initial mass of the white dwarf, Meo, is lar.ger than 1.2 M0 , the central region is compressed only adiabatically and thus is cold when the white dwarf mass becomes 1.4 the white dwarf is sufficiently massive and cold at the onset of accretion, carbon M0 . If burning will be ignited in the center when density is as high as 1010 g cm-3,6)

Accordingly, the ultimate fate of accreting C+O white dwarfs depends on M and the inintial mass of the white dwarf Meo, as summarized in Figure 1. M denotes the growth rate of the C+O white dwarf mass irrespective of the composition of the accreting matter. A similar diagram for the O+Ne+Mg white dwarfs is shown in Figure 2. Neutron Star or in Figure 1 indicates a region of parameter space where neutron star formation by NS white dwarf collapse is expected. The evolution of the white dwarfs in these three regions is summarized as follows:

~~1) For M > 2.7 x 10-6 M0 yr-1, off-center carbon burning is ignited by rapid compres sional heating.15) The C+O white dwarf is peacefully changed into an O+Ne+Mg white 141~~

~~Figure 3: Structure of the ac creting white dwarf in the density -c+otemperature plane as a function of time for the model with M 10-6 M0 yr-1 = 2 x~~

and Meo = 1.0 M0 •15> A heat wave propagates fromthe hot outer layer to the central region. Car bon burning is ignited at rela tively high central density before the center is heated up. The thin solid lines shows the adiabat fol lowed by the central point for an 7.5 initial temperature of 107 K. For lower (higher) initial temperature, the ignition density is higher (lower) as far as the heat wave does not

~~7.0 reach the center. The dotted curve~~

~~4 5 6 7 8 9 10 is an approximate ignition line of Log p (g cm-3) carbon burnig defined in Fig. 4.~~

Figure 4: Evolutionary path of at the center of accreting - (Pc, Tc ) ----- white dwarfsfor twocases. - j c+o \ -6 ------, For M 10-s M0 yr-1, M=4xl· 0 M 0 yr-I ' = 4 x 8.5 '-.., carbon deflagration is ignited at ', (off - center ignition l ' relatively low density (Pc 3 x ' 109 g cm-3 . This model"" is in \ ) Carbon Ignition /, \ good agreement with many of the \ \ observed features of Type Ia su \ I pernovae. For M 10-10 8.0 2.5 x /\ M0 yr-1, carbon =burning is ig 6 I Tc+c=I0 yr \ nited in the solid core (r > 170: below the dotted line when the �\ ) . central density is as high as i · Pc ··1I � 1010 g cm-3• For comparison, 7.5 r=110 ... the ignition point of off-center car ...... I I \... / bon burning is shown for M = I 4 · . · .. ·· I 10-6 M0 yr-1•15) The dashed . I x ·· .. · . I I curve is an approximate ignition

...... · I line where the rate of carbon burn I 7. 0 I ing is equal to the rate of . Ec+c /' ... I neutrino losses for (center l Y Ev T > 2 x = 2.5 x 0- 10 M yr-1 108 K and / M I e = T Ec+c 106 yr forrc +c cp 108 K = T � 2 x (cp 7 8 10 is the specific heat . 9 ) 3 log p (g cm- ) 142

dwarf through off-center carbon burning.17•18) The resulting O+Ne+Mg white dwarf will collapse to form a neutron star if the Chandrasekhar mass is reached.7) s 2) For 2.7 x 10-6 M0 yr-1 > M > 4 x 10- M0 yr-1 and Meo > 1.2 M0 , a central density as high as 1010 g cm-3 is reached by adiabatic compression if the white dwarf is sufficiently cold at the onset of accretion.19) For M > 10-6 M0 yr-1, the lower mass limit is not 1.2 M0 , but 1.0 M0 •15) An example of such an evolution is given in Figure 3, where M 10-6 M0 yr-1.15) = 2 x

3) For M � 10-9 M0 yr-1 and Meo > 1.13 M0 , the white dwarf is too cold to initiate a helium detonation.13•20•21) Eventually pycnonuclear carbon burning starts in the center when reaches - 1010 g cm-3• An evolutionary path of for a model with M Pc Pc - Tc = 10-10 M0 yr-1 and Meo 1.16 M0 is shown in Figure In this model, the outer 2.5 x = 4. layer of 0.24 M0 is composed of helium.

The fate of white dwarfs in other regions in Figure 1 is described in §3, numerical simulations of carbon defiagrations initiated at high densities are discussed in §4, and in §5 we make some concluding remarks.

~~3. MODELS FOR SUPERNOVAE OF TYPE Ia AND lb~~

~~3.1 Type Ia Supernovae~~

s For relatively high accretion rates (2.7 x 10-6 M0 yr-1 > M > 4 x 10- M0 yr-1 ), a carbon defiagration starts in the white dwarf's center at a relatively low central density - 109 g cm-3 .16) The defiagration wave then propagates outward at (Pc 3 x ) convective a subsonic velocity and incinerates the material of the inner layers to nuclear statistical equilibrium (NSE) . When the defiagration wave arrives at the outer layers (Mr > 0.7 M0 ), the density it then encounters has already decreased below 108 g cm-3 due to the expansion of the white dwarf. At such densities, the peak temperature attained behind the defiagrationfr ont is too low to process the material to NSE. The products of explosive nucleosynthesis depend on the temperature and density at the defiagrationfront and, thus, vary from layer to layer. In the center, iron peak elements are produced. particular, In about 0.6 M0 of 56Ni is synthesized. In the outer layers, intermediate mass elements such as Ca, Ar, S, Si are produced. The white dwarf is disrupted completely and no neutron star residue remains.16•22) 143

~~The carbon deflagration model can account for the light curves, early time specta, and late time spectra of Type Ia supernovae as follows:1•2>~~

~~1) The theoretical light curve based on the radioactive decays of 56Ni and 56Co into 56Fe fits the observations well. 2,23,24)~~

2) The synthetic spectum at maximum light is in excellent agreement with the observed 7• spectum of SN 1981b 25) as seen in Figure 5.26•2 39) The feature near 6125 A is clearly identified as the Si II line that is a sigature of Type Ia supernovae (see discussion concerning Type lb below).

3) At late times, the outer layers are transparent and the inner Ni-Co-Fe core is exposed. Synthetic spectra of emission lines of [Fe II] and [Co I] agree quite well with the spectra observed at such phase. 22)

~~Therefore, there is good evidence that Type I supernovae are exploding white dwarfs.~~

~~3.2 Type lb Supernovae~~

~~Recent observations indicate that there exists another kind of Type I supernovae, designated Type lb (SN Ib).28-32) The SN lb spectra lack hydrogen lines (definition of SN~~

I) and are characterized by both the lack of the 6125 A Si fe ature at maximum-light spectra and the appearance of oxygen emission lines at late times.32•33) More than 5 M0 ,34l and as much as 15 M0 ,32) of oxygen has been inferred from the late time spectra. These signatures have led to the currently popular idea that the progenitors of SN lb are Wolf Rayet stars.28•32-35) However, such a large mass of oxygen may yield a theoretcal light curve whose decline is too slow to be compatible with SN lb observations.28•36) In addition, Wolf-Rayet death rates and the SN lb frequency might be incompatible.28)

Branch and Nomoto 38) have suggested that the observed spectra are better explained by an accreting white dwarf model. In Figure 6, the maximum-light spectrum of SN 1984128) is compared with a synthetic spectrum. The expansion velocity of matter at the photosphere is assumed to be 8,000 km s-1. Two of the absorption lines in the red are identified as He I lines 39) and other features are well explained as Fe II lines. In addition, ultraviolet features can fit with a synthetic spectrum of Co II and Fe I lines if the photoshperic velocity is 12,000 km s-1•40> The above interpretation of the early spectrum together with the presence of the oxygen lines in the late time spectrum suggests that Fe, 144

4000 5000 6000 7000 8000 WAVELENGTH Figure 5: The maximum-light spectrum of SN 1981b (top)25l is compared to a synthetic spectrum forthe carbon defiagration model 16) 15 days after the explosion. 26) this model outer layer is assumed to be mixed. Terrestrial absorption features in the observedIn spec trum are indicated.

~~x ::J ....J LL.~~

~~� 0 ....J lJ')~~

~~C\J~~

4000 5000 6000 7000 WRVELENGTH CRl Figure The maximum-lightspectrum of the Type SN 19841 in NGC 991 upper 28l 6: lb ( ) is compared with a synthetic spectrum (lower) based on resonant-scattering lines of He I and Fe superimposed on a continuum.38) the synthetic spectrum the blueshifted II In absorption component of He I A6678 appears near 6500 A and He I A5876 appears near 5850 A. Other features are produced primarily by Fe II lines. 145

Co (decaying), and He are in the outer high-velocity layers and that oxygen and some other intermediate mass elements are in the inner layers. In other words, the composition structure of SN Th's appears to be that for SN Ia's inverted.

The existence of such high velocity Fe and Co is difficult to explain with the Wolf Rayet model. Branch and Nomoto 38) have speculated that the progenitors of SN differ lb from the progenitors of SN Ia in having a lower accretion rate, i.e., M 10-8 M0 < 4 x yr-1• For such low accretion rates, the helium shell flash grows into a detonation. The outcome may be more like a single detonation than the double detonation obtained in the spherical calculations 41•42) because the off-center flash will occur at a point rather than all over a spherical shell. The outer helium layer will burn to mostly 56Ni with a trace He and be ej ected into space. The inner C+O core will remain unburned due to non-spherical effects and a part or most of the C+O will be ej ected. Since the ej ected mass of 56Ni will be as small as 0.1 - 0.3 M0 , the peak luminosity of this model is lower than that for SN Ia by a factor of 2 This result is consisttent with the observations of SN Ib.28-31) - 6.

This single detonation scenario requires that M be lower than that needed forthe carbon deflagration model of SN Ia. This requirement may be inconsistent with the fact that SN have been seen in only spiral galaxies, usually in their star-forming regions. lb However, if the white dwarf accretes matter with an efficiencyof only 0.03 - 0.1 43) from a wind (10-6 - 10-7 M0 yr-1) of a relatively massive(4 - 7 M0) red giant companion,44) the model would be consistent. Further, this scenario is consistent with the radio observations of SN in that they can be explained by the interaction of supernova ej ecta with the lb circumstellar shell. 31•45•46)

Both Wolf-Rayet and white dwarf models for SN should be tested by quantitative lb comparison with observations based on theoretical light curves, synthetic spectra, and multi-dimensional hydrodynamical calculatons of off-center detonations.

~~3.3 Dim Type I Supernovae~~

an off-center single detonation occurs on a very massive white dwarf - 1.1 If (> M0 ), the resulting supernova will be rather dim, because the accumulation of only a small amount of helium (- 0.01 - 0.1 M0) can lead to the helium detonation. 21) most cases, In an unburned C+O core will be left behind as awhite dwarf. Such dim supernovae 47) are more likely to be associated with O+Ne+Mg white dwarfs since their masses are larger than - 1.2 M0 (see §5). 146

~~4. COLLAPSE INDUCED BY CARBON DEFLAGRATION AT HIGH DENSITY~~

~~4.1 Conductive Defiagration~~

As mentioned in §2, there are two scenarios in which a carbon defiagrationis initiated in the center when the central density is as high as 1010 g cm-3• In one, the accretion rate is lower than 10-9 M0 yr-1 and the initial white dwarf mass, Me o, is larger than 1.13 the other, M 10-8 yr-1 and M0 . In > 4 x M0 Me o > 1.2 M0 . At densities as high as 1010 g cm-3, the carbon defiagration may not lead to an explosion since electron capture is much fas ter at these high densities than at the lower densities encountered in the models of SN Ia. Moreover, if the central part of the white dwarf is in the solid state, the propagation mode of the burning front could be different. the solid is strong enough, convection will be suppressed and the burning front will If propagate as a conductive defiagration wave 5•6> though more study is needed on this point. The propagation velocity of a conductive defiagration wave is given approximately by the expression, / / 112, where denotes the width of burning front, Vdef - 6 rn -(u cvrn) 6 the nuclear burning timescale, the conductivity, and the specific heat.48•49) This Tn u Cv 9 gives 100 km s-1 at 1010 g cm-3, which is about 0.01 •.4 ) Here the Vdef - p - v v. is sound speed, equal to 1.0 - 1.3 104 km s-1 between 109 - 1010 g cm-3• x p = Whether the white dwarf explodes or collapses depends on whether, behind the de fiagration wave, nuclear energy release or electron capture is faster. A white dwarf whose mass is close to the Chandrasekhar mass has an adiabatic index close to 3, so that even a small energy release can cause substantial expansion.49) However, a slight pressure de crease due to electron capture will easily induce collapse. is low (high) enough If Vdef and/or the central density is high (low) enough, a carbon defiagration will lead to collapse (explosion). The outcome is rather sensitive to and the central density. Vdef

The results of a numerical simulation of a conductive defiagration started at high central density ( "" 1010 g cm-3), with M 2.5 x yr-1 and 1.16 Pc = 10-10 M0 Meo = M<:J , are shown in Figure 4. Here Xe = Xo = 0.5 and we have assumedthat no chemical separation occurs. Pycnonuclear carbon burning commences in the solid region and turns into thermonuclear runaway as aresult of the temperature rise. Throughout the simulation, convection neglected. is 147

~~1.4~~

~~1.2 A Conductive~~

~~1.0 Deflagrotion Wove B .. 0.8 ::;; � ::;; 0.6~~

~~0.4~~

~~0.2 c~~

~~0 0.2 04 0.6 0.8 1.0 1.2 1.4 1.6 1.8 I (sec)~~

~~Figure 7: Propagation of the conductive defiagration wave. The location (Mr) of the defiagrationfront is shown as a function of time, t, for three cases (A, B, C) of parametrized conductivity.~~

~~Explosion~~

~~"' I 9 E 0 "'~~

~~cf: "' � 10 c B Col lapse~~

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 (sec ) I Figure 8: Change in the central density of the white dwarf associated with the propagation of the conductive defiagrationwave . Relatively slow propagation in Cases B and C leads to the increasein i.e., collapse of the white dwarf. On the other hand, faster proapagation in Case A inducesPc, the explosion of the white dwarf. 148

The actual simulation of a conductive defiagration requires extremely fine zoning.49l Instead of employing a grid whose fineness would slow the calculations unduly, we have parametrized the conductivity to obtain a range of reasonable With these, we have lldef· explored the range of possible hydrodynamical responses of the white dwarf. Figure 7, In the location of the defiagration front as a function of time, after initiation is plotted for t, three cases A, B, C). addition, Case D of the slowest propagation has been calculated. ( In The average for CasesA, B, C, and Dis about 0.15, 0.1, 0.06, and 0,01, respectively. llder/118 Figure 8, the evolution of the central density, for Cases A - C is plotted. In Pc,

~~4.2 Cases of Collapse~~

As Figure 8 indicates, in Case B, the central density increases as the defiagration front propagates outward. When the defiagrationfront has reached 0.9 0.6 M, "" M0 (t "" s , is as high as 1011 g cm-3• Clearly, the white dwarf now undergoes quasi-dynamic ) Pc contraction (not yet free-fall collapse) because electron capture on NSE elements rapidly reduce the electron mole number, Y. , behind the defiagration wave. This effect dominates the opposing effect of nuclear burning. In the central region of 1010 g cm-3, typical Pc "" values of Y0 are 0.06 s and 0.16 s for Y. "" 0.5 and 0.47, respectively. At Tee (= /1"Y01) t = 0.16 s, Y0 has dropped to 0.42 at the center. Because of the decrease in the electron capture rate in the central region, electron capture is fas test at the deflagration front and thus the density there is important. Case B, the density at the front is gradually decreasing but In is still as high as 109 g cm-3 at 0.9 and is as short as "" 0.3 s at Y0 4 x M, = M0 , Tee ( = 0.5). Moreover, once the contraction of the white dwarf begins, photodissociation becomes important, further promoting collapse.

Case C, the contraction is much more gradual than in Case B because the defla In gration wave is slower. When reaches 1011 g cm-3, the burned mass is only 0.13 Pc M0 (Figs. 7 and 8). Case D, forwhich - 0.01 is close to the actual conductive deflagration In lldef ( 118) speed, it takes 155 s to reach "" 1011 g cm-3• At 155 s, the mass of the burned Pc t = region is only 0.03 M0 and Y0 - 0.39. 149

~~4.3 Caseof Explosion~~

~~On the other hand, in Case A, decreases as the defiagrationpropagates outward. By Pc the time the front has reached Mr "" 1.2 M0 , the total energy of the white dwarf is already~~

1.2 lQ51 ergs and it is clear that it will be completely disrupted. Nuclear energy release x dominates electron capture because the front's density, and henceits electron capture rate, decreases as the front propagates outward. The expansion of the burned core of the white dwarf decreases the density and temperature of the entire star. Once this expansion is substantial, it is impossible for electron capture to induce reimplosion. Only for initial central density as high as 3 1010 g cm-3, similar to those in the detonation case, x ll) would reimplosion be a possible outcome.

~~Because of the expansion, when the defiagration front has reached Mr = 1.0 - 1.16~~

~~M0 , its density is aslow as 108 - 107 g cm-3• Therefore, some intermediate masselemen ts, such as Ca, Ar, S, and Si, are synthesized.16) When the defiagration wave arrives at the~~

baseof helium layer (Mr = 1.16 M0 ), it turns into a helium detonation because helium has a large Q-value and a low ignition temperature. Despite the expansion of the white dwarf, detonation wave does not die and it processes most of the matter to 56Ni. Were it not for the Ca - Si layer sandwiched between the two 56Ni layers, the final outcome for Case A would be similar to the outcome for the double detonation supernovae,41•42> where both carbon and helium layers are burned to 56Ni. This type of supernovae should not be very frequent since they ej ect too much neutron-rich iron peak matter into the Galaxy. 24,so)

~~4.4 Convective Defiagration~~

carbon ignition at high densities occurs for 10-8 M0 yr-1 and Me o If M > 4 x > 1.2 M0 , adiabatic compression may have already melted the solid core when carbon is ignited. Convective defiagration would then develope, though conductive deflagration could still dominate in the central region.49) Even for the solid core, propagation of the defiagrationwave not necessarily due to conduction alone since convection could influence is the melting the solid core.51) To investigate these cases, a set of numerical experiments hasbeen performed with the above model, but under the assumption that the defiagration 150

wave is propagating by convection in fluid layers. Our treatment of convection is the same asthat employed by Nomoto et al., 16) i.e., Unno's 52) time-dependent mixing length theory with a parameter /Hp where is the mixing length and Hp is the pressure scale a = l l height.

For 0.7, the propagation velocity is as slow as 0.06, 0.09, and 0.11 a = Vder/v. � when the defl.agration reaches Mr / M0 = 0.2, 0.4, and 0.6, respectively. As expected, the white dwarf collapses as in Case B. On the other hand, for 1.0, 0.10, a = Vder/v. � 0.15, and 0.20 at Mr / M0 0.2, 0.4, and 0.6, respectively, and the white dwarf explodes = completely. Since a value for of 0.7 is preferred in the low density carbon defl.agration a model of SN la (§3), 16) a plausible choice for in the present context may be 0.7, not a 1.0. (For both low and high central densities, the carbon defl.agration with 1.0 grows a = into a detonation in the outer layer and incinerates almost the entire star to the iron peak. This is incompatible with observations of SN Ia.16l) Therefore, for plausible choices of the parameter, a carbon defl.agration initiated at high densities will result in white dwarf a collapse, not explosion.

~~5. CONCLUDING REMARKS AND DISCUSSION~~

We have demonstrated that if a carbon defl.agration is initiated in the center of the white dwarf when Pc "" 1010 g cm-3 and the propagation velocity of the defl.agration if wave is slower than a certain critical speed, Vcrit, the outcome is collapse, not explosion.

For Vcrit, complete disruption results (and the ej ecta contain too much neutron-rich Vdef > matter). The value of Vcrit depends on Pc at carbon ignition. For Pc "" 1 x 1010 g cm-3, Vcrit 0.15 A lower Pc implies a lower Vcrit Below a certain critical density (perhaps, � v•. · 6 - 109 g cm-3),12) even extremely slow defl.agrations results in explosions. our � 8 x In case of Pc "" 1 1010 g cm-3, for both conductive and convective defl.agrations x Vdef < Vcrit and, therefore, collpasewill result.

Such a high central density reached two regions of the Me o plane of Figure is in M - 1. One defined by 4 10-s M0 yr-1 and Meo 1.2 M0 , while the other is is M > x > defined by 10-9 M0 yr-1 and Me o 1.13 M0 . The frequency of such systems M < > 151 may be small. First, if hydrogen-rich matter accretes at 10-9 M0 yr-1, nova-like M < explosions will prevent the white dwarf mass from growing.53) The hydrogen flash can be avoided if the companion star is a helium star.54•55) Secondly, massive C+O white dwarfs (> 1.2 M0 ) may be rare.56) The formation of such white dwarfs might be prevented if the precursor star lost its hydrogen-rich envelope by either a stellar wind or Roche-lobe overflowbefore its degenerate C+O core could grow substantially.

~~As seen in Figure 2, the accretion-induced collapse is the outcome for a wider range of parameter space for O+Ne+Mg white dwarfs.7> The initial mass of the white dwarf,~~

MoNeMg, is larger than 1.2 M0 .9•57•58l many cases, MoNeMg is very close to the � In Chandrasekhar mass, so that only a small mass increase is enough to trigger collapse. However, an O+Ne+Mg white dwarf is formed from an 8 - 10 M0 star.57) The number of such systems may be significantly smallerthan the number of systems containing C+O white dwarfs whose precursors are 1-8 M0 stars, perhaps, by four order of magnitude.44) Even so, the number of low mass X-ray binaries is much smaller than the number of SN I and the statistics may be consistent.59)

A hydrodynamical calculation of such a white dwarf collapse has not been carried out. Its collapse should be similar to the collapse of the O+Ne+Mg cores of 8 - 10 M0 stars,60-62) but some differences are anticipated. both classes of collapse, the white In dwarf or the core contains nuclear fuel (C+O or O+Ne+Mg) which ignites during infall. Electron captures occur only in the NSE layer behind the burning front and, therefore, the region of small is confinedto a central region which grows gradually. The collapse Y. is slower than the collapse of the iron core of a massive star until the burning front has propagated to roughly 0.8 M0 . 60> Afterwards the collapse accerelates quickly. in � Y. the NSE region of collapsing white dwarf is smaller than in iron cores because the Y. entropy at the burning front is high. These two effects result in a homologous core whose mass is smaller and an outer infalling layer which is less dense than is the case in iron core collpase.60> Such a structure has two effects on the bounce shock. First, the binding energy of the rebounding core is smaller and, hence, the shock wave is initially weaker. 63•64) Secondly, the low density in the outer layers makesthe shock propagation easier. Which effect dominates depends on the details of collapse hydrodynamics. 152

The location and propagation speed of the burning front may have important effects on the hydrodynamics. The initial composition and entropy of the collapsing star may be the determining factor. During collapse, nuclear burning is ignited when the temperature, which is increasingdue to adiabatic compression, reaches the ignition temperature. the If white dwarf is composed of C+O, the ignition temperature and density for carbon are lower than for oxygen. At lower densities, effects of nuclear energy release is larger. On the other hand, a white dwarf has much lower entropy than a red-giant core. For lower entropy, the ignition of nuclear fuel is delayed until higher density is reached. Without calculating the collapse, we don't know whether mass is ej ected.

~~Even if no mass is ej ected, a neutron star will be formed because the residue's mass~~

1.4 M0 baryon mass , 1.3 M0 gravitational mass is smaller than the maximummass ( ( ) � ( )) of a neutron star. Nevertheless, it is important to know whether some mass is ej ected by the bounce shock and, if mass is ejected, what its composition is. some 56Ni is ej ected, If the white dwarf collapse can be observed as a dim Type I supernova. Otherwise, the collapse would be silent, because most of the explosion energy would go into the kinetic energy of expansion. The interior temperatures would be too low to produce a significant optical light curve. the shock wave is strong enough, some neutron-rich species will be If ej ected. This might be an important site of some neutron-rich isotopes. 65•66) Mass ej ection will affect the binary evolution after the explosion and the results can be compared to the observed neutron star binary systems.4>

~~ACKNOWLEDGEMENT~~

It is a pleasureto thank Drs. S.H. Kahana, G.E. Brown, A. Yahil foruseful discussion and hospitality during my stay in Brookhaven and Stony Brook. I would like to thank Dr. A. Burrows for thereading ofthe manuscript and comments. I also would like to thank Drs. D. Branch, J.C. Wheeler, and R. Harknessfor inf ormative discussion on Type I supernovae during my visit to Univ. of Oklahoma and Texas. This work has been supported part in by the U. S. Department of Energy uRder Contract No. DE-AC02-76CH00016. 153

~~REFERENCES~~

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33) Filippenko, A.V., and Sargent, W.L.W. 1985, Nature, 316, 407. 34) Begelman, M.C., and Sarazin, C.L. 1986, Ap. J. {Letters), 302, L59. 35) Chevalier, R.A. 1986, Highligh ts of Astronomy, in press. 36) Woosley, S.E. 1986, Saas-Fe Lecture Notes. 37) Branch, D. 1986 Ap. J. {Letters), 300, L51. 38) Branch, D., and Nomoto, K. 1986, Astr. Ap., in press. 39) Wheeler, J.C., and Harkness, R. 1986, in Distances of Galaxies and Deviations from the Hubble Flow, ed. B.M. Madore and R.B. Tully (Dordrecht: Reidel), in press. 40) Branch, D., and Venkatakrishna, K.L. 1986, Ap. J. {Letters), in press. 41) Nomoto, K. 1982b, Ap. J., 257, 780. 42) Woosley, S.E., Taam, R.E., and Weaver, T.A. 1986, Ap. J., 301, 601. 43) Davidson, K., and Ostriker, J.P. 1973, Ap. J., 179, 585. 44) Then, I. Jr., and Tutukov, A.V. 1984, Ap. J. Suppl., 54, 335. 45) Sramek, R.A., Panagia, N., and Weiler, K.W. 1984, Ap. J. {Letters}, 285, L59. 46) Chevalier, R.A. 1984, Ap. J. {Letters}, 285, L63. 47) Branch, D., and Doggett, J.B. 1985, A. J., 270, 2218. 48) Buchler, J.R., Colgate, S.A., and Mazurek, T.J. 1980, Colloq. C2, suppl. 3, 41, C2-159. 49) Woosley, S.E., and Weaver, T.A. 1986c, in IA U Colloq. 89, Radiation Transport and Hy drodynamics, ed. D. Mihalasand K.H. Winkler (Dordrecht: Reidel), in press. 50) Nomoto, K., Thielemann, F.-K., and Wheeler, J.C. 1984, Ap. J. {Letters), 279, L23. 51) Mochkovitch, R. 1980, Thesis, University of Paris. 52) Unno, W. 1967, Pub. Astr. Soc. Japan, 19, 140. 53) MacDonald, J. 1984, Ap. J., 283, 241. 54) Savonije, G.J., de Kool, M., and van den Heuvel, E.P.J. 1986, Astr. Ap., 155, 51. 55) Then, I. Jr., and Tutukov, A. 1986, Ap. J., submitted. 56) Law, W.Y., and Ritter, H. 1983, Astr. Ap., 123, 33. 57) Nomoto, K. 1984c, Ap. J., 277, 791. 58) Nomoto, K. 1984d, in Problems of Collapse and Numerical Relativity, ed. D. Bance! and M. Signore (Dordrecht: Reidel), p.89. 59) Webbink, R.F. Rappaport, S., and Savonije, G.J. 1983, Ap. J., 270, 678. 60) Hillebrandt, W., Nomoto, K., and Wolff, R.G. 1984, Astr. Ap., 133, 175. Hillebrandt, W. Ann. New York Acad. Sci. , 422, 197. 61) Burrows, A., and Lattimer, J.M. 1985, Ap. J. (Letters), 299, L19. 62) Baron, E., Cooperstein, J., a.lid Kahana, S.H. 1986, private communication. 63) Brown, G.E., Bethe, H.A., Bayµi, G. 1982, Nucl. Phys., A375, 481. 64) Lattimer, J.M., Burrows, A., and Yahil, A 1985, Ap. J., 288, 644. 65) Hartmann, D., Woosley, S.E., and El Eid, M.F. 1985, Ap. J., 297, 837. 66) Takahashi,Y., Miyaji, S., Parnell, T.A., Weisskopf, M.C., Hayashi, T. and Nomoto, K. 1986, Nature, in press. 155

~~NUCLEOSYNTHESIS IN THE NEIGHBORHOOD OF A BLACK HOLE~~

~~Sandip K. Chakrabarti Theoretical Astrophysics, 91125 California Institute of Technology, Pasadena, California, USA.~~

ABSTRA CT The preliminary results from simulations of nucleosynthesis inside a thick accretion disk around a black hole is discussed as a function of the accretion rate, the viscosity parameter and the mass of the black hole. Results for the Bondi accretion case are also presented. Taking the case of a an d a cen 10 M 106 M tral Schwarzschild hole, detailed evolution of a representative element of matter as it accretes into the hole is presented in the case when the initial abundance (at the outer edge of the disk) is same as the solar abun dance. It is suggested that such studies may eventually shed light on the composition of the outgoing jets observed in the active galaxies and SS433. 156

I. INTRODUCTION Recently, through detailed numerical simulations Chakrabarti, Jin and Arnett1l (CJA); and Jin, Arnett and Chakrabarti2) (JAC) have suggested that in an wide range of the parameter space as spanned by the accretion rate, mass of the hole and the viscosity parameter, it is possible to have a considerable amount of nucleosynthesis within the matter accreting into the hole. These calculations are carried out using an approximate model of the thick disk surrounding a black hole. From such analysis one hopes to provide at least partial answers to a large number of questions some of which are: a) Is it possible to infer the composition of the observed jets in active galaxies? b) Conversely, could the observed composition of jets (as inferred from line emission measurements) be used to probe the inside story of an active galaxy, in particular, can one put some constraint upon the "unknown" viscous mechanism c) Could the combined effects of the 9 nucleosynthesis in the neighborhood of galactic centers be sufficient to influence the cosmic abundance? Whereas the answers to all the questions are not decisive yet, we believe that eventually the answers may be affirmative. In some sense such a study is similar to the study of volcanic activities by the Geophysicists. The debris of a volcano provides informa tion about the geophysical activities including the constituents and the thermodynamic condition deep inside the earth. The jet matter is essen tially the debris of the active galaxies. In the present paper, I shall briefly summarize the CJA and JAC papers. In JAC the central temperature of the disk 0.25 are considered. Work on even higher temperature cases is T 9 < under way (Arnett, Chakrabarti and Jin, in preparation). In addition, for completeness, I shall briefly discuss the case of Bondi accretion on a hole and also when the hole is rotating. The plan of the paper is the following: In the next section the thermodynamic condition inside a thick accretion disk around a Schwarzschild hole will be briefly discussed. The thermo dynamic path for Bondi accretion case is taken from Chakrabarti3) by put ting angular momentum of matter to be zero in the rotating wind solution in axisymmetric space-time. In section III, the major nuclear reaction which may take place under these conditions will be examined. In section IV, two particular cases will be studied where the detailed analysis of the change in the composition of the accreting matter as it accretes towards a central hole of 101110 and 106.AtJ are provided. Finally, in section V, some implications of these results are discussed. The discussions here will be somewhat biased in the sense that the presense of a quasi stable thick torus configuration is assumed around the blackhole despite the fact that recent linear stability analysis by Papaloizou and Pringle4), 5) apparantly forbids the existence of such tori. The justification could be that, a) thick disks are known to exist b) the above mentioned analysis are done 5), 7l, for infinitesimallythin non-accreting tori, c) the growth of linear pertur bation may be limited by nonlinear effects. Furthermore, the parameters 157

concerning the distribution of the angular momentum which are most favorable for nucleosynthesis and which shall be considering below fall ( I ) very near the boundary between the stable and unstable disks. Thus, even if disks with "near flat" angular momentum distribution turned out to be unstable, our discussions below will not be affected.

II. Thermodynamic Conditions inside a Thick Disk Ever since Abramowicz et. al.8) suggested the possibility of the forma tion of the radiation supported thick accretion disks around black holes, various versions of the theory has been proposed (see e.g. Paczynski and Willa 9 I shall use the suggestion by Chakrabarti where a simple )). ID) prescription is provided for an exact solution in any stationary axisym metric space-time. The distribution of the specificenthalpy h will be taken from equation (2. 6b of this paper which is given by, l ) n 2 2 2 2 = constant ( 1) hut I 1-c 2A n- 1 n- where, Ut is the specific binding energy of the matter in the black hole geometry, denotes the von-zeipel parameter, and n are constants ,\ c describing the specific angular momentum distribution = n If one l c ,\ . assumes that the heat generated in the disk interior is being steadily brought towards the surface of the disk by convective elements preserving angular momentum and if the convective process is so efficient that the specific energy hut is constant along the surfaces of constant angular momentum, then specific entropy s also remains constant over those sur faces. We shall assume below that entropy density is constant throughout the disk. We shall choose the equation of state to be = K Here and p p'l. p p are the isotropic pressure and the matter density respectively and is y the adiabatic index. For isoentropic gas K is a constant when the gas is homogeneous in composition. In our case, to get a distribution of thermo dynamical variables to a first order we shall assume K to be strictly con stant. In the range of temperature and densities we shall be interested here, the gas is nondegenerate and non relativistic. The pressure of infal ling matter will be contributed by both gas and radiation. The single fluid assumption will be made, which is valid for high accretion rate11l. When the angular momentum distribution of the matter inside the disk is supplied, the pressure, density, temperature at various points inside the disk can be calculated by using equation (1) and from the equa tion of state mentioned above as a function of (3, the ratio of the gas pres sure to the total pressure. The local values of or T at some point in p, p the disk does not depend upon the mass of the hole. But the global proper ties of the disk (such as the mass, luminosity, .. etc.) do depend upon the hole mass. Figure 1 shows the density and temperature at the center of a typical disk for various values of (3. Also shown are the entropy density s, 158

~~2.7e•3~~

~~self gravity~~

~~B 1 x I I 2.6e -1 soQ 2e+14~~

~~B 1 x 2 6e-5~~

~~'!' '!' og("fc) I Jog(A)~~

~~B 1 x 2 6e-09~~

~~2 6e- 13~~

0 2 3 4 5 6 7 B 9 10 I og(M/M0) ----'7 Fig. The thermodynamic condition of the center of a thick disk in Schwarzschild1: geometry and for mass of the hole (rin = 5.98 re = 14) up to 10 The shaded region in the upper right corner contains the points10 [email protected] The shaded region in the lower left corner contains theMdisk points > Mhole when. the opacity due to Thompson scatter ing is less than unity. In the vertical shaded region on the left 31'fG.Also shown are {3, the ratio of gas to total pressure, the Mholeentropy < density, and the optical depth due to Thomson scattering.s

~~1' z O'1 1,~~

~~R ...~~

~~Fig. The meridional cross-section of a thick disk showing the ele mentary2: volume sandwiched between the two surfaces and u2 ) of constant angular momentum and 2. (a1 l 1 l 159~~

the ratio of gas to total pressure the optical depth near the center of {3, Tr the disk. The optical depth inside a realistic thick disk is probably more than 103 to 104. In all such diagrams f3 and hence p and T remain con p, stant on horizontal lines. The oblique line on the right hand corner separates the diagram into two regions. The line is drawn where the disk mass is same as the hole mass. Because of the possibility of local gravita tional instabilities it is not clear if a stable disk formation is possible in the region where self gravity dominates. So this region in the parameter space will be avoided. The oblique line in the lower left corner separates optical depth 1 region from 1 regions. The boundary conditions Tr < Tr > for which the calculations of the thermodynamical quantities have been made are: r = 103,T 104 Kat the outer edge of the disk. The center of = the disk is at r = 14.00 and the inner edge is at r = 5.98. The correspond ing c and n are given by 2.287 and 0.24 respectively. This choice maxim izes the central temperature of the disk for the same accretion rate. Details are discussed in CJA. The accretion into a hole depends upon the viscosity of the gas. The usual procedure of describing viscosity, namely, the parameter 2 ex. model 1 ), is probably an over-simplification.Neverth eless, we shall stick to such a description. In JAC a number of cases have been discussed with various viscosity parameters and the accretion rate. The outcome of the simulation is very sensitive to these parameters. Thus, if indeed the com position of jet tells us anything about the composition of the disk near the hole, as is hoped, these results may severely limit the uncertainty in the viscosity parameters provided the mass of the central hole is roughly known. The constraints upon the accretion rate is imposed separately13) 14l. Figure 2 shows the meridional cross-section of a thick accretion disk Let a and a2 denote two surfaces of constant angular momentum and 1 l 1 l 2 respectively. Let M denote the accretion rate. Assume that no matter is lost from the surface of the disk. If Vr denotes the average radial velocity through one such surface drawn at r, then from the conservation of mass, one has,

u, 47TTVr pd a = 47TTVr� (2) M "' J0 where, � denotes the 'column' density of the disk, a denotes a parameter describing length along the surface of constant angular momentum meas ured from the equatorial plane (a = away from the hole) and as being z its value on the surface. I shall assume an equatorial accretion !5), 16) This assumption makes the calculations much simpler because one can. get � from 160

(3) where, the subscript denotes the corresponding value on the equatorial e plane and z 0 denotes the half thickness of the accreting layer. Usually it is taken to be the half thickness of a thin disk, i.e.,z rv /a , where, v 0 =

equation, the disk half thickness turns out to be z 0 = r ( ( v a) ) 1 + ¢1 2 112 . O With this half thickness, the ratio 2 is closer to unity within a few per JP epdz cent throughout the disk. Thus our simplifiedmodel mimics a thick disk more closely than the averaging employed by previous workers. Due to viscosity, angular momentum is transported radially outwards. From the difference in torque exerted on the surfaces and a2 one can a calculate the net rate of angular momentum transport. The1 derivation will be avoided here (see CJA for details). We shall find it convenient to work in terms of the dimensionless accretion rate defined to be the accretion m rate M divided by the critical accretion rate Mer· One can combine the mass and the angular momentum transport equations to obtain the accretion velocity at r as, and the residence time tr _I__ Vr Vr = (l ) f':,! ��pm Vr (l - P lin)P Since the specific angular momentum l scales as the mass of the exholep M, whereas the pressure and density p are independent of p the mass, we obtain, in particular, M /ex. Once vr is known from a tr � given viscosity parameter the accretion rate can be calculated from ex, m above mentioned equations. Figure 3 shows the variation of the accretion rate measured in the unit of the critical accretion rate when is kept ( ) ex fixed at 10-6. The gas pressure to the total pressure ratio is how ex= {3 ever, kept constant over the horizontal lines. The pressure temperature p, T and density also remain constant over the horizontal lines as they are p independent of the mass of the hole. The residence time tr given in the diagrams are the full residence time of the accreting matter, rather, not the time to cross from the center to the inner edge. This time only gives an estimate of the time scale during which important nuclear reactions may be taking place inside the disk. The diagrams clearly shows that for a given viscous mechanism, higher temperature is attainable at the center of the disk for a lighter mass hole.

III. Major nuclear reactions inside a thick disk In the previous section we observed that the central temperature of the radiation supported thick accretion disk could be more than 109 degrees depending upon viscosity parameter, the accretion rate, and the 161

~~2 7e•3 Bl~~

~~8 I 2 6e -1~~

~~81 2 6e-5~~

~~t t log(l;,l I og(R) 2 6e-09~~

~~B I x I 05_.__-r--,--,----,....--r--,--,---,-----,------jr- 2 6e- I 3 8 10~~

Fig. The variation of the accretion rate when the parametei:- is chosen3: to be 1 throughout the diagram.m The unshadedex region 10 100 representso-6 the region available for thick disk forma tion� (Blandfordrh. � 1985) The fixed fixes the accretion velocity near IX the center The residence time calculated from re - rin ) (vc). (tr = ---- is also shown in the diagram. For a different the unshadedv ,strip moves parallelly right or left depending upon whetherex new value o� is lower or higher than The crosses indicate the. points. for whicha: the simulation is reported1 o-6. in section IV. central hole mass. Figure 4 roughly summarizes the major nuclear reac tions which are possible inside a disk simultaneously at a different dis tance from the hole. At regions with temperature 0.02 chain is Tg < PP slow but dominant process. As matter approaches the hole, in presence of trace carbon (which may be formed by triple alpha reactions) or oxygen, CNO cycle is triggered 9 0.1) which is quickly defeated by hot CNO (T l>3 cycle rate when the proton capture rate of 13N becomes larger than its positron decay rate (T 9 1>30.25). At even higher temperature region 0.5) CNO bi-cycle and rp -process takes place17l. The later process (T9 > starts when the alpha capture rate of 150 becomes comparable to its posi 9 tron decay. The 1 F so formed rapidly captures proton and heavier ele ments are produced (hence the name rp process; this is similar to the classical r process where rapid neutron capture takes place.) Under some circumstances the process may also become important when all the ini ex tial proton is depleted. At a even higher temperature photodisintegration becomes inevitable. 162

~~f--- '(- d1sintegrat1on Tg I I 0~~

Mg21 • Mg24 lp,1l (a,pl f--- rp Process l�D� 19 t 20 2 . ·�'"" N• N• N• 3 t 1 9 20 21 (p al/ (J,Pl N• N• N• �"' ·,�·> F 11,al 18 F 1 9 f----- CNO B1-C�cle Tg > 5 0 017 f----- HCNO Cycle Tg N IS > 0 3 e t f----- CNO Cuc I 12 1 Tg > c c 1 3 c •4 0 I

~~3a reaction~~

~~Chains~~

Fig. The basic reactions of the hot cycle and the cause of its breakdown4: is shown in this diagram. CNO Arrow indicates the flow of a reaction. So far, the issue of the possible convective instabilities has not been addressed. The instability may be turned on due to highly temperature sensitive energy generation processes near the equatorial plane. Qualita tively one can derive the condition for such overturning in the following way. In the case of the thin. disk the outgoing flux is approximately given by, �A{ and pressure G:L: where, is the column density. F "" z, p "" 3 z, L: Thus forf a fixed and at a fixedR, we have F and On the other L: � z p � z, hand, the flux due to energy from nuclear burning is given by,

� n where 4 for chain, for CNO cycle, 40 Fburn (pT )L:, n = PP n = 16 n = for triple alpha reaction, etc. at For ion pressure supported disk, T "" T•· For equilibrium, this must be so that temperature must vary p � pT, � z, _z 1) as � � z,. ,2 , Thus, Fbu- � - , This implies that for gas pressure T , .• (Zn p z dominated disk,n,_, must be for no overturning to occur. For radiation ;;; 1 2!'.. - 1 supported disk, and similar argument shows that, Fburn p � T 4 � z 4 implying that the no-disruption condition is 8, Thus, at least for n ;;; PP chain disk should be stable against convection. For thick disks the central 163

temperature is usually higher than that of a star, so, becomes smaller n for any particular reaction. Thus, the thick disks are more stable against convective overturning. In reality, the net nuclear energy generation rate can be much less compared to the gravitational energy release. Hence small higher burnings may not cause instability. n

~~IV Numerical Simulation of the Nucleosynthesis IN THICK DISK AROUND SCHWARZSCHILD HOLE: The simulation starts with matter near the outer edge of the disk assumed to be of solar~~

-4

-5

-6

-7

-8

-9

~~-10 ;;; -11 �!§ � -12~~

~~E -13~~

~~- 1 4~~

~~-15~~

~~-16~~

~~-17~~

~~-18 0~~

~~log(TIME) in Seconds 164~~

~~0.0829 0.1041 0.1401 ,-----.�--.-�--,�-,�,---,,-----,�--,-� --,�.,-�.----,0.2135� --.-�--,�',y-� q.3737 o.o~~

~~He4~~

~~-1.0~~

~~"' u -2.0 � 016 s !:! "" a �~~

~~-3.0~~

~~4.3 (146) 4. (116) 4.48 (84) 4.57 (50) 4.65 39 log(TIME) in Seconds~~

Fig. 5ab The variation of composition of accreting matter in a thick accretion disk around a OMoblack hole as a function of time. The parameter near the center1 is a) for deuterium and neutron, b)a other elements with abundance10- higher5. than In parenthesis the radial coordinate in the unit of Schawarzschild10- radius4. is shown In the upper axis the temperature of matter is also displayed. The cross mark on the upper axis indicates the location of the disk center.

composition. The center of the disk is at and the inner edge at T = 14 5.98. The network contains 256 isotopesc till Ge72. Figures 5a and 5b T = showin the variation of the composition of matter as it accretes towards a 10.Ati hole. In Fig. 5a the changes in deuterium and neutron are shown and in Fig. 5b other elements with abundances higher than 10-4 are shown. The parameters chosen at the center are: 1 o-5 and 10. The cen e< = m = tral temperature is 0.3737. The corresponding point in the parame T9 = ter space is shown in Fig. 3. We observe that almost entire deuterium is burnt out before 200 via PP chain. Proton burning via CNO cycle T = becomes significant at about 146 begining of Fig. 5b but the sub T = ( ) stantial proton burns only after hot CNO becomes comparable at about 50. The entire amount of 160 goes to 150 via T = 160 (p ,y)17F ({3+v)170(p ,y)18F (p ,cx)150 . Only 56Fe remains almost intact during the whole process. 165

Fig. 6 shows the variation of composition in a thick disk around 106Mg central hole. The parameters are: o: 10-8, and 100. The central = m = temperature is 0.2105. The corresponding point in the parameter T9 = space is shown in Fig. 3. The behavior of deuterium and neutron is similar to the previous case. Otherwise, some reactions are very much different. Until r i"3 180, the p capture rates of 13C and 14N remains so low com pared to that of 12C that they keep piling up and 12C decays down. Ulti mately, 13C itself becomes 14N by capture. This goes on till an equili p brium is reached (see plateau of 14N at r i"3 140). At around this region the lower p capture rate of 170 compared to that of 160 causes it to pile up at the initial stage but soon both the rate goes up and becomes comparable. 160 is depleted and 14N is formed via 160 (p ;y)17F (f3+v)170(p ,o:)14N until another equilibrium is established (see plataeu of 14N after r i"3 90). Finally, when all the protons are depleted, o: capture reaction starts. As a result, a major final product becomes 180 at the expense of 14N .

~~0. 2105 0.0262 0345 0.0489 0.0789 o. -0.0 ------~~

~~He4~~

~~-1 .0~~

~~;;;~~

~~§-2.0 � 016 �"" 0 --<~~

~~-3.0~~

~~12.0 (246) 12.16 (195)~~

~~log (TIME) in Seconds~~

Fig. The variation of composition of accreting matter in a thick accretion6: disk around a 106.Afeblack hole as a function of time. The parameter near the center is 10-0. In parenthesis the radial coordio: nate in the unit of Schawarzschild radius is shown. In the upper axis the temperature of matter is also displayed. The cross mark on the upper axis indicates the location of the disk center. 166

IN BONDI ACCRETION: Since the time scale for the Bondi accretion is much shorter than that of a disk accretion, the nuclear reaction was very little. Two cases have been simulated: a) central hole of mass 1 OM with accre tion rate 800 and temperature at the critical radius 100) is m = (re =

T9 = 0.015 and b) central hole of mass 106M with the accretion rate 6000 and temperature at the critical radius 100) is m = (re = T 9 0.0025. The simulation is continued till 2.5 is reached. Only in = r = the first case, some deuterium is burnt through the PP chains. Significant 0 fiows 1 0 1 ) occur after matter reaches 30. In the second case the ( > - r = fl.owof reactions was never significant. IN KERR GEOMETRY: Probably all black holes have some angular momentum. For an extreme Kerr hole the horizon is at 1 and the rh = stable circular orbits exist all the way to the horizon. Hence the center of a disk also lies very close to it. More binding energy is released (42% as opposed to only 6% for the Schwarzschild hole case) as matter goes deeper into the potential well. What this means is that the central temperature of a disk is much higher for a similar set of parameters. Accordingly more nucleosynthesis is expected. However, no simulation has been carried out so far.

V Discussions The thermodynamic conditions as mentioned in section II (also 9 see18),l ) ) clearly indicated that under suitable conditions considerable thermonuclear reactions may take place inside a thick disk. We have demonstrated this in the previous section. The effects of shocks which are believed to be significant, have not been considered here. Nucleosynthesis in the neighborhood of a hole may have interesting consequences. The processed matter may be present in the jet. These nuclei can be brought to excited state by collision of highly relativistic protons in the jets. The observation of the line emissions from the jet or from the quasars may thus shed light upon the constituents of the disk and its evolutionary his tory. Lamb et. al.2D) have reported observation of gamma ray lines at 1.495 Mev and 6.695 Mev in the spectra of the regions of SS433 which have been tentatively identified as cascade de-excitation of 150 21) or 24Mg and 160 lines22l. Yet more convincing are the EXOSAT results of G. Stewart (reported by Fabian23l) who observed strong iron-emission line at about 7kev in the approaching component of the jet of SS433. The final over abundance of 150 and high abundance of 56Fe in our simulation for a 10 solar mass hole could be suggestive although it is argued24) that probably the viscous parameter is very close to 0.1. Ulrich et. a!.25) have reported observation in the UV spectrum of the Seyfert galaxy NGC4151 showing variable lines tentatively identified as the redshifted and the blue shifted components of CIV 1550 presumably emitted in both branches of a two sided jet. Clearly, such'A observations require closer investigation. We hope to be able to understand these in near future. 167

I am thankful to Dr. W. D. Arnett and Mr. Liping Jin for a very exciting collaboration during which much of the work was completed This research was supported partly by NASA grant NAG-W123 with the University of Chi cago and partly by NSF grant AST 8415355 and a Tolman fellowship at Cal tech.

REFERENCES Chakrabarti, S.K., Jin, L., and Arnett, W.D. 1986, AP.J. , (In Press) 1. 2. Jin, L., Arnett, W.D., and Chakrabarti, S.K. 1986,Ap.J. (submitted) 3. Chakrabarti, S. K. 1986, Ap . J. , , 582. 303 4. Papaloizou and Pringle , 1984, MN RAS , , 721. 208 5. , 1985, MNRAS , 799. ______213 , 6. Margan, B. 1984, Ann. Rev. Astron. Astrophys., , 507 . 7. Katz, J.I, 22 1986 (preprint). 8. Abramowicz, M.A., Jaroszynsky, M., and Sikora, M. 1978, Astr. Ap . , 63 321. 9. Paczynski, B., and Witta, P. 1980,Astron. Ap. , 23. 88 , 10. Chakrabarti, S.K. 1985, Ap. J. , 1. 288 , 11. Rees, M.J. 1984, Ann Rev. of Astron. Astrophy. , , 47 1. 22 12. Shakura, N.l. and Sunyaev, R.A. 1973 Astron. Ap. , 337. 24 , 13. Blandford, R. D., 1985, Active Galactic Nuclei , J. Dyson (Ed.), Univer sity of Manchester Press, UK, p. 281-299. 14. Begelman, M.C. 1984, Proceedings of the Santa Cruz Summer School Conference (preprint). 15. Paczynski, B. and Abramowicz, M.A. 1982,Ap. J. 897. ,253 , 16. Rozyczka, M. and Muchotrzeb, B. 1982,Acta Astron , 285. 32 , 17. Wallace, R.K. and Woosley, S.E., 1981,Ap .J. , (Supp .ser. ) , , 389. 45 18. Blandford, R.D. 1985, Numerical Astrophysics , J.M. Centrella, J.M. LeBlanc and R.L. Bowers (Eds.) 19. Begelman, M.C. 1984, VLEI and Compact Radio Sources R. Fanti, K. Kellermann, and G. Setti (Eds.) 20. Lamb, R.C., Ling., J.C., Mahoney, W.A.,Riegler, R:-C., Wheaton, W.A., and Jacobson, A.S. 1983, Nature , 37. 305 , 21. Boyd, R.N., Wiescher, M., Newsom, G.H., and Collins, G. W.,Il. 1984, Ap. J. (Lett ), , L9. 276 22. Ramaty, R., Kozlowsky, B., and Lingenfelter, E.R. 1984, Ap.J, L13. 283 , 23. Fabian, A.C., 1986, Nature , ,451. 319 24. Katz, J.I. 1980,Ap. J. (Lett. ), 236 ,Ll27. 25. Ulrich, M.H., Altamore, A., Boksenberg, A., Bromage, G.E., Clave!, J., Elvius, A., Penston; M.V., Perola, G.C., and Snijders, M.A.J. 1985, Nature , ' 747. 313

~~169~~

~~BLACK HOLES AND DISK DARK MATTER~~

~~Dennis Hegyi Department of PhysicsJ., University of Michigan Ann Arbor , Michigan 481 09~~

~~ABSTRACT~~

Two independent approaches are used to place constraints on the amount of dark ma ss in the gal acti c disk in the form of black holes . Gas accre tion by bl ack holes leads to X-ray emi ssion which should not exceed the upper limi ts on the observed soft X-ray background . Al so, metals produced in stel lar processes that lead to black hole formation should not exceed the observed disk metal abundance . Based on these constraints , it appears unl ikely that the mi ssing disk mass could be contained in black hol es . 170

~~I. Introduction~~

~~There are several length scal es In the uni verse on which there is or~~

~~may be mi ssing mass. On the largest scal e, that of the uni verse Itsel f, it~~

~~is diffi cult to underst and how gal axies devel oped based on the observed~~

~~cosmol ogical mass density in lumi nous matter. Al so, the upper limits on~~

~~the am pl itude of perturbations present at recombi nation as deduced from~~

~~measurements of the cosmi c background radiation suggest more mass than has~~

~~been found in lumi nous matter. To reconci le these apparent di screpancies ,~~

~~it Is necessary to introduce dark matter. Thus , on a cosmologi cal scal e it~~

~~appears necessary to hypothesi ze the ex istence of subl umi nous or~~

~~nonl umi nous mass. In fact , however, it is possible to avoid the necessity~~

~~of introduci ng cosmol ogical dark matter by al lowi ng for reheating of the~~

~~intergal actic med ium after gal axy formation. Reheati ng would smooth out~~

~~perturbations In the intergal actic medium left over from gal axy formation.~~

~~Thus, there may be no compel ling re ason to int roduce dark matter on a~~

~~cosmol ogi cal scal e, but there is a need for dark matter on a vari ety of~~

~~smal ler scales based on arguments which are independent of the cosmol ogi cal~~

~~arguments.~~

~~On the next smal lest scal e, cl usters of gal axi es , it is quite cl ear~~

~~that there is mi ssing mass. It has been known for some time that there~~

~~exi sts a missing mass probl em for cl usters . 1)~~

~~Conti nui ng to smal ler length scal es , a good case can be made for~~

~~missi ng mass in el liptical gal axi es . 2) , 3) Neverthel ess, some additional~~

~~cl ari fi cation would be helpful to demonstrate that the observed mass~~

~~bel ongs to the gal axi es rat her than to the cl usters wi thi n whi ch they are~~

~~found . Also on gal actic scales , an excel l ent case can be made for mi ssing~~

~~mass in the hal os of spi ral gal axi es . 4)~~

~~Fi nal ly, on the scal e of the disk of the gal axy , a recent~~

~~rei nvestigation by Bahca1 1 5) of a probl em fi rst discussed by Oort6 l 171~~

confi rms Oort 's conclusion that it is necessary to postul ate the ex istence of some unseen mass to satisfy the dynamics of the disk. Bahcal l found the total mass density in the sol ar nei ghborhood by fi nding the gravitational potenti al due to the di sk necessary to expl ai n the scal e height of stars in the vi ci nity of the disk. Assumi ng that the unseen matter is di stributed like the light in the di sk, Bahcal l fi nds that he cannot account for about one-half of the total deduced mass .

Havi ng deduced that dark matter exists on several di fferent scal es , it is interesting to consider constrai nts that can be pl aced on the natu re of the mi ssing mass. On the cosmological ;cal e, arguments for non-baryoni c matter have been made in order to decrease the timescale for gal axy formation so that they may form from the smal l baryoni c seeds observed at recombi nation in less than a Hubble time. Al so , primordi al nucl eosynthesis arguments7 1 limit the fraction of the cri tical density in baryons , nB , to be less than n There is very little mi ssing baryoni c cosmological B <0.2. mass that can be incl uded in this limit. On the other hand , thi s limi t is only margi nal ly inconsistent wi th an n for cl usters of gal axi es . It <0.3 would be di fficult to exclude baryoni c matter in cl usters based on nucleosynthesis arguments.

~~At the present time, no detai led arguments exi st to indicate the~~

~~nature of the dark matter in el liptical gal axi es . However, it has been~~

~~argued8) ,9) that halos of spi ral gal axi es are not baryoni c. These~~

~~arguments do not exclude the possibility of bl ack holes in hal os .~~

~~The subject of this paper is the dark matter in the gal actic disk.~~

~~The local dark matter cannot be we akly interacti ng matter like, for~~

~~exampl e, neutri nos or axi ons , si nce the matter must have dissipated some~~

~~energy to be confi ned to the disk. The only candidate for the local dark matter at the present time is baryonic, but the form whi ch the baryons take~~

~~is unclear. Recently, Bahcal l, Hut and Tremai nelO) have shown that if the 172~~

~~dark matter were bl ack holes wi th a mass greater than 2 they wou ld Me, disrupt we akly bound bi n ary star systems and on that basis exc luded them as~~

~~a candidate for the dark matter.~~

~~Here we shal l argue that the local dark matter is not composed of~~

~~bl ack holes of mass less than 2 At the present time it is di fficul t to �. avoid the conclusion that the local dark matter consists of pl anets or~~

~~possibly whi te dwarfs. An interesti ng aspect of thi s conclusion is that at~~

~~least two di fferent types of dark matter are necessary to sol ve the mi ssi ng~~

~~mass probl ems .~~

~~In this paper two di fferent arguments are used to limit disk dark~~

~~matter in the form of bl ack ho les. If the dark matter is in bl ack hol es,~~

~~it would accrete interstel lar gas and emit X-rays . Though some of the~~

~~X-rays would be absorbed by the interstel lar gas itself, enough of the fl ux~~

~~would be detectabl e to set an interesting upper limit on the mass of bl ack~~

~~holes in the gal actic disk. The second argument is based on the producti on~~

~~of metals in stars as they are formi ng bl ack hol es . The constrai nt that we~~

~~are imposing is that the production of metals duri ng the formation of bl ack~~

~~hol es does not appreciably exceed the sol ar abundance . Recause the~~

~~production of metals is rel ated to the slope of the initial mai n sequence~~

~~whi ch is expected to be simi lar to that in the sol ar nei ghborhood , we can~~

~~compare the deduced limits on the slope wi th the observed sl ope. As we~~

~~shal l see thi s al so limits the mass al lowabl e in bl ack ho les. In the~~

~~remai nder of the discussion bel ow, an overvi ew of arguments that were~~

~~originally presented by Hegyi , Kol b, and Ol ive ll wi ll be di scussed . )~~

~~II. Accretion into Bl ack Hol es~~

~~Though a hal o composed of bl ack holes cannot be excl uded because they~~

~~accrete little gas , the same arguments cannot be used to exclude di sk bl ack~~

~~holes. Halo bl ack holes pass through the gal actic disk at hi gh vel ocity so 173~~

they both spend little time in the di sk and gi ve gas molecules in the di sk a very smal l momentum impulse. Therefore hal o bl ack hol es accrete little gas . Rl ack holes in the di sk, however, spend most of thei r time in the disk and al so travel through the interstel lar medium at rather smal l velocities. Thus , they are capable of accreting much more gas.

~~Consi der a bl ack hole of mass M moving at supersoni c vel ocity v through the interstel lar medium havi ng a density n. It wi ll accrete mass at a ratel2) .~~

~~M 107 (M/l\;:> ) 2 (n/cm-3) ( 300 s -l/v) 3 g s -1 ( 2.1) Km~~

~~The lumi nosity due to accretion is c 1) (n =~~

~~L € M (2. 2) = where € is the efficiency wi th whi ch matter is converted to radi ation.~~

2 Expression (2.1) is only valid for a capture radius, re ap 2 GM/v , which is at least several mean free paths because (2.1) assumes that matter wi ll travel al ong streaml i nes and col lide behi nd the bl ack ho le after wh ich it then falls into the hol e. If the mean free path were not sufficiently smal l relative to re ap • col lisions would never occur. Thus , there is a lower limi t on the velocity of the bl ack hole for which (2.1) is appl icable whi ch corresponds to - 0.5 s -1 for typi cal interstel lar densities. If Km one considers the magnetic fi eld embedded in the interstel lar medium, the cut off vel ocity for which (2.1) is appl icable wi ll be sti ll lower.

~~Substituti ng n= 1.85 cm-3 and veloci ty v 20 s -1 the < Km 5) , lumi nosity is~~

~~= 8 x 1031 € (M/�)2 erg s -1 (2. 3) L~~

~~As may be seen from (2.1), Ma v -3, so that smal ler vel oci ties are wei ghted more heavi ly in the comput ation of M. Bahcal l •s5) analysis showed that az , 174~~

~~the velocity dispersion of the dark matter, constrai ned crz to be less than~~

50 s -1 . Consideri ng the v-3 wei ghti ng , the effective mean velocity to Km be used fo r the computation of is 13 s-1 . Thus , our choice of M � Km v 20 Km s -1 is conservative. < Ou r model for a radi ating bl ack ho le assumes a spheri cal surface of

~~radius R radi ati ng like a bl ackbody. Any real model would not have perfect~~

~~spheri cal symmetry and would not be a perfect bl ackbody radi ator. Either~~

~~departure from the assumed model would result in a hotter radi ator which~~

~~would emi t harder X-rays wh ich would be more easily detectabl e. Thus ,~~

~~calcul ations based on a spheri cal bl ackbody model underestimate the number~~

~~of detected X-rays .~~

~~A bl ackbody radi ator of radius R expressed as a multiple of the~~

~~Schwarzschi ld radi us, Rs , havi ng temperature T, has a lumi nosity~~

~~L 29 (R/R 2 2 (T/30 ev 4 erg s -1 = 9.14 x 10 s ) (M/Mc;i) ) (2.4)~~

~~with a differential lumi nosity~~

~~3 dl 35 2 2 E 4 -1 1. 7 x 10 (R/R ) (M/M ) erg KeV s dE = s 0 exp (E/T) _ 1~~

~~X-ray observations have been used to set an upper limit on the temperature~~

~~of the radi ation emitted by accreting bl ack holes as a function of radi us~~

~~and mass. Equi val ently, the upper limit on temperature can be rel ated to~~

the efficiency of co nverting mass into radi ation. It is expected that e, the radi ation efficiency is 0.1.13) ,14) ,15) As may be seen in e • in ref. 11, if R 2 R -2 if M ( 1 M0 whi le Figure = s , is greater than 10 e if R 5 R , is greater than o-2 for M 35 Si nce 0.1, then = s l e < Mc;i. € •

~~either R 5 Rs or M 1 Mc;i--either option is unl ikely. > < 175~~

~~III. Bl ack Hole Formation and Metalicity~~

In thi s section we outline a cal cul ation for the amount of metals ejected back into the interstel lar medium by a disk popul ation of stars with mass in the range (8-100) that leave bl ack ho le remnants. We M:;, assume that the stel lar initial mass function is of the form

~~+(M) M - (1 (3.1) a + x) where + (M.) is the number of stars that formed per unit vol ume per unit mass. Val ues of the slope parameter range from 1.616) to 2.017 ) to x~~

~~2.318) in the sol ar nei g hborhood .~~

~~The calcul at ion proceeds as fol lows . Fi rst , it is necessary to fi nd the mass fraction in metals of a star 's ej ecta as a function of its mass~~

assumi ng that it leaves a 1-2 bl ack hole remnant . Arnettl9) has M:;, publ i shed hi s cal cul ations of the ejected mass fraction in metal for stars in the mass range (8- 100) If these values are integrated over the I'\;>. inti al mass function in (3.1) , and two constrai nts are proposed : (1) 50%

of the di sk mass is in bl ack holes wi th mass {1-2) 110 and (2) the overal l metal licity of the disk cannot appreci ably exceed the sol ar val ue, Z < 0.025, the slope parameter is found to be 6. . Thi s substantially x x > 7 exceeds the observed val ue 2. in the sol ar nei ghborhood . x � 3

~~It is expected that the initial mass function for bl ack hole~~

~~progenitors should reasonably match the local initi al mass function. Thus ,~~

~~it is diffi cult to understand how (1-2) M:;, bl ack hol es could supply the~~

~~missing disk mass. 176~~

~~References~~

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~~COSMIC BURST OBSERVATIONS GAMMA-RAY J.-L. ATTEIA : Centre d'Etude Spatiale des Rayonnements 9, Avenue du Colonel Roche BP 4346 31029 TOULOUSE CEDEX~~

Ab stract : More than 400 bursts have now been detected; this paper reviews the main observational facts regarding their temporal structures, energy spectra and localizations and shows how these characteristics are related to a neutron star origin of gamma-ray bursts. The experiments planned in the near future, and the areas in which significant progress are expected, are presented. 178

~~• • •~~

~~• • •• -� ' t . , • • . .. .;. ,· ' •~~

~~·: .. ·� •~~

~~·. :-··~~

'· ··. � • , ' .><- 1 ' ·: ..... ' ·., . . . .. • . • • . I , .:-: :. · . . ;...... �. ,._ , _ ... . •' ·• ·· ..1 ...... � ,. " .. : ' . . .. . • .... ·C,I • .. ,... • ',-4>" • • -Enlargement of Palomar Observatory Sky Survey plate showing the June y-ray burst error box (the region common to the intersection of the annuli, indicated by an arrow). 1374, 1979 13 179

~~INTRODUCTION~~

~~The first gamma-ray bursts were detected as rapid increase in gamma-ray~~

flux by the Vela detectors (in the range 200 keV - 2 MeV) , and since the first l) publication in 1973 , hundreds of bursts have been recorded by numerous experiments, providing us with a large number of light curves and energy spectra. It is generally agreed that gamma-ray burst sources are neutron stars; thus it is interesting to note that more than 400 bursts have now been detected , a number which is comparable to the number of known pulsars or of known binary X-ray sources containing neutron stars.

~~Because of their neutron star origin, gamma-ray bursts are directly related to several important topics :~~

- Stellar evolution : what portion of the neutron star population becomes bursters ? In many models bursts are due to the accretion of matter on the 2 3) neutron star (either the sudden infall of gas • or an 4 5) asteroid • , or slow, continuous accretion yielding 6 7) thermonuclear flashes • ). This brings up the question of the source environment : is the neutron star alone does it have an ? accretion disk or a dwarf companion In any case, the ? evolutionary path leading to such obj ects may be interesting and unusual.

- Matter and radiation under extreme conditions : The production of gamma rays may result from an unusual combination of high temperature, strong magnetic field and gravity. Therefore gamma-ray burst spectra may give new insight into the physical processes taking place under these conditions.

- Distribution of the sources : We are not yet able to determine the distance to the sources. If they are nearby obj ects (with distances less than a few hundred parsecs) , then a non-negligible fraction of neutron stars evolve into gamma-ray bursters, and this can give us an estimate of their density near the Sun. If they are very distant

~~(with distances up to 100 kpc ) we have to explain the high S ) velocity needed to ej ect them so far from the galactic plane . 180~~

~~I) THE OBSERVATIONAL STATUS~~

~~Experiments presently in use give two kinds of data : - Light curves (or time histories) with a resolution of a few milliseconds.~~

~~- Energy spectra, with a time resolution of � 0.25 s.~~

A) Time histories An important point is the great diversity encountered in gamma-ray burst light curves (Fig. la-ld) bursts can display a single peak or (more frequently) several peaks ; the total duration can vary between 50 ms and 100 s (with a typical value of a few seconds) and fluctuations can occur very quickly (on timescales of few milliseconds) or not (several seconds and more) . This wide range of gamma-ray burst characteristics presently seems hard to explain if all the bursts are described with a single model .

~~50 50-280 KEV 40~~

~~< 30 N (fJ co E- z 20 z ::::l < 0 (") ---, u 10 "I co :::i " 10 15 20 TIME, SECS~~

~~80 60-300 KEV 60~~

~~m N (l) � 40 z a: ::::l (L 0 (") < u 20 " I lD :::i 10 15 20 TIME , SECS 181~~

~~�:::'°"� .. 0 15 30 45 60 15 TIME , SECS~~

~~600~~

~~(f) 400 E--- 2 =:) 0 u 200~~

~~0 15 30 45 60 15 TIME , s.~~

~~Fig, la - ld : Examples of burst time histories; note the great variety in temporal evolution.~~

Various attempts have been made to classify bursts using their temporal 9 and ref , therein) characteristics , and many convincing results have been obtained, but the physical significance of such work is not yet clearly understood, Presently two results seem well established : 182

- The decay times of short (t 1 s) , single-peaked events tend to < be equal to their rise times or a little bit longer l O) , - Few periodicities are found in gamma-ray burst light curves 2 ll) cases are 8.0 s and 4.2 s periods in GB790305b and 12) GB771029 respectively ; some evidence for several second modulations are also present in the data of the Signe experiment (aboard Venera 11,12,13,14 and Prognoz 7 and 9) . These periods, if of rotational origin, provide strong evidence for gamma-ray burst emission by old magnetized neutron stars. Moreover, these period values may indicate that sources are neutron stars in binary systems since they can slow down more rapidly than isolated neutron stars .

B) Spectra : Just as the light curves are highly variable, so are the burst energy l3) spectra. Barat et al. using data from the Signe experiment , found significant variations in spectra taken with 250 ms temporal resolution. This trend also appears in data obtained by the Konus experiment on the Venera 14) spacecraft . Figure 2 illustrates a "generic" energy spectrum when integrated over 1 second or more. Generic means that it summarizes the main characteristic traits found in burst spectra up to now. To check the reality of the features displayed here, a continuum fit is needed. A first attempt made by Mazets et 15) al . indicated that a simple thermal bremsstrahlung law with 2 parameters -l (N(E) dE = A E exp (-E/kT) dE) provided a good representation between 30 keV and 1 MeV , for spectra integrated over 4 s, this law gives values of kT > varying from 150 to 450 keV . Since then, many authors have pointed out that spectra can be correctly fit (at least between a few keV and 1 or 2 MeV) by 16) assuming various other physical processes such as thermal synchrotron or l inverse Compton . In any case it is not yet known whether instantaneous ?) burst spectra are described by a simple law : as pointed out by Hameury et al. a physical description of the energy dissipation following a lB) , thermonuclear flash at the surf ace of a magnetized neutron star indicates that the spectrum may be the sum of various components, namely a blackbody with a temperature of few keV plus inverse Compton and synchrotron contributions . Under these conditions , wh ile the reality of the features indicated on Figure 2 is no longer doubted, their level of significance is hard to estimate. The emission feature around 400 keV is observed in about 10% of the spectra; it appears as short flashes (6 t 250 ms) which tend to be correlated < with the peaks of the time histories. This emission is usually interpreted as a 183

+ - gravitationally redshifted e /e annihilation line . The 20% redshift corresponds to the theoretical value for a neutron star and strongly reinforces the idea of a neutron star burst origin. The 200-400 keV FWHM generally indicates a temperature well below that of the continuum and this fact leads to the conclusion that either the emission mechanism is non-thermal or the line 19) and the continuum come from different regions of the neutron star (we shall address this question below, in connection with the high energy tail observations) . A similar problem is raised by the low energy absorption features, first lS) reported by Mazets et al. They are observed in about 20% of the spectra with a typical width of 10-20 keV, independent of the continuum temperature . They are generally interpreted as cyclotron absorption lines in the atmosphere 12 of a strongly magnetized neutron star (B 9 10 G) . ZO) The high energy tails in burst spectra, recently found by Matz et al. in Solar Maximum Mission (SMM) data are an important characteristic since more than 20% of the bursts display an emission beyond 2 MeV. This component is correctly fitted by a power law and , when present , shows no high energy cut-off Zl) (at least up to 6 MeV) . Golenetskii et al . have pointed out that this high + - energy portion is probably an extended wing of the broad e /e annihilation line . One interpretation may be that this tail is a superposition of several + - 8 e /e lines emitted by plasmas with temperatures varying between 10 and lO lO keV (either in time or in space) , or by plasmas with a non-thermal energy distribution. Absorption due to pair production by high energy photons in strong magnetic fields means that the observed photons have to be emitted in a 12 region of low magnetic field (B 10 G) , or almost parallel to the field if 12 < B > 10 G. In the first case we are confronted with 2 emitting regions, while the second implies a beaming of the high energy photons (angles 20° with < respect to the magnetic field) . The fluence contained in the > 400 keV region can represent more than half of the total fluence (i.e. for E > 30 keV) of the burst ; however when averaged over all the events (including those with no high energy tail) the ratio 8(>400) / S(>30) falls to 10-20%. The link between these features is not clear since no correlation was found between the rapid variations displayed by the continuum, the low energy features and the high energy tail (this fact leads to rapidly changing hardness ratios during bursts) . Finally, several authors have reported as a common characteristic the 22 23 24) observation of X-ray emission (at a few keV) by gamma-ray bursters • • . The onset seems to be simultaneous in X- and gamma-rays , but the X-ray emission is clearly longer than the gamma-ray burst (several tens to hundreds of 23) seconds) . Some evidence for X-ray precursors may exist , but it is only of 184

~~marginal significance. The total fluence in the X-ray range represents a few percent of the gamma-ray burst fluence.~~

� Illustration of a "generic11: gamma-ray burst energy spectrum. As explained in the text , this figure put together the characteristic features displayed by burst spectra when integrated over a few seconds (the instanta neous spectral shape is not yet known , and may be very different).

C) Localizations : About 100 localizations of gamma-ray burst sources have been obtained either by the Konus experiment 2 with a typical accuracy of a few degrees or 5) by arrival time analysis using an international network of near earth and interplanetary satellites, which gives an accuracy of a few tens of arc and ref · therein) minutes 26 . With the latter technique, an accuracy reaching the arc-minute level is obtained for several intense events every year. We will first address the results of these precise locations .

~~- Counterparts~~

~~Despite numerous searches in the optical range up to V magnitude ** 23-25 , 185~~

27) no quiescent burster counterparts have yet been identified If sources are rather nearby objects (with distances less than 1 kpc) , they can only have degenerate dwarf companions . Likewise, in the IR domain no counterpart has been detected up to K magnitude 28) 19

A striking fact was the discovery by Schaefer (on a plate taken in ** 29) 1928) of an optical flash in the direction of the 1978 November 19 burster rd For an assumed duration of 1 s, this transient would have reached 3 magnitude. Since then Schaefer has found 2 more flashes in gamma-ray burst 30) error boxes (for a total examined exposure time of 2.7 yr) . These events indeed seem to be emitted by gamma-ray burst sources since a search 34 times longer (in yr .sr) done in regions containing no known burster has revealed no such flash. Moreover, a 5 month photometric survey of the GB790305b field has revealed 3 optical transients of mag 8-10 possibly associated with the gamma 31) burster . These observations have created more questions than answers : - Do gamma-ray burst sources also emit optical bursts - Are the gamma-ray and optical bursts simultaneous ? What kind of mecanism can increase the light emission so dramatically If optical bursts are currently emitted by gamma-ray burst sources, they should provide new information as significant as good positions or optical spectra. Therefore several experiments dedicated to this study are now in operation, they will be explained in Section II.

In the X-ray range, 6 sources were observed by the Einstein observatory ** and by Exosat, none displaying a point source . These observations give 32) constraining limits on steady accretion rates . They are shown on Figure 3 as a function of the assumed distance to the source; they depend on the area over which accretion takes place and on the value of the interstellar -12 absorption of X-rays. In any case the upper bounds vary between l0 and -15 10 M0/yr (for distances lower than 10 kpc) , values which are orders of -10 magnitude below those currently found in X-ray bursters ( ..- 10 M0/yr) . As 32) pointed out by Pizzichini et al. , a slightly different interpretation is possible within the framework of the thermonuclear model : the observations allow us to calculate the accretion rate per unit area, which is the critical parameter of the model. 3 observations out of 5 cannot be explained by the thermonuclear model unless there is some additional effect, such as beaming of the gamma-ray flux, cutoff of the accretion after a burst, or emission of the accretion energy with a spectrum harder than a blackbody. 186

~~°' >- 12 .... 10- .. 6 APRIL 1979 GRB REGION x: w EINSTEIN OBSERVAT ION >-- <( 14 "' 1 f z 52 t:; � 10-16 <(~~

~~DISTANC E IKpcJ~~

Fig 3 Einstein observation (in the .15 - 4.5 keV range) of the 1979 April 6 burster.: The lack of X-ray point source in the gamma-ray burst error box provides upper limits to the surface temperature of the neutron star (lower curve) and to the polar cap accretion rate (upper curve , assuming 2 S 3.2 km ). These limits, which are a function of the assumed distance of P = tfi� source, give constraints of great significance for thermonuclear models.

- Galactic distribution : Another study concerns the galactic distribution and recurrence timescale of the gamma-ray burster population. As shown on Figure 4, this distribution is essentially isotropic and does not exhibit the influence of the galactic structure. This indicates that sources are either very close (with characteristic distances around 300 pc) or very distant (with distances equal to or greater than 50 kpc) . If the sources are distributed in an extended galactic halo , an interesting consequence is that collimated intruments with -S -2 moderate improvement in sensitivity (S�lO erg.cm ) would probably be able to detect an excess number of bursts in the direction of nearby galaxies (M31, LMC , SMC) . 187

� : Distribution of 86 gamma-ray burst sources (in galactic coordinates) . This distribution is essentially isotropic , indicating that the observed sources are not affected by the galactic structure.

Repetitions : up to now only 2 sources, including the peculiar GB790305b burster, have been observed to recur on timescales of days or months. The GB790305b burster presents 2 interesting characteristics : A 164 day period is possible in the 15 already observed weak 33) recurrences . - The luminosity function of the recurrent bursts is not representative of the "classical" gamma-ray burst population (indeed, if we assume that this luminosity function is representative of the whole burst population, 18 st repetitions should have been recorded in the data of the 1 international 26) network of detectors ). Therefore we can undoubtly exclude this event (and most probably the second) from the subset of normal gamma-ray bursts. Considering that no repetition was observed among the 80 located sources in the second catalog of 26) gamma-ray bursts from the international network , and making reasonable assumptions about the burst luminosity function, leads to a repetition time of 10 years or so (although a repetition time as short as one year is still compatible with the observations if we consider a luminosity function with a great maj ority of weak bursts) . 188

~~II) EXPERIMENTAL PROGRESS.~~

~~A) Large area detectors~~

Starting in 1988, large scintillation detectors will fly on the SIGMA 2 experiment (8 CsI blocks 2400 cm each, aboard the Soviet GRANAT spacecraft) 2 and on BATSE (8 NaI (Tl) blocks 2025 cm each, aboard the Gamma Ray Observatory) . They will allow the recording of light curves with integration times of 1 ms or less. This point is important since present experiments cannot detect short timescale variability (At 20 ms) except in some very intense 34) < events (e.g. Lares et al . who recently discovered a burst displaying several spikes about 10 ms wide) . Also very important is the ability of large detectors to record spectra with integration times of tens of ms rather than seconds, since spectral lines are generally smoothed when integrated over 1 s 13) or more . Finally, SIGMA and BATSE (as well as balloon borne detectors) will achieve better sensitivity and provide an estimate of the Log(N(>S) )-Log(S) curve to ? -2 10- erg.cm , which should yield information on the galactic distribution of the sources.

~~B) Spectroscopy~~

Several experiments are planned which will record spectra in extended energy ranges (compared to the usual 50 keV - 2 MeV range) WATCH , ASTRO-C, PHOBOS and SAX will all have good temporal resolution and 9> spectral capability in the few kev range and should detect several tens of bursts . PHEBUS (a French experiment aboard the GRANAT spacecraft, consisting of 6 35> BGO detectors) and, in some cases, GRO will provide spectral information up to 100 MeV with an improvement of one order of magnitude in sensitivity. Another very promising technique is high resolution (1 keV over the 10 keV - 10 MeV range) spectroscopy using high purity Ge semiconductors, in the near future (1986 - 1988) , only balloon flights are planned.

~~C) Localizations~~

Several very precise (tens of arcseconds) localizations will be obtained starting in 1988 using data from the gamma-ray burst detectors aboard ULYSSES (which will be launched towards Jupiter) , PHOBOS (towards Mars) , PVO (around Venus) and, around the Earth, SMM, GRANAT and GRO . This improved accuracy is 189

necessary to perform deep observations in the optical, radio and X-ray ranges , as well as to look for optical flashes on archival plates . X-ray experiments, as WATCH or SAX, will also provide positions with an accuracy varying from several arcminutes to 1 degree. The expected numb er of localizations is about in the month mission of the WATCH experiment and 0 3 9 about 20 - 30 per year for the SAX spacecraft The SIGMA experiment will 9> . also provide arcminute positions and good spectra for some 5-10 bursts arriving in the field of view of the gamma camera (6°x 7 ° ) .

If optical bursts are actually associated with gamma-ray bursters (which is probable) several experiments will allow a good positioning of the sources (with an accuracy of l ). They include the GMS (several 20 cm telescopes " 9> pointed towards known burst sources), the ETC 6 (which is a wide field array 3 ) of CCD cameras devoted to sky surveillance, with a limiting magnitude of 11 for a 1 s optical burst), and the Ondrejov network of cameras for meteor 37 > detection (with a limiting magnitude varying from to 8 for a 1 s flash) . 6

~~CONCLUSION.~~

An important point to keep in mind when addressing the gamma-ray burst question is their essentially transient nature : note, for instance, that the bulk of the results presented here come from observations in the gamma-ray range (where special detectors were developed for transient event studies), and that no conspicuous quiescent counterpart has yet been found at any wavelength. Two points now seem clear : the neutron star origin of gamma-ray bursts and the existence of several models capable of explaining the general characteristics of this phenomenon. Nevertheless the most important fact probably lies in the number of new features inferred from the present data, that is : - Evidence for an "instantaneous" spectral shape different from the presently observed one. - Existence of a rapidly variable high energy tail associated with the presence of the 511 keV line . - Probable transient optical emission by gamma-ray bursters. - Existence of faint variable obj ects in gamma-ray burst error boxes . - Significant evolution of the luminosity on millisecond timescales. - Periods or characteristic timescales of several seconds in long time histories. 190

~~- 2 examples of repeating burst sources over intervals of few months.~~

~~The promise of the future experiments is that they may place these different features in perspective and provide us with an almost complete set of data at several wavelengths. 191~~

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~~195~~

~~A MODEL FOR SOFT X-RAY TRANSIENTS~~

~~J. M. Hameury l . A. R. King2 . J. P. Lasota l.3~~

- Observatoire de Paris. Section de Meudon . Departement d'Astr ophysique Fondamentale. F-92 195 Meudon Principal Cedex. France 2 - Department of Astronomy. University of Leicester. Leicester LEl 7RH. UK 3 - lnstitut d'Astrophysique de Paris. 98 bis Bd. Arago. F-75014 Paris. France

~~ABSTRACT~~

Soft and ultrasoft X-ray transients are generally believed to be close binaries where the primary is a compact object C black hole or neutron star> and the secondary fills its Roche lobe. We propose here that the transient soft X-ray events are due to a mass loss instability that arises in the secondary star. as a result of X-ray illumination of its atmosphere. We find that. for accretion rates M in the range - lol2 - lol6 g s-1 . the stellar atmosphere is unstable. In the quiescent phase. the red dwarf does not completely fill its Roche lobe: the accretion rate is as low as O 12 - l O 13 l g s-1 . but is sufficient to heat up the external convective layers of the red dwarf close to the Lagrangian point L They slowly expand: when M reaches the unstable range. l. matter flows at a rate - 0 17 g s-1 through L l. The mass loss instability ceases when l the Ll region is shielded by the accretion disc : by then. the heated layers have been transferred to the disc . The outburst Itself stops when the whole disc has been accreted on to the compact object. Both computed time scales and luminosities are in good agreement with observations. 196

~~I - INTRODUCTION~~

Transient X-ray sources are divided into three classes . depending on their spectra . Hard X-ray transients are massive binaries Csee e. g. Rappaport. 1982) . and will not be discussed here. Although soft and ultrasoft X-ray transients ( SXT's> were discovered in the 1970's. their nature is still not well understood. Detailed reviews of the observations are given by White et al ( 1984) for the X-ray data. and by Bradt and McClintock < 1 984) tor the optical data. We shall summarize here only the most important properties of these objects. They are probably X-ray binaries that turn on for a few months. with a recurrence time of the order of a year or more . The total energy emitted during the outburst is approximately 1044 ergs. with a maximum luminosity in the range 1037 - 1038 erg s- 1 : during the quiescent phase. the X-ray flux is lower by at least 2 to 6 orders of magnitude. yielding accretion rates which could be as low as 1012 g s-1.

During the outburst. the emitted spectrum of ultrasoft transients is approximatively thermal. with a temperature of about one keV: there are however two spectral components : a blackbody. and a high energy power law tail that can extend up to 100 keV. and becomes comparatively stronger as the emitted flux decreases (Wilson and Rothschild. 1983: Cooke al . 1984; Parmar et al . 1985al . This is et . . reminiscent of the properties of accreting black holes candidates . such as Cyg Xl .

et which exhibits the same behaviour in the high and low states (White al . . 1984) . The idea that ultrasoft X-ray transients are low mass binaries where the companion is a black hole is strengthened by the recent determination of the mass function of

~~A0620-00. McCllntock and Remillard C 1985) found that the mass of the compact object is at least 3. 4 MG. with a most probable value of 7 MG .~~

On the other hand . it seems that soft X-ray transients . that have a comparatively harder spectrum in outburst are low mass binaries where the compact object is a neutron star. This is certain In some cases. for example Aql X-1. Gen X-4. or EXO 0748-67. since type I X-ray bursts were observed during the decay phase ( Koyama et al. 1980; Matsuoka al. 1981> or during maximum (Parmar et et al . . 1985bl . In the brightest sources. two spectral components are observed : a thermal one and a so-called unsaturated comptonized spectrum. which becomes comparatively stronger as the source weakens. The hard component could be. for instance. radiated by a very hot. optically thin corona around the neutron star. and so It might well be that most of the X-ray fiuK during the quiescent and unobservable phase is emitted in the hard X-ray range. 197

In the following. we shall use the generic term 'soft X-ray transients' for both soft and ultrasoft transients . This is legitimate since the difference arises only in the nature of the compact object. which. as we shall see . does not affect the model proposed here.

Optical counterparts have been detected in a few cases : during the outburst. most of the emitted light comes from an accretion disc. while in quiescence. the spectrum is that of a late type main sequence star < K typel . Indications of orbital modulation are found in some cases. with periodicities of a few hours. The clearest case is EXO 0748-67 : the X-ray light curve exhibits almost total eclipses with a period of 3. 8 hr. If one assumes that the red dwarf fills its Roche lobe. one finds a mass of 0. 3S M0• corresponding to a MS main sequence star. In general. the masses of the companions are not well known; we shall consider here the particular case of a relatively massive star

~~Models that have been proposed to explain soft X-ray transients frequently involve disc instabilities~~

It has also been suggested that the site of the instability could be In the secondary Itself. and not in the accretion disc . This Instability could be an Ionisation instability as proposed by Bath < 197Sl for dwarf novae . or the result of illumination of the companion atmosphere by X-rays emitted by the primary

certain range of accretion rates . a stable equilibrium is impossible. In section Ill. we discuss the structure of the heated envelope of the red dwarf in the Roche potential. both in the vicinity of the Lagrangian point L and far from L 1. where the gravitational l. potential is approximately spherical . Because of its relatively long Kelvin-Helmholtz time. which ca n exceed the observed time scale of luminosity fluctuation in those sources. the envelope need not be in thermal equilibrium. In section IV. we propose a possible application to X-ray transients : the low and high states would correspond to the two possible quasi-equilibria of the limit cycle of the atmosphere. while motion along the equilibrium curve would be the result of the slow expansion of the outer convective layers.

~~STABILITY OF AN ILLUMINATED ATMOSPHERE II -~~

X-ray heating of the companion atmosphere has been invoked by Osaki C 1985) as an explanation for the superoutbursts of the SU UMa stars. with a possible application to soft X-ray transients. King and Lasota C 1984> also put forward the same mechanism to explain the high and low states In magnetic cataclysmic variables. Anderson C 1975) proposed earlier that this type of instability could be responsible for the high and low states of the system HZ Her/Her X- 1. The analysis of mass transfer was however generally carried out using the spherical potential of an isolated star; here. we shall take into account the full Roche potential. and we shall see that this results in significant differences with the previous studies. In addition. we show that the situation is very different depending on whether most of the accretion luminosity is emitted in soft or hard X-rays.

In the quiescent phase of soft X-ray transients. most of the X-ray flux is emitted in the hard energy range. While this is almost certain in the case of ultrasoft X-ray transients. this assumption is more speculative is the case of soft transients. According to Monte Carlo calculations by Felsteiner and Opher < 1976) . hard X-rays can penetrate down to Thompson optical depth of the order of 10 before losing their energy. For late type stars . the photosphere is located at a column density of about 5 g cm-2 CAiien. 1973) Ci. e. Thompson optical depth - 2l ; this value remains almost unchanged in the Roche potential C see below) . Therefore. X-rays emitted during the quiescent phase can penetrate slightly below the photosphere; this allows the absorbed X-ray flux to be reradiated as a blackbody. and a hot. optically thin corona does not form . as it would be the case if most of the X-ray flux were emitted below a few keV

analysis Is therefore inapplicable to these starsl . The effective temperature T of the heated reg ion is such that the emitted blackbody flux balances the stellar flux $• plus the absorbed X-ray flux Cl-axl$x. where ax - 0. 3 is the X-ray albedo at norma l incidence. At the Lagrangian point L 1. $x is given by :

~~( 1} where is the efficiency for hard X-ray production. M the accretion rate and d the ri distance from the L 1 point to the compact object.~~

~~The mass overflow rate of the Roche lobe fi lling secondary star is C Lubow and Shu. 1975) :~~

~~( 2} where Q is the effective cross section of the mass transfer throat at the Lag rangian~~

~~point L 1. P the mass density at L 1. and C C R Tl 1 /2 the isothermal sound L 1 s = g velocity. Rg being the gas constant. Because the effective gravity vanishes at Ll . the density does not vary e>~~

~~( 3 }~~

where Is the density at the base of the Isothermal atmosphere. the distance of PO t:.r the bottom of the isothermal atmosphere C being defined as the ma> to the Ll point, and H the scale height given by :

~~p c - = 8 T 2 H 8 1 .59 x 10 Phr ( --}l/ cm ( 4 ) 1/2 4 2rr (A + 1/2) 10 K~~

A where P = Phr >< 1 hour Is the orbital period. and a numerical factor given by Lubow and Shu (1975) . ranging from CM / M 0 or a» to CM IM = 1). In Eq . <4> . we 4 2 1 = B 2 1 have taken A constant. and equal to for simplicity. This does not introduce a large B error since A has a very broad ma>

~~( 5 }~~

~~The effective cross section Q Is given by Meyer and Meyer-Hofmeister: 200~~

~~1018 ,...... _ - I t/J 16 B � 10~~

~~"" E-< < 14 c:: 10 z = 7 A 0 M M0 e::: 1 12 M2 = 0.69 M0 "" 10 7.8 hr c::u = u P < T0 = 3000 K 1010~~

~~2 9 9 9 0 10 3 10 4 10~~

~~t:i.r (cm) Figure Accretion rate versus t.r for 0. l Tl = l~~

~~(6) where k 7 is a dimensionless constant. M and M are respectively the masses in - l 2 solar units of the compact object and the red dwarf. and Dis the orbital separation .~~

4 Equation <2> together with the condition rrT = Cl - ax> x allows one to * + determine the temperature of the isothermal atmosphere and the accretion rate. once the distance i:.r to the base of this atmosphere is known . Figure l shows M as a function of i:.r for 0. as In the case of a neutron star or black hole primary with Tl = l. a hard X-ray spectrum. The surface temperature is taken to be 3000 K and the orbital period 7. 8 hr. which are the parameters of the soft X-ray transient A0620-00 < McClintock et al. . 1983> for which a KS companion was detected in quiescence. The 3000 K temperature corresponds to the effective temperature at the point . It Is seen that In the first case. the equilibrium curve MCt.rl has an inverted S shape; for t.r in the range 2. 04 x 109 - 2. 48 109 . three solutions are x found. The equilibrium on the central branch Is thermally unstable. while the two others are stable. Therefore. values of the accretion rate between 3 lol3 g s-1 and x 4 x lol6 g s-1 are not physically accessible. The MCt.r> curve is analogous to the l. viscosity-surface density curve in accretion discs. where a limit cycle occurs . 201

We have computed the MC Ml curve for a variety of parameters. and found that the upper bound of the unstable range of accretion rates depends rather weakly on the orbital period . with values of the order of a few times 101 6 g s-1 . i.e. slightly

al greater than the average accretion rate of SXT's . and well above likely values for the quiescent accretion rate. The lower bound of the unstable range M corresponds to a value of of the order of unity. as expected . The exact A <1>xt<1>. value is 1. 16 for the parameters considered here.

~~It must be noted that. although this critical ratio is relatively constant. the absolute value of the accretion rate depends rather sensitively on the orbital~~

~~parameters. As an example. changing M 1 from 7 M0 to 1. 4 M0~~

~~STRUCTURE OF THE HEATED ENVELOPE Ill -~~

In order to find the timescales of the limit cycle (i. e. duration of the on and off states> . one has to determine the reasons for secular motion along the equilibrium curve. We shall see In this section that. because of the illumination of the red dwarf atmosphere. Its outer envelope In the region Is no longer adiabatic and in thermal Ll equilibrium; it slowly expands. and this expansion is responsible for secular changes of the accretion rate .

~~1 - Unilluminated case~~

~~We have computed the structure of the envelope and atmosphere in a Roche potential by solving the standard equations:~~

1 dP p = - r ( 7 ) dr g( ) er dT4 4 (8) 4>conv + 3 K p dr where g is the effective gravity e. taking into account the full Roche potentlall. P Ci. the pressure. the density. the opacity. the total stellar flux and the p K "'• conv convective flux. for which we adopted the mixing length formula given by Paczynski 1969> . valid for both optically thin and optically thick turbulent eddies. For we C K. used the tables of Alexander C 1 975> at low temperatures: for temperatures greater than 1 o4 K. we used the analytical approximation of Christy 1966) . which is much C less accurate. but happens to be used only In the fully convective reg ion. where 202

~~= 7 M0 M2 = 0.69 M0 7.8 hr P = Lir 9 = 2.13 10 cm~~

pressure Figure 2 Structure of an uniluuminated KS main sequence star orbiting a compact object. Dotted line : radial structure near L 1: solid line : radial structure far from the L 1 point. almost all of the stellar flux is carried by convective motions.

We used the algorithm of Paczynski Cl969) to solve equations <7> and <8> . The main difficulty of this problem is that. because the gravity varies over the stellar surface. is not constant over the whole star. and is therefore unknown . 4>.

On the average. the red dwarf filling its Roche potential has a radius Av given by Paczynski. 1 971>: c 2 R = 1.63 x lOlO �2 /3 p f3 cm v hr (9) The stellar structure far from L 1 can be computed under the assumption that the presence of the primary star does not change much the gravitational potential of the secondary. This structure is therefore that of a main sequence isolated star of radius Av . In order to determine <1>. in the vicinity of L 1 . we used the prescription of Papaloizou and Bath C 1 975> : since the deep layers of the envelope are fully convective. their specific entropy S is constant: in particular. S along the line of centres must be equal to the value of the entropy calculated far from L 1 assuming spherical symmetry. This determines in the L1 region. <1>.

~~Figure 2 shows the pressure - temperature diagram along the line of centres 203~~

of an unilluminated K5 star orbiting around a 7 M0 black hole with a period of 7. 8 hr. In this case. the distance t;.r of the region of optical depth 10 to the Ll point is 2. 13 x io9 cm. The structure far from the Lagrangian point (spherical modell is also shown for comparison. and It Is seen that differences arise only in the very outer regions. where the temperature gradient is superadlabatlc Ccolumn densities less than 500 g cm-2. However. $_. Is only 5. 3 x 1 o9 erg cm-2 In the L 1 region. and l. 8 x iol O erg cm-2 elsewhere. This makes the Ll region much more sensitive to illumination than the rest of the star.

~~Let us finally note that the thermal structure of the dwarf companion is rather insensitive to the assumed mass of the primary Cfor a given orbital period) . since.~~

~~from Eq. C9l. Rv is lndependant of M 1 . and since the parameter A Cwhich determines the gravitational potential in the L 1 vicinity) varies extremely slowly with~~

~~the ratio M 1 IM2 .~~

~~2 - Size of the L 1 region~~

~~In principle. the effective temperature over the whole stellar surface can be found using the procedure used in the Ll region. i. e.~~

of the order of the solar mass. numerical computations have shown that Tell varies as ga. with a"'0. 08 C Lucy. 1 966) . Assuming a power law dependence In our case too. and using only the results of the structure along the line of centres and in the spherical case. yields values of a of 0. 10 for the K5 dwarf. similar to the value quoted

~~above. The determination of T elf over the stellar surface then reduces to the computation of the effective gravity at the photosphere.~~

Assuming again A 8 and expanding the Roche potential to second order gives: � = [ 1 + 0.58 ( �)2 ] 112 (10) where go is the effective gravity at the photospherlc point along the line of centres. located at a distance t;.r from L 1. and I Is the distance measured along the equipotential. This expansion Is valid provided that g remains small as compared to 204

~~= 7 M0 /~~

~~= / M2 0.69 M0 / = / P 7.8 hr~~

~~I I~~

~~3 10~~

2 2 10- L-l-1..LIWJJJ.-L.LLJ.llJIL._J._LLJ.llJll.-...1....l.J.J.JJJ!J_.J....1..J..l.Wll.-LI..l.J..IWJ 1 0 3 4 5 7 9 10 10 10 106 10 108 10 pressure Figure 3 Comparison of the Illuminated red dwarf structure in the Roche potential with the unilluminated situation. The solid curve shows the relative temperature difference t.TIT at constant pressure for an Illuminating X ray flux equal to the stellar flux at the Lagrangian point. Also shown is the local Kelvin-Helmholtz time (dashed linel the spherical gravity. wh ich Is more than 10 times g . From Eq. one deduces 0 < l Ol. that g. and therefore Taff · varies over a scale I= 2. 3 t.r. The surface over which the luminosity is depressed compared to the mean stellar value Is thus rrl2 = 17 e,r2 . and represents - 10-3 of the total surface. As expected . this is about the size of the effective cross section Q for mass transfer through the Lagrangian point.

~~3 - Envelope response to illumination~~

Illumination of the red dwarf leads to energy deposition below the photosphere. so that all of the absorbed X-ray flux can in principle be reradiated as quasi-blackbody emission . The set of equations 7l - = e( r (ll dr ) ) the energy deposition rate at radial position r. If. for simplicity. one wt1crc ei n is assumes that all of the X-ray flux is absorbed at a fixed column density. then rl is a e< delta function: below that point. the flux is the unperturbed stellar flux . : above. It is - ax> x· Figure 3 shows the structure along the line of centres of the K5 red ct>._ + < l dwarf illuminated by an X-ray flux equal to the stellar flux at the Lagrangian point ct>._ L when thermal equilibrium is reached. It can be seen that in these regions the l. 205

whole depth of the envelope is affected by illumination. and that the temperature rises by - 10% everywhere. This is a consequence of the fact that the X-ray flux can penetrate down to the convective layers . It is well known CSchwarzschild. 1958l that. contrary to radiative layers. convective ones are very sensitive to boundary conditions.

Because the thermal content of the whole envelope is large. thermal equilibrium will not be reached on timescales comparable to the recurrence time of soft X-ray transients. Figure 3 also shows the variations of the Kelvin- Helmholtz time

~~TK-H In the envelope. Here. we define TK-H as :~~

p C TH p p (12) ,. where Cp is the specific heat at constant pressure. and Hp the pressure scale height. The flux in Eq . C 12l is taken to be the stellar flux .si nce illumination results in a heating of the external layers . and hence in a reduction of the temperature gradient. leading to a decrease of the convection efficiency. The deep layers are therefore

~~heated by the stellar flux itself. which justifies Eq . Cl2l . Note that TK-H is a local quantity. and not the timescale required to heat up the whole envelope above a given~~

~~level. For this reason. TK-H can decrease with increasing depth.~~

Figure 3 represents therefore an extreme case where heating has been effective for an infinite time. For a heating time of one year. the actual thermal structure will be that of Fig. 3 only for pressures less than 4 x 107 dyne cm-2. AT/T decreasing rapidly to zero at greater depths.

~~IV - APPLICATION TO SOFT X-RAY TRANSIENTS~~

We suggest that soft X-ray transients are due to an Illumination instability in the red dwarf envelope. This instability. discussed In Section II, arises provided that the externally imposed accretion rate Is in the range - 1 O12 - 2 x 1O16 g s-1 . This 1 falls within the observed values ciol 4 - 1 01 6. 5 g s- . White et al. . 1984l . It also falls within the expected values resulting from shrinking of the Roche lobe under the effect of gravitational radiation.

~~During the quiet phase. the accretion rate is given by the lower portion of the S curve of Fig. 1. and is comparable to the stellar flux at the Lagrangian point. As 206~~

discussed in section Ill. the subphotospheric layers in the vicinity of L 1 heat up. and expand. In the case of the KS dwarf. column densities up to 2 x 104 g cm-2 are heated by X-ray illumination within one year Csee Fig. 3l . and expand. The total expansion of these layers can be estimated as 1. 5 x 108 cm. which brings the base of the atmosphere from 2. 13 x 109 cm to 1. 98 x 1 o9 cm from L 1. i. e. in the unstable regime. The outburst of mass transfer ceases when shielding of the Ll region by the accretion disc is effective. and the X-ray transient event stops when the whole disc has been accreted on to the compact object. This is quite different from what has been proposed by Osaki C 1985) for SXT's. since he assumed that the outburst stops only when llr has increased up to point B where the upper branch of equilibrium

~~We shall now examine in some more details these various phases.~~

~~1 - Quiescent phase~~

The limiting value of the accretion rate is - 101 2 - 1013 g s-1 in all cases. leading to X-ray fluxes that are too small to be detectable. the more so as most of the flux is emitted in the hard X-ray range. In the most stringent case of A0620-00. the upper limit on the X-ray flux is 1032 erg s-1 . for an assumed bremsstrahlung spectrum with kT 1 keV C Long et al . 1981 . If the spectrum is. as expected. much = . l harder. then this upper limit must be raised significantly. In particular. if the spectrum is similar to that of 4U 1630-47 during decline C power law with photon number index - -1 . Parmar et al . . 1985) . almost all of the X-ray energy is emitted outside Einstein IPC spectral window. Therefore. values of the accretion rate as large as 3 x 1013 g s-1 which are predicted by our model cannot be excluded. Note also that the quiescent X-ray flux depends rather sensitively on the mass of the compact object : changing M 1 from 7 Me to 1. 4 Me results in a decrease of the quiescent accretion rate by a factor 5.

One might think that. since the X-ray flux at the Lagrangian point L 1 is about 1 /2 of the stellar flux at L 1. strong optical modulations should be observable. which is not the case C McClintock et al . 1983) . It must be realized that is large only in .

~~(13) 207~~

where x < L l > is the X-ray flux at the Lagrangian point. <<1>.> the average stellar flux. that is approximately three times the stellar flux at Ll in the case of the KS star. and - O. 3S is the X-ray albedo averaged over the red dwarf surface . Therefore. the amplitude of the modulations resulting from this effect would be Jess than 0. 02 mag . lower than the observed value CO. 2 mag> by one order of magnitude. In fact. these observed periodic fluctuations are very likely due to a combination of ellipsoidal variations and gravity darkening.

One also expects the disc to contribute to the optical luminosity of the system . If one assumes that 10% of the accretion luminosity <- 1033 ergs) is emitted in the optical range. then the optical luminosity of the disc amounts to a few percent of the stellar luminosity. This is in good agreement with recent observations rnovaisky. 198S) showing 10% optical variability on a 30 mn timescale in A0620-00; it could indicate that the disc contributes to at least 10% of the optical luminosity.

~~2 - The outburst~~

When the distance of atmospheric layers to L l reaches the critical point A. t;.r a mass transfer instability occurs. The rise time is governed by the accretion disc viscous time scale. which is of the order of a few days . provided that the disc is far from a steady state CLightman. 1974 . Bath and Pringle . 198 1) . This agrees with the observed rise time.

~~During the outburst. the accretion disc thickens; it will ultimately shield the L l region. thus quenching the instability. The opening angle of an a-disc Is given by CShakura and Sunyaev. 1973) :~~

. 0 1 10 3/2 r h .6 x -2 a- 3/ 8 M 2 10 / M� 1 1 ( 14) r 10 8 - 10 max [ g s ] [ �cm )1/ 8 where h is the thickness of the disc and r max its size. Shielding is inefficient during the quiescent phase (the size of the disc shade over the stellar surface is at least 20 times smaller than the effective cross section for mass transfer in the case of the KS star as well as the MS one> . However. when the accretion rate reaches a value close to the Eddington limit. shielding is efficient. This effect is increased by the Illumination effect on the disc Itself. Moreover. if the accretion rate exceeds a value of the order of l 0 17 g s-1 . shielding by the outflowing material Itself becomes important

~~The instability quenches when the disc becomes thick enough. The mass contained in it can be roughly estimated as CShakura and Sunyaev. 1973> :~~

. 7/10 � 5/4 24 -4/5 l/4 M M = 3 . 2 10 a M ( 15 ) D x l 18 -1 11 [ 10 g s ] [10 cm] and thus a mass of the order of 1024g is accreted on to the compact object during the outburst. corresponding to a total emitted energy of about 1044 ergs. again in good agreement with the observations.

The total duration of the outburst is the time required for the disc to be accreted on to the neutron star. This time has been estimated to be of the order of a month by various numerical computations Clightman. 1974. Bath and Pringle . 1981) . provided that is close to unity. Moreover. the predicted and observed a variations of luminosity are in fair agreement. Note that. because of disc shielding. the outburst stops well before the system arrives to the higher turnover point Bon the equilibrium curve

Since the mass of the subphotospheric layers which have been heated during quiescence is smaller than the total mass transferred to the compact object. the red dwarf has . after the outburst. the same thermal structure as at the beginning of illumination. and the whole process starts again. The recurre·nce time is the time required to heat up the envelope in the L 1 region so that the atmosphere is brought into the unstable regime. This time depends of course on the value of �r after the outburst; however. on long time scales. the system must adapt so that the average accretion rate matches the shrinking rate of the Roche lobe. Since a negligible amount of matter is accreted between outbursts. th e average recurrence time is:

~~= � - T l 10 yr ( 16 ) where is the amount of mass transferred during the outburst. and is the � externally imposed average accretion rate .~~

~~V - CONCLUSION~~

We have shown that soft X-ray transients can be due to a mass loss instability in the secondary star. as a result of illumination of its atmosphere by the X-ray flux emitted by the compact object. During the quiescent phase. the subphotospheric layers are slowly heated by an X-ray flux that is comparable to the stellar flux in the 209

vicinity of the Lagrangian point. These layers expand and ultimately bring the atmosphere in an unstable regime. The outburst of mass transfer ceases when shielding by the accretion disc prevents the X-ray flux from reaching the Ll reg ion. The rise and decay time. the total emitted energy. the recurrence time as well as the value of the X-ray flux in quiescence are in good agreement with the observations.

It Is possible that in some cases . shielding by the disc is not efficient enough at the maximum of luminosity. In that case. the duration of the limit cycle would be much longer. and one expects the X-ray source to remain stuck in the on-state for an extremely long time. as required for to increase by such an amount that the high M D.r solution ceases to exist. This time is of the order of 106 - 107 yr. The accretion rate in the high state is in the range 1016 - 1O18 g s-1 . and some of the luminous low mass X-ray sources could well be explained by this mechanism. On-the other hand. one also expects that a correspondingly large number of low mass binaries are in a very low state. i. e. unseen. with accretion rates less than 108 g s-1 . This would in fact significantly raise the number of such sources. since the ratio of sources in high and low states is the ratio of outburst to average accretion rate. This idea does not of course exclude the possibility that a number of the bright galactic low mass X-ray sources are binary systems where the companion is an evolved star .

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~~LIST OF PARTICIPANTS~~

~~ALY Jean-Jacques DPhG/SAP CEN-Saclay 91191 GIF SUR YVETTE CEDEX FRANCE~~

~~ATTEIA Jean-Lu c CESR BP 4346 31029 TOULOUSE CEDEX FRANCE~~

~~BARKAT Zalmat Dept of Astronomy University of Texas AU STIN TX 78746 USA~~

~~BONNET-BIDAUT Jean DPhG/SAP CEN-Saclay 91191 GIF SUR YVETTE CEDEX FRANCE~~

~~BRAUN Arie Racah Institute of Physi cs The Hebrew University of Jerusalem 91904 JERUSALEM ISRAEL~~

~~CANAL Ramon Depto de Fisica Modem a Universitad de Granada 18001 GRANADA SPAIN~~

~~CESARSKY Catherine lnstitut de Recherche Fondamentale CEN-Saclay 91191 GIF SUR YVETTECEDEX FRANCE~~

~~CHAKRABARTI Sandip K; Theoretical Astrophysi cs, (130-33) California Institue of Technology PASADENA CA 91125 USA 212~~

~~CHARDIN Gabriel DPhPE/SEPh CEN-Saclay 91191 GIF SUR YVEITE CEDEX FRANCE~~

~~COLGATE Stirling MS 275B Los Alamos Nati onal Laboratory LOS ALAMOS NM 87544 USA~~

~~CRANE Philippe European Souther n Observatory Karl Schwarzs child-Strasse 8046 GARCHING bei MUNCHEN FEDERAL REPUBLIC OF GERMANY~~

~~DERMER Charles D. NASA Goddard Space Flight Center, code 665 GREENBELT MD 2077 1 USA~~

~~EICHLER David Dept of Physics Ben Gurion Univ. of the Negev, Box 653 84 120 BEER-SHEVA ISRAEL~~

~~ELBERT Jerome Dept of Physics University of Utah SALT LAKE CITY UT 84 112 USA~~

~~FERRANDO Philippe DPhG/SAP CEN-Saclay 91191 GIF SUR YVETTE CEDEX FRANCE~~

~~FRIEDJUNG Michael Institut d'Astrophysique 98 bis, Bd Arago 75014 PARlS FRANCE~~

~~FUJIMOTO Masayoki Max Planck Institut for Physik und Astrophysik Karl Schwarzs child-Strasse 8046 GAR CHING bei MUNCHEN FEDERAL REPUBLIC OF GERMANY 213~~

~~GAISSER Thomas Bartol Research Foundati on University of Delaware NEWARK DE 197 16 USA~~

~~GLASNER Shimon-Ami Racah Insti tute of Physi cs The Hebrew University of Jerusalem 91904 JERUSALEM ISRAEL~~

~~GORET Philippe DPhG/SAP CEN-Saclay 91191 GIF SUR YVETTE CEDEX FRANCE~~

~~HAMEURY Jean-Marie Dept d'Astrophysique Fondamentale Observatoire de Paris- Section de Meudon 92195 MEUDON PRINCIPAL CEDEX FRANCE~~

~~HEGYI Dennis Dept. of Physi cs, Randall Laboratory University of Michigan ANN ARBOR MI 48109 USA~~

~~HILLEBRANDTWo lfg Max Planck Institut fi.ir Astr ophysik Karl-Schwarzschild-Strasse 8046 GARCHING be i MUN CHEN FEDERAL REPUBLIC OF GERMANY~~

~~ISERN Jordi Dept de Fisi ca, Tierra y Cosmos Diagonal 647 08028 BARCELONA SPAIN~~

~~LABAY Javier Dept de Fisica, Tierra y Cosmos Diagonal 647 08028 BARCELONA SPAIN~~

~~LANDE Kenneth Dept of Physi cs Univ. of Pennsylvania PHILADELPHIA PA 19104 USA 214~~

~~LASOTA Jean-Pierre Institut d'Astrophysique de Paris 98 bis, Bd Arago 75014 PARIS FRANCE~~

~~LIVNE Eli Racah Institute of Physics The Hebrew University of Jerusalem 91904 JERUSALEM IS RAEL~~

~~MARCK Jean-Alain Dept d'Astrophysique Fondamentale Observatoire de Paris - Section de Meudon 92195 MEUDON PRINCIPAL CEDEX FRANCE~~

~~MOCHKOVITCH Robert Institut d'Astrophysique de Paris 98 bis, Bd Arago 75014 PARIS FRANCE~~

~~NOMOTO Ken'Ichi Dept of Physics Brookhaven National Laboratory UPTON NY 11973 USA~~

~~PALLA Francesco Osservato1io Astrofisico Arcetri Largo E. Fermi, 5 50125 FIRENZE ITALY~~

~~RAMA TY Reuven NASA Goddard Space Flight Center GREENBELT MD 2077 1 USA~~

~~SHAVIV Giora Dept of Ptlysics Israel Institute of Technology 32000 HA1FA ISRAEL~~

~~SUTHERLAND Peter Dept of Physics Mc Master University HAMILTON ONTARIO L85 4M l CANADA 215~~

~~SVOBODA Robert Dept of Physics University of California IRVINE CA 927 17 USA~~

~~TENORIO-TAGLE Guillermo Max Planck Institute fiir Astrophysik Karl-Schwarzschild-Strasse 8046 GARCHING bei MUNCHEN FEDERAL REPUBLIC OF GERMANY~~

~~TRUMPER Joachim Max Planck Institut fiir Extraterrestrische Physik Karl Schwarzschild-Strasse 8046 GARCHING bei MUNCHEN FEDERAL REPUBLIC OF GERMANY~~

~~TUCHMAN Yitzchak Racah Institute of Physics The Hebrew University of Jerusalem 91904 JERUSALEM ISRAEL~~

~~WEEKES Trevor Center of Astrophysics - Wipple Observatory Harvard Smithsonian, P. 0. Box 97 AMADO 85629 AZ USA~~

~~YODH Gaurang Dept of Physics and Astronomy University of Maryland COLLEGE PARK MD 20742 USA~~