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A spectroscopic investigation of dwarf novae during the early rise of outburst
Mansperger, Cathy Sue, Ph.D.
The Ohio State University, 1990
Copyright ©1990 by Mansperger, Cathy Sue. All rights reserved.
UMI 300 N. Zeeb Rd. Ann Aibor, MI 48106 A SPECTROSCOPIC INVESTIGATION OF DWARF NOVAE
DURING THE EARLY RISE OF OUTBURST
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Cathy Sue Mansperger, B.S.P.A., M.S.
* * * * *
The Ohio State University
1990
Dissertation Committee: Approved by
R.H. Kaitchuck
A.E. Slettebak
R.F. Wing Adviser G.H. Newsom Department of Astronomy Copyright by Cathy Sue Mansperger 1990 ACKNOWLEDGMENTS
I would like to thank Arne E. Slettebak, Robert F. Wing, and
Gerald H. Newsom for serving on my committee, and for their comments and helpful suggestions. I would also like to thank George W. Collins
II for helping me find a job. Appreciation goes to John Cannizzo for his useful comments and for directing me to Mineshige's paper. I acknowledge the AAVSO visual data sent by the Director, Janet A.
Mattei. I would also like to express my gratitude to Gerald Dyck and
Elizabeth 0. Waagen for the aid they gave me during the observing runs which allowed me to catch these dwarf novae during the preoutburst stage. I would especially like to thank Ronald H. Kaitchuck, not only for his invaluable assistance with the research throughout this study, but for his moral support and patient guidance during the past five years.
il VITA
January 16, 1962 ...... Born - Columbus, Ohio
1984 ...... B.S.P.A., The University of Georgia, Athens, Georgia
1984-1985...... Research Assistant, Space Telescope Science Institute, Baltimore, Maryland
1985-1986...... Teaching Associate, The Ohio State University, Columbus, Ohio
Summer, 1986 ...... Research Associate, The Ohio State University, Columbus, Ohio
1986-1987...... Teaching Associate, The Ohio State University, Columbus, Ohio
Summer, 1987 ...... Research Associate, The Ohio State University, Columbus, Ohio
1987 ...... M.S., The Ohio State University, Columbus, Ohio
1987-Present ...... Head Teaching Associate, The Ohio State University, Columbus, Ohio
PUBLICATIONS
Mansperger,C.S.1987, "Spectroscopy of the Dwarf Nova RX And in Outburst and Quiescence", M.S. thesis,The Ohio State University.
Kaitchuck,R.H.,Mansperger,C.S.,and Hantzios,P.A.1988, "Spectroscopy of the Dwarf Nova RX Andromedae from Quiescence to Eruption", Astrophysical Journal,330,305.
iii Scott,J., Mansperger,C.,Brainerd,T.,and Saizar,P.1988, Sample Examination Questions for Introductory Astronomy Courses, 2nd ed. (Edina, MN: Burgess International).
Mansperger,C.S.,and Kaitchuck,R.H.1990, "Spectroscopy of the Dwarf Nova TW Virginis Caught on the Rise to Outburst", Astrophysical Journal,in press.
FIELDS OF STUDY
Major Field: Astronomy
Studies in Cataclysmic Variables with Dr. R. H. Kaitchuck.
iv TABLE OF CONTENTS
ACKNOWLEDGMENTS...... ii
VITA ...... iii
LIST OF TA B L E S ...... vii
LIST OF FI G U R E S ...... viii
CHAPTER PAGE
I. INTRODUCTION ...... 1
II. OBSERVATIONS...... 20
RX A n d ...... 25 SS C y g ...... 36 KT P e r ...... 40 AH H e r ...... 45 AR A n d ...... 50 TW V i r ...... 53 Summary of Preoutburst Behavior ...... 58
III. COMPARISON WITH OTHER OBSERVATIONS ...... 61
Quiescence...... 63 Rise to M a x i m u m ...... 65 M a x i m u m ...... 65 D e c l i n e ...... 67
IV. DISCUSSION OF PREOUTBURST STAGE ...... 69
RX And: 1985 December...... 69 RX And: 1987 Oc t o b e r ...... 70 SS Cyg: 1987 Ju n e ...... 70 KT Per: 1988 Se p t e m b e r ...... 71 AH Her: 1988 Se p t e m b e r ...... 71 AR And: 1988 Se p t e m b e r ...... 72 TW Vir: 1988 Se p t e m b e r ...... 72 S u m m a r y ...... 72
V. COMPARISON WITH T H E O R Y ...... 81
v CHAPTER
VI . CONCLUSIONS
BIBLIOGRAPHY LIST OF TABLES
TABLE PAGE
1. Physical Data for Program S t a r s ...... 22
2. Observational Data for Program S t a r s ...... '23
3. Observed Spectral Changes During the Preoutburst S t a g e ...... 58
4. Outburst Coverage of Dwarf Novae ...... 64
5. Model Line Emitting Regions During Preoutburst . . . 78
6. Final Model Parameters for TW Vir, Black Body M o d e l ...... 87
7. Final Model Parameters for TW Vir, Stellar Atmospheres Model ...... 90
8. Final Model Parameters for RX And, Stellar Atmospheres Model ...... 100
vii LIST OF FIGURES
FIGURE PAGE
1. Light curve of the dwarf nova SS Cyg based on AAVSO visual observations. For a complete AAVSO light curve from 1896-1985 see Mattei et al. (1985)...... 10
2. The surface density (E) vs Temperature (T) relationship from Smak (1984a)...... 13
3. IDS light curve for the 1985 December RX And outburst...... 26
4. The AAVSO light curve for RX And during the 1985 December outburst. The horizontal lines along the bottom of the plot indicate the times of the IDS spectroscopic observations...... 27
5. Equivalent width of H-beta emission versus UT for RX And on 1985 December 15 (left), and 1985 December 16 (right)...... 28
6. Gray-scale image of RX And on 1985 December 15 (top) and 1985 December 16 (bottom) scaled to show the extreme emission line wings. Orbital phase runs down the image. Note the narrowing of the H-beta line from phase 0.6 to phase 0.84. He II 4686 may also have narrowed...... 30
7. Gray-scale images of RX And for 1985 December 18 (top) and 1985 December 19 (bottom). Note the apparent splitting of the H-beta emission line between the phase 0.7 and 0.2. On the 19th the H-beta emission line seems to have a two-component structure...... 31
8. Approximate B mag vs UT for RX And on 1987 October 16 (left) and 1987 October 18 (right)...... 32
viii FIGURE PAGE
9. Line flux of the H-beta emission line vs UT for RX And on 1987 October 16 (left) and 1987 October 18 (right)...... 33
10. Mean spectra of RX And on 1987 October 16 and 18...... 34
11. FWHM of the H-beta emission vs UT for RX And on 1987 October 16 (right) and 1987 October 18 (left)...... 35
12. Mean spectra of SS Cyg on 1987 June 18-19...... 37
13. Mean spectra of SS Cyg on 1987 June 20-22...... 38
14. Line flux (top) and FWHM (bottom) of H-beta emission of SS Cyg. Data set 1 is the averaged data from 1985 August and September. Data set 2 is the averaged data for 1987 June 18, and data set 3 is the averaged data for 1987 June 19...... 39
15. IDS light curve of KT Per on 1988 September 15-23...... 41
16. Mean spectra of KT Per on 1988 September 15-17. The spectrum for the 16th is represented by a dotted line to distinguish it from the 15th...... 42
17. FWHM (top) and line flux (bottom) of H-beta emission for KT Per during preoutburst...... 43
18. Mean spectra of KT Per on 1988 September 19-20, and 1988 September 22-23. The spectrum for the 23rd is represented by a dotted line to distinguish it from the 22nd...... 44
19. IDS light curve of AH Her for 1988 September 17-23...... 46
20. Mean spectra of AH Her on 1988 September 17 and 1988 September 19-21. The spectra for the 20th and 21st are represented by dotted lines...... 47
21. FWHM (top) and line flux (bottom) of He I 4471 emission for AH Her during preoutburst...... 48
22. Mean Spectrum of AH Her on 1988 September 22. . . . 49
ix FIGURE PAGE
23. IDS light curve of AR And for 1988 September 16-22 51
24. Mean spectra of AR And on 1988 September 18-22 52
25. IDS light curve of TW Vir for 1989 March 28-April 1 ...... 54
26. Mean spectra of TW Vir on 1989 March 28 (a) and 1989 March 29 (b), and 3:30 to 5:55 UT (c), 6:00 to 7:15 UT (d), 7:20 to 8:35 UT (e), and 8:40 to 10:00 UT (f), 1989 March 30...... 55
27. Mean spectra of TW Vir on 1989 March 31-April 1 ...... 56
28. FWHM (top) and line flux (bottom) of H-beta emission of TW Vir on 1989 March 28-29...... 57
29. Continuum level at 4600 A (top), Balmer line flux (middle), and Balmer FWHM (bottom) vs time for SS Cyg from Clark, Capel and Bowyer (1984)... 62
30. Slope of continuum from 4510 through 5060 A vs UT for TW Vir on 1989 March 30 (top), and continuum flux at 4750 A vs UT for TW Vir on 1989 March 30 (bottom)...... 83
31. Color index vs UT for TW Vir on 1989 March 30. . . . 84
32. Slope of the continuum from 4510 through 5060 A vs time (top), and continuum flux at 4750 A vs time (bottom) for the model which treats each disk annulus as a black body...... 88
33. Color index vs time for the model which treats each disk annuli as a black body...... 89
34. Slope of the continuum from 4537 through 5025 A vs time (top), and continuum flux at 4750 A vs time (bottom) for the model which interpolates in a table of model stellar atmosphere intensities...... 91
35. Color index vs time for the model which interpolates in a table of model stellar atmosphere intensities...... 92
x FIGURE PAGE
36. Slope of the continuum from 4510 through 5060 A vs UT for RX And on 1985 December 17 (top), and continuum flux at 4750 A vs UT for RX And on 1985 December 17 (bottom)...... 96
37. Color index vs UT for RX And on 1985 December 17...... 97
38. Slope of the continuum from 4537 through 5025 A vs time (top), and continuum flux at 4750 A vs time (bottom) for the model which interpolates in a table of model stellar atmosphere intensities...... 98
39. Color index vs time for the model which interpolates in a table of model stellar atmosphere intensities...... 99
xi CHAPTER I
INTRODUCTION
Cataclysmic variables are close interacting binary systems
consisting of a white dwarf and a companion (secondary) star. The
fact that these systems have short periods was established from radial velocity studies done by Kraft (1962, 1963, 1964). Most cataclysmic variables have periods between -25 min and 8 hr (Ritter 1987). The
companion star is usually a G, K or M main sequence star (Patterson
1984; Ritter 1982), but can also be a giant or even another white
dwarf (Wade and Ward, 1985). The secondary has a distorted tear-drop
shape due to tidal and rotational forces.
Surrounding both stars in every binary system is a figure-eight shaped inner critical surface along which the total potential of the combined centrifugal force due to the rotation of the system, and gravitational force from the two stars, remains constant. The portion of this surface which surrounds each individual star is referred to as that star's Roche lobe. The point where the two Roche lobes meet is called the inner Lagrangian point (L-^) . At this point the net force for a test particle at rest in the system frame is zero. Anything sitting at that point will stay there as long as no other force acts upon it. The least perturbation in the direction of either star, however, will cause that material to fall towards that star. The
1 secondary in a cataclysmic variable (CV) has filled its Roche lobe and
is, therefore, losing mass to the white dwarf through (Smak 1971a;
Warner and Nather 1971). Due to the high angular momentum of the gas
stream passing through and the small size of the white dwarf, the
gas does not fall directly onto the white dwarf. The stream is narrow
enough that it will closely follow the trajectory of a singe particle
(Lubow and Shu 1975). The Coriolis force will cause the material to
flow at an angle to the line between the stars of the binary system
instead of falling straight towards the white dwarf. When the mass
transfer first begins to take place between the two stars, a disk will
form in some of these system in the following manner. If the white
dwarf does not have a strong magnetic field the flow of the stream
will be uninterrupted, allowing the stream to miss the white dwarf and
flow around it forming a ring. This ring forms a circular shape,
since a circular orbit has the least energy for a given angular
momentum. Viscous forces will cause some of the material in the ring
to lose energy and, therefore, fall deeper into the potential well,
i.e. move closer to the white dwarf. For angular momentum to be
conserved some of the material in the ring will be forced to move outward. This model for accretion disk formation has been presented by Pringle (1985). The spreading of the ring will continue until tidal and gravitational forces won't permit the material to move any farther outward. As the disk material comes close to filling the
Roche lobe of the white dwarf, it will try to take on a distorted tear-drop shape just as a star would. This will cause tidal torques to act on the outer particles, transferring their angular momentum to 3
the secondary star. Hence, the outward spreading is stopped. In this
way an accretion disk is formed which will nearly fill the Roche lobe
of the white dwarf.
The point on the disk where the stream impacts is referred to as
the hot spot, or bright spot (Smak 1984a; Wade and Ward 1985). Some
of the kinetic energy of the stream is dissipated at this point,
causing the hot spot to be luminous (Smak 1984a). There are,
therefore, five possible emitting regions in these systems: the white
dwarf, the cool companion, the disk, the hot spot, and the stream. In
systems where there is a strong magnetic field the gas is funneled
along field lines onto the magnetic poles forming an accretion column
(Wade and Ward 1985).
In the disk forming systems, it is believed that most of the
energy emitted arises from the disk. This is determined by analyzing
the light curves of eclipsing systems (Smak 1971a; Warner and Nather
1971, 1972; Nather and Robinson 1974; Warner 1974). The radiation
produced by the disk is due to viscous heating (Pringle 1985). The nature of the viscosity is not well understood. It is, however, the mechanism by which angular momentum is transported outward, allowing material to be transported inward and hence accreted onto the white dwarf, liberating its gravitational potential energy in the form of light (Pringle 1985). The coefficient of kinematic viscosity (i/) is the ratio of the shearing stress to the velocity gradient (Symon
1971). If the source of viscosity is turbulence, v can be written as
1. v ~ Aturbvturb where Atur^ is the size of a turbulent cell and vturb t^ie cell#s velocity. The cell has to be smaller than the thickness of the disk.
Also, it is usually assumed that the velocities of the cells are subsonic. The viscosity can now be written as
2 . v — acsH
where cg is the sound speed in the disk and H is the height of the disk, a must be less than 1 by the above arguments. This parametrization of the viscosity was first presented by Shakura and
Sunyaev (1973). Making this assumption results in the uncertainty of v merely being transferred to the uncertainty of at.
The disk has a wide range of temperatures, the coolest being at its outer edge, and the hottest being at the boundary layer with the white dwarf. From accretion disk theory and Stefan's law, Wade and
Ward (1985) estimate that these temperatures range from 2000K-50000K.
From these temperature estimates, the disk should radiate from the soft X-ray region to the near infrared, 50A-10000A. Emission lines are often observed in these systems. The lines present in the visible are hydrogen, neutral helium (He I), once-ionized helium (He II), and once-ionized calcium (Ca II). Once-ionized iron (Fe II) is also sometimes seen (Wade and Ward 1985). Since the dominant energy source is the disk, it is thought that these emission lines arise from the disk. Also, in.eclipsing systems it has been observed that the emission lines tend to weaken or disappear completely while the disk is being eclipsed (Warner & Nather 1972; Greenstein and Kraft 1959; Schlegel, Kaitchuck, and Honeycutt 1984). The strengths of the lines
imply that only a fraction of the disk is involved in producing the line emission. According to Wade and Ward (1985), the strengths of the emission lines for a typical dwarf nova, a subclass of CVs, 19 indicate a line-emitting region with a mass of « 10 g, while a 23 typical quiescent disk mass is « 10 g. It is often assumed that the line-emitting region is in the outer cooler part of the disk, which is optically thin to the continuum (Williams 1980; Tylenda, 1981).
The emission lines have broad wings, and this broadening increases with the inclination of the system. Also, AA/A is constant for a given atomic species. AA is the line width. Both of these things are what would be expected if the lines were broadened by
Doppler shifting. In addition to this, the lines are sometimes double peaked (Honeycutt, Kaitchuck, and Schlegel 1987). Therefore, it is usually assumed that the lines are rotationally broadened and that the disk is undergoing Keplerian rotation (Smak 1984a), i.e. v a r'^/2 .
The total contribution to the line at each radial velocity within the disk will depend on the area of the disk which has that radial velocity. Within a Keplerian disk, the two surfaces of constant radial velocity which have the largest areas are the ones which touch the two ansae of the disk (Smak 1981). Therefore, the radial velocities measured from the peaks of the lines are those of these two points on the disk. The wings of the lines arise from the innermost parts of the line-emitting regions where the orbital velocities are highest. If one assumes the disk is axially symmetric, then the radial velocity measured from the disk lines will be that of the white dwarf. This is because the rotational effects of each side of the
disk will balance each other. Thus the radial velocity measured from
the line center will reflect only the orbital velocity of the disk as
a whole. Therefore, if one were to determine how the radial velocity
from the disk line changed throughout one orbit, one would obtain a
radial velocity curve for the white dwarf.
When spectra have been plotted against phase, as in a gray-scale
image (see Fig. 6 and 7), an s-shaped emission line superimposed on
the broad emission line from the disk has been observed in some
systems (Honeycutt, Kaitchuck, and Schlegel 1987). Throughout one
orbital period, the s-wave moves from the red peak to the blue peak,
then back to the red peak. This emission has been attributed to the
hot spot and is referred to as the s-wave. The effect occurs because
the hot spot is concentrated on a small portion of the disk which will
exhibit only a limited range of radial velocities at any one time.
Therefore, the radial velocities seen in the hot spot will reflect the vector sum of the velocity of the disk at the hot spot and the orbital velocity of the system. That is why the amplitude for this line will be different from that of the line which arises from the entire disk which reflects only the orbital motion of the white dwarf.
The disks in these systems are usually assumed to be thin in the
direction perpendicular to the orbital plane (the z direction) and
axially symmetric. These assumptions make the structure of the disk a
one dimensional problem. It is also assumed that there is no self gravity in the disk. That is, the dominant gravitational body is the white dwarf. As in stars, the gravitational force exerted on the disk must be balanced by the gas pressure in the disk. It can be shown
that in order for hydrostatic equilibrium to be maintained in the z
direction, the disk must be flared. That is, the scale height of the
disk will increase with increasing radius. From the above
assumptions, including that of a Keplerian disk, and the given
parametrization of the viscosity, the structure of the disk can be
represented by 8 equations with 8 unknowns:
3. p — S/H (definition of surface density)
4. H — cs(R/GM)^/2R (pressure scale height) 2 5. cg — P/p (sound speed)
6. P — pkTc//xmjj + 4ctTc 4/3c (equation of state)
7. 4aTc4/3r - (3GMm/8jrR3) (1 - (R^/R)1/2) (thermal equilibrium)
8. t - SK (definition of optical depth)
9. i/S- (m/3jr) (1 - (R^/R)1/2) (mass conservation)
10. i/ — otCgH (parametrization of viscosity)
R* is the radius of the white dwarf, and K is the Rosseland mean opacity. The unknowns are density (p), surface density (S), disk height (H), sound speed (cg), gas pressure (P), temperature at z — 0
(Tc), opacity (r), and viscosity (i/). These equations are a function of the mass of the white dwarf (M), the mass transfer rate (m), the radius within the disk (R), and a. These structure equations will hold only for a stable disk. Equation 9 is derived from the differential equation for the conservation of mass using the boundary layer of the disk to obtain a boundary condition in the following way. The material in the disk is rotating at Keplerian velocity.
Therefore, the velocities within the disk will increase with decreasing R. However, the white dwarf cannot be rotating at
Keplerian velocity or it would break up. Therefore, the material actually being accreted onto the white dwarf must be rotating at less than the Keplerian velocity. There must be a circle in the disk, close to the white dwarf, at which the velocities within the disk turn over and start to decrease with decreasing R. The region of the disk interior to this circle is called the boundary layer. It can be shown that the rest of the disk will radiate only half of the energy which is expected from the gravitational binding energy of the material being accreted unto the white dwarf. The other half of the energy is supplied by the boundary layer. For a full discussion of accretion disks see Pringle (1981), Verbunt (1982), or Frank, King, and Raine
(1985).
There are seven types of CVs: nova, recurrent nova, dwarf nova, nova-like, polars, intermediate polars, and anti-dwarf nova. Only three of these undergo outbursts. The eruptions of novae and recurrent novae are due to the ignition of hydrogen gas which has built up on the surface of the white dwarf (MacDonald, Fujimoto, and
Truran 1985; Prialnik 1986). This is a nuclear reaction which results in the ejection of some of the material that has accreted onto the white dwarf. Unlike novae, the outbursts in dwarf novae take place in the disk rather than on the surface of the white dwarf. This has been established by observing eclipsing dwarf novae during outburst
(Warner, 1974). During outburst, the primary eclipse still occurs when the disk and white dwarf are being eclipsed, so that the outburst
cannot be taking place on the secondary. The duration of the primary
eclipse is the same as during quiescence. If the outburst were taking
place on just the white dwarf, then the time in which the maximum
amount of light is obscured would be much shorter than the time it
takes for the disk to be eclipsed.
Dwarf nova outbursts are quasi-periodic, with amplitudes of 2-5
mag in the visual. These outbursts recur on time scales of a few days
to a few months and last for a few days to a few weeks (Wade and Ward
1985). Figure 1 shows the light curve for a "typical" dwarf nova, SS
Cyg. The data were provided by the American Association of Variable
Star Observers (AAVSO). All AAVSO data for this study were provided
by J. Mattei (1986, 1988a, 1988b, 1989 personal communication). It
has been noted that in most dwarf novae there is a correlation between
the time between outbursts and the outburst amplitude. The longer a
system goes without having an outburst, the brighter the outburst will
be. Also, systems with longer orbital periods decline from maximum
brightness at a slower rate than those with shorter orbital periods.
Both of these correlations are presented by Smak (1984a). During the
outburst, the Balmer emission lines typically disappear and are
replaced by broad absorption lines. As the outburst progresses,
emission lines tend to appear in the bottom of the absorption troughs.
These lines become stronger throughout the decline while the
absorption lines weaken (Wade and Ward 1985).
Dwarf novae fall into three subclasses. The first are U Gem
systems which go through the relatively simple cycle of quiescence Apparent Visual Mag O 00 Figure 1. Light curve of the dwarf nova SS Cyg based onCyg visualSS Lightcurveof based AAVSO thedwarf nova 1.Figure 650 observations. For the complete AAVSO light curve from 1896-1985from lightcurve Forcomplete the AAVSO observations. e atie l (1985).seeetal. Mattei • • 99 99 C» •• • • 700 •• m uin ae 2300 ) + (2439000 DateJulian 5 0 850 800 750 • • 9m 99 • m 900
O 11 then outburst. SS Cyg is an example of this subclass. The second are
Z Cam systems which, in addition to exhibiting quiescent and outburst states, experience standstills. During a standstill the brightness of the system remains approximately half way between those of outburst and quiescence for periods of weeks to months. These standstills begin during the decline from maximum. They do not, however, occur during every outburst. Finally there are SU Ursae Majoris dwarf novae which undergo superoutbursts as well as regular outbursts. These superoutbursts are less frequent and longer lasting than normal outbursts.
There are currently two theories as to the cause of dwarf nova outbursts. One is that there is a sudden increase in the rate of mass transfer from the secondary due to dynamical instabilities. These are triggered by ionization zones which develop in the atmosphere of the secondary due to heating from the disk (Bath 1973, 1975; Bath et al.
1974; Bath and van Paradijs 1983; Papaloizou and Bath 1975). These regions would occur on the face of the star near L^.
The second theory is that an instability builds up in the disk itself (Osaki 1974; Meyer and Meyer-Hofmeister 1982; Faulkner, Lin, and Papaloizou 1983; Cannizzo and Wheeler 1984). Osaki first presented this possibility because there is a discrepancy in the observed ratio of the hot spot luminosity to the disk luminosity during quiescence. The theoretical hot spot and disk luminosities are
11. Lg * (1/Rs)m 12
12. Ld » (1/R*)ih
where Rg is the distance between the hot spot and the center of the white dwarf. Given typical values for Rg and R*, Lg/Ld should be
-1/100. The observed Lg/Ld ratio is ~1 (Smak 1971b). Osaki suggested that the disk in quiescence is too faint because material that impacts the disk at the hot spot remains stored in the outer part of the disk.
At some critical density an instability causes much of the material to be suddenly accreted onto the white dwarf producing the dwarf nova outburst.
To understand how the disk instability could take place, one needs to examine how the surface density of the disk behaves with changing effective temperature. It has been shown that regardless of the value picked for o and the position within the disk, the surface density - temperature (T) relationship will have approximately the same shape (Smak 1984a). Figure 2 shows the "standard" S - T relationship from Smak (1984a). As can be seen, in general as E increases, T increases. This is because as S increases there are more interactions between particles which increases the viscosity.
Therefore, the temperature will rise (Cannizzo and Kaitchuck 1950).
This can be represented mathematically by combining the thermal equilibrium (7) and mass conservation (9) equations to get
13. 4ctTc 4 / 3 t = (9GM/8R3)j/S.
Since M is constant for a given system, for a given R this becomes 13
HEATING
CLING '
lo q X
Figure 2. The surface density (s) vs Temperature (T) relationship from Smak (1984a).
( 14
14. Tc^ oc i/Et .
As long as the opacity is not a strong function of temperature, Tc and
S will be directly correlated. Indeed, Faulkner, Lin, and Papaloizou
(1983) have shown that for large Tc and a small optical depth at z - 0
(rc), and for small Tc and rc -*■ 1, Tc a E3/2 and Tc a S^/3
respectively. The AB and CD branches correspond to these conditions.
These regions in which the slope is positive are in thermal equilibrium. If either region were cooled for some reason the viscosity will become less efficient. Thus, material would not be transported out of the region as quickly and E would increase. This in turn would increase the viscosity which would raise the temperature, returning the region to its original state. By similar arguments, if the region were heated it would also return to its original state. At temperatures in which there is partial hydrogen ionization, however, S will decrease with increasing T. This is because the increasing ionization of hydrogen increases the opacity and the opacity becomes very temperature dependent, K « T in zones of partially ionized hydrogen. From this and the definition of optical depth (eq. 8)-, the above relation between temperature and S becomes
15. Tc6 a 1/(j/S2) .
So now E will decrease with increasing temperature. Another result of the ionization of hydrogen is the onset of convection. Faulkner, Lin, 15
and Fapaloizou (1983) showed that for TQ = 6000K and high rc , T «
s -9/14 Hoshi (1979) rigorously showed that the bend in the curve is
due to the partial ionization of hydrogen. This region in which the
slope is negative is thermally unstable. If the region is cooled
slightly, the opacity will drop tremendously. This will allow more
heat to escape, causing the temperature to drop even more, which will
lower the opacity further, and so forth. The opposite will occur if
the region is heated. Once the hydrogen is fully ionized, the opacity
will follow Kramer's rule
16. K a pT"3 '5.
Convection will stop and £ will begin to increase with increasing
temperature again.
Smak (1984b) explains why the different regions on the T - £
curve are or are not in thermal equilibrium in the following way.
Models to the left of the T - £ relation are in a state of cooling and
contraction, while those to the right are in a state of heating and
expansion. If a region of the disk is forced to heat up from the CD or AB branch, it will simply cool until it falls back down on the branch where it came from. However, if a region of the disk is forced to heat up from the BC branch, it will be forced to continue heating until it reaches the AB branch. The converse is true if the region is t forced to cool down.
Consider a localized annulus in the outer part of the disk.
Suppose that the local mass transfer into this annulus causes the 16
temperature to be below B but above G on the figure. The region will
be unstable and the least perturbation will cause it to drop down to
the CD branch or go up to the AB branch to find a state of thermal
equilibrium. For the sake of argument, let us say it fell to the CD
branch. This will cause the incoming mass transfer rate to be higher
than the local outgoing mass transfer rate. Thus, the local surface
density will increase, causing the region to move up the CD branch.
Once it reaches C it will be forced to move up to the AB branch to
remain in thermal equilibrium. This will create a situation in which
the incoming mass transfer rate is smaller than the local outgoing mass transfer rate. Therefore, the surface density will decrease and the region will move down the AB branch. Once it reaches B it will be forced to drop to the CD branch and the cycle will continue. If this local instability causes a heating wave to propagate throughout the disk, the disk will go through a cycle of quiescence then outburst, with the disk being in quiescence while it's on the CD branch, and in outburst while it's on the AB branch. The energy in this wave comes from the release of the material which is stored outside the instability zone.
There are many predictions which the disk instability model makes that can be checked observationaly. One is that it predicts two types of outbursts, called type A and type B outbursts. The type A outburst begins in the outer part of the disk and moves inward. A type B outburst occurs when the instability takes place in the inner parts of the disk and then moves both inward and outward. In the case of the type A outburst, the increased viscosity will transport a large amount 17
of the material in the outer disk inward. Since the surface density-
wili be dropping in the outer disk, this region will not be
excessively heated. In the inner parts of the disk, however, the
surface density will be rising, increasing the temperature. Also, the
inner region corresponds to the AB branch in Figure 2. Therefore, the
corresponding T for a given S will be much higher than on the CD
branch, i.e. in the outer part of the disk. The inner part of the
disk is therefore much hotter than the outer part. During a type A
outburst it would be expected that the rise in continuum brightness
would first be seen in the longer wavelengths produced by the outer
disk, and then later seen in the shorter wavelengths produced by the hotter inner disk. For type B outbursts, all wavelengths should be
affected at about the same time. Outbursts have been observed which
fit both of these descriptions (Smak 1984a).
The disk instability model also predicts that dwarf nova outbursts will take place only in systems where the mass transfer is below a certain rate. This is because the temperature at the outer edge of the disk must be below the ionization temperature of hydrogen in order for the instability to exist within the disk. If the outer edge of the disk is above the critical temperature, then the entire disk will be in thermal equilibrium and there will be no instability.
The mass transfer rate for dwarf novae has been observed to be below this rate (Smak 1983; Warner 1987). The disk instability theory also predicts how the radius of the disk will change during an outburst.
During a type A outburst there is an increase in the flow of material inward. Thus, for angular momentum to be conserved the material 18
remaining in the outer disk must move outward, hence the disk will
expand. This will happen in a type B outburst only if the heating
wave reaches the disk's outer edge. The accretion disk of U Gem has
been observed to expand during outburst (Smak 1971a; Warner and Nather
1971). The modulated mass transfer theory on the other hand requires
the disk to shrink. This is because the gas in the stream has less
angular momentum than the gas at the outer edge of the disk (which
receives the angular momentum transported outward from the material
that is being accreted in the inner part of the disk). Thus, the
increased mass flow in the low angular momentum stream will cause the
material in the disk to move inward for angular momentum to be
conserved. A major problem with the disk instability theory is that
it does not explain the observed large lag between the rise of the
optical flux and the rise of the ultraviolet flux (Hassall et al.
1983; Schwarzenberg-Czerny et al. 1985; Verbunt et al. 1987; Polidan
and Holberg 1984; Cannizzo et al. 1986). The observed lag exceeds
that predicted by the type A outburst. By the standard disk
instability theory, once the instability has set in, the resulting
heating wave should almost instantly raise the temperatures in the
regions of the disk it has passed through to &10,000K. Hassall (1984)
concluded that during the early part of the outburst in VW Hyi, the predominant luminosity comes from a large region with a temperature of
-6000K.
To understand how outbursts occur it is useful to study the early stages of the outburst. The changes that take place in the continuum and the emission lines can help in determining which parts of the disk 19
are being affected just before the outburst. Also, the rate of change
in the continuum level indicates the progression of the outburst
through the disk. The objective of this study is to observe as many
dwarf novae both just prior to and during the outburst as possible.
To do this, two large blocks of telescope time were reserved. During
these times dwarf novae which were currently in a quiescent state but were "due" to go into outburst were monitored in an effort to observe any subtle changes that may take place in these systems before the rapid rise of outburst. The success rate of the project was quite high. In seven cases, dwarf novae were observed during the time period desired. In the case of TW Vir the system was caught during the actual transition from quiescence to outburst. There has been only one other instance of a dwarf nova being followed from quiescence into outburst (Clarke, Cabel, and Bowyer 1984). At no other time has the early outburst behavior displayed by TW Vir been seen.
There have been other studies in which dwarf novae have been observed during more than one stage of their outburst cycle. However, these observations are seldom taken continuously over the outburst cycle to allow transitions between the stages to be observed. RX And and KT Per have both been studied during quiescence and outburst by
Clarke and Bowyer (1984). SS Cyg has also been observed during these two stages by Hessman et al. (1984). Schoembs and Vogt (1981) took data of WX Hyi during quiescence, the rise to maximum, and the decline to minimum. In the same study they also observed VW Hyi during maximum and the decline. All of the above observations will be discussed further in Chapter III. CHAPTER II
OBSERVATIONS
All of the observations were made with the 1.8 meter Perkins
telescope of the Ohio State and the Ohio Wesleyan Universities located
at Lowell Observatory in Flagstaff, Arizona. The data were gathered with The Ohio State University image dissector scanner (IDS)
spectrograph. The IDS is used to make spectroscopic observations of
faint objects. The instrument is controlled by a CAMAC interfaced to
a PDP 11/34 computer. Since the IDS is a dual-beam instrument, the
object plus sky and sky alone can be observed at the same time. This makes for more efficient use of observing time as well as allowing the
sky spectrum to be subtracted accurately. Initially, the light
gathered from the telescope is passed through a spectrograph of a
Cassegrain design. The Schmidt-Cassegrain Camera of the IDS then collects the diffracted light. The resulting spectra are directed onto the photocathode of a three-stage image tube. Dark current in this assembly is reduced by circulating cooled methanol around the first photocathode. The image tubes produce an amplified image on the output phosphor of the last tube. Due to the decay time of phosphor, the images will be stored for a few milliseconds. An image dissector will convert the photons emitted by the phosphor to electrons. It will then scan the spectrum on the phosphor every 4.3 ms by imaging
20 21
sections of it onto the dissector aperture with focus and scan coils.
The photoelectrons from the cathode of the dissector are collected by this aperture and amplified to a 5-volt level. The decay time of the phosphor is long enough that no detected photon will go uncounted. A detected photon can, however, be counted more than once. Finally, the scanning results are transmitted to counting circuits. The output is digital and the detector has a linear response. See Byard et al.
(1981) for a complete description of the IDS.
A spectral resolution of 2.7 A was obtained, and an aperture size of 7" was used. The observations were made in the bandpass of -4250A-
5050A. For each night of observations at least one standard star was observed so that, when sky conditions permitted, the data could be flux calibrated. Most of the observations were made from 1988
September 14-23 (UT), and from 1989 March 22 through April 1 (UT).
During both runs, objects were monitored which were "expected" to go into outburst. This was determined with the help of the visual observers of the AAVSO, especially Gerald Dyck. There are also two previous observations of RX And and one of SS Cyg used in this study, where the early outburst happened to be caught. These observations were made in 1985 December by Kaitchuck and Hantzios, 1987 October by
Kaitchuck, and 1987 June by Kaitchuck respectively. This makes a total of seven cases in which the desired part of the outburst cycle was successfully observed. These were seen in RX And (twice), SS Cyg,
KT Per, AH Her, AR And, and TW Vir. In the case of TW Vir, the system was actually caught in the transition between the early outburst stage and the rapid outburst stage. Table 1 gives physical data for each 22
Table 1
Physical Data for Program Stars
■s— Obj ect Orb. Per. Outburst Per. i ml/m2 ml (davs) (davs)
RX And 0.2098930b 14° 51 + 9d 2.4 ± .7d 1.14 ± .33d
SS Cyg 0.275130e 50° 37 + 5e 1.72 ± .05e 1.20 ± .10e
KT Per - 17° - - -
AH Her 0.258116® 19c 46 + 3® 1.25 ± .08® 0.95 ± .10®
AR And - 25c - - -
TW Vir 0.18267d 26f 43 + 13d 2.30 ± 0.6d 0.91 ± . 25d
a ‘ average time between outbursts k- from Kaitchuck 1989 c * from G. Dyck 1988 personal communication d * from Shafter 1983 e * from Hessman et al. 1984
from G. Dyck 1989 personal communication
® ‘ from Horne, Wade, and Szkody 1986 23
Table 2
Observational Data for Program Stars
Object UT Date Obs. # spectra int. time Comments
RX And 12-15-85 44 200 s Thin clouds t t 12-16-85 42 200 s Thin clouds II 12-17-85 58 200 s Photometric t t 12-18-85 76 200 s Photometric I t 12-19-85 68 200 s Photometric II 12-20-85 46 200 s Photometric SS Cyg 6-18-87 42 240 s Photometric I t 6-19-87 40 240 s Photometric II 6-20-87 38 240 s Photometric II 6-21-87 44 240 s Photometric I t 6-22-87 36 240 s Photometric RX And 10-16-87 44 200 s Photometric I t 10-18-87 68 200 s Photometric If 10-19-87 100 200 s Photometric KT Per 9-15-88 40 200 s Photometric II 9-16-88 2 200 s Photometric II 9-17-88 10 200 s Photometric II 9-19-88 26 200 s Photometric 11 9-20-88 36 200 s Photometric t t 9-22-88 20 200 s Photometric tr 9-23-88 4 200 s Photometric AH Her 9-17-88 10 200 s Photometric II 9-19-88 20 200 s Photometric II 9-20-88 20 200 s Photometric II 9-21-88 18 200 s some clouds t t 9-23-88 16 200 s Photometric AR And 9-16-88 20 300 s Photometric II 9-18-88 58 200 s Photometric II 9-19-88 34 200 s Photometric II 9-20-88 34 200 s Photometric II 9-21-88 14 200 s some clouds It 9-22-88 10 200 s Photometric TW Vir 3-28-89 36 300 s Photometric It 3-29-89 50 300 s Photometric tl 3-30-89 60 300 s Photometric t t 3-31-89 74 200 s Photometric It 4-01-89 68 200 s thin clouds 24
object observed. Table 2 gives details for each night of observation
for each of these objects.
Each night 2-4 likely objects were observed. Ideally each object
would be monitored for a full orbit if the orbital period was known.
However, this was not always possible since the objects were not
necessarily above the horizon for a full orbit after twilight's end.
Time restraints sometimes prevented full orbital coverage for an
object if all the program stars for the night were to be observed. It
is desirable to be able to detect any changes with orbital phase in
these systems, so short exposures were taken, 200-300 s. This is so
that orbital effects would not be confused with non-orbital behavior.
Therefore, several spectra were taken of each object each night, typically 10-70.
In each of the cases where sufficient observations were made of the system before the rapid rise of outburst there appears to be some sort of transformation taking place within the disk. This was indicated either by a change in the continuum, or changes within the lines, or in some cases both. From this it appears that at least in some systems there is a transition phase between quiescence and outburst. This phase will be referred to as the preoutburst stage.
The preoutburst stage begins up to four or five days before the outburst takes place and continues right up until the outburst.
During this time, there are changes taking place within the system which do not normally occur during quiescence. These changes are, however, subtle and are not the sort of dramatic transformations that one sees during outburst. It is very likely that the preoutburst 25
behavior is closely associated with the triggering mechanism for the
outburst. Each observed preoutburst is discussed in detail below.
RX And
RX And is a Z Cam type dwarf nova. The system is not eclipsing.
Its apparent average V mag is 12.6 during minimum, 10.9 during
outburst, and 11.8 during standstill. The first observation of RX And
used in this study was made from 1985 December 15-20 (Kaitchuck,
Mansperger, and Hantzios 1988). On the nights of the 15th and 16th
there were high thin clouds. Thus these nights were not strictly' > •- «•
photometric. The next four nights, however, were. The IDS and AAVSO
light curves for this time are shown in Figures 3 and 4. The times of
our observations are indicated on the AAVSO light curve. The light
curve from the IDS is obtained by summing the fluxes across the
bandpass excluding the emission and/or absorption lines and then
converting these summed fluxes to an approximate B magnitude. On
December 15th and 16th the system was in quiescence. December 17th
the system was in outburst and continuing the rise to maximum.
Maximum was reached on the 18th. This is determined from looking both
at the AAVSO light curve and at the IDS light curve. The decline had begun by the 19th, and continued through the 20th.
On the 16th the Balmer emission lines were narrower than they were on the 15th. The FWHM of the lines were determined by fitting them with Lorentzian profiles. Figure 5 shows how the lines were changing with respect with the continuum. The gray-scale images for these two nights shows the narrowing of the lines quite clearly (Fig. o
• •
ro
414 415 416417 418 419 420 Julian Date (2446000 + )
Figure 3. IDS light curve for the 1985 December RX And outburst. Julian Date (2446000 + )
The AAVSO light curve for RX And during the 1985 December outburst. The horizontal lines along the bottom of the plot indicate the times of the IDS spectroscopic observations. EW (A) Figure 5. EW of H-beta emission versus UT for RX And on 198515for December on EW of emission RX H-beta UT And versus 5.Figure X n E v U fr 0 / 5 2/1 1 H0 for UT EW vs AndRX (left), (right). 198516December and UT (hr) X n E v U fr 0 2/16 1 H0 for UT EW vs AndRX 00 to EW (A) Figure 5. Equivalent width of H-beta emission versus UT for RX And on 1985offoron emission And Equivalent RX width H-beta versus UT 5. Figure 04 CO o o o X n E v U fr j 12/15 2 1 Hj8 for UT EW vs AndRX eebr1 (left), (right). 15198516 andDecember December X n E v U fr / 12/ 6 /1 2 1 H/3 for UT EW vs AndRX oo ro 29
6). These images were made by first co-adding the data into 25
orbital phase bins, and then writing each of the co-added spectra to a
Raytheon 910 Line-Scan Recorder. This device produces 16 shades of
gray with full black representing maximum flux. The AAVSO light
curve shows that the continuum level was slightly higher on the 16th
than it was on the 15th. It is difficult to use the IDS light curve
to determine this, since these nights were not strictly photometric.
On the 17th broad absorption lines had appeared with only the
slightest trace of emission in the absorption troughs. By the 18th
the Balmer emission lines had reappeared, and were blended with the
absorption lines. From the gray-scale image, there appears to be two
components to the Hj8 emission line. On the 19th there is definitely a
double structure to the emission lines. The gray scale images for
these two nights are shown in Figure 7. One is a narrow straight
line, the other is a broader s-shaped line which has been called the
s-component, not to be confused with the s-wave. This same structure may appear on the 20th, but since there was not full orbital coverage
for that xiight, it is difficult to tell. During a 1987 January
outburst of RX And, Szkody, Piche, and Feinswog (1990) also observed
that the H/9 emission line consisted of two components.
RX And was observed a second time on the nights of 1987 October
16, 18, and 19. All the nights were photometric. On the 16th and
18th the system was in quiescence. On the 19th it was in outburst.
The spectra for the 16th and 18th were coadded into groups of 2-3 spectra to improve the signal-to-noise ratio. Throughout the 16th the continuum level is rising, while the strength of the H/? emission line N&rtlZ RESOLUTION ■** 1 VERT RESOLUTION * 0 N SPECTRA « 23 M NRAPS - 12 . PlR»T PIXEL ■ 1 SLACK LEUEL * $60 HUtTE LEVEL • 49§ ROLL OVE& PIXELS? * N ONE MAX *X ANb» lS-bE 6 -SS
m i M i
MORI2 RESOLUTION - 1 VERT RESOLUTION - 8 H SPECTRA - 2 8 N WRAPS - 12 FIRST PIXEL ■ 1 SLACK LEVEL - 360 WHITE LEVEL • 490 ROLL OVER PIXEL8? - N ONE MAX R X A ND/ 1 6 -DEC-B 3 4 3 0 0 4 4 0 0 4 9 0 0 4 4 0 0 4 7 0 0 4 « 9 0 0 - 4 7 0 0 9 0 0 0 i.i i i i i _ ~.2t 48 =-.68 68 •',',1 I - * T i - ; < • I. . , • ’ ■
t *;•*: > m w I :« Figure 6. Gray-scale image of RX And on 1985 December 15 (top) and 1985 December 16 (bottom) scaled to show the extreme emission line wings. Orbital phase runs down the image. Note the narrowing of the H-beta line from phase 0.6 to phase 0.84. RX AND# 1S-DEC-0S
R X AND# 1 9 —DEC—S 3
Figure 7. Gray-scale images of RX And for 1985,December 18 (top) and 1985 December 19 (bottom). Note the apparent splitting of the H-beta emission line between the phase 0.7 and 0.2. On the 19th the H-beta emission line seems to have a two component structure. iue8 ApoiaeBmgv TfrR n n18 coe 6 (left)1987Bfor16 and 1987 Approximate on mag vs UT October RX And 8.Figure 14.5 14 13.5 . - 5 7 6 5 4 . . . 1 • • X n Mg s T 16 /1 0 1 UT vs Mag AndRX • t • • — —r i— • - L coe 8 (right). 18October 1 1 1 1 UT (hr) • • • ilit i i | r • • • • . 1 . _ L - _ L - -j - i - i • • • - ■ • ■ . * in V T-* K) in . . “ • • X n Mg s T / 8 0/1 1 UT vs Mag AndRX • - |- _ ' • ' • • j 6 _ .. 1 __ ... 1 ______
----- • • UT (hr) . i 1 ______• • • ------• 8 L J ------• • • • • 1 -- RX And Line Flux for H/S Emission 1 0 /1 6 RX And Line Flux for H/ff Emission 10/18
CO N I E o • • CO E* cn a>
X Z3
o U— i— i— i— i- i— ■ ■ « ■ i
UT (hr) UT (hr)
Figure 9. Line flux of the H-beta emission line vs UT for RX And on'1987 October 16 (left) and 1987 October 18 (right).
U) U5 Fx (10~16 ergs s~1 cm~z A“ o o 04 O ro o 4300 Figure 10. Mean spectra of RX And on 1987 October 16 and 18.16and1987 spectra on of October Mean RX And 10.Figure 4400 4500 604700 4600 Wavelength (A) 804900 4800 10/18/87 10/16/87 5000 CO FWHM (A) Figure 11. FWHM FWHM 16oftheemissionfor1987 H-beta onOctober vs UT RX And 11.Figure • * X n FH fr 0 msin 16 /1 0 1 Emission H0 FWHM And for RX 5 7 6 5 4 1 1 1 J 1 1 1 1 1 1 1 1 1 J 1 1 1 1 1 1 1 • • • • • • • • • (right) (left).1987 and18 October T h) UT (hr) UT (hr) • • • • • ” • 4 0 | - • * m S' o £ 2 X u 20 • - ■ • X n FH fr / Eiso 10/ 8 /1 0 1 H/3 Emission FWHM And for RX w A •• • • --- • •. • • . ••• 8 6 1 . 1 . 1 ------• • • a w • • 1 • ------• • 1 ------• • 1 • — - • • ui is decreasing (Fig. 8 and 9). On the 18th the average continuum level is higher than it was at the end of the night on the 16th, and the average Balmer emission line strength is less than that on the 16th. The averaged spectrum for each of these nights are shown in Figure 10. From this figure, it can also be seen that some of the He I lines have disappeared by the 18th. While the Balmer emission lines weakened between these two nights, the FWHM of the lines remains constant (Fig. 11). The line widths and strengths were determined by fitting the lines with a Lorentzian profile. The behavior of the lines is the reverse of that in the 1985 December outburst of RX And, in which the Balmer emission lines narrowed. Hence, it seems that even in the same system, outbursts differ from one another. On the 19th absorption lines were present, with weak emission appearing in the absorption troughs. SS_ Cyg SS Cyg is a U Gem dwarf nova. During quiescence it has an approximate V mag ranging from 12.1-11.4. Its average outburst mag is ~8.2. SS Cyg was observed on 1987 June 18-22. Sky conditions were photometric for each night. The first two nights the system was in quiescence. The averaged spectrum for each of these two nights is shown in Figure 12. These are shown along with the averaged spectrum for data taken for SS Cyg during 1985 August and September when it was in quiescence. On the 20th it was in outburst. The system remained in outburst for the duration of the observing run. The averaged spectra for the June 20-22 are shown in Figure 13. This figure shows F x (10~16 ergs s“r c m ' 2 k~1) O 200 400 Figure 12. Mean spectra1987 Cyg onof SS18-19. Mean June 12.Figure 45004300 4400 4600 Wavelength (A) 4700 8050004900 4800 8/85&9/85 6/19/87 6/18/87 OJ 00 5000 6/21/87 4900 4800 4700 Wavelength (A) Wavelength 4500 4600 4400 Figure 13. Figure 13. June Mean 20-22. of SS Cyg on 1987 spectra 4300 0002 0002 0001 o 0-Y gjwo f_s s6xa n J Qi) Xj 0 1 | 1 1 1 39 ft • 7 • • E o • . 09 • E • © - - X ■ ■ 3 • ft E • • « c a * * 0 1 2 3 4 Data Set o< w O Data Set Figure 14. Line flux (top) and FWHM (bottom), of H-beta emission of SS Cyg. Data set 1 is the averaged data from 1985 August and September. Data set 2 is the averaged data for 1987 June 18, and data set 3 is the averaged data for 1987 June 19. 40 that He II A4686 is present in emission with absorption wings. On the 22nd there was a flat field spike at ~4686 A.. This feature was smoothed out, but it is not known how much the strength and shape of the He II A4686 emission line was affected by it. During the first couple of nights, it appears that the continuum level was higher than it had been during other observations taken during quiescence. This is evidence that on these nights the system was in preoutburst rather than quiescence. Also, the continuum level rose between the 18th and the 19th as it has been observed to do in other systems during preoutburst. Furthermore, absorption was present on both of these nights, an unusual occurrence for a dwarf nova during quiescence. The H/3 emission lines were double peaked. The spectra for each of these nights were coadded into 25 phase bins. The double peaks were present in each phase bin for each night. Thus, this feature is probably real. Again, the data from 1985 August and September don't show this. Gaussian fits were made to the H)9 emission line for the combined 1985 data. Double Gaussian fits were made to the H/3 emission and absorption lines for the 18th and 19th. The strength and width of the emission line on June 18 and 19 appear to be comparable to that during quiescence (Fig. 14), but it is difficult to tell how much the fits to these lines are being affected by the underlying absorption (Kaitchuck, Mansperger, and Hantzios 1988). KT Per KT Per was observed on nine nights during the 1988 September observing run. All nights were photometric. From September 15-17 the o> 418 420 422 424 426 428 430 Julian Date (2447000 + ) Figure 15. IDS light curve of KT Per on 1988 September 15-23. * * I 1 I • ■ i * | ■ i "i T" j" I *11 i r 1 |” i '" i ■ i “ i | i '■ i 11 i p i i 1 i i j i i ■ i O in 9/17/88 * '■ 9/15/88 9/16/88 ' O 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 16. Mean spectra of KT Per on 1988 September 15-17. The spectrum for the 16th is represented by a dotted line to distinguish it from the 15th. ■p* N5 Figure 17. FWHM (top) and line flux (bottom) of H-beta of (bottom) flux line (top) and FWHM 17. Figure line Flux (10“14 ergs cm”2 s”1) FWHM (A) N n i 4 5 6 7 18 17 16 15 14 14 • -■ ■ • emission for KT Per during preoutburst. during Per KT for emission ♦ ih (UTdate) Night ih (UT dote) Night 1 * • 1 • * ♦ - • in 9/18/88 *» I co CO 9/20/88 I o >• 9/22/88 ISZ'^VVwwULaV,>!> * 9/23/88 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 18. Mean spectra of KT Per on 1988 September 19-20, and 1988 September 22-23. The spectrum for the 23rd is represented by a dotted line to distinguish it from the 22nd. 45 system was in quiescence. On the 19th it was in outburst. The decline of the outburst began by the 20th, indicating this outburst was weaker and shorter than normal. The IDS light curve for this outburst is shown in Figure 15. On the 17th the continuum level was higher than it was on the 15th and 16th (Fig. 16). The FWHM for the H/3 emission line on the 17th is smaller than on the 15th. However, the line flux decreases then increases again. It is even stronger on the 17th than it was on the 15th (Fig. 17). The line strengths and widths were measured by fitting the lines with Gaussian profiles. Unlike many of the other outbursts, the Balmer emission lines were still quite strong on the 19th. They dominated over the absorption lines. The averaged spectra for the nights of the 19th, 20th, 22nd, and 23rd are shown in Figure 18. AH Her AH Her is a Z Cam dwarf nova. The system has an apparent V mag of 13.9-14.7 while in quiescence, -11.3 while in outburst, and 12 while in standstill. AH Her was also observed during the 1988 September observing run. The first four nights the system was in quiescence. On the fifth night it was in outburst. The IDS light curve is shown in Figure 19. In the nights before the outburst, the continuum level rose and then dropped again. Averaged spectra for these nights are shown in Figure 20. The apparent mag of AH Her has been observed to vary with orbital period (Moffat and Shara 1984). Each night the system was observed there ttas very little orbital coverage. Also, a different part of the orbit was covered each night. N • • • • • • • t m 420 422 I 424 426 428 430 Julian Date (2447000 + ) Figure 19. IDS light curve of AH Her for 1988 September 17-23 ■p- ON i ~ ' |— i— i— i— i— |— i ■ i i r | i t -i r | i i i i | i— i i i | i i i i | i i i i | i i i 9/19/88 9/20/88 9/17/88 9/21/88 o — 1 —1* 1 1 1 * -1- 1 1 1 1 - * * * 1 1 ‘ 1 * 1 • ■ * 1 1 ■ 1 1 ' 1 ‘ ‘ 1 ‘ * ■ * ■ 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 20. Mean spectra of AH Her on 1988 September 17 and 1988 September 19-21. The spectra for the 20th and 21st are represented by dotted lines. Figure 21. FWHM (top) and line flux (bottom) of He I 4471 I (bottom) ofHe flux (top)line and FWHM 21. Figure line Flux (10“15 ergs cm“2 s"1) FWHM (A) O O CM o emission for AH Her during preoutburst. during for Her AH emission 18 ih (UTdate) Night 1816 ih (UTdate) Night 20 20 22 F x (10~1S ergs s'"1 c m ~ s a "1) 90 100 110 120 304700 4300 Figure 22. Mean Spectrum 22. Mean of1988September on AH Her Figure22. 4400 4500 4600 Wavelength (A) 4800 905000 4900 ■o VO 50 Therefore, it is hard to tell whether or not the changes in brightness observed during this run are due to orbital effects, or if they are changes with time, or both. Also, the 21st was not strictly photometric, so it is not known how much of an effect this had on the continuum level. There were no significant changes in the Hj8 emission line, either in the width or the strength. The He I A4471 emission line, however, does seem to be affected. The line shows very similar behavior to that of H/9 emission line in KT Per during the preoutburst stage. The strength of the line drops between the 17th and 19th, then increases on the 20th, and 21st (Fig. 21). This is inversely correlated with the strength of the continuum level during this time. The width of the He I A4471 emission line drops slightly throughout the preoutburst stage. The lines were fitted with both Lorentzian and Gaussian functions. Each method showed the same behavior. Also, as in KT Per, the Balmer emission lines were still quite strong during the first observed night of outburst, the 23rd, (Fig. 22) although they do not dominate over the absorption lines. AR And AR And was observed during the 1988 September observing run. On the 16th the system was observed to be in quiescence. By the 18th it had gone into outburst. Throughout the night of the 18th the continuum level was rising. Maximum was reached on the 19th. The system was three times brighter than it had been the night before. The decline began on the 20th and continued through the 22nd. The IDS CO •• 420 422 424 426 428 430 Julian Date (2447000 + ) Figure 23. IDS light curve of AR And for 1988 September 16-22. i i ( i i i i I i i i i" p i i i ~i i*" i i i i * i " i ~| i' i' i "» ~'i ~i " i * |*~ r* v *i' 9/19/88 9/20/88 9/21/88 9/18/88 Q I . ■ I . ■ ■ ■ I ■ ■ ■ ■ I ■ ■ ■ ■ 1 ■ ‘ ■ * 1 t -± _ t . . I I- ». 1- -I .1 ... - ■ . I 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 24. Mean spectra of AR And on 1988 September 18-22. Ln ro light curve for this outburst is shown in Figure 23. Unfortunately, not enough coverage of the preoutburst stage was observed in this system to determine if there were any subtle changes taking place before the rapid rise began. The averaged spectrum for the 18th shows strong Balmer absorption lines with no emission present. The Balmer emission did not begin to reappear until the 20th. Averaged spectra for each night of outburst are shown in Figure 24. TW Vir TW Vir is an U Gem dwarf nova. The system has an apparent V mag of 15.8-16.3 while in quiescence, and an apparent V magnitude of -12.2 while in outburst. TW Vir was observed during the 1989 March-April run over five consecutive nights from March 28 through April 1. The IDS light curve for this period is shown in Figure 25. The first four nights of observations the sky conditions were photometric. On the fifth night, however, there were high thin clouds which thickened as the night progressed. On the 28th and 29th the system was in quiescence. At the beginning of the observations on the 30th the system was brighter than it had been the nights before, but It still showed the classical signature of a CV in quiescence. As the night progressed, though, it went into the rapid rise stage of outburst. The emission lines disappeared, and broad absorption lines appeared in their place. The continuum level doubled in strength during the 2.5 hr of the rapid rise that were observed that night. Figure 26 shows the averaged spectra for the 28th and 29th. To give a sense of how the spectrum changed with time on the 30th, the spectra for that night CO • • 00 1 1 . 635614 614.5 615 615.5613.5 616 616.5 617 617.5 618 Julian Date (2447000 + ) Figure 25. IDS light curve of TW Vir for 1989 March 28-April 1. 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 26. Mean spectra of TW Vir on 1989 March 28 (a) and 1989 March 29 (b), and 3:30 to 5:55 UT (c), 6:00 to 7:15 UT (d), 7:20 to 8:35 UT (e), and 8:40 to 10:00 UT (f), 1989 March 30. in in 4 / 1/89 4300 4400 4500 4600 4700 4800 4900 5000 Wavelength (A) Figure 27. Mean spectra of TW Vir on 1989 March 31-April 1. Ul On Figure 28. FWHM(top) and line flux (bottom) of H-beta of (bottom) flux line and FWHM(top) 28. Figure Flux (10~14 ergs cm”2 s”1) FWHM (A) n - in IO CM O 1 64 1 616 615 614 613 1 64 1 616 615 614 613 • * - • • » - • • - ■ ■ ■ ■ > - • • emission of TW Vir on 1989 March 28-29. March 1989 on Vir TW of emission • ♦ t I uin ae 2400 ) 4 (2447000 Date Julian uin ae 2400 ) 4 (2447000 Date Julian T" “T " T " -.1 , _ - T 1 __ • • • i • • T 1 _ L _ i - - - - 57 58 were binned together into time bins of 1.25 to 2.5 hours and are also shown in Figure 26. Maximum was reached on the 31st. On this night emission lines were present in the absorption troughs. By April 1 the decline had begun. The mean spectra for the 31st and 1st are shown in Figure 27. The emission lines were becoming stronger and more dominant over the absorption lines. Between the 28th and the 29th the Hj9 emission line weakened. However, the width of the line remained constant to within the errors (Fig. 28). While the H/9 emission line that was present on the 31st and 1st is comparable in strength to the line on the 28th and 29th, it is much narrower. Summary of Preoutburst Behavior The sorts of spectral changes that were observed to take place during preoutburst include a rise in the continuum, and a narrowing or weakening of the emission lines. Also, there were instances when the emission lines became weaker and then increased in strength during the preoutburst. These findings are summarized in Table 3. As can be seen in the table, the continuum rose during 5 of the preoutbursts. The continuum wasn't observed to rise in AR And, but there wasn* t enough coverage of the preoutburst stage to detect it if it had. In AH Her orbital effects may have kept a rise in the continuum level from being detected during the preoutburst. In KT Per, AH Her, and one observation of RX And some of the emission lines narrowed. In KT Per and AH Her, the line which became narrower weakened then recovered in strength during the preoutburst. In KT Per the Hp emission line actually was stronger by the end of the 59 Table 3 Observed Spectral Changes During the Preoutburst Stage Object Date Continuum Lines Lines Lines Weakened Rose Narrowed Weakened then Recovered RX And 12/85 XX RX And 10/87 XX SS Cyg 6/87 X KT Per 9/88 X X X AH Her 9/88 X X > AR And 9/88 TW Vir 3-4/89 XX preoutburst than it was at the beginning. The third preoutburst in which the lines narrowed was the December 1985 RX And preoutburst. Since the nights during the preoutburst weren't photometric, it cannot be determined if there was a change in the line strength. Also, only two nights of preoutburst were observed in RX And, whereas in the other two systems where the lines became narrower there were 3 to 4 nights observed. So it may be that there wasn't enough coverage to see the lines weaken then become stronger again in this preoutburst of RX And even if skies had been photometric. In the TW Vir and October 1987 RX And preoutbursts the Balmer emission lines weakened, but their widths remained constant. None of these sorts of changes have been reported to have been observed in dwarf novae during quiescence. In all but two of the outbursts observed, the Balmer emission lines completely or almost completely disappeared at the beginning of the outburst. The two systems in which the emission lines remained fairly strong are KT Per and AH Her. These systems also showed similar behavior in the lines during the preoutburst. From this, it seems that there is most likely something occurring within the disks of these systems up to five days before the actual outburst begins. It also seems that the transformation taking place within the disk may vary from preoutburst to preoutburst, even within the same system. CHAPTER III COMPARISONS WITH OTHER OBSERVATIONS As mentioned earlier, it is difficult to catch and observe the preoutburst stage. Usually dwarf novae are observed during minima then later they are observed during outburst. It is rare that the progress of a dwarf nova is followed from a quiescent state into outburst. Therefore, it is rare that the preoutburst stage would be observed. Also, the changes that take place during this time are subtle. Without high time or spectral resolution they may not be detected. Thus, it is not surprising that the preoutburst stage has gone all but unnoticed before this study. It was, however, observed in SS Cyg by Clarke, Capel, and Bowyer (1984). They observed the rise to maximum to take place in two stages. During the first stage, which lasted for three to five days, the continuum brightened by a factor of two per day. During this time the H lines both weakened and narrowed. They referred to this stage as the slow rise phase. Figure 29 shows the behavior of the continuum level at 4600A, the Balmer peak flux, and the Balmer line FWHM throughout the preoutburst and outburst. This figure is from Clarke, Capel, and Bowyer (1984). In none of our observations did the emission lines both continuously weaken and narrow. 61 62 SS CYG OUTBURST CYCLE VARIATIONS CONTINUUM AT 4 6 0 0 A _ 05 t* BALMER FEAK FULIX aALMER UNE FWHM E 1000- Figure 29. Continuum level at 4600 A (top), Balmer line flux (middle), and Balmer FWHM (bottom) vs time for SS Cyg from Clarke, Capel, and Bowyer (1984) . 63 As mentioned in Chapter I, there have been a number of other observations of dwarf novae during outbursts. In some cases the system was also studied during quiescence, but they were not monitored continuously from quiescence into outburst. These observations include outbursts of RX And and KT Per (Clarke and Bowyer 1984), VW Hyi and WX Hyi (Schoembs and Vogt 1981), and an outburst of SS Cyg (Hessman et al. 1984; Hessman 1986). More recently there have been other outbursts of RX And (Szkody, Piche, and Feinswog 1990) and KT Per (R. K. Honeycutt 1990 personal communication). These outbursts occurred in 1987 January and 1987 December respectively. Table 4 gives the stages during which each of these systems was observed. The observations of KT Per made by Honeycutt began the night before the rapid rise started. Therefore, the system may have been in the preoutburst stage on that night. However, the system needed to be observed for more than one night before the outburst to detect the changes in the spectrum that have been associated with the preoutburst because these changes usually occur over a period of days. Comparisons between these observations during the stages of quiescence, the rise to maximum, maximum, and the decline will be discussed below. The preoutburst stage has already been discussed above. Quiescence In all of the observations of each system mentioned above, the quiescent spectra are dominated by strong Balmer emission lines. In both of the observations of RX And from this study weak He II A4686 64 Table 4 Outburst Coverage of Dwarf Novae Observer Obiect SDect. Res. CA} Outburst Coveraee Clarke & Bowyer RX And 3.5-10 Q.M (1984) Clarke & Bowyer KT Per 3.5-10 Q.M (1984) Clarke, Capel, & SS Cyg 4 Q,P,R,M,D Bowyer (1984) Hessman et al. SS Cyg 1.75 Q.M.D (1984) Honeycutt KT Per 2.5 P,R,M,D (1990) Schoembs & Vogt VW Hyi (3) M,D (1981) Schoembs & Vogt WX Hyi (3) Q.R.D . (1981) Szkody, Piche, & RX And - M Feinswog (1990) This Study RX And 2.7 P,R,M,D This Study RX And 2.7 P,R This Study SS Cyg 2.7 P,R,M,D This Study KT Per 2.7 P.M.D This Study AH Her 2.7 P,R This Study AR And 2.7 P,R,M,D This Study TW Vir 2.7 P,R,M,D a ‘ The stages of the outburst cycle are represented by the following: Q for quiescence; P for preoutburst; R for the rise to maximum; M for maximum; and D for the decline from maximum. 65 emission is present. He I A4471 is quite common during quiescence. It is present in TW Vir, AH Her, the 1987 and 1988 observations of KT Per, and the 1985 and 1987 observations of RX And. Rise to Maximum Broad Balmer absorption lines are present in each case. The emission lines disappear almost completely during this stage in all of the systems except for AH Her. In the 1987 outburst of KT Per the emission lines reappear before maximum is reached. This stage was not observed in the 1988 KT Per outburst. Therefore, the behavior of the Balmer emission lines for that outburst is unknown. He II A4686 emission appears in AH Her and in the outbursts of SS Cyg seen by Clarke, Capel, and Bowyer (1984), and Hessman et al. (1984). Hessman (1986) suggests that this emission is due to the hot spot. This would support the theory that an increase in the mass transfer rate triggers the outburst. He II A4686 emission disappears in both of the RX And outbursts from this study. It is fairly common for He I A4471 to be present in absorption at this stage. It is seen in the 1984, 1985, and 1987 RX And spectra, as well as in the AH Her, and the 1987 SS Cyg data. Maximum By this stage, well defined emission lines have appeared in the bottom of the absorption troughs in all of the outbursts except that of AR And. In a number of cases the emission lines were measured and found to be narrower than the lines present during quiescence. This was true for the 1984 and 1985 RX And outbursts, the 1984 KT Per outburst, the SS Cyg outbursts observed by Clarke, Capel, and Bowyer (1984) and Hessman et al. (1984), and the 1989 TW Vlr outburst. The Balmer emission lines were determined to be stronger in SS Cyg during maximum than during quiescence by both the Clarke, Capel, and Bowyer, and Hessman et al. studies. Hessman (1986) theorized that during outburst the Balmer emission arose more from the hot spot than from the entire disk. This would explain why the lines are narrower, and why the emission lines are 199° ± 4° phase shifted from the companion's absorption lines. It must be remembered, however, that the underlying absorption makes it difficult to fit and measure these emission lines (Kaitchuck, Mansperger, and Hantzios 1988). In both the 1988 and 1987 KT Per outbursts, the emission lines are relatively strong and the absorption lines are relatively weak compared to the other systems. He II A4686 emission line is strongest in SS Cyg at this stage, and the line is even present in absorption. This line appears as weak emission in the 1985 outburst of RX And at this time. He I A4471 absorption appears in AR And, the 1987 SS Cyg outburst, and TW Vir. It is at this stage that the H/9 emission line first shows a double structure in the 1985 RX And data. The gray-scales from the 1987 October RX And outburst also suggest that there are two components to the H/3 emission line. Szkody observed this same structure in a 1987 RX And outburst. The 1987 SS Cyg and 1989 TW Vir data show a double structure to the emission lines as well, but the two lines could not be successfully deconvolved in either case. 67 Decline Weak emission lines appear in AR And and, as in most other systems, the emission lines strengthen throughout this stage. The exception to this is VW Hydri. In this system the emission lines weaken during this time until the spectrum appears practically featureless. The lines then begin to increase in strength again, recovering by the end of the decline. It is during this stage that the two components of the Hy9 emission line become the most well defined in the 1985 RX And data. One line is narrow and intense with a very small amplitude. The other is a broader line with a very high radial velocity amplitude. It has been suggested that the first line (the stationary component) arises from the face of the secondary at L^, and that the second line (the s- component) is either due to the stream flowing over the disk and impacting with it at its far side, or to gas being pushed through L3 (Kaitchuck, Mansperger, Hantzios 1988). There have been cases where an s-wave component has been detected within the Balmer emission line. Hessman (1986) found such a component in SS Cyg. He attributed this to chromospheric emission from the companion star. Schoembs and Vogt determined that scatter in the radial velocity curve for WX Hyi is due to a marginal s-wave. These comparisons show that there are many similarities between dwarf novae in all of the different stages. There are, however, subtle differences too. Each system seems to behave slightly differently from the rest, making it somewhat unique. Also, the same system does not always behave the same from one outburst to another. 68 It may be, therefore, that there is not just one answer to the question of what causes the outbursts seen in these systems. There may be a number of factors which play a part in the outburst cycle of a dwarf nova. Study of the preoutburst phase may help determine what some of these factors are. Chapter IV discusses the possible interpretations of what is being observed during preoutburst. CHAPTER IV DISCUSSION OF THE PREOUTBURST STAGE In Chapter II the details of the spectral changes that were observed to take place during the preoutburst stage were presented. In this chapter possible interpretations to these observations will be discussed. As mentioned in Chapter II the behavior of these systems varied from preoutburst to preoutburst even in the same system. Each preoutburst will be discussed separately and then comparisons will be drawn between them. RX And: 1985 December From the AAVSO light curve it was estimated that the rapid rise v» began at around 17 UT on the 16th. Therefore, the system was observed from 37.5-11 hr before the rapid rise started. During this preoutburst, the Balmer emission lines narrowed. The FWHM of the H£ line went from 16.9 A on the 15th to 16.1 A during the second half of the 16th. This isn't a great change, but this measurement and the gray-scale images for these two nights (Fig. 6 ) seem to indicate that the line did indeed become narrower especially toward the end of the night of the 16th. Gaussian fits to the H/? line show that the line actually increased in strength between the two nights. However, it must be remembered that neither of these nights were photometric. 69 70 Therefore, the line fluxes cannot be completely trusted. The EWs were dropping during these two nights (Fig. 5), but this could be due to the continuum rising, as the AAVSO data show, rather than the line weakening. RX And: 1987 October The AAVSO light curve shows that the rapid rise began at about 11 UT on the 18th. This means that the system was observed from 49-2 hr before the rapid rise. In this case, the strength of the line decreased while the widths of the lines remained fairly constant (Fig. 9 and 11). SS Cvg: 1987 June The AAVSO light curve shows that the rapid rise may have started at about 12 UT on the 19th. Therefore, the system was observed for up to about 30 hr before the rapid rise began. This preoutburst is unusual in that Balmer absorption lines are present (Fig 12). The outburst itself was also unusual. The rise to maximum was much slower than normal. It may be that the observations taken on the 18th and 19th were actually of the rapid rise and not of the preoutburst. It is difficult to determine this from the AAVSO light curve. The presence of absorption means that somewhere within the disk the densities are high enough that the region has become optically thick. Emission lines are still present, though, indicating that there are still regions in the disk which are optically thin. The emission line-emitting region may be relatively unchanged. Since accurate fits 71 cannot be done to the lines, however, this is difficult to know for certain. In Chapter I it was mentioned that the emission lines are assumed to arise from the outer parts of the disk. If this is true, then the observations seem to imply that the region of the disk interior to the emission line-emitting region has been affected. KT Per: 1988 September From the AAVSO light curve it was estimated that the rapid rise began at about 0 UT on the 12th. This means that the observations took place from 63-12 hr before the rapid rise began. The Balmer emission lines narrowed during this preoutburst as they did in the RX And 1985 December preoutburst (Fig 17). The line fluxes decreased then increased again during the preoutburst. AH Her: September 1988 The rapid rise began at around 12*1 UT on the 22nd, as shown by the AAVSO light curve. Therefore, the observations took place from about 126-31 hr before the rapid rise. In this case the Balmer lines showed no changes, but the He I A4471 emission line showed much the same behavior as the H/3 emission line did in KT Per (Fig 21) . This implies that the same things may have been going on in the disk of AH Her as in KT Per, only they are taking place where the He I lines are formed instead of where the Balmer lines are formed. 72 AR And: 1988 September As mentioned earlier, there was not enough coverage of the preoutburst stage to detect any spectral changes that may have occurred before the outburst. The system was observed for only one night before the rapid rise began. Furthermore, since AR And is so dim during quiescence the signal-to-noise ratio for that night is very low. This makes it impossible for any changes taking place during that one night to be detected. TW Vir: 1989 March-Aoril From our observations the rapid rise was determined to begin at around 7*1 UT on the 30th. Therefore, this system was observed from about 50 hr before the rapid rise started right up until it actually began and beyond. During this preoutburst, the H/? emission line decreased in flux while retaining its width (Fig 28), much the same as in the 1987 October RX And preoutburst. Summary With the exception of SS Cyg, there appear to be two basic types of behavior during the preoutburst. In the first type, the emission lines become weaker while the widths of the lines remain fairly constant. This was seen in RX And (1987 October) and TW Vir. The second type of behavior involves a narrowing of the line. In these cases, by the end of the preoutburst the line was as strong if not stronger than it was at the beginning. This is what was seen in RX And (1985 December), KT Per, and AH Her. Both of these preoutbursts 73 are accompanied by a rise in the continuum. The narrowing of the lines in RX And (1985 December), KT Per, and AH Her is consistent with the wings of the lines disappearing. Also, the gray-scale image of RX And (Fig 6 ) strongly indicates that the wings of the H£ emission lines are no longer present. If one assumes a Keplerian disk, the disappearance of the wings of the lines means that the inner part of the line-emitting region is being affected. Since the intensity of the cores of the emission lines during these preoutbursts appears unchanged it would seem that the outer part of the disk is not being influenced by the same mechanism as the inner part of the line-emitting region. This could mean that the part of the disk that produces the wings of the lines has become so hot that all the hydrogen is ionized, or that the region has become so cold that all of the hydrogen electrons are in their ground states. It could even mean that there simply is no longer any material in this region of the disk. _ This would be the case if the inner part of the disk had collapsed onto the white dwarf. The continuum rising would indicate that heating is taking place somewhere within the disk. That doesn't mean that the line-emitting region is the area that is being heated. However, cooling taking place within the disk is inconsistent with this rise in continuum. Also, if the inner disk were to collapse, there would be a sudden large increase in the energy output. Therefore, it seems most likely that the heating of the inner parts of the disk causes the emission lines to narrow and the continuum level to rise. 74 In KT Per and AH Her the lines narrowed throughout the preoutburst while becoming weaker, and then increasing in strength again. The disappearance of the line wings would explain the initial behavior. It does not, however, account for the lines regaining their strength later in the preoutburst. It could be that there were regions farther out in the disk that were initially too cool to produce line emission. If these regions were heated slightly, this may cause them to start producing line emission. The strength of the emission lines could increase due to this, even if the innermost parts of the line-emitting region were no longer producing line emission. This indicates that there may be a heating front moving from the inner parts of the disk to the outer. The observed rise in the continuum is consistent with a rise in temperature. In AH Her the Balmer lines weren't affected but the He I lines were. This could mean that as of 1989 September 21, the front reached the hotter inner regions where the He I lines are produced, but had not yet reached the cooler outer part of the line-emitting region where the Balmer lines are produced. Unfortunately the system was not observed on the 22nd due to clouds, which based on the AAVSO light curve was the last night of the preoutburst phase. It may be that the effects of the heating front on the Balmer line producing region could have been seen on that night. To determine if this was a reasonable explanation for what was observed in AH Her, a program was written which calculates line profiles from Keplerian disks given an inner and outer radius for the line-emitting region within the disk. The idea was to qualitatively explain how the radii of the line-emitting region varied during the 75 preoutburst, not to determine the actual values for these radii. Many simplifying assumptions were made. The disk was assumed to be optically thin in the lines. Therefore, the energy of the line emission as a function of wavelength (E(A)) emitted by the disk can be written as (based on Smak 1981) dr 17. E(A) = 2He f J [v(r)2sin2i - V2 ]1/ 2 rl where e is the volume emission coefficient, i is the inclination of the disk, H is the thickness of the disk, r is the radius within the disk, and r^ and are the inner and outer radii of the line-emitting region. The orbital velocity (v(r)) and the radial velocity corresponding to a given A (V) are 18. v(r) = (GM/r)1/ 2 19. V — c(A - A )/A where M is the mass of the white dwarf. e was assumed to be constant throughout the line-emitting region and zero elsewhere. H was assumed to be constant as well. Of course, e and H will both vary with R, but these assumptions will not affect the sense of how the line-emitting regions moved within the disk. The input parameters for the program are: e, M, i, H, the rest wavelength of the line, and the inner and outer radii of the line- emitting region. The line-emitting region was then divided into 2 0, 0 0 0 sections and the integral was solved by summing the products of the average E(A) of each section and the section width. The total E(A) from the disk was found for every 0.2 A in the range of ±100 A from the rest wavelength for the line. These values could be plotted to produce a line profile in which the width and strength could be examined. The program also calculated a flux and FWHM for the line. In this way the inner and outer radii of the line-emitting region could be adjusted to see how the line shapes and strengths would change. The inclination and mass of the white dwarf for AH Her are known (see Table 1). From the parameters for the system the separation between the two stars, and hence the radius of the Roche lobe around the white dwarf, can be found. These were a — 1.42 x 10^® cm, and RL1 " 5 .66 x 1010 cm. Therefore, the radius of the disk could be as large as 5.66 x 10^® cm. The thickness of the disk was O estimated to be Rp/100, or 5 x 10 cm. The inner and outer radii of the line-emitting region were then adjusted until the program produced a line with the same FWHM as the data for the first night within the errors. After this was done, an e was chosen so that the line flux would be the same as the data within the error. The radii were then adjusted to produce a line with the same FWHM and flux as the data from the last night of the observed preoutburst. The same e was used as in the first night. The final values for these radii will of course depend on the e chosen. They would also change if e and H were 77 treated as functions of R. However, the sense of how the radii changed throughout the preoutburst will not change. Also, while these radii are rough estimates, it is reassuring that they are reasonable values for this system. On the first night it was found the inner and outer radii were 1.0 x 1 0 ^ cm, and 2.0 x 10^® cm respectively. The last night these radii were 3.5 x 10^® cm and 3.9 x lO'*'® cm. Both of these regions are well within the Roche lobe of the white dwarf. These numbers imply that a heating front had reached out to 3.5 x 10^® cm in the disk by the end of our observations of the preoutburst. This leaves room for hydrogen emission to be taking place beyond where the heating front has reached. The front may have moved even farther out in the disk by the end of the preoutburst. This is a simple model, and is not meant to be an exact representation for what is happening in the disk of AH Her during the preoutburst. It is merely establishing that what is seen is consistent with the picture presented above. The same calculations were preformed for the RX And (1985 December) and KT Per outbursts. The system parameters are not known for KT Per so typical parameters were chosen to use in the program. The results are shown in Table 5. In both cases, line-emitting regions were found which would reproduce the observed data and were within the Roche lobes of the systems. The radii for these regions changed in the same sense as they did in AH Her. If one assumes a Keplerian disk, the lines weakening while retaining their widths would be consistent with the inner boundary of the line-emitting region remaining stationary while the outer boundary 78 Table 5 Model Line-Emitting Regions During Preoutburst Object Roche lobe Line Night Inner Radius Outer Radius AH Her 5.66 X 1 0 10 cm He I 9/17/88 1.0 X 1 0 10 cm 2.0 X 1 0 10 cm tt 11 tt 9/21/88 3.5 X 1 0 10 cm 3.9 X 10^® cm KT Per 5.00 X 1 0 10 cm H/9 9/15/88 1.0 X 1 0 10 cm 2.0 X 1 0 10 cm 11 11 tt 9/17/88 1.4 X 1 0 10 cm 2.3 X 10^® cm RX And 5.52 X 1 0 10 cm E/3 12/15/85 2.7 X 1 0 10 cm 4.2 X 1 0 ^® cm II II tt 12/16/85 3.5 X 1010 cm 4.5 X 1010 cm RX And tt E/3 10/16/87 1.8 X 1 0 10 cm 2.6 X 1 0 ^ cm II tl 11 10/18/87 1.8 X 1 0 10 cm 2.55 j : lO^cm TW Vir 4.5 X 1 0 10 cm H/9 3/28/89 1.5 X 1 0 10 cm 2.2 X 1 0 10 cm If tt tt 3/29/89 1.5 X 1 0 10 cm 2.0 X 1 0 10 cm moves inward within the disk. This is what was seen in RX And (1987 October) and TW Vir. The same program mentioned above was used to test this hypothesis. The results are also shown in Table 5. The final radii for the line-emitting region given in the table correspond to the last observations taken during the preoutburst stage. They are not necessarily the final radii at the end of the preoutburst. It was possible to reproduce the observed widths and strengths of the lines with reasonable radii for the line-emitting regions. When the inner radius was held steady while the outer radius was moved inward, it was found that the FWHM of the line remained nearly constant. So the observations are consistent with the model that the outer part of the disk is being effected first, and that the front which is causing the line emission to cease is moving steadily inward. Again, this could mean that the outer part of the disk has become so hot that all the hydrogen is ionized, or that it has cooled to the point all the hydrogen electrons are in their ground states. It could also mean that the outer part of the disk has collapsed onto the inner part of the disk. The continuum level rose in these cases too, implying heating taking place somewhere within the disk. Also, if the outer part of the disk had collapsed there would be a sudden large increase in intensity. Therefore, it seems most likely that the first possibility mentioned above is the correct explanation. These two types of preoutbursts seem to correspond well with the type A and type B outbursts mentioned in Chapter I, p. 16. Indeed, these observations would tend to support the disk instability theory. This is because the preoutburst begins tens of hours before the outburst does. It would be difficult to explain how the disk knows that much ahead of time that an increase in the mass transfer rate is about to occur. We know that an increase in mass transfer didn't happen before or during the preoutburst, because if it had the hot spot would be much more luminous. Also, if a change in mass transfer were causing the preoutburst, it should always affect the outer regions of the disk first. This study shows that there are preoutbursts which seem to be taking place in the inner disk, but not affecting the outer disk. Neither the standard disk instability model nor the mass transfer model, though, explains the small but definite increase in the continuum level during the preoutburst. The continuum was seen to rise in all the preoutbursts except those of AR And and AH Her. There was not enough coverage of AR And to detect such a rise. Orbital effects and non-photometric skies may have kept a continuum level rise from being observed in AH Her. Therefore, it may be that the continuum rose in all of these preoutbursts. This rise indicates that there is a slight heating which takes place within the disk before the outburst actually occurs. This heating is consistent with a front moving through the disk as mentioned above. The front, however, does not heat the disk up to the temperatures seen during outburst. It seems to be more of a "warming" front which only raises the disk temperatures slightly. A good model for dwarf nova outbursts would need to explain this rise in the continuum level and these fronts moving throughout the disk before the outburst occurs. CHAPTER V COMPARISON WITH THEORY Mineshige (1988) has developed a model which will provide for the slight rise in the continuum observed before the outburst. His model deals with outbursts which start at the outer edge of the disk and move inward, although the same principles could be applied to an outburst that started in the inner parts of the disk and moved outward. In his model the region of the disk where the outburst begins does not immediately rise up to the hot equilibrium state. While the mid-plane temperature will rise fairly quickly, increased opacity in the ionization of hydrogen and helium and the increased thermal time scale will cause the rise in effective temperature to be halted at Te££ -6000K. This part of the disk will remain at that effective temperature for ~24 hr. Mineshige referred to this as the "stagnation stage." During this stage the "warm" front created by the instability propagates inward. The effective temperature in each region of the disk it passes through will be raised to ~6000K. The outer part of the disk where the warm front began is not in a stable state. Therefore, it will eventually rise to the hot equilibrium state. This will produce a "hot" front which will move both inward and outward in the disk. Since the velocity of the front depends on temperature, the hot front will travel faster than the warm front, 81 82 and it will eventually overtake and merge with it. The warm front will have propagated about a third of the way into the disk when this happens. This may explain the small rise in the continuum seen during preoutburst. The preoutburst seen in TW Vir was used to test this model. This data set was chosen because the observations made on 1989 March 30 seem to be that of a transformation from one phase into another. At the beginning of that night the continuum was ~3.5 times brighter than it was on the previous nights (see Fig. 26), yet it shows little or no change during the first 2.5 hr of observations. Then suddenly the continuum begins to rise very drastically. If Mineshige's theory is correct, then it may be that we were observing the end of the stagnation stage and the beginning of the hot stage during this night. The spectra of TW Vir for the night of the 30th were co-added into bins of 2-3 spectra to improve the signal-to-noise ratio. This gives a time resolution of 16.7 minutes. The spectra were then fit with a straight line through the wavelength range of 4510-5060 A excluding 4820-4910 A to avoid contamination from the H)9 emission and/or absorption line. From this the slope of the continuum and the continuum level at 4750 A were found for each time-binned spectrum. These are shown in Figure 30. From the figure it can be seen that there was little or no change in the slopes until about 7*1 UT. Then very suddenly the slopes began to decrease quite rapidly, showing a significant change in just 17 minutes. The fluxes on the other hand showed a much more gradual change throughout the night. The color indices versus UT for this night are shown in Figure 31. These were -.. 1 — ....T ------«“ ---- 1------1------r 83 ♦ • • • • * ■ * ♦ • ♦ ♦ • ♦ • ♦ s< ♦ • ♦ * • o » — o x — o. in • ♦ ♦ « .2 * ♦ in . 4 • • 4 * £ •• o 1 __ i______1______i— ---- 1 .— I T 6 8 10 UT (hr) UT (hr) Figure 30. Slope of continuum from 4510 through 5060 A vs UT for TW Vir on 1989 March 30 (top), and continuum flux at 4750 A vs UT for TW Vir on 1989 March 30 (bottom). Color Index o in o « 3 Figure 31. Color indexfor198930. Color on TW Vir vs UT March 31.Figure 4 5 6 UT (hr) 7 8 9 10 00 •P* 85 calculated using the following formula 20. color index = -2.5(log(flux(4510A)) - log(flux(5060A))). Once the slopes and fluxes were measured the test was then to see if Mineshige's model could reproduce these slopes and fluxes on the same time scale. In order to do this a program was written that employed the parameters of Mineshige's model to make model spectra of an accretion disk at different times throughout the preoutburst and outburst. This was not an attempt to reproduce Mineshige's detailed model. The idea was merely to see if the physical aspects of his model could be used to approximate what was seen in TW Vir. This program would adjust the temperature of each region of the disk for every time step throughout the outburst in accordance with Mineshige's parameters. Note that this is a more sophisticated program than the one mentioned in Chapter 4 where e, and hence T, remained constant over the line-emitting region. From Mineshige's paper the velocities of the warm and hot fronts were estimated. The velocities were assumed to be constant throughout the disk. Also, the final temperatures of the disk regions after the hot front had passed through them were calculated as a function of radius from the paper. The mass of the white dwarf and the mass transfer rate that Mineshige used in his models are probably about the same in TW Vir. The free parameters for the program were: the temperature of the disk during quiescence, the temperature of the warm front, the radius the warm front reached when the hot front began, the 86 radius the hot front began at, and the disk radius. The disk was divided into 500 annuli. The temperature of each annulus at any time during the preoutburst and outburst will depend on which fronts have or have not moved through it. To begin with, each annulus was assumed to radiate like a black body. The contribution from each annulus was then summed together to produce a model spectrum at each time step during the preoutburst and outburst. These time steps were 1.2 x 10 s. During the first time step of the program the disk is in quiescence. The second time step is when the warm front begins. The program continues until the hot front has reached the boundary layer between the disk and the white dwarf. This corresponds to the time of maximum. The absolute values for the flux will depend on the distance to the system and its inclination. Neither of these are well known for TW Vir. Therefore, the fluxes were adjusted so that the continuum level and slope of the 28th matched those of the first time step in the model. The final temperature of each annulus after the hot front passed through it was increased by a factor of 2.1 so that the slopes of the model spectra would decrease as quickly as those of TW Vir after 7 UT on 1989 March 30. The free parameters of the model were adjusted until a good fit to the data was found. It was determined that a change in the free parameters of 100 K in the temperature and 0.005 disk radii changed the resultant spectra by a significant amount. It was necessary to slow down the speed of the hot front by 14% so that the fluxes would not increase too fast after the hot front began. The final values for the free parameters are in Table 6 . Figure 32 shows the resulting 87 continuum flux and slopes. It's assumed that in TW Vir the hot front ■ I. began when the slopes sharply decreased at -7 UT. Therefore, the night of the 30th spans from 4 hours before the hot front began to 3.5 hours after. For the sake of comparison, Figure 32 spans this same time interval. The color indices determined for the model spectra are shown in Figure 33. The inner Lagrangian point was calculated from the parameters of the system given by Shafter (1983). It was found to be 6.1 x 1010 cm. This means that the outer disk radius given in Table 6 is well within the Roche lobe of the white dwarf. Table 6 Final Model Parameters for TW Vir, Black Body Model Parameter______Value______ Initial temperature ...... 6200 K Temperature of warm front ...... 9400 K Radius of warm front when hot front begins ...... 0.63 disk radii Initial radius of the hot front ...... 0.999 disk radii Outer radius of disk ...... 1.9 x 10^® cm Speed of warm front ...... 0.785 x 10^ cm/s Speed of hot front ...... 1.90 x 10^ cm/s The program was modified so that it would calculate the flux from each annulus using stellar atmosphere intensities instead of those of a black body. This was done with the help of a look-up table which contained fluxes from model atmospheres (Kurucz 1979) at given temperatures and wavelengths. The program would interpolate within Figure 32. Figure Slope (int/A) 5x10”15 10”14 1.5x10”14 -IQ"17 -5x10"18 • • 1 • • « •• vs time (top), and continuum flux at 4750 A vs A 4750 at flux continuum (top), and time vs disk annuli as a black body. black a as annuli disk each treats which model for the (bottom) time Slope of the continuum from 4510 through 5060 A 5060 through 4510 from continuum the of Slope 8x10 8x10 “ T — i ■ • ie (sec) Time ie (sec) Time * — i — ------9x104 9x104 9x104 9x104 L 1 ---- • • 1 ---- • • r- • • • • 10 • I ° • - ■ • ' • • « « 88 Color Index .x0 814 .x0 914 .x0 105 9.5x104 9x104 8.5x104 8x104 7.5x104 o m Figure 33. Color index vs time forindexastreatseach disk theannuli time which Color vs model 33.Figure h black body.black ie (sec) Time • • 90 the table to find the flux at any given temperature for various wavelengths. The velocity of the warm front in this model was the same as in the black body model. In this case, the velocity of the hot front did not have to be altered from that derived from Mineshige's paper. The final disk temperature of each annulus was increased by a factor of 1.6 from Mineshige's final disk temperatures. The free parameters which gave the best fit to the data are given in Table 7. The resulting model slopes and continuum fluxes are shown in Figure 34. The resulting color indices are shown in Figure 35. Table 7 Final Model Parameters for TW Vir, Stellar Atmospheres Model Parameter Value Initial temperature ...... 5600 K Temperature of warm front ...... 7500 K Radius of warm front when hot front begins .... 0.58 disk radii Initial radius of the hot front ...... 0.96 disk radii Outer radius of disk ...... 1.9 x 10'*'® c m Speed of warm front ...... , 0.785 x 10^ cm/s Speed of hot front ...... 2.20 x 1 0 5 cm/s Both models were able to reproduce the shapes of the continuum slope and flux curves. The only deviations from Mineshige's model are the temperature of the warm front, which was 60% or less, the final temperatures of the disk annuli at maximum, which were increased by no more than a factor of about 2 , and the velocity of the hot front, O Ll __ I__ T 9x104 10® 1.1x10* Time (sec) x T- 1 1 1 1 ----- 1------r in • » • • • • • • • • • m • » • O • S • 1 _JL_ 9x10 10° 1.1x10* Time (sec) Figure 34. Slope of the continuum from 4537 through 5025 A vs time (top), and continuum flux at 4750 A vs time (bottom) for the model which interpolates in a table of model stellar atmosphere intensities. Color Index o 0 in Figure 35. Color index vs time for the model which interpolates inofa interpolates table indexfor Color time thevs modelwhich 35.Figure 1 « 1 1 * I 1 1 1 * | — “ i i i i | r * ■ 1 I 1 1 1 1 I 1 * 1 1 1 1 > x0 9514 0 10x0 1.1x10s 1.05x10s 105 9.5x104 9x104 model stellarintensities. atmospheremodel i e (sec) Time ------i ------i ------• • r ro VO 93 which was decreased by 14% in the black body model and not changed at all in the stellar atmosphere model. Both models show a kink in the flux curve as well as in the slope curve at -7 UT . The data don't show this. This may simply be due to the crudeness of the model. The model which uses stellar atmosphere models required the least amount of adjustments from Mineshige's model. Also, the temperatures this model gives for the disk annuli after the warm and the hot fronts moved through them are closer to that of Mineshige's than those from the black body model. This is not surprising since Mineshige treated each annuli as a stellar atmosphere. There are two time scales involved in this model. One is the time interval between the start of the warm front and the start of the hot front. The other is the time it takes for the hot front to reach the boundary layer between the disk and the white dwarf (i.e., the time it takes for the system to reach maximum) . In the case of TW Vir it isn't known when the warm front began. We do know, however, that it started sometime between the last observation of 1989 March 29 and the first observation on the 30th. Therefore, limits of 4-21 hr can be placed on the time interval. The time interval from both of the models is in fair agreement with this. In the model using black bodies, 24.8 hours passed between the time the warm front started and the time the hot front started. In the model using stellar atmospheres this time was 28 hr. From the IDS light curve of this outburst (Fig.25) it appears that the system was still getting brighter at the beginning of observations on the 31st. About half way through the night the luminosity leveled off. Therefore, the time 94 period from the start of the hot front until maximum is about 24 hr. Again, this is in good agreement with the models. In the black body model it took 26.7 hr for the hot front to reach the boundary layer. In the model using stellar atmosphere models it was 22.2 hr. This data set and comparison with Mineshige's model is presented in Mansperger and Kaitchuck (1990). Since this transition wasn't seen in any other system it is difficult to apply the same model to them. In the 1985 December outburst of RX And, however, much of the rise to maximum was observed on the 17th. Since observations were taken on the two previous nights, reasonable guesses can be made about when the two fronts started. The warm front probably began sometime between the nights of the 15th and the 16th. From the AAVSO light curve (Fig.4) it appears that the hot front began between the Julian dates of 2446416.100 and 2446416.440, or between 14.4*1 and 22.6*1 UT on 1985 December 16. 17*1 UT was chosen as the time the hot front most likely began simply because this time best fit the data. Therefore, the IDS data on the 17th begins 9.9 hr into the hot phase. The spectra for this night were co-added into groups of 2-3 spectra to improve the signal-to-noise ratio. This gave a time resolution of 10.8 minutes. The data from 3.3 to 4.6 UT were thrown out because it was decided that the IDS sweep positions had drifted. The sweeps were relocated before further data were taken. This means that the data collected before 3.3 UT are somewhat questionable. Straight line fits were made to the remaining co-added spectra across the wavelength range of 4510-5015 A excluding 4570-4660 A and 4820- 95 4905 A to avoid contamination from an absorption feature which is present around 4615 A and the H/9 absorption line. The slope and continuum flux at 4750A were determined from this. The results are shown in Figure 36. Color index versus UT are shown in Figure 37. The model using stellar atmosphere intensities was used to try to reproduce these data. The absolute flux was scaled so that.the model slope and fluxes at maximum would match those from the night of 1985 December 18 for RX And. The final temperatures of the disk regions after the hot front passed through them were adjusted to be a factor of 1.34 greater than Mineshige's temperatures so that the model slopes would decrease as fast as the observed slopes on 1985 December 17. In this case the disk was divided into 100 annuli, and the time steps were 2.0 x 10 s. The resulting model slopes and fluxes are shown in Figure 38. The resulting color indices are shown in Figure 39. Table 8 shows the free parameters which were used to get the best fit. From the parameters for this system (Shafter 1983) the Roche lobe was 10 calculated to be 5.52 x 10 cm. Therefore, the outer radius of the disk given in Table 8 is well within the Roche lobe for the system. RX And reached maximum light sometime between the last observation on 1985 December 17 and the first observation on the 18th. If one assumes the hot front started at 17 UT on the 16th, then it must have taken it between 14.6 and 33.1 hr to reach the boundary layer. In the model this time was 20.1 hr. In the cases of both TW Vir and RX And Mineshige's model seems to successfully reproduce the observations. Of course the model used here is a simple one. The best method to determine how well this Figure 36. Slope of the continuum from 4510 through 5060 A 5060 through 4510 from continuum the of Slope 36. Figure Fx (tO "14 erg cm"2 e"1 Jl"1) Slope (ln t/1 ) o O CM o • • sU o XAdo 95Dcme 7 tp, and (top), 17 December 1985 on And RX for UT vs continuum flux at 4750 A vs UT for RX And on And RX for UT vs A 4750 at flux continuum 95 eebr1 (bottom) 17 December 1985 4 T (hr) UT T (hr) UT 6 8 96 Color Index o CM in 0 in I 1 * Figure 37. Color Index vs UT for RX And on 1985 December 17.Indexfor Color 1985 onDecember vs RX UT And 37.Figure T (hr) UT VO „ I— t— I— -I ■ » ■ t ■ ■ ■ . I 1ff5x10 1.25x10 1.3x10* 1.35x10* 1 Time (sec) CM 1.2x10 1.25x10 1.35x10' Time (sec) Figure 38. Slope of the continuum from 4537 through 5025 A vs time (top) , and continuum flux at 4750 A vs time (bottom) for the model which interpolates in a table of model stellar atmosphere intensities. Color Index in *“ in Figure 39. Color index vs time for the model which interpolates ininterpolatesaof table index for Color timethewhich vs model 39.Figure I ■ • * - • ■ • • • - • • . - • • model stellar atmosphere intensities.stellar atmospheremodel .51 1.3x10° 1.25x10 _ i .. i _ . L —r- r — 1 • ■ L, 1— - , -L ■, • ------ie (sec) Time ' ------• 1 1 • • 1.35x10® I — 1 ______• _ U « 1 • - - VO VO 100 Table 8 Final Model Parameters for RX And, Stellar Atmospheres Model Parameter______Value______ Initial temperature ...... 5700 K Temperature of warm front ...... 7900 K Radius of warm front when hot front begins ...... 0.60 diskradii Initial radius of the hot front ...... 0.99 disk radii Outer radius of disk ...... 1.67 x 10^® cm Speed of warm front ...... 0.785 x 10^ cm/s Speed of hot front ...... 2.20 x 10^ cm/s theory fits the data would be to run the full Mineshige model at very small time steps. This would require large amounts of computing time, and was beyond the scope of this study. CHAPTER VI CONCLUSIONS This study was an attempt to observe and analyze dwarf novae just before outburst to establish the existence of a preoutburst stage. This is a phase that dwarf novae are thought to undergo which is neither quiescence nor outburst. The observational part of the study was quite successful. Dwarf novae were observed both just prior to and during outburst seven times. In one case there weren't enough data obtained before the outburst to study any preoutburst effects. In each of the other observations there is compelling evidence that these systems are going through a phase different from either outburst and quiescence. This phase was observed in every instances where enough data were collected to detect it. This does not prove that the preoutburst stage takes place in every system before every outburst. It does, however, indicate that the preoutburst stage is not a rare or fluke event which occurs only in one dwarf nova, or even one type of dwarf nova. This phase was observed in both U Gem and Z Cam objects. There were no SU Ursae Majoris objects which were caught during the crucial time to determine if they also exhibit the preoutburst stage. The characteristics of the preoutburst are a small rise in the continuum and changes in the emission lines. The continuum was seen to rise in five of the seven preoutbursts. There weren't enough data 101 to determine if this occurred in AR And. In AH Her orbital effects may have kept such a rise from being observed. The emission lines which are affected were usually the Balmer lines. However, there was one case where the Balmer lines remained unchanged while the He I A4471 emission line was affected. The observed change in the emission lines vary from outburst to outburst even within the same system. One change observed was a narrowing of the line, while the line strength ultimately was as great or greater than it was at the beginning of the preoutburst. In two of these cases the strength of the line decreased then increased again. Another change is a weakening of the emission lines while the line width remained fairly constant. These differences in the emission line behavior indicate that the preoutburst is taking place at different regions within the disk. When the line narrowed throughout the preoutburst, it would seem the changes took place in the inner parts of the line-emitting region and the mechanism causing these changes moved outward. In the cases where the lines weaken while their widths are unchanged, it would seem that the preoutburst took place in the outer part of the line-emitting region which caused a front to move inward. Both situations require a "warm" front to move through the disk to produce the observed results. Any successful model for these outbursts must explain the behavior seen during the preoutburst. Such a model must especially account for the rise in continuum observed during this stage. The evidence for the preoutburst occurring in different regions in the disk supports the disk instability theory more strongly than the modulated mass transfer model. The standard disk instability model 103 doesn't, however, explain the behavior of the continuum during the preoutburst. Mineshige's model does this by including a stagnation stage to the standard disk instability model. In his model there are two fronts which pass through the disk during the outburst. One is a warm front which raises the temperatures of the disk regions it passes through to 6000 K. These parts of the disk are not in thermal equilibrium. The outer disk where the warm front begins stays at this temperature for about 24 hr. After this time that area of the disk rises to the hot equilibrium state. This produces a hot front which spreads through the disk. If this happens the continuum level would begin to rise slightly about 24 hours before the rapid rise of outburst begins. In order to test Mineshige's theory two simplistic programs were written which incorporated Mineshige's prescription. These models adjusted the temperatures of the disk regions based on which fronts had passed through them. In the first model the resultant flux for each disk region was determined assuming that it radiated as a black body. The fluxes from each.region were then summed together to produce model spectra for different times throughout the preoutburst and outburst. In the second model the resultant flux for each disk region was determined by using model stellar atmosphere intensities. The slopes and intensities for the model spectra were compared with those of TW Vir and RX And from the 1985 December outburst. The data for TW Vir spanned from 4 hr before the hot front began to 3.5 hr after. In RX And it was not so easy to determine exactly when the 104 fronts started. However, it is believed that the data from the 17th spans about 10-14.5 hr after the hot front began. The free parameters of the model were adjusted until a good fit was made to the data. In both cases the shapes and values of the slope and flux curves were successfully reproduced. For TW Vir the model using stellar models did a better job of reproducing the data and had fewer variations from Mineshige's model. Overall the agreement between the model and the data is quite good. The time scales involved in these models also agrees well with the time scales observed in these systems. There are some problems with fitting Mineshige's model to the data. For instance, the model flux curves show a sharp kink at the time the hot front turns on. The data for TW Vir do not show this. Instead there is a gradual increase in the flux throughout this time. The RX And data don't cover this time. This is a small detail, though, and for the most part Mineshige's model does quite well at reproducing what is seen both in TW Vir and RX And. Mineshige's model is currently the only model which can explain the behavior of the preoutburst stage. Therefore, not only does the preoutburst stage exist, it does appear to give insight as to the cause of dwarf nova outbursts. Certainly further study into this phase would be useful. It would be interesting to determine if this preoutburst always occurs in every system. It may be that it occurs only in some systems. It may also be that In a given system it takes place only part of the time. It would also be interesting to see if SU Ursae Majoris objects exhibit preoutburst to establish if they are unique to U Gem and Z Cam 105 systems. Two different preoutbursts toolc place in the same system. Further study may show if this is common or if certain systems tend have only one type of preoutburst. There may even be more than two types of preoutburst. Obtaining additional details about preoutbursts could provide further insight into the reason for dwarf nova outbursts. 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