Neutron Stars in Binary Systems G. Borner, Munich (Max-Planck Institute for Physics and Astrophysics)

The discovery of a 58 keV line fea­ sources, and sources showing irre­ already been established that they are ture in the spectrum of the X-ray gular fluctuations (as e.g. Cyg X-1 on members of a binary system (several source HerX-1 by J. TrÜmper and his a timescale of milliseconds) appear are listed in Table 1), i.e. they are in colleagues from Tubingen & Garching less exotic than the flare-like objects, orbit around an optical companion. (Germany) in 1976 '), as reported in which appear, reach a peak lumino­ As long as there is no evidence to Europhysics News, 8 (1977) 5, is the sity, and then fade away as if they the contrary, we may live happily with latest exciting news from the rapidly had never been. But most peculiar are the assumption that all other galactic expanding field of X-ray astronomy. the burst-like sources, which emit X-ray sources are also binary systems Cosmic X-rays are completely absor­ their X-rays in short term bursts of a with mass flow, and we may wait bed by the earth's atmosphere, and few seconds duration, with no appa­ confidently for further candidates to therefore the observing instruments rent periodicity involved. The theorists Table 1. have to be placed in the outer layers do not hesitate, however, to invoke Most of the energy is liberated or outside the atmosphere. Up to equally exotic images, when they try deep inside the gravitational well, i.e. 1970, balloon and rocket flights had to explain the observations. Although on the stellar surface, if the compact led to the discovery of about 30 X-ray we are far from understanding these object is a neutron star, or within a sources. But then, in December 1970, X-ray stars completely, we have lear­ few Schwarzschild radii, if the object NASA launched the Uhuru satellite ned quite a bit during the past years. is a black hole. In both cases, for 1 which was devoted entirely to X-ray Some general, fairly obvious, but not solar mass objects, distances are astronomy. This was the big step necessarily compelling conclusions $$ 106 cm. A proton in free fall on to

forward, because within less than 2 (there is always a more complicated a 1 Mo object would have a kinetic years, Uhuru had found about 100 fairy tale with the same outcome) can energy of 100 MeV at such a dis­ galactic and about 50 extragalactic be drawn immediately from the data : tance. If one thermally radiates away X-ray sources. About 90 % of these The rapid variability on timescales the energy in X-rays of a few keV, i.e. galactic sources apparently constitu­ of seconds or milliseconds (cf. Table at temperatures of 7 $$ 107 to 3x107 K, ted a new class of stellar objects 1) suggests that a compact object from areas with such typical dimen­ with an X-ray luminosity exceeding (white dwarf, neutron star, black hole) sions, one finds luminosities of 1036 - the sun's total luminosity by a factor is involved. The energy source for the 1038 erg/s. 5 of 10 . This was substantiated by X-rays comes from gas which accre­ This is in good agreement with the satellite observations in later years. tes in the deep gravitational well of observations. Talking only of black The new satellites also revealed the compact object, flowing over from holes and neutron stars is, of course, new types of galactic X-ray stars, so a companion star, which is not com­ unfair to the white dwarfs, which can that now one knows of a large variety pact. This view is supported by the also satisfy the constraints imposed of types, of which regular pulsating fact that for 10 X-ray sources, it has by the data. But accretion on white

Table 1

Source Short term variability Long term variability Optical candidate Distance Luminosity (2-10 keV) (kpc) (1036 erg)

HerX-1 1.24 s pulsations X-ray eclipses (1.7d) HZ Her ; 2-6 1 -10 (6 kpc) (3U1653 + 35) 35d modulation 1.7d binary long-term on-off

Cen X-3 4.84 pulsations X-ray eclipses (2.1 d) double ellipsoidal 6-9 10-30 (9) (3U1118-60) extended lows light variation Ob star

Cyg X-1 Irreg. var. in times slow transition HDE 226868 2.5 3-10 var (3U1956 + 35) of milliseconds between 2 distinct 5.6d binary spectral states

Vela X-1 283 s pulsations flares, eclipse HD 77581 2 10 (3U0900-40) (282.8913 ± 0.0004) (8.95d)

SMCX-1 0.71 s pulsation X-ray eclipses, 3.9d SK 160 60 30 - 300 (3U0115-73) extended lows 13 mag.

ScoX-1 Irreg. var. min slow (~ 10 min-h) ScoX-1, blue 1 -2 10 (3U1617-15) flares 0.787d period

A0620-00 none appears in outbursts optical 1 100 lasting $$ 1 year Identification (1967 & 1975) no period determined tures of the X-ray source (in Fig. 1, therefore that HerX-1 is a neutron star. a schematic drawing of the gas flow It also establishes that neutron stars is presented). Table 1 (ref. 2) con­ really have the large magnetic fields tains several regularly pulsating X-ray expected for them from theoretical sources, with pulse periods in the considerations of stellar collapse, and range of 1.24 s (HerX-1) - 283 s (Vela from the slowing down of the pulsars X-1). The time-keeping mechanism is by the emission of electromagnetic probably rotation of the compact ob­ dipole radiation. Meanwhile a second ject, which means rotation of a neu­ experiment by Trümper ef al. has tron star at least for the fast rotators. confirmed the results of the first mea­ The observed pulses must be produ­ surements, and other observers have ced by an asymmetry in the infall also obtained evidence for a line fea­ of matter, and the obvious way to ture in the spectrum of HerX-1. achieve this is to have inclined to the The large value of 5. 108 T also in­ axis of rotation, a stellar magnetic dicates that the line emission is a field, which guides the matter down, quantum effect. In strong magnetic such that only certain hot spots on fields, the motion of the electron per­ the surface accrete. As these hot pendicular to the field is quantized, spots move through our field of vision, similar to the quantization of the elec­ we see X-ray pulses. tron orbits in an atom. The energy difference between two adjacent or­ Fig. 1. — Schematic drawing of accretion bits or levels is $$ωB_ where ωB = from a stellar wind and Roche Lobe Measurement of the Magnetic Field overflow with disk accretion. of a Neutron Star B B What information do we gain from eBlmc is the classical gyration fre­ dwarfs produces keV X-rays only, if observations on the physics of the quency. A spin reversal of the elec­ the infall is radial ; the observed accretion process close to a neutron trons has the same energy difference period changes are very difficult to star ? The spectrum of the radiation 2π h ωB. So there are two excited explain, and strong magnetic fields, emerges from a complicated and in­ states with the same energy diffe­ as measured by Trümper 1), cannot tricate interaction of many distinct rence with respect to a ground state : be supported by white dwarfs. With features, such as hot plasmas accele­ a higher orbit quantum number, or a accretion on to neutron stars or black rated by a strong gravitational field, different spin direction of the electron holes, about 10% of the rest mass guided by a rotating magnetic field, on the same orbit. Transitions into the energy of the infalling gas is conver­ finally hitting a neutron star surface ground state from the first excited ted into X-rays. Thus the accretion of very high density. There are so state in this system of Landau levels rates do not have to be very large : many parameters unknown, that a produce the observed line. The emis­ 8 10 sion of higher harmonics should also 10- Mo/a to 10- Mo/a is sufficient quantitative picture of the accretion to give the powers observed. process is not available, one only be possible. There is, indeed, an indication of an enhancement in the These or larger mass-transfer rates knows that it must be quite compli­ observed spectrum around 110 keV, can easily occur in close binary sys­ cated. where one would expect the second tems. Three different mechanisms There are great hopes, however, for harmonic to occur. may be important : an improvement of the theoretical i) A massive companion expanding situation, due to the measurement by Fig. 2. — Measurement of J. Trümper et across the critical equipotential the group of J. Trümper. They have al1) showing the spectrum of the HerX-1 surface between the two stars observed the regularly pulsating pulses and of OSO-8 (Aug. 75) showing the total spectrum. — Roche lobe overflow — could source HerX-1 for about 4 hours in a transfer mass at a rate of 10-6 balloon flight from Palestine/Texas on 3 Mo/a to 10- Mo/a. May 3, 1976. The spectrum for the ii) A stellar wind, I.e. an atmosphere pulsed flux they have obtained is streaming radially outwards, as shown in Fig. 2. There is strong evi­ expected from Ob or Be stars, can dence of a spectral line feature at 58 ±

have a magnitude of 10-6 Mo/a. 5 keV, which has an intensity of The accretion rate on to the or­ 3.10 -3 cm-2 s-1, that is several percent biting neutron star or black hole of the total pulsed flux. The best es­ 9 would then be about 10- Mo/ a. timate of the line width is ≤ 12 keV. iii) A feedback mechanism, where the The most likely explanation for this heating of the companion by X- line seems to be in terms of an elec­ rays, produces the mass flow ne­ tron cyclotron emission, because ato­ cessary to substain the X-rays, mic or nuclear emission mechanisms may also be possible. Such a fail to produce the high intensity re­ mechanism may be applicable to quired. If the line emission is due to the HerX-1 system. the radiation of electrons spiralling It is probable that because of the around the magnetic field lines of the angular momentum of the accreting star, then the line frequency is a gas, the mass flow will lead to the direct measure of the magnetic field formation of an extended flat disk strength. 58 keV corresponds to a around the compact object (the disk magnetic field of B = 5.108 T. Such will probably be smaller in the case a high value of the magnetic field of a stellar wind). The physics of the can only be expected for a neutron accretion disk determines many fea- star. This experiment establishes The pulsed continuum radiation starts to dominate around a radius of above 25 keV can be fitted by an ex­ 1000 km, and the X-rays come from ponential spectrum of $$ 8 keV cutoff, a region near the neutron star surface and the 58 keV cyclotron line is sitting with a radius of 10 km. The whole on top of it, assuming it is seen in region of this extended magneto- emission. It is likely that the hot plas­ sphere affects the formation of the ma emitting the X-rays is optically X-ray pulses. In that sense, the line thin with respect to the continuum measurements provide an invaluable radiation (the free-free absorption diagnostic tool in determining details coefficient is much smaller than the of the accretion mechanism on to a Thomson scattering coefficient). The neutron star. absorption coefficient at the cyclo­ tron frequency is, in contrast, much Mass Determination of Neutron Stars larger and the black body intensity in in Binary Systems the emission line should be reached Besides the observations of spectra causing the line to stand out above and pulse shapes, and hence a value the continuum. It is thus not a contra­ for the magnetic field of a neutron diction to assume an electron tem­ star, the existence of these X-ray perature in the accretion channel sources in binary systems, allows the right above the neutron star surface, determination of their masses within greatly in excess of the average kT rather narrow limits. For regularly of 8 keV. In fact kT should be greater c pulsating sources such as HerX-1, one than ~ 40-50 keV, to populate the can, from the Doppler shift of the Fig. 3. — Masses of neutron stars for higher Landau levels sufficiently and X-ray pulses, obtain radial velocities various realistic equations of state derived excite the line. It is difficult to under­ from a 2-body potential using many-body and finally a value for the mass techniques ; taken from ret. 5, where com­ stand how the protons transfer several 3p 3 function (M sin i) / (Wx + Mp)2, which plete references can be found. percent of their kinetic energy to the depends only on the mass of the electrons. Coulomb collisions and optical companion Mp1 on the angle i collective plasma excitations may be between the normal to the orbital the X-ray source orbits the star, we important. It is only fair to say that plane and the line of sight, and on see the ellipsoid head on (minimum the excitation mechanism for the line the mass of the X-ray source M In light) — sideways (maximum) — head is not understood at present. x. several cases (Table 2) the optical on — sideways during one revolution. On the other hand, one can already companion has been identified, and A precise analysis of these light draw some conclusions from the ob­ its mass can be derived from the curves is quite involved, but it clearly served line width. If the main broading spectral type within certain limits. depends very strongly on the mass mechanisms are Doppler broadening Then one needs information on the ratio of the two components 2). and self-absorption, both depending angle of inclination from other obser­ From Doppler shifts of spectral lines on the angle of the line of sight of the in the optical, one can determine a vations, to determine Mx. mass function (M3 sin3i) / (M + /W )2 observer with the magnetic field, the The source HerX-1 shows periodic X p x small width enforces the conclusion occultations with a period of 1.7 d. even for nonpulsating X-ray sources. that the cyclotron line is seen from a The optical companion, Hz Her, ex­ The regularly pulsating source, Vela direction close to perpendicular to hibits regular variations by two magni­ X-1, allows a determination of an the fields, i.e. the radiation must show tudes in phase with the X-ray eclipses. optical as well as an X-ray Doppler a fan-like pattern. The same mecha­ This means that the light variations shift, and thus the mass value for this nism is probably responsible for the are caused by irradiation from the source is determined very accurately. appearance of pulses in the other X-ray source. For the mass function The results of this light curve ana­ spectral regions, since pulse shape, lysis (Avni & Bahcall2), are listed in one finds a value of 0.85 Mo. The phase and duty cycle are similar in the spectral type (late A to F) gives — to­ Table 2. One can see that neutron continuum and the line. This fan-beam gether with sin i = 1, which seems star masses (i.e. masses of regularly is of course very plausible, because plausible from theoretical considera­ pulsating X-ray sources) are within along the accretion columns the pho­ the theoretical limits of 0.2 - 2.5 M . tions of the 35 day cycle of this o tons are dragged downwards, making It is interesting to note that the masses source: Mx = 1.7 - 2.2 Mo and

it much easier for the radiation to seem to be rather high (≥ 1 Mo) a Mp = 0.7 - 1.4 Mo and a distance of escape sideways than upwards. 5 kpc, cf.2). fact which may be relevant with regard There are potentially great rewards For sources, where the irradiation to the evolutionary history of these in this observation, rewards for the by X-rays of the optical companion is objects. theorist, but more work is required negligible, one can find sinusoidal Black Hole in Orbit to arrive at a quantitative model for variations in the optical light curve the formation of the pulses. The flow with twice the orbital period. These In Table 2 we find a minimum mass pattern of the plasma in the neutron are due to an ellipsoidal deformation Mx = 8.5 Mo for Cyg X-1. This inno­ star's magnetic field, i.e. the structure of the star by the X-ray source. As cent looking fact has made this object of the accretion column, determines one of the most widely discussed in recent years. the opacities in the various directions, Table 2 the structure of the hot spot, and White dwarfs have masses less than therefore also the region where the Source Mx/Mo Mopt/Mo 1.4 Mo, and also the masses of neu­ line originates. The plasma flow In HerX-1 $$ 1 $$ 2 tron star models do not seem to turn is influenced by the interaction CenX-3 0.6-1.8 16-20 exceed a maximum of 2.5 — 3 Mo (cf. SMCX-1 2.2 - 4.2 26 - 30 Fig. 3). These models have been cal­ of the disk of incoming gas with the Vela X-1 1.3-2.2 20-28 neutron star's magnetic field. The field Cyg X-1 8.5-15 23-45 culated with many-body methods from fluctuations occur on a time-scale of plosions leave a neutron star as a milliseconds, indicating an extension remnant. One possible mechanism of the source of ≤ 100 km. The ave­ would be the collapse (electron cap­ rage spectrum changes between two ture) of an iron core above the Chan- distinct states of low and high inten­ drasekhar limit. But an iron core sity for the soft X-rays between 2 and would require a rather massive initial 6 keV. These are puzzling properties, configuration. Smaller mass stars but so far they are not understood. It seem to get completely disrupted in is also not clear whether the accre­ a SN explosion, because of explosive tion on to a black hole has charac­ C12 burning. So the evolution of sys­ teristic features which distinguish it tems such as HZ Her-Her X-1, which

from other accretion processes. The­ contain only 3 Mo, is ill understood. refore the evidence for a black hole Model calculations also indicated that in orbit rests on the somewhat indi­ it is difficult to obtain the correct rect argument about its mass excee­ binary periods. ding the mass limit of other compact As the secondary evolves further it objects. will eventually overflow the Roche lobe, and cover the X-ray source. It may then be possible that the com­ Evolution pact source spirals inward inside the How do neutron stars in binary secondary, blowing a lot of mass out systems come into being ? For the of the system, until finally it orbits a massive systems with a massive blue white dwarf like core. The core may supergiant as the companion, an evo­ undergo a supernova explosion too, lution along the lines of Fig. 4 may leaving a binary system of two neutron Fig. 4. — A possible evolutionary se­ have occurred (after ref. 3). stars, or a neutron star and a black quence lor a binary system3). After the primary (the more massive, hole. This could be the story of the and therefore more rapidly evolving) birth of a binary pulsar as PSR 1913 + 16. of initially 25 Mo, say, has burnt its a 2-body potential which is attractive hydrogen core, contraction and hy­ at large separation and becomes re­ drogen shell burning sets in, during Binary Pulsar pulsive at short distances. But large which phase the hydrogen envelope The pulsar PSR 1913 + 16 has been extrapolations from the density re­ of the primary is almost completely discovered in 1975 by Hülse & Tay­ gime accessible by laboratory experi­ transferred to the secondary (of ini­ or4) (parameters in Table 3). It is in ments with nuclei, had to be made in tially lower mass, say 8 Mo, and the­ a very narrow binary system : (projec­ the derivation of the precise shape, refore less rapidly evolving). The pri­ ted along the line of sight, the peria- especially of the repulsive part of the mary is then a helium star with helium stron Is Ro $$ 7 x 1010 cm). A normal 2-body potential. So the reliability of core burning, and M ≤ 4 Mo. Its life­ star cannot fit in, therefore the pul­ this upper mass limit for neutron stars time after the onset of oxygen burning sar's companion must be a small could be questioned. The Cyg X-1 is much less than the thermal time- object, either a compact object or a mass determination instigated theore­ scale of the envelope (neutrino emis­ helium dwarf. If the companion really tical investigations into absolute upper sion cooling). is a compact object, then this system mass limits using only assumptions Then the core collapses before the is a unique laboratory for tests of such as positive density, positive pres­ star reaches its critical Roche lobe. general relativity. A precise clock (the sure-density gradient, but no specific This collapse and supernova explo­ pulsar period) in orbit presents the equations of state for densities above sion, will not disrupt the system, be­ opportunity of measuring relativistic normal nuclear density. In addition, cause the secondary is still unevolved, effects such as periastron advance, these limits were investigated in Ein­ and has a much larger mass. The spin precession, effects of gravitatio­ stein's theory of general relativity as remnant is a black hole or a neutron nal radiation on the orbital parame­ well as in other more exotic theories star, which may for some time appear ters. of gravitation. When astrophysicists as a pulsar. The radial Doppler shifts have been indulge in such free speculations, the The secondary then evolves away measured and the mass function has result is to be expected : no absolute from the main sequence, to a blue been obtained. The periastron ad­ upper mass limit seems to exist. But supergiant, produces a strong stellar vance has recently been found to for the more conservative mind, con­ wind, and by accretion on to the amount to 4°/a. If this is due only tent to stay within the limits of Ein­ compact object, the X-ray source to relativity, one knows the sum of stein's theory, an absolute upper mass appears. the masses to be 2.8 Mo. Another limit of 5 — 8 M seems to exist. This o There are some difficulties with this measurement, e.g. of the spin preces­ then has the consequence that Cyg general picture. It is still unknown, sion, would determine all system para­ X-1 is the first established represen­ under what conditions supernova ex­ meters. Any further measurement of tative of the sinister class of black holes, collapsed objects which hide behind an event horizon, through Table 3 Binary Pulsar PSR1913 16 which no radiation can escape. Only when they accrete matter they beco­ Period 0.0590301 ± 0.0000002 s Flux at 430 MHz 0.006 ± 0.003 Jansky me visible through the radiation of the Eccentricity of orbit 0.6 hot plasma which surrounds them. Longitude of periastron 179° Rate of advance of periastron 4o/a The radiation from Cyg X-1 has Projected semimajor axis a1 sin i = 1.00 ± 0.02 solar radi peculiar characteristics. Short-term Mass function f(m) = 0.13 ± (0.01) Mo a relativistic effect, would then also be a test of Einstein's theory of gra­ vitation. Universiteit van Amsterdam The group for Atomic Physics in the Zeeman Conclusion Laboratorium has a vacancy for a It is fascinating to see how, star­ ting with the discovery of the pulsars, many more and ever more exotic senior research astronomical objects involving neu­ tron stars have been found. These associate (m/f) massive bodies of densities inacces­ sible in terrestrial laboratories, seem to be set up in such a variety of celes­ who will participate in current activities (term analysis of spectra and laser spectroscopy), tial systems that their properties can with the special duty to take charge of be unravelled step by step. These are theoretical support. Applicants should be good times for astrophysicists. qualified specialists in the field of theoretical atomic structure and spectroscopy and have a References good knowledge of experimental methods. 1. TRÜMPER, J., PIETSCH, W., REPPIN, Educational duties include the teaching of C, VOGES, W., STAUBERT, R., and theory of atomic spectroscopy at an advanced KENDZIORRA, E., Ap. J. Letters 1978 (in press) level and coaching of graduate students. Command of the English language is 2 "X-Ray Binaries" Proc. of NASA Symp. mandatory while a reasonable knowledge of at GSFC (Maryland) (1975). This volume has been used as a standard reference Dutch is expected to be acquired during service. for the data presented. Applications with curriculum vitae, list of publications and names of referees to be 3. VAN DEN HEUVEL, E.P.J, and HEISE, J. Nat. Phys. Sci. 239, 1972, 67 received before July Ist, by Dr. P. F A. Klinkenberg 4. TAYLOR, J.H., HULSE, R.H., FOWLER, Zeeman Laboratorium LA., GULLAHORN, G.E., and RANKIN, J.M., Ap. J. 206, 1976, L53 Plantage Muidergracht 4 I0I8 TV Amsterdam - The Netherlands. 5. BORNER, G., Springer Tracts in Mod. Phys. 69 (1973) 1

Lattice Dynamics M. Balkanski, Paris (Chairman, Condensed Matter Division) An International Conference on Lat­ tential energy of electrons, in simple ening and lattice instabilities in d-band tice Dynamics was held In Paris, Sep- metals at least, is small compared to metals pointing out a strong corre­ tember 5-9, 1977, sponsored by EPS, their kinetic energy : the ratio can lation between such behaviour and a IUPAP and SFP. The programme of then serve as a small parameter. The high density of states at the Fermi this conference reflected recent de­ electronic response to core displace­ level associated with the d-states, and velopments in this field, a large part ments can be described in terms of a also with the occurrence of relatively simple complete set of equilibrium being devoted to phase transitions re­ high Tc in superconductivity. Model lated to mode softening and central functions and yield a unified formula­ calculations considering several qua­ peak. The remarkable developments tion of microscopic lattice dynamics si-degenerate d-bands at the Fermi of non-linear physics have also pene­ both in metals and non-metals. A level yields, for Nb, the characteristic trated the field of lattice dynamics : a rigorous "first-principle" calculation dips in the longitudinal branches session was devoted to solitions. has yet to be performed. The effort along [100] and [111]. The dip along Much interest seems to focus on in this direction is nevertheless inter­ [111] is probably related to the "cen­ phonon driven phenomena : super- esting for at least two reasons : mi­ tral peak" observed in Nb and Nb-Zr conductivity, ferroelectricity, melting croscopic theory should help us un­ alloys. NbC and TaC show also pro­ and to non perfectly (ill) condensed derstand in detail how the dynamical nounced softening type anomalies in matter, defects in materials, disor­ spectrum of solids arises from their the acoustic modes reproduced well crystal and electronic structures em­ dered phases, amorphous solids and by the same model. It has also been ploying Fermi surface effects, co- liquids and materials of specific inter­ pointed out that the response func­ valent, ionic, metallic binding, etc. est like superionic conductors. tion X (q), peaks in NbC due to Fermi The second reason is that such theory c Instead of an overall account of the surface nesting features, which occur should connect the same macroscopic Conference a few significant contri­ also at the position of the anomalies. physics to related properties such as butions in the fields of Microscopic This may indicate correlation between superconductivity, crystallographic Theory, Solitons and Electron-Phonon the electron-phonon matrix elements phase transitions, optical and trans­ Interactions are summarized. and the electronic structure. port properties and the like. A similar coincidence with regard Microscopic and Model Theories S.K. Sinha 1) advocates the approach of Lattice Dynamics using the density response function to peaks in Xc (q) and the position in Microscopic calculations of phonon of the electron system. With the formu­ q of the maximum softening, is men­ dispersion curves are much simpler in lation using this approach, he exami­ tioned in the "charge-density-wave" metals than in non-metals. The po- nes the occurrence of phonon soft­ materials, e.g. the layered transition