PART VII. NEUTRON STARS

TIMING EFFECTS IN ROTATING NEUTRON STARS

Ethan J . Schreier

Center for Astrophysics Harvard College Observatory and

Smithsonian Astrophysical Observatory Cambridge, Massachusetts 02138

INTRODUCTION

I n this talk, 1 will be discussing observations of rotating neutron stars, and in particular, what we can learn about neutron stars from studying various timing effects. I intend to concentrate on the observations and their immediate interpreta- tions; other papers will be concerned with more of the theory. In the spirit of this session, 1 will try not to deal with observations which are primarily concerned with binary companions, third body effects, general relativistic orbit corrections, or anything else which doesn’t directly concern neutron star structure, except where these effects offer alternative explanations. Furthermore, the topic of neutron star masses and particularly limiting masses will be dealt with in the following paper.

I n reviewing the radio pulsar literature of the last two or three years, I find little new observational data which directly bear on neutron star structure. The binary pulsar is much more exciting for its implications about mass, evolution, and rela- tivistic effects. However, certain x-ray pulsar data have recently been interpreted in terms of the response of the star to accretion torques with direct application to determinations of magnetic fields and possibly moments of inertia. I will thus con- centrate on these data, drawing parallels with the radio pulsars as appropriate.

EXISTENCE O F PULSATIONS

The first and most important thing which is learned about neutron stars from the study of timing effects is their existence. The original arguments associating the radio pulsars with neutron stars are well known. The regularity of the periods indicated massive objects; the rapidity of the pulsations, the small pulse widths, and the required luminosity indicated a compact object, with an intense gravita- tional field. As shorter period pulsars were discovered, it became more and more difficult to invoke higher harmonics of pulsating white dwarfs, leaving rotating magnetized neutron stars as the logical model. There was the further consistency between the magnetic field required for pulsar emission via accelerated charged particles, and the field predicted for a neutron star from the contraction of the pre- supernova star. Finally, there was the association of the Crab pulsar with the SNR.

The discovery of x-ray pulsars led to parallel arguments. The pulsations of Centaurus X-3 as seen in the U H U R U data in early 1971-in excess of lo3’ ergs/ sec turning on and off every 4.8 seconds-again indicated a condensed object. Its presence in a binary system was recognized from Doppler measurements and occultations. At about the same time, the fast-fluctuating source Cygnus X - l was

44 5

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- c 3 -

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Annals New York Academy of Sciences

x -

in C

+ - 2 8 3 s 3 - 6 k e V 3 1 1 0 9 0 0 - 4 0

I 5 - 15 keV Al118-61 405 s

6-12keV GX301-2 696 s

1 . 5 - 5 k e V 3 U 0 3 5 2 ' 3 0

0.0 0.5 1.0 1.5 2 .o Pulse Phase

FIGURE I . Pulse profiles of nine x-ray pulsars. (From Rappaport & J O S S . ~ By permission or Narure.)

Schreier: Timing Effects, Neutron Stars 441

optically identified with a spectroscopic binary, and Her X-l was found with char- acteristics very similar to those of Cen X-3. Thus the early predictions of accreting compact objects as x-ray sources were confirmed; the now canonical model of a rotating magnetized neutron star accreting matter from a close binary companion appeared. Although it was also proposed that an accretion driven pulsating white dwarf could explain the 4.8 second pulsating source Cen X-3, to explain the 1.2 second pulsations of Her X-l higher harmonics of characteristic white dwarf periods were needed. The recent discovery of pulsations of SMC X-l (Lucke et al . ’ ) , with a period of 0.72 seconds and most of the power at 0.36 seconds, makes a white dwarf model even harder to support.

The long period x-ray pulsars also cannot be explained on the basis of vibrating white dwarfs without making the mass very low, although this doesn’t rule out rotating magnetized white dwarfs. As shown in FIGURE I , nine binary x-ray pul- sars have now been observed, with periods ranging from 0.7 to 835 seconds (cf., Rappaport and Joss’). It is not yet obvious whether the gap between the fast pul- sars ( T 6 5 sec) and the slow pulsars ( T 2 100 sec) indicates two distinct distribu- tions. Rappaport and Joss pointed out th2t no systematic change i n pulse shape or characteristics with period exists; this would argue at least for the same type of objects in both. However, the complexity of time varying detailed pulse shapes, envelopes, and energy spectra has still not been explored in depth.

It should be noted that a principal argument used against neutron stars as the compact objects in binary x-ray pulsars no longer holds. It has been shown theo- retically that it is possible for the supernova that leads to a neutron star not to disrupt a binary system (Wheeler et d3). And there is, of course, the further ob- servational proof that a binary radio pulsar does exist. It has also been shown that in the cases ofCen X-3 and Her X-I, the resultant eccentricity can be removed on a time-scale consistent with reasonable x-ray emitting lifetimes (Lecar et d4).

THE 35-DAY PERIOD OF HERCULES x-1 The first kind of x-ray pulsar variability which was interpreted in terms of

neutron star structure was the 35-day period of Hercules X- I . One of the causes originally suggested for this behavior was precession of the neutron star moving the pulsar beam into and out of our field of view (Brecher’). A second model in- voked the precession of the neutron star causing the 35-day cycle via a magneto- spheric valve-accretion could only take place when the magnetic pole was close enough to the accretion disk in the orbital plane (Pines et ~ 1 . ~ ) . I n both cases, Pines et aL6 pointed out that free precession required a solid core for the neutron star. However, recent x-ray data have ruled out neutron star precession as the cause of the 35-day period. Various reports of emission during the low-state include the U H U R U data ofJones and Forman,’ where a definite increase in intensity is seen at the midpoint of the low-state (FIGURE 2) . Pulsations are detected, and the spec- trum during the low-state is consistent with that of the high-state. Thus, pulsed emission is always present, and we can reverse the argument: any neutron star precession must be less than about 15” (the actual number must reflect a beam shape). The likely model for the 35-day behavior now involves non-changing x-ray emission from the neutron star, with varying attenuation and obscuration by the precessing accretion disk (FIGURE 3). Models along this line have been discussed

448 Annals New York Academy of Sciences

-- --

t

0 8 t

(A31 9-21 aN033S/SlNn03 31VlS 3Sdll33

Schreier: Timing Effects, Neutron Stars 449

(hex 9 - 2 ) aN033S/SlNn03

450 Annals New York Academy of Sciences

by Katz,' R o b e r t ~ , ~ Petterson," and Gerend and Boynton." This precession is tied to the primary and could lead to orbit precession; in fact there is some evidence for a 35-day Doppler effect on the pulsations (Fechner and .loss,'* Deeter and Boynton13).

LONG-TERM PERIOD CHANGES

Although the existence of rapid pulsations suggested the basic models for both x-ray and radio pulsars, the study of the long-term period changes gave much needed confirmation and to some extent began to give some information about the neutron stars themselves. It also helped that by the time this long-term information was collected, enough objects had been discovered to allow reasonable discussions of the distribution of periods, rates of period change, types of companion stars, etc.

The universally observed slowdown of the radio pulsars immediately suggested the source of the radiated energy. The comparison of observed slowdown rates with the energy loss of the pulsars, and particularly with the luminosity of the Crab nebula, via E = 112i1, gave an estimate for the moment of inertia consistent with the numbers expected for neutron stars. The further assumption of magnetic dipole radiation as the means of braking led to magnetic fields on the order of lo'* gauss, again consistent with expectations.

The general speed-up of the x-ray pulsars, first observed for Cen X-3 by U H U R U in early 1972, and not contradicted by any of the binary pulsars, showed that rotation was not the energy source. It was, rather, consistent with the picture of accretion from a binary companion onto a magnetized rotating neutron star.

HERCULES X - l PULSE PERIOD

I 2 3 7 8 2 (

D C

0

W m - I 23781 ' D

Lz W

a I 237811 w u)

0

J 3 a

I23780

I I I

UHURU

A S A S - 3

o s o - 8

1971 I 1972 ' 1973 ' I974

FIGURE 4. Speed-up of Her X-l pulse period, 1971-75. Error bars are are smaller than plotted points.

' 1975

u: those not shown

Schreier: Timing Effects, Neutron Stars 45 I

I I 1

c 0 0 4 841- VI

0 UHURU

A ARIEL 5

1

0

4 8 4 0 - a W ul

4 4 8 3 9 -

4 8 3 8 -

4 8 3 7 -

1971 I 1972 I 1973 1974 I 1975

FIGURE 5 . Speed-up of Cen X-3 pulse period, 1971-75. Error bars are smaller than plotted points.

Although the orbital angular momentum which is transferred to the x-ray emitter via an accretion disk can either speed i t up or slow i t down on the average, depend- ing on the relative rotation directions, the observations indicate tha t for all sources yet observed the spin a n d orbit momenta a re in the same sense.

T h e da ta for three o f the well-determined speed-up rates a re shown in FIGURES 4-6. T h e Her X-I da ta include the original U H U R U data and the recent measure- ments by Becker et d." and Joss er d." T h e Cen X-3 figure is from Fabbiano and Schreier." T h e S M C X- l da ta a re from Henry and Schreier17 a n d include the U H U R U . N R L , and SAS-3 data .

T h e rates of speed-up can be used to further a rgue against white dwarfs a s the compact objects in these systems. On the basis o f Cen X-3 and Her X - I , t he first two binary pulsars known, Gursky and Schreier" showed that the speed-up rates were more consistent with neutron stars than with white dwarfs. Th i s a rgument has been extended to all the x-ray pulsars recently by Rappapor t a n d Joss." More detailed calculations i n the case of Cen X-3, Her X-I, and S M C X-l have been carried out by Fabb iano and Schreier" and by Henry and Schreier.17

T h e basic a rgument assumes tha t all of the mat te r in Keplerian motion a t the inner edge of the accretion disk transfers its angular momentum t o the magneto- sphere a t that point. T h e speed-up rate is then proportional to the accretion rate and inversely proportional to the moment of inertia:

where the mass accretion rate M i s determined by the x-ray luminosity, the AlfvCn

452 Annals New Y ork Academy of Sciences

0 718 I UHURU 0 APOLLO-SOYUZ A SAS 3

0,141 I I I I I I I I I I I I I I I I I I 1000 1500 2000 2500 3

JD - 2440000 0

FIGURE 6. Speed-up of SMC X-l pulse period, 1971-76. Error bars are la.

radius RA is determined by the balance between the pressure of the accreting matter and the magnetic pressure, w, is the spin rate, and w,(R, ) is the Kep- lerian angular velocity a t the Alfvtn radius. (See References 16 and 17 for further definitions and discussion.)

It was an interesting coincidence that the two sources first considered-Cen X-3 and Her X-I-were both found to be spinning up by less than the predicted amount. However, the fact that the ratio of crudely calculated speed-up rates agreed with observation, and the fact that the corresponding white dwarf calcula- tion could not explain the speed-up, led Gursky and Schreier to offer this as back- ing the neutron star model. The discrepancy can be understood in terms of com- peting slowdown torques, as discussed by Elsner and Lamb" and Fabbiano and Schreier.16 Furthermore, it appears that these two fast pulsators are the excep- tion. Rappaport and Joss'' have summarized period change data on eight x-ray pulsars. They plotted the speed-up rate vs. 7L376/7 (FIGURE 7); the solid line shows the dependence predicted by the model for neutron stars with M = 1M, , B = 10" gauss and R = R, = lo6 cm. The general trend of the data is thus in good agreement with the model using typical parameters of neutron star systems. In the case of white dwarfs, the much larger moment of inertia would predict a parallel line 2.5 decades lower.

These calculations also supply implicit evidence that accretion disks exist for these sources. This would not be remarkable in the case of typical semidetached Roche lobe models, e.g.. Her X-I. However, it has been argued that accretion disks are unlikely in the case of massive companions with stellar winds, e.g., Cen X-3 and SMC X-1. The above discussion has been used by Gursky and Schreier," Schreier et U I . , ~ ' and others to indicate that Cen X-3 does have an accretion disk.

Schreier: T iming Effects, N e u t r o n Stars 45 3

It is also in keeping with the current thinking on evolution which predicts a nearly filled Roche lobe at the x-ray-emitting stage of evolution of massive x-ray binaries (e.g., Ziolkowski;” van den Heuvelz3).

DETAILED PERIOD BEHAVIOR

It is the detailed period behavior of the pulsars which, in turn, gives detailed information about the neutron stars, from the standpoint of both torques and re- sponse. The existence of radio pulsar glitches and lower amplitude pulsar noise had to be explained, via crustquakes, corequakes, magnetospheric instabilities, or other probably less likely causes; and the subsequent response of the neutron star to the glitches had to be interpreted, via crust-core coupling constants, moment of inertia ratios, etc. Furthermore, variability of the pulses and of dispersion measure had to be interpreted, in terms of magnetospheric irregularities. Again, there are direct parallels with x-ray pulsar studies. In this case, the “glitches” may be due to changes in accretion torques; by studying these, we learn about accretion mecha- nisms, magnetic field strength, and some characteristic moment of inertia. With more refined data, there will be the possibility of studying crust-core coupling and

-6 I I I I I I

- I 0 I 2 3 4 log (P% 6’7)

FIGURE 7. Speed-up rates of eight x-ray pulsars, log PIP plotted versus log (PL6/’) . Straight line indicates predicted speed-up rates for disk accretion onto a neutron star with typical parameters. Accretion onto a white dwarf would predict a parallel straight line (slope = I ) with y intercept at about -7, i.e., 2.5 decades lower than line shown. (From Rappaport & J O S S . ’ ~ By permission of Nature.)

454 Annals New Y ork Academy of Sciences

relative moments of inertia. The variability of pulse shapes, phases, and spectra again indicates magnetospheric effects; much of this behavior may be due to changing matter flows a t the magnetospheric boundary, as suggested by McCrea and Lamb24 and by Basko and S ~ n y a e v . ~ ~ It must be stressed, however, that it is difficult to separate accretion effects from neutron star effects; torques must propagate from the companion star through a stellar wind, an accretion disk, or both. The only x-ray pulsar glitches yet observed are on the scale of days or weeks.

where the general problem of fluctuating accretion torques is treated; they con- sider the time scale and magnitude of arbitrary accretion torques acting on the magnetosphere necessary to produce a given observed response. This response can shed light on the neutron star structure-the moment of inertia and crust-core coupling-just as in the case of radio pulsar glitches. However, a t this time, i t is hard to decouple the unknown details of the neutron star structure from the un- known details of the accretion torques.

The long-term pulse period curves of both Her X-l and Cen X-3 show signifi- cant fluctuations about the average speed-up rates (FIGURES 4 and 5); both sources have shown local slowdowns on occasion. Although apsidal advance and third- body effects have been proposed (Thomas;27 Brecher and Wasserman2*), they d o not seem that likely. The Her X-l period variations are not that smooth, and other effects would have to be considered as well. F o r Cen X-3, some of the data can be explained by a third body; however, the balance between accretion and dissipative torques discussed below is more consistent with the data.

The one instance where there is good coverage of a reversal in period change is in the Cen X-3 data of August to October 1972. As seen i n FIGURE 8, the period was decreasing with an equivalent T / T of - - year-', a factor of 3 to 4 faster than average (indicated by the dashed line), and within a factor of 2 of the maxi- mum speed-up rate predicted from the model given earlier. This fact itself confirms the fact that the average speed-up rate of Cen X-3 is only some fraction of the maximum rate. Within the course of a month, the period stopped decreasing and started slowing down at nearly the same rate. At the same time, the intensity changed from about 250 counts/sec during the speed-up period to about 175 counts/sec during the constant period week, then to about 130 counts/sec during the slowdown, and finally it increased to about 200 counts/sec at the very end of the observing interval. We thus go back to the idea that the long-term average rate of period change is due to a near balance between the speed-up torque of the accreting matter and dissipative slowdown torques. Short-term fluctuations are then explained by small changes in the balance. Although other dissipative torques (e.g., trapped magnetic fields in the accreting matter) can be imagined, we find the natural balance between the AlfvCn radius and the corotation radius is an effective and self-consistent means of countering the accretion torque. I f the star rotates faster, the corotation radius decreases in relation to the Alfvkn radius, and the magnetic field lines extending outside the corotation radius accelerate the accreting matter, possibly ejecting it from the vicinity of the neutron star (FIGURE 9). The neutron star thus experiences a braking torque. The importance of this process as a means for holding the rotation period near an equilibrium was noted by David- son and O ~ t r i k e r * ~ ; other authors, including Pringle and R e e ~ , ~ ' Lamb et and

One can follow the approach to the data of the Illinois group (cf., Lamb et

Schreier: Timing Effects, Neutron Stars 455

1

FIGURE 8. Detailed period 4 8 4 0 8 0 -

change of Cen X-3 during ; August-October. Two-day period 2

Dashed line shows average S-year speed-up rate. v)

1972

averages and la errors are shown. 5 a W

9 4 84075 a

4 84070

lllarionov and S u n y a e ~ ~ ~ have also discussed the relation between accretion rates and rotation period.

We consider an amoun t of' matter Am just outside the AlfvCn radius r, , orbit- ing with Keplerian angular velocity [ W k ( r A ) = (crn,/rA3)1/2, where m, is the neu- tron star mass]. I f wk is less than the neutron star angular velocity w, = 2 T / T , the matter will be sped up, undergoing an increase in angular momentum Amr,*(w,, - w k ) . The neutron s ta r must lose this same angular momentum, with

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where the denominator includes a rough estimate of the neutron s tar moment of inertia. I n order to calculate the magnitude of thc effect, we must know wk and

456 Annals New Y ork Academy of Sciences

r,; obviously, wk must be significantly less than w, in order for the braking torque to occur without requiring the ejection of a large amount of matter.

The AlfvCn radius is defined via the balancing of magnetic pressure and ram pressure of the infalling matter. I f we specify the neutron star radius and mass, and the x-ray luminosity, we can choose a magnetic field such that the AlfvCn radiusequals the corotation radius. For Cen X-3, a magnetic field of 5 x 10I2 gauss gives an AlfvCn radius of 4 x LO’ cm, corresponding to a corotation period of 4.8 seconds. A decrease in luminosity (due to a possible decrease in stellar wind density) would then increase the AlfvCn radius and cause matter to be ejected (cf. FIGURE 9). Thus, if L went to 1 x ergs/sec, the Alfven radius would increase to5.3 x 10’ cm, with the fractional difference between the new Keplerian and corotation angular velocities being about 1/4. The amount of accelerated matter Am necessary to slow down the neutron star by the observed amount is calculated to be Am = 1 x 10-”M, corresponding to A = 2 x IO-’M (year)-’. Since the x-ray luminosity requires accretion rates of the order of a few IO-’M (year)-’, we see that the acceleration and ejection of some appreciable fraction of the accreting material will slow down the rotation rate by the observed amount. It is significant that a decrease in the x-ray luminosity during the “slowdown” portion of the observing interval is observed, consistent with the above remarks, indicating a decrease in the accretion rate by about 50 percent or less.

A scenario for the overall process could be as follows: The stellar wind density is initially high, with a large accretion rate and a large spin-up torque. The wind density then decreases, increasing the AlfvCn radius. This causes matter to be ejected, slowing down the neutron star, and further decreasing the accretion rate. The slowdown will proceed until the stellar wind density again increases or possi- bly until accelerated matter (which has not left the system) builds up to a density sufficient to decrease the AlfvCn radius.

In the above interpretation, in order to balance the observed accretion rate, we had to use a magnetic field of about 5 x lo’* gauss. We thus see that in sources with this behavior, the luminosity during periods of rapid speed-up determines a lower limit on the magnetic field, assuming known mass and radius.

A spin-up rate for SMC X-1 has also recently been determined (Henry and S ~ h r e i e r ’ ~ ) . In TABLE I , we list the observed and predicted spin-up rates for SMC X-I, Cen X-3, and Her X-I. The errors on the predicted numbers are domi- nated by the inaccuracies in the masses of the neutron stars determined from the binary systems.

The predicted maximum spin-up rate of SMC X-l is close to the observed value; this is not true for Her X-1 and Cen X-3. It is significant that the slowdown mechanism is not operating strongly in S M C X-l since the observed speed-up is consistent with both the higher luminosity and lower pulsed fraction of the source. The luminosity of SMC requires that an order of magnitude more matter be ac- creted onto the neutron star, a s compared with Cen X-3 or other stellar wind binaries; we don’t expect a significant amount of mass to be ejected. The difference between Cen X-3 and SMC X-l can be explained by a change in the relative mag- netic field strengths; a weaker field for SMC X-l would lower the Alfvin radius with respect to the corotation radius, yielding a more efficient accretion process and larger spin-up torque. A smaller field for SMC X-l would not only explain the lack of braking torque but would also be qualitatively consistent with a lower

Rsyn ' 'A

Normal accretion, i / r < 0

Rsyn < RA

Matter ejected, +/T > 0

Synchronous radius: = r w2 2 R s y n = (4.3X1O8) X (418)2/3 -

FIGURE 9. Schematic of speed-up/slowdown model. T o p part shows situation with high accretion rate causing high luminosity and Alfvtn radius inside corotation radius resulting in large speed-up rate. Lower part shows situation when accretion rate has decreased. Alfvtn radius is now outside corotation radius; some matter is sped up and ejected, neutron star slows down, and luminosity decreases.

TABLE I SPEEDUP RATES OF SMC X-I, CEN X-3, AND HER X-l

- P I P

P I O - ~ year-' - L (2-35 keV) eres s- ' I s Predicted Observed

7.7 ~t 0.8 + I 4 -2.5

-7

SMC X- I 51 0.7 16

Cen X-3 5.0 4.84 22 + I 4 2.8

Her X - l I .5 I .24 1 . 1 f 0.2 0.03

457

458 Annals New York Academy of Sciences

pulsed fraction and wider pulses, as observed, due to the reduced channeling of the accreting matter.

In summary, we find that x-ray pulsar observations d o extend the study of neutron star structure, since the accretion torques supply the external stimulus necessary to kick the neutron star; we can then watch the response and determine magnetic fields and moments of inertia. However, this in turn necessitates certain care in treating the data: the response behavior must be decoupled from the torque behavior. It is also useful to note that most of the relevant information thus far obtained is rather old-the extended U H U R U observations of Cen X-3 and Her X-1. Although increased time and spectral resolution is of course appropriate, careful monitoring of sources over many binary periods is essential for detailed timing studies.

ACKNOWLEDGMENTS

Certain of the work discussed here has been done with G. Fabbiano and P. Henry. Useful discussions with R. Giacconi, H. Gursky, and W. Tucker are also greatly appreciated.

[NOTE ADDED IN PROOF: I t has been pointed out by Y . Avni (private com- munication) that the range of masses for Cen X-3 is significantly larger than assumed in the above calculations (and by Fabbiano and Schreierl' and Henry and Schreier"). This has the effect of increasing the error bars on the pre- dicted speed-up rate; in particular, if the mass exceeds 2 M a , the predicted rate becomes comparable to the observed average rate. However, this in no way affects the observational fact that local speed-ups are observed at a factor of 3 larger than the average rate, demonstrating the variability of the torque acting on the neutron star.]

REFERENCES

I .

2. 3. 4 . 5. 6. 7. 8. 9.

10. 1 1 . 12. 13. 14.

15. 16. 17.

LUCKE, R., D. YENTIS, H. FRIEDMAN, G . FRITZ & S . SHULMAN. 1976. Astrophys. J .

RAPPAPORT, S. & P. Joss. 1977a. Nature 266: 123. WHEELER, J . , C. MCKEE & M . LECAR. 1974. Astrophys. J . Lett. 192: L71. LECAR, M . , J . C. WHEELER & C. F. MCKEE. 1976. Astrophys. J . 205: 556. BRECHER, K. 1972. Nature 239: 325. PINES, D., C. PETHICK & F. K . LAMB. 1973. Ann. N.Y. Acad. Sci. 224:237. J O N E S , ~ . & W. FORMAN. 1976. Astrophys. J . Lett. 209: L131. KATZ, J . 1973. Nature 246: 87. ROBERTS, W. 1974. Astrophys. J . 187: 575. PETTERSON, J . 1975. Astrophys. J . Lett. 201: L61. GEREND, D. & P. BOYNTON. 1976. Astrophys. J . 209: 562. FECHNER, W. & P. Joss. 1977. Astrophys. J. Lett. 213: L57. DEETER, J . E. & P. E. BOYNTON. 1976. Astrophys. J . Lett. 210: L133. BECKER, R. H., E. A. BOLDT. S. S. HOLT, S. H. PRAVDO, R . E. ROTHSCHILD, P. J .

Joss, P. C., F. LI, Y.-M. WANG & D. HEARN. 1977. Astrophys. J . 214: 874. FABBIANO, G. & E. SCHREIER. 1977. Astrophys. J . 214: 235. HENRY, P. & E. SCHREIER. 1977. Astrophys. J . Lett. 212: L13.

Lett. 206: L25.

SERLEMITSOS, B. w. SMITH & J . H. SWANK. 1976. Preprint.

18.

19. 20. 21.

22. 23. 24. 25. 26.

27. 28. 29. 30. 31. 32.

Schreier: Timing Effects, Neutron Stars 459

GURSKY, H. & E. SCHREIER. Neutron Stars, Black Holes and Binary X-ray Sources.

RAPPAPORT, S. & P. Joss. 1977b. Nature 266: 683. ELSNER, R. F. & F. K. LAMB. 1976. Nature 262: 356. SCHREIER, E. & G . FABBIANO. 1975. Symposium on X-ray Binaries. Goddard Space

ZIOLKOWSKI, J . This volume. V A N DEN HEUVEL, E. P. J. This volume. MCCREA, R. & F. K. LAMB. 1976. Astrophys. J . Lett. 204: LI 15. BASKO. M . Y. & R. SUNYAEV. 1976. Preprint. LAMB, F. K., D. PINES & L. SHAHAM. 1975. Symposium on X-ray Binaries. NASA/

Goddard Space Flight Center, Greenbelt, Md. THOMAS, H. C. 1974. Astrophys. J. Lett. 191: L25. BRECHER, K . & I . WASSERMAN. 1974. Astrophys. J . Lett. 192: L125. DAVIDSON, K. & J . P. OSTRIKER. 1973. Astrophys. J . 179: 585. PRINGLE, J . & M. J . REES. 1972. Astron. Astrophys. 21: I . LAMB, F. K., C. J . PETHICK & D. PINES. 1973. Astrophys. J . 184: 271. ILLARIONOV, A. F. & R. A. SUNYAEV. 1974. Preprint.

H. Gursky & R. Ruffini, Eds. D. Reidel Pub. Co. Dordrecht, Holland.

Flight Center, Greenbelt, Md.