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387 Paperpresented at the 13th Int. Conf. on and Gravitation Cordoba, Argentina, 1992: Part 2, Workshop Summaries

Relativistic

Richard H. Price

Department of University of Utah Salt Lake City, UT 84112 USA

Abstract. Work reported in the workshop on relativistic astrophysics spanned a wide varicy of topics. Two specific areas seemed of particular in— terest. Much attention was focussed on sources, especially on the waveforms they produce, and progress was reported in theoretical and observational aspects of disks.

The title “relativistic astrophysics” is rather broad, and has illedeiined boundaries separating it from the concerns of other branches of relativity, and of other workshops at the conference. As l interpret it, the subject should be driven (although sometimes indirectly) by observations. On this basis the following topics would seem to be some of the interesting devel» opnients in the past year or so: (i) The discovery of the isotropy of y—i‘ay burst sources suggests a cosmologicalorigin. (ii) The identification of blaclehole candidates in compact matu— systems, systems with signatures rather different from Cygnus Xel, is a sign of ration ol. the field. (iii) There is increasing evidence that our own has a mass concentration near its center, suggesting a central , and/or other strongefield phenomena. (iv) Data from the llubble telscope confirm the longstanding belief that there is a mass cusp at the center of M87. (v) Recent work, especially the numerical simulations by Shapiro and Teukolsky [1], reported at this conference, presagc the down, {all of cosmic censorhip. What are the astrophysical consequences of Shapiro-'l‘eukolsky spindle singularities? Along with these new, or reactivated, problems there remain some venerable issues, problems on which progress continues, and on which further work is needed. We are still far from having an adequate understanding the physics of accretion disks around black holes. Perhaps related to this is one of the Classic question of relativistic astrophysics: the central structure of active galactic nuclei. The range of subjects covered was broad and somewhat scattered. I shall review here two subjects, which were well represented: sources of gravitational radiation, and accretion disks/toroids. Both, are questions the “long-standing problem” variety. The first of these, gravitational wave sources, was a subject of marked concentration in the workshop, and was the focus of five of the thirteen oral presentations. The focus,

(a 1997i lOP PublishimT Ltd 388 General Relan'vily and Gravitation J 992

in fact, was rather narrow. The great interest in details of source waveforms leaves no doubt that the anticipated advent of laser interferometer gravitational wave detectors is having a considerable impact. One presentation holds out an interesting hope of tying together observations of gravitational waves and the recent discoveries about 7-ray bursts. Perhaps the reason these bursts have not created the same flurry among relativists as among astrophysicists is that in the 20 or so years since they were first discovered the bursts have been assumed to be dramatic, but not relativistic, events involving strongly magnetized neutron . All this has changed with the findings of BATSE (Burst and Transient Source Experi- ment) on the Compton GRO ( ) [2]. There are two important features of bursts that it has discovered: (i) the bursts are distributed isotropically, and (ii) plots of number of bursts vs. burst strength show a fall off at low strength. These results almost certainly point to sources at z N 1. At this point the field is open for much speculation, and the data leave room for some differences of interpretation. For one thing, the PVC (Pioneer Venus Orbiter) which has higher threshold (and different energy range) than BATSE has been monitoring strong 7»ray bursts since 1978. A com~ parison of the strong burst data of PVC with the extensive statistics of weak bursts from BATSE suggests a deficiency of weak bursts that points to evolution of the source population and rules out early sources [3]. The way the data are to be interpreted is an open question. There might, for example, be two different classes of phenomena contributing to the observations. The nature of the source is a question that is open even wider. Exotic possibilities, such as stars made of strange , have been suggested [4], as has the tidal disruption of an ordinary by a massive ( 1W ~ 108MB) black hole [5]. Perhaps the favored modeleat least the most conservative modeleis that of the coalescence of two compact objects, either a binary as suggested by Piran [6] and others, or a neutron star— black hole binary, as suggested by Paczynski [7]. The expected frequency of neutron—star coalescences is on the order of 10—6 year“1 per galaxy) which would be compatible with the rate at which bursts are being detected. The energy requirement for a 2 ~ 1 burst is around 1050 ergs, and would be compatible with the expected 1053 ergs for a binary coalescence. This all should, of course, means that 7—1‘ay bursts are of great potential interest to relativists, since coalescence of compact binaries is also the presently favored source of detectable gravitational waves. At the workshop David Nicholson reported on work with Schutz that points out how this can be exploited for gravitational wave (GW) observations. In particular, the 7—ray burst and the GW burst for the coalescence should coincide within 1 sec The pattern matching necessary for the search for GW bursts would be simplified by searches limited to the data within 1 sec of an observed 7-ray burst. This allows, for example, the use of a finer mesh of filters and improved sensitivity. The detection of a burst by BATSE would provide directional information on the burst source, and would therefore constrain the form of the signal arriving in GW detectors. Monte Carlo simulations were used by Nicholson and Schutz to explore the magnitude of the improvement to be gained from a search for coincident bursts. They find (for an optimally configured detectors) that 2 GVV detectors would be able to detect a binary neutron star coalescence out to z = 0.4. Other work reported at the workshop was also motivated by the problem of the pattern matching necessary to find GW signals from coalescing binaries. Very recent Relativistic astrophysics 389 results by the CalTech [8] show that much improved detailed understanding of the final inspiral of compact binaries will be needed if astrophysical information is to be efficiently extracted from GW waveforms. Larry Kidder reported on work with Will and Wiseman [9] on one facet of the progress that will be needed. They study the existence of innermost stable orbits for compact binary systems. The approach is a hybrid of (post)2- Newtonian analysis [so that (post)5/2 radiation damping is omitted] and test body effects from the Schwarzschild geometry. The results show that, for a given mass of the binary pair, the radius of the innermost stable orbit is 20% larger for an equal mass binary than for the test body case. The need for more precise predictions of source waveforms was part of the motiva- tion for the presentation, by Alan Wiseman, of a study with Will of “heredity effects” in GW phenomena. These are nonlinear effects that in general require integration over the past history of the system. Another motivation was the relation of this work to the “Christodoulou nonlinear memory” [10]. A gravitational wave train is said to have “memory’7 if the strain hU-(t) is different after the the passage of the waves than it was before the arrival of the waves. In principle, this would leave the free masses of a GW de- tector in positions different from their positions before the waves arrived, and the shifted positions would constitue a souvenir of the burst, the “memory.” In practice this DC offset of the burst would be swamped by noise, but it can be inferred by measurement of the low frequency content of the burst, the components of the burst at frequencies below any characteristic frequency of the source. A major reason for the interest in GW memory is the recent correction of a widespread and longstanding conceptual error concerning its calculation. Only 1/1" con- tributions to hi, are radiative; for the memory only the initial and filial values of h;, are needed; before and after the strong accelerations producing the fat middle of the burst, the stress energy is simply that of “particles” moving at uniform velocity; the 1/r fields of these particles is just the Coulomb fields due to their masses, and those contributions are completely within the scope of linear theory. It was therefore the common wisdom that the calculation of the memory produced by an astrophysical event required only linearized gravity theory, even for a strong field events like black hole collisions. As long as the waves were weak at the detectors, it was thought, linearized theory should suffice for calculations of the memory. Christodoulou [10], with a rigorous mathematical analysis, showed that this was wrong, that there are in fact nonlinear contributions to the memory that are of the same order as the linear contributions. It was quickly shown to be equivalent, for waves from astrophysical sources, to including the emerging GWs themselves as part of the source [11][12]. Though this nonlinear part of the memory is present in principle, it is a separate question whether it could be detected. Preliminary model calculations [12] suggest that detection with laser interferometers will be very difficult, but may be possible. A presentation by Viqar Husain dealt with an aspect of GW waveforms not directly related to binary coalescences. Model calculations of GWS from strong-field sources, black holes or relativistic stars, have shown that GW wavetrains tend to be dominated by “quasinormal” (QN) ringing, oscillations at complex (i.e., damped) frequencies which are characteristics of the spacetime of the black hole or relativistic star. This QN dominance has some apparent parallels with normal mode phenomena. In Newtonian theory, for example, a stellar model with no fluid dissipation would have hydrodynamical motions consisting of a superpostion of the normal modes of the star. Given the initial conditions 390 General Rela/ivily and Gravz'la/ion 1992

of the system one can calculate the amplitude of excitation of each mode, and subsequent motions of the system are always the same superposition of these normal modes. The dynamics of the system is in this way relatively easily extracted from the initial data. The damping of the modes could then be calculated to find the imaginary part of the damped normal mode frequency. These simplifications of calculation and understanding follow from the propery of “completeness” normal modes. Intuition suggests that the same sort of picture, in some sense, must apply for QN dominated sources, at least for not-very—relativistic stars described with general relativity. There is, however, a crucial mathematical difference between normal modes and QN modes. Completeness and other useful properties of normal modes follow from the fact that they are solutions of a self—adjoint problem. For QN modes the causal boundary condi— tion of outgoing waves gives a problem which is not self»adjoint (the complex frequency eigenvalues are a sure sign of this) and for which none of the familiar features of normal mode systems are guaranteed to be valid. There is then no guarantee of completeness, but neither is there a prohibition against it, and consideration of not—very—relativistic stars argues for some sort of completeness [l3]. But what sort? Hnsain[l/l] uses a model problem of mechanical system with radiative damping. Special features of the system make a complete analysis straightforward and allows some insights to be gained about the sense in which QN modes can be complete. The results show that, for the model, the QN modes are complete for initial data that is “purely outgoing,” that is, initial data that. generate no ingoing waves at large distances. For such data the excitation of the QN modes, and the subsequent motions of the system can be extracteda from the initial data. It is likely that this result can be extended to an approximate description of a relativistic stellar model. One presentation at the workshop dealt with aspects of GVVS much broader than that ol' waveforms. An analysis of the exterior Schwarzschild geometry by Kundu had led him to claim [15] that when propagating in the neighborhood of a body of mass M, the amplitude of GWs of frequency w is smaller by a factor V/l + Lo2G'2M2/4eG than what would have been expected on the basis of the qn.’nlrnpoln formula. This would mean, for example, that waves from a binary coalescence with w : 103 Hz at the center of a galaxy with a mass of 1011M.) will be suppressed by nine orders of magnitude. Knndu’s analysis assumes that the quadrupole moment of the radiating source is described by 1/)8, the coefficient of the 7"5 part of the Newmanel’cnrose quantity ‘Ilo. This is known to be the case for stationary spacetimes, and for linearized gravity, but on the basis of a scalar model calculation Kozamch 6! (1] [l6] have argued that 1/)8 does not describe the source quadrupole; rather, in the scalar model the analog of $8 is “enhanced” with respect to the quadrupole, and this enhancement cancels Kundu’s calculated suppression. A gravitational source calculation [17] has been done to show that for GWs from a source at the center of a galaxy the only effects due to the mildly curved are those small effects that are expected. On the other hand, Kundu has presented the basic formalism for a source calculation of $8, and finds no enhancement [18]. At the workshop Jorge Pullin reported that all results are now reconciled. For quadrupole-dominated sources there is indeed an enhancement of $8 which cancels Kundu’s suppression. Thus, long sources deep inside a massive galaxy will be detectable on the outside with negligible suppression. Sources far (many ) from the center of the galaxy will suffer a strong suppression of the radiation in the “quadrupole mode,” if by Relativistic asMop/lysics 39]

“quadrupole” is meant the formal (,7 = 2 mode with respect to the center of of the galaxy. But sources far from the center, even if they are slow motion sources, will have their radiation dominated by high order E—pole moments. The mathematics of the suppression is therefore correct, but if does not affect any sources of astrophysical interest. The second topic of concentrated interest at the workshop was accretion disks. Studies of disks around holes has, so far, always featured some approximations. In particular, Abramowicz 61‘. a] [19] studied self-gravitating disks around pseudo—Newtonian black holes and found evidence that massive disks would be unstable; Wilson [20] studied non—self—gravitating disks around Kerr holes and found no evidence on instability. At the workshop Shogo Nishida reported work, with Eriguchi and Lanza, on a nu— merical code that is able to handle a rotating black hole and toroid in equilibrium. The numerical approach uses the full equations of general relativity and is not limited in the range of masses or angular velocities. The particular results reported assume that the toroid is made of a perfect fluid obeying a polytropic equation of state and having a uniform distribution of angular momentum. Studies were reported on several interesting strong—field phenomena such as the appearance of ergotoroids, and the absence of evir dence for prolate black holes. But the results which were probably ()f most immediate astrophysical interest were those on stability. By considering sequences of models with fixed total angular momentum Nishida et a! conclude that selfegravitating disks are in fact unstable if (for their model assumptions) the toroid mass is greater than 10% of the hole mass. It is generally thought that massive black holes play a crucial role in the energetics of active galactic nuclei, though the nature of the mechanism is not Clear. A conservative model assumes that the angular momentum of infalling matter leads to the formation of an accretion disk, and uses “staudaidl7 accretion disk theory to produce the AGN energy and the high energy part of its observed spectrum. The predicted spectra depend on details of the disk (thick vs. thin, source of ) and of the dominant radiative processes. A careful and extensive study was made by and lV’ialkan [21] of what kind of agreement with observation could be achieved by such a conservative approach. They assumed physically thin and Optically thick disks around both Schwarzschild and rapidly rotating ((1 : 0.998) Kerr holes, and included the general relativistic effects on the emerging radiation (gravitational and Doppler boosting, focussing) and inclination effects. The results were compared with 60 and AGNs selected for well deter— mined spectra, and the spectra were corrected for reddening, intergalactic absorption and other observational effects, to arrive at an estimate of the inherent spectrum generated directly by the energy source. For each object the black hole mass, the accretion rate and the inclination angle were varied to achieve a best fit. Sandip Chakrabarti, reporting at the workshop on work with Wiita, noted that the overall results were quite good but that in several cases (he concentrates on 1202+281 and 2130+099) the models predict too little emission in the far UV. (It should be noted, however, that the Sun-Malkan models even more clearly predict too much UV emission in other cases, in particular 1421+330.) Chakrabarti has argued that the conditions necessary for the formation of standing shocks will often be present in accretion disks, and that these shocks can have significant observational effects [22]. At the workshop he pointed out that such shocks will result in a hotter inner disk region with the potential to produce greater UV than the Sun—Malkan models. He presented results for geometrically thin, optically thick disks around Schwarzschild holes. General relativistic effects on boosting and focussing emis— 392 General Relativity and Gravitation J 992

sion were omitted (and were found to be important by Sun and Malkan only for rapidly rotating Kerr models). The results [23] do indeed show better agreement in the UV than the Sun-Malkan models7 and suggest that standing shocks may indeed play some role in some AGNs and quasars.

References

[1] Shapiro S L and Teukolsky S A 1991 Phys. Rev. Lett. 66 994—7 [2] Meegan C A et al 1992 Nature 355 143-6 [3] Fennimore E E, Epstein R 1, Ho C, Klebesadel R W and Laros J 1992 Nature 357 140—141 [41 Haensel P, Paczyr’iski B and Amsterdamski P 1991 Astrophys J. 375 209—215 [51 Carter B 1992 Astrophys J. 391 LS7~L70 [6] Piran T 1992 Astrophys J. 389 L457L48 [7] Paczynski B 1991 Acta Astron. 41 257 Lindley D 1991 Nature 354 20721

[81 Cutler C, Bildstein L, Flanagan E, Markovic D, Sussman G and Thorne K 1992 reported at workshop C1 of GR13

[9] Kidder L E, Will C M and Wisernan A G 1992 submitted to Class. Quantum Grav. Letters [101 Christodoulou l) 1991 Phys. Rev. Lett. 67 148679 [111 Thorne K S 1992 Phys. Rev. D45 5207524 [12] Wiseman A G and Will C M 1991 Phys. Rev. (Rapid Communications) lt29/1579

[131 Friedman J 1991 in Recent Advances in General Relativity eds. A. Janis and .1. Porter (Boston: Birkhauser) [141 Price RH and llusain V 1992 Phys. Rev. Lett. 68 197376 [151 Kundu K 1990 I’roc. It. Soc. London A431, 337 Kundu K Ohio University report (unpublished) [16] Kozameh C, Newman E T and Rovelli C 1991 Phys. Rev. D44 551*554 [17] Price R, H and Pullin 1992 Phys. Rev. in press [181 Kundu K 1992 submitted to Proc. R. Soc. [191 Abramowicz M A, Calvani M and Nobili L 1983 Nature 302 597 [201 Wilson D B 1984 Nature 312 620—621 [211 Sun W—H and Malkan M A 1989 Astrophysical J. 346 68~100 [22] Chakrabarti S K 1990 Theory of Transonic Astrophysical Flows (Singapore: World Sci- entifie)

[23] Chakrabarti S K and Wiita P .1 1990 to appear in Astrophysical J. Letters