arXiv:astro-ph/0207270v1 12 Jul 2002 lycle bakhl addts aehge masses higher have of range candidates” the hole in “black called ally ain fteXryeiso niaetepeec fa of presence the indicate emission (10 X-ray pul- strong periodic the obtained stable of is First, surface observations. sations of material types a two of from The presence horizon. the i.e. event an hole, of by black evidence formed material a is or a surface ) whose possessing quark object a an star or star a neutron either (a X- surface is in component systems compact binary the ray that believed generally is It Introduction 1. trmse r l ocnrtdaon h “canonical” the M around 1.4 concentrated of all value bimodal Neutron are a 1998). (at masses Nolan show & star form masses Shahbaz their binaries Miller, (see objects: X-ray distribution ev- of in direct types two is bodies evidence least) there compact of However, that absence”. “Absence prove of idence horizon. not evidence event does not an absence is of their presence surface, the solid a of presence horizon. obvious event an an are of object absence compact the the of accumu- of proof surface matter the bursts in at X-ray occurring lated of explosions observations black thermonuclear Second, a - system. of the presence the in excludes hole theorem “no-hair” the of h aiu aso eto o ur)sa,wihis which than star, higher quark) are (or than neutron larger masses a never their of that mass is maximum bodies the holes massive black more McCaughrean being the suspecting of & for Cuby reason Greiner, The and 2001). 2001 McClintock & wl eisre yhn later) hand by inserted be (will Astrophysics & Astronomy lhuhXryplain rXrybrt niaethe indicate bursts X-ray or pulsations X-ray Although 2 Abstract. Accepted / Received 4 1 3 fbigabakhole. black accurate a very the being trace of will of existence which the observations, fundamentall future of is favour to also in proof ones, such strong that very here sometimes argue We proposed. been nttt fAstronomy of Institute nvri´ iree ai ui,Prs6 Paris Curie, Marie et Universit´e Pierre eateto srnm n srpyis hlesUniver Chalmers : Astrophysics, email and Astronomy of Department ntttdAtohsqed ai,9bsBueadArago, Boulevard : 98bis email Paris, de d’Astrophysique Institut mi : email oosrainlpofo h lc-oeevent-horizon black-hole the of proof observational No 9 − 10 ⊙ [email protected] [email protected] [email protected] eety eea aso bann bevtoa ro of proof observational obtaining of ways several Recently, 15 ∼ hra h eodcaso ois usu- bodies, of class second the whereas ∼ ae .Abramowicz A. Marek )mgei ed hc ytevirtue the by which field, magnetic G) o1 M 18 to 5 M 3 ⊙ seeg agd ta.1994). al. et Salgado e.g. (see aucitno. manuscript ⊙ oansKepler Johannes seeg aaa,Garcia Narayan, e.g. (see 1 , 3 , nvriyo iln G´ora, Poland Zielona of University , 4 oe Klu´zniak W lodek , ytedtiso h pctm erco oysuspected body a of metric spacetime the of details the ly rudabakhl,tesoe nrywl els forever lost forms be will ADAF energy an stored If the flow. hole, not black the a is in around matter stored accreting but away the radiated from remov- effi- torques momentum radiative viscous angular by low ing released energy very which with in ciency describe ADAFs ADAFs by Proof 2. event- of Yi existence & the prove Narayan to horizons. used 1995; be can al. 1995a,b) et 1994, Abramowicz The (ADAFs; Accretion Dominated collaborators. Flows Advection of and properties that Narayan is claim been Ramesh has “posi- by This existence. a attempted event-horizon’s wish the rather of would proof of tive” One favour in existence. argument black-hole persist— satisfactory the would very a matter M not bulk low is 10 “unlikely” hadronic unrealistically than which require at larger densities would masses this with Q-—because bodies that low. likely this densities have al. to et matter Bahcall baryonic by allows given (1990) interactions sub-nuclear mean-field nuclear The of of “Q-stars.” description configurations so-called the entertain are to These density. willing is one aeilsraecnhv assa iha 0M 10 as high as masses with have stars can that surface showed material (1990) 1987). of a Selipsky Ipser equation & & causality-limit Friedmann Lynn 1974; a Bahcall, Ruffini by & described (Rhoades state be to taken is ε a eepesda 8 as expressed be can 0 vn oio,btte antpoei.Ti applies This it. prove cannot they but horizon, event stefiuildniyaoewihteeuto fstate of equation the which above density fiducial the is 51 ai,France Paris, 75014 lhuh ssonb ilre l 19) ti un- is it (1998), al. et Miller by shown as Although, ngnrl h aiu aso opc body compact a of mass maximum the general, In mosbe bevtoscnpoiearguments, provide can observations impossible: y iy 1-6G¨oteborg, Sweden 412-96 sity, 2 , 3 n enPer Lasota Jean-Pierre and , h xsec fbakhl oioshave horizons black-hole of existence the . 4 ε 0 / 10 14 cm g 3 − 3  − 1 / 2 M ⊙ where , ⊙ ⊙ are if , 2 Abramowicz, Klu´zniak, Lasota: No proof of event-horizon under the , whereas if the accreting body is of the argument) that ADAFs are subject to mass loss a “star” this energy must be radiated away once matter and therefore the dimness of quiescent SXTs could result lands on its surface. Therefore, the argument runs, black from the low accretion rate onto the compact object - holes should be dimmer than neutron stars, quark stars, most of the matter being lost with the wind. However, as etc., if in both cases an ADAF is present. shown by Menou et al. (1999), such wind models do not The best systems in which this hypothesis could be offer an explanation of the difference between tested are the so-called Soft X-ray Transients (SXTs) neutron-star systems and those presumed to contain black which are close binary systems undergoing rare and pow- holes. In fact, these authors also pointed out that the qui- erful outbursts but spending most of their life in a low escent luminosity of neutron-star binaries is not consistent luminosity quiescent state (see Tanaka & Shibazaki 1996 with the assumption of a ∼ 10% radiative efficiency. Since for a review). In SXTs, like in Low-Mass X-Ray Binaries the attempt to apply to these systems the windy-ADAF (LMXBs) in general, a compact body accretes matter lost model of Quataert & Narayan (1999) failed, they proposed by a Roche-lobe filling low-mass stellar companion. The that the action of a magnetic propeller could be answer. accreting matter forms a disc whose instabilities trigger However, a compelling signature of this effect has yet to outbursts (see Lasota 2001 for a review of the instability be found. model). Narayan, McClintock & Yi (1996; see also Lasota, Despite of this, Abramowicz & Igumenshchev (2001) Narayan & Yi 1996 and Narayan, Barret & McClintock suggested that the observed differences between quies- 1997) proposed that quiescent SXT discs are truncated cent of accreting black holes and neutron and that the inner accretion flow forms an ADAF. This stars is well explained by the occurrence in such systems hypothesis has been recently vindicated from the theoreti- of a CDAF (Convection Dominated Accretion Flow; see cal point of view by Dubus, Hameury & Lasota (2001) and Narayan, Igumenshchev & Abramowicz 2000) instead of is supported by observations (see Done 2002 for a review). an ADAF. They found that for low viscosities accretion Narayan, Garcia & McClintock (1997) compared qui- flows around compact bodies form ADAFs only in their escent luminosities of SXTs supposed to contain black innermost regions but are convectively dominated at radii 2 2 holes with those of neutron-star SXTs and realized that, R ∼> 10 RS (where RS = 2GM/c is the Schwarzschild in accordance with the prediction of the ADAF model, radius). In such flows emission comes mostly from the systems containing black-hole “candidates” are dimmer. convective region; the radiative efficiency is independent −3 They came to the conclusion that they found evidence for of accretion rate and equals εBH = 10 . Assuming that the presence of event horizons. the efficiency of accretion onto a is εNS ≈ This conclusion has been challenged by Chen et al. 0.1 one obtains the observed ratio between black-hole (1998) who asserted that the relative dimness of black-hole and neutron-star luminosities. Unfortunately this cannot candidate systems was due solely to Narayan et al. (1997) be the correct explanation of the luminosity difference comparison method. Things were clarified by Lasota & (Lasota 2002) because, as mentioned above, neutron stars Hameury (1998) who suggested comparing systems with in quiescent transient systems do not seem to accrete with similar orbital period on the assumption such systems a 0.1 efficiency. would have similar accretion rates – the ADAF model Another class of argument asserts that X-rays in qui- asserting only that accreting black holes should be dim- escent SXTs are not emitted by the accretion flow. mer than neutron stars for the same accretion rate. The Brown, Bildsten, & Rutledge (1998) suggested that, in new method showed, however, the same effect (Lasota & neutron-star systems, most (or all) of the quiescent X-ray Hameury 1998; Menou et al. 1999), recently confirmed by luminosity is not due to accretion but results from cooling Garcia et al. (2001): black holes (candidates) are dimmer of the neutron-star crust heated by nuclear reactions. This than systems known to contain neutron stars, or at least crust-cooling model does not seem to be in perfect agree- stars with surface. ment with observations showing two spectral components This is a very strong argument in favour of the presence and a variable flux (see Rutledge et al. 2002 and refer- of event horizons, in fact this is the most conservative ences therein). If the crustal-cooling model were right it conclusion. However, it is not a proof. would imply different X-ray emission mechanisms for the two classes of quiescent SXTs. However, luminosity vari- 3. Arguments against evidence based on relative ations observed also in quiescent black-hole systems (see dimness of candidates e.g. Garcia et al. 2001) would rather suggest a common origin. Attempts to ascribe quiescent X-ray luminosity in The arguments against the claim that the relative dimness black-hole systems to active stellar companions (Bildsten of black-hole candidates is the proof of existence of event & Rutledge 2000) are not based on a sound theoretical horizons are of two, not unrelated, types. First, it has been foundation (Lasota 2001) and have been refuted by obser- argued that the accretion flow in quiescent SXTs are not vations (Garcia et al. 2001). represented by ADAFs. Menou (2001) presented an argument based on the Narayan & Yi (1995a) and Blandford & Begelman settling-flow model of Medvedev & Narayan (2001) in (1999) argued (see however Paczy´nski 1998 and which the accretion flow arrives with very low angular mo- Abramowicz, Lasota & Igumenshchev 2000 for criticism mentum at the surface of a rapidly rotating compact ob- Abramowicz, Klu´zniak, Lasota: No proof of event-horizon 3 ject. The X-ray luminosity is then due to rotation-energy composed of matter whose properties have been described loss by the accreting body. This requires viscous con- by Bahcall et al. (1990) but also more compact configura- tact between this body and the accreting matter. Menou tions whose microscopic properties are not known at all. (2001) pointed out that if black-hole candidates had, con- Therefore there is no reason to assume that the surface of trary to neutron stars, radii smaller than the inner-most such objects is composed of ordinary matter and is in the stable orbit the accretion flow would be supersonic and temperature range required for X-ray bursts to occur. The viscous contact impossible. Black-hole candidates would stellar surface could be too cold to support a thermonu- be dimmer because unable to lose their rotational energy. clear runaway. As a matter of fact, the accreted matter Finally, we note that very compact objects with a sur- could be converted right away to a more exotic form, as face would be dimmer than less compact objects, simply it would be on contact with quark matter in the color- because of redshift and light bending. If the surface is be- locked phase (Alford, Rajagopal & Wilczek 1998, Rapp low the photon orbit, the fraction of “outward moving” et al. 1998), or with the skin of a (Mazur & photons which escape to infinity is in the Schwarzschild Mottola 2001, see below). This could happen even at zero metric density, contrary to the hypothesis advanced by Narayan 1 2 & Heyl (2002). No nuclei, no bursts. ∆Ω 27 (1 − R /R) / =1 − 1 − S . (1) 2π  4 (R/R )2  S 5. For the lowest possible value for a causality-limit equation Mazur and Mottola (2001) have recently found a new of state R/RS =9/8, this factor and the redshift squared yield a luminosity at infinity which is equal to only 0.040 static, spherically symmetric, solution of Einstein’s field of the luminosity at the source. equations. A gravastar, as it is called, has the standard vacuum Schwarzschild exterior, and an interior filled with matter that has the equation of state ρ = −p. The interior 4. Absence of X-ray bursts is described by the de Sitter solution, and is matched to Three of the SXTs show millisecond pulsations, and two of the exterior vacuum solution in a very thin shell of thick- −33 them are X-ray bursters. They all have very short orbital ness on the order of the Planck length, λP =1.6 × 10 periods, 2 hr in the case of SAX J1808.4-3658 (Wijnands cm. The gravastar has no horizon or singularity. Its rigid and van der Klis 1998; Chakrabarty and Morgan 1998), surface is located at a radius just slightly greater than the 43.6 min for XTE J1751-305 (Markwardt et al. 2002), and gravitational radius, R∗ = RS + fλP , f ∼ 2. 42 min for XTE J0929-314 (Galloway et al. 2002). It is per- There are several purely theoretical objections that one fectly well understood that occurrence of coherent pulsa- could raise against gravastars, none of them conclusive. tions or of type I X-ray bursts is incompatible with the For example, stellar-mass gravastars have entropy smaller presence of an event horizon, so none of these sources can than ordinary stars with the same masses and this would be found on the list of black hole candidates, even though require extremely efficient cooling before gravastars could their masses are unknown. form during stellar collapse. observational However, it is true, as pointed out by Narayan & Heyl There is no way to distinguish what may (2002), that none of the longer (binary) period SXTs, with seem to be a Schwarzschild black-hole from a gravastar. a measured mass function greater than 3M⊙ is a type I To see this, let us denote the surface redshift by 1/2 1/2 burster. Narayan & Heyl (2002) compute instability of RS fλP accretion onto a hypothetical 10M⊙ star with a surface ε = 1 − = . (2)  R∗   R∗  of radius between (9/8)R and 3R , and report that for S S For astrophysically interesting gravastars, with mass a range of accretion rates compatible with observations 5 greater than M⊙, i.e., R > 3 × 10 cm, this quantity of X-ray novae, the star is expected to give rise to an X- S 9 2 is very small, ray burst if the accreted column density is 10 g/cm ≤ −19 Σ ≤ 1011 g/cm2. From this, the authors conclude that ε< 10 ≪ 1. (3) black hole candidates cannot have a surface, as they do The power of any radiation emitted by the surface of not exhibit X-ray bursts. a gravastar is greatly reduced because only the radiation One concern is that the authors do not present the within the solid angle 27ε2/4 around the normal to the results separately for the lowest column density consid- surface escapes to infinity. Further, because of gravita- ered, 109 g/cm2, and the higher values 1010 g/cm2 and 11 2 tional redshift, the power of radiation received by a distant 10 g/cm —for a 10M⊙ star with a 3RS radius, the mass observer is only ε2 of what was emitted at the gravastar’s transferred in the transient outburst ∼ 6×1024 g/cm2 cor- 9 2 surface. Therefore, the power emitted from the surface is responds to 6 × 10 g/cm , so the X-ray burst expected at reduced by one of the higher column densities may, in fact, not occur 4 −75 during a SXT outburst. However, there is a more funda- ε < 10 (4) mental doubt as to the relevance of the result. by the time it reaches a distant observer. One should con- Since the minimum radius of Q-star is 1.4 RS (Miller et clude that a gravastar with mass greater than M⊙ is to a al. 1998), Narayan & Heyl (2002) consider not only objects distant observer as black as a black hole. 4 Abramowicz, Klu´zniak, Lasota: No proof of event-horizon

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