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Astron. Astrophys. 323, 382-386 (1997)

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4. Spectral signatures of compact objects

In Fig. 4a, we schematically show our present understanding of the accretion flows onto compact objects. The Keplerian or sub-Keplerian flows at the outer boundary become increasingly sub-Keplerian close to the inner boundary. On the black hole horizon, and presumably at the naked singularity, the radial velocity approaches the velocity of light (C90b; Chakrabarti 1996c) and since even in the extreme case the sound speed is less than this, the flow must be supersonic at the inner boundary. In the case of accretion onto a neutron star however, the flow is subsonic on the inner boundary. CT95 and Titarchuk et al. (1996) pointed out that in the limit of high accretion rates (where the Thompson scattering opacity [FORMULA]) the eigenvalue of the corresponding radiative transfer equation in presence of convergent fluid flow is given by,


where, [FORMULA] is the location of the inner boundary in units of the Schwarzschild radius. In terms of this eigen value, the energy spectral index [FORMULA] [ [FORMULA] ] is found out to be,


[FIGURE] Fig. 4. a Schematic view of generalized solutions on compact objects where flows close to the objects are sub-Keplerian Bondi type (with or without shocks). b Variation of the soft state spectra in three types of compact objects. In neutron stars (NS) and naked singularities (NSing) the soft state spectra should not have the weak hard tail, while the black holes should have this feature.

In the case of a black hole accretion: [FORMULA] and [FORMULA] ; and one obtains [FORMULA], very similar to what is observed in black hole candidates (Sunyaev et al. 1994; Ebisawa et al, 1996). If [FORMULA] is chosen (which corresponds to the last photon orbit and is probably more physical) the corresponding value is [FORMULA]. In the case of high accretion rates on neutron stars, [FORMULA] giving rise to [FORMULA]. The spectrum at higher energies is thus completely flat. In the case of a naked singularity, [FORMULA], and the spectrum in higher energies is also flat, independent of the accretion rate as long as the post-Keplerian flow (with or without shock waves) has [FORMULA]. Naked singularities may be similar to black holes in the hard states, when the accretion rates are smaller, while similar to neutron stars in soft states although the soft bump is cooler unless the neutron star accretion itself is isothermal (as is possible when shocks are present; see, Shapiro & Salpeter, 1975). These aspects of spectral properties are shown qualitatively in Fig. 4b.

As far as the total energy of radiation is concerned, one could distinguish these objects as well. Since the flow has to dissipate its energy at the hard surface of a neutron star, the luminosity of neutron stars would still be proportional to the accretion rates provided magnetic field is weak enough; non-linear interaction with magnetic fields (Illarionov, & Sunyaev, 1975) may change this conclusion. On the contrary, in a black hole accretion, luminosity could be very small since the flow disappears through the horizon (for instance, constant energy flows of C89 have, strictly speaking, zero luminosity). In a naked singularity, there is no horizon, and extremely hot matter very close to the origin may cause thermonuclear flashes and matter should be at least partially luminous also. However, the detailed physics is not very well understood since one must take into account quantum effects.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998