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Astron. Astrophys. 333, 583-590 (1998)

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2. Properties of low mass black hole binaries

It is useful to summarize the properties of the six X/O transients with low mass companions and mass functions indicating [FORMULA]. The properties most important to the present discussion are listed in Table 1, and are extracted from the observational reviews of Tanaka & Lewin (1995), Tanaka & Shibazaki (1996) and Zhang et al. (1997) and the references therein. Some synthesis and extrapolation to common energy bands has been made; for example the masses [FORMULA] and [FORMULA] are generally quite uncertain; when only one digit has been given the masses may be uncertain by [FORMULA] %.


Table 1. Properties of low mass BHB transients

It is important to note that these systems have been discovered over a period of [FORMULA] 20y with widely differing instrumental capabilities. Nevertheless, it has become clear that the low mass black hole binaries display many striking similarities and it is therefore appropriate to estimate the population of these sources as a homogeneous class. The class of X/O novae is larger than the six well-studied examples described below. In Tanaka & Lewin (1995) and Tanaka & Shibazaki (1996), [FORMULA] 12 other (generally fainter) X-ray transients with properties similar to the known low mass BHB are listed as possible BH systems, but do not have measured mass functions. Additionally, the transients GRO 1655-40, 1E1740.7-2491 and GRS 1915+105 are likely black holes. GRO 1655-40 is a dynamical BH candidate, but it is not considered here since it has an intermediate mass ([FORMULA]) secondary; further these three sources do not display the characteristic isolated outburst behaviour of the low mass systems. To complete the roster of BH candidates one should mention the classical persistent systems Cyg X-1, LMC X-1 and LMC X-3 which all have high or intermediate mass secondaries.

2.1. X-ray outbursts: fluxes and spectra

The X-ray outbursts of identified black holes have a rather similar appearance, with a rapid rise to a peak luminosity that can approach the Eddington limit in soft X-rays, followed by an exponential decay back to quiescence on a timescale [FORMULA]. There may be a faint precursor before the main outburst and the decay may be interrupted by smaller `reflares' spaced by several [FORMULA]. The similar basic behaviour has lead several authors to conclude that these are disk instability transients. For example, King, Kolb and Burderi (1996) have shown that LMXB transient behaviour corresponds well to predictions of the disk instability model. This picture is applied in Sect. 2.3.

Although these X/O novae are often referred to as `Soft X-ray Transients', the spectral behaviour of the outbursts has been divided into two classes. The first class (UP) is indeed soft, with an ultra-soft (U) component dominating below 10keV at maximum and a variable high energy power-law (P) tail. In the late stages the burst often transitions to a hard state dominated by the P component. The high energy power-law index varies over an appreciable range ([FORMULA]). A second class of BH transients has been discovered, for which the U component is weak or absent and the luminosity is dominated by the power law component, even near burst maximum. In these cases the spectrum appears to be hard ([FORMULA]). Since sky monitors discovering X-ray transients survey in quite different bands, it is important to consider the hard and soft flux separately. In Table 1 the estimated soft (2-6keV) and hard (20-300keV) component fluxes of the six transients at maximum are listed, interpolated from data in Tanaka and Shibazaki (1996) and references therein. Note that for the UP class in particular the maximum fluxes in the two bands may occur at different times. For UP sources with poorly observed hard fluxes ([FORMULA]) the estimate [FORMULA] is used. For the P sources it is seen that [FORMULA]. The fluxes are highly variable on short timescales, even at maximum.

2.2. Optical outbursts

The optical outbursts of the black hole transients are a product of reprocessed X-rays from the central accretion disk. This leads to light curves with characteristic decay constants of [FORMULA] (King and Ritter 1997). Modern outbursts of X/O novae confirm that the optical flux decays more slowly than the X-rays, although earlier outbursts of 2023+338 had [FORMULA] (the time for a decay [FORMULA]) of [FORMULA] the 1989 [FORMULA] rather than the [FORMULA] predicted by King & Ritter. There is a general correlation between the X-ray outburst flux and the optical peak magnitude, but apparently details of the disk affect the reprocessing of flux into blue optical light. Previous outbursts of two of these systems were recorded on archival sky survey plates (eg. Duerbeck 1987). For these sources an approximate recurrence time is thus known. The historical optical outbursts showed low amplitude and slow decay with brightness fluctuations (nova class Bb), similar to the optical outbursts observed during the modern X-ray selected events.

2.3. Recurrence times

These outbursts are held to be equivalent to the dwarf nova eruptions of white dwarf cataclysmic variables in the accretion disk instability model (e.g. Huang and Wheeler 1989, King & Ritter 1997). In this model the viscosity, and hence local energy release, of the disk is controlled by the ionization state of hydrogen. The system initiates an outburst when the largely neutral, low viscosity disk exceeds a local density threshold, causing a transition to a `hot' high viscosity state with large mass flows. The energy released in accretion onto the central source irradiates the outer disk (King & Ritter 1997), ionizing the gas and forcing the disk to remain in the high [FORMULA] state until the ionized zone is depleted of mass and the disk can return to its quiescent `cool' configuration. In this picture the `re-flares' of the disk occur when heated outer regions accrete through the central zone on a viscous timescale. Neutron star accretors do not generally show this behaviour as the hot central object continues to irradiate the disk even as the accretion decreases so that the disks remain in the hot outburst state. In this way the presence of an event horizon (i.e. a black hole) is central to the existence of large amplitude X/O outbursts.

Since, according to King & Ritter (1997), the heated disk must be accreted for the outburst to cease, a simple prescription for the recurrence time is


where the disk mass [FORMULA] (with [FORMULA] the pre-outburst disk density, a typical disk radius [FORMULA] cm and [FORMULA]) is replenished on a timescale [FORMULA] by mass transfer from the secondary [FORMULA] at rates near [FORMULA] /y. The disk radius can be related to the binary parameters; since the average Roche lobe radius is [FORMULA] for these high mass ratio systems and the disk around the primary extends to [FORMULA], one has a disk radius [FORMULA], where [FORMULA] is the total system mass in solar mass units and [FORMULA] is the binary period in days. In long period BHB, however, King & Ritter (1997) note that the outer disk may not be sufficiently heated by the central flux to become ionized and achieve high viscosity. For [FORMULA], an Eddington-limited mass accretion rate of [FORMULA] /y and standard parameters for a BH irradiated disk, their estimates give a maximum heated radius of [FORMULA] cm. This is larger than the full disk radius for all of the observed systems except GS 2023+33. As there is good evidence that this X/O nova reached an Eddington-limited luminosity in outburst, in this system [FORMULA] is taken to be [FORMULA].

For all of these binaries we have [FORMULA]. For the short period systems mass transfer is driven by loss of angular momentum. Considering first GR losses one has


with the stellar masses in [FORMULA], and [FORMULA] the orbital period in days. In many short period binary systems, `magnetic braking' (Verbunt and Zwaan 1981) is also believed to play a role, giving


At longer periods the system is driven by nuclear evolution of the secondary. King, Kolb and Burderi (1996) give the convenient expression


for secondaries well off the main sequence.

GS 2023+338 clearly has mass transfer driven by evolution of the secondary. For the systems with [FORMULA] h angular momentum losses should be driving them to shorter periods. If the secondary mass is near the low end of the allowed range, however, significant mass loss must have occurred. Further, it is also clear that for 1705-250 and 1124-683, at least, the secondaries must be somewhat evolved to maintain Roche lobe contact. It is generally assumed that nuclear evolution ceases at initial Roche lobe contact, but there will be a range of periods for which modest evolution of the secondary can occur before angular momentum capture and spiral-in. The orbital period would be reduced below that normally expected for the evolved star core mass, and the nuclear evolution-driven transfer rate should provide an upper limit in this case. Detailed models are needed to compute precise transfer rates.

Following the discussion above, the model outburst recurrence times can be computed for the low mass BH binary systems. Table 2 lists [FORMULA] (in y) for the mass transfer rates (2.2)-(2.4). For objects with earlier outbursts recorded on sky survey plates, the observational [FORMULA] estimate is also listed. In the case of GS 2023+338, nuclear evolution-driven transfer is assumed to replenish the inner heated disk. For the binaries with [FORMULA] it is clear that standard magnetic braking of the form above gives unacceptably small [FORMULA], since observations indicate that typical recurrence times must be at least several decades. As an example, for 0422+32 Castro-Tirado et al. (1993) find [FORMULA] y by searching for similar outbursts on archival sky survey plates. On the other hand for the slightly evolved systems, the GR-driven recurrence times are quite long; MB, especially with somewhat reduced efficiency, may be acceptable. To be conservative the standard [FORMULA] will be determined by the observed recurrence time where available, or by GR losses for the short period systems and nuclear evolution-driven recurrence rates for [FORMULA]. Some check on the disk replenishment picture can be obtained from estimates of average mass transfer rates. McClintock et al. (1995) estimate a continued transfer rate of [FORMULA] /y for A0620-003 from the accretion disk emission, about [FORMULA] the rate for the [FORMULA] estimate above.


Table 2. Recurrence timescale estimates

It is interesting to speculate why MB appears to be inefficient in the short period systems - with the high primary mass and large mass ratio, tidal forces may suppress convection in secondaries with normally convective envelopes, reducing any associated magnetic wind. An examination of secondary spectra for evidence of coronal activity may provide opportunities for testing this idea.

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Online publication: April 20, 1998