X-ray Transients: Hyper- or Hypo-Luminous?

The disk instability picture gives a plausible explanation for the behavior of soft X-ray transient systems if self-irradiation of the disk is included. We show that there is a simple relation between the peak luminosity (at the start of an outburst) and the decay timescale. We use this relation to place constraints on systems assumed to undergo disk instabilities. The observable X-ray populations of elliptical galaxies must largely consist of long-lived transients, as deduced on different grounds by Piro and Bildsten (2002). The strongly-varying X-ray source HLX-1 in the galaxy ESO 243-49 can be modeled as a disk instability of a highly super-Eddington stellar-mass binary similar to SS433. A fit to the disk instability picture is not possible for an intermediate-mass black hole model for HLX-1. Other, recently identified, super-Eddington ULXs might be subject to disk instability.


INTRODUCTION
Many bright X-ray sources are strongly variable. It is now largely accepted that much of this variability results from the thermal-viscous disk instability (see Lasota 2001, for a review). The instability -originally discovered for dwarf novae, which are accreting white dwarf systems -results from the presence of ionization zones of hydrogen in the accretion disk (helium in some some ultracompact systems). The disk is forced to alternate between quiescence, when the disk is cool and faint and hydrogen predominantly neutral, and outbursts in which the disk is hot and hydrogen ionized. If the accretor is a neutron star or black hole, the X-rays produced by central accretion keep the disk in the hot state and only allow a return to quiescence on a viscous timescale.
Although some of the properties of this model remain to be worked out, in particular the duration of the quiescent phase, its predictions for outburst behaviour are robust enough to allow quantitative tests (Coriat, Fender, & Dubus 2012). We show here that there is a simple connection between the accretor mass, the peak luminosity at outburst and the decay time of the outburst, if this is well-defined by observations. If central irradiation is able to keep the whole disk in the hot state the outburst indeed has a fast-rise, exponential decay (FRED) shape (King & Ritter 1998;Dubus, Hameury, & Lasota 2001).
The connection we consider is particularly useful for uncovering the properties of varying X-ray sources which are too distant, or whose distance is too uncertain, to study easily in other ways. Here we apply it the the X-ray populations of elliptical galaxies, and to the stronglyvarying X-ray source HLX-1, whose nature remains uncertain.

OBSERVABLE PROPERTIES OF DISK INSTABILITIES
Two observable properties characterize the disk instability picture for X-ray transients. First, the maximum accretion rate (at the start of the outburst) is that of a (quasi)steady X-ray irradiated disk accreting at constant rate of ∼ 3Ṁ + crit (R d ), whereṀ + crit (R d ) is the value of the minimum critical accretion for a hot, irradiated disk at its outer radius R d (see e.g. Fig. 31 in Lasota 2001).
This fixes the critical accretion rateṀ max through the relation (Lasota, Dubus, & Kruk 2008) m −0.64+0.08 log C−3 g s −1 (1) where C = 10 −3 C −3 is a constant characterizing the outerdisk irradiation by the point-like source centered at they accretor (Dubus et al. 1999), m is the accretor mass in solar units, α < s1 the standard viscosity parameter, and R d = R d,11 10 11 cm is the disk outer radius. Taking C −3 = 1 (Dubus, Hameury, & Lasota 2001) and ignoring the very weak dependence on α, one getṡ FRED-type X-ray transients typically have disk radii ∼ 10 11 cm, corresponding to orbital periods of ∼ 10 hr. The second observable property is the decay time for the X-rays: in soft X-ray transients (unlike dwarf novae), disk irradiation by the central X-rays traps the disk in the hot, high state, and only allows a decay ofṀ on the hot-state viscous timescale (King & Ritter 1998;Dubus, Hameury, & Lasota 2001). This is Here the Shakura-Sunyaev viscosity is ν = αc 2 s /Ω, where c s ∝ T 1/2 c is the sound speed, T c the disk midplane temperature, and Ω = (GM/R 3 ) 1/2 . This gives Taking the critical midplane temperature T + c ≈ 16300 K corresponding toṀ + crit (Lasota, Dubus, & Kruk 2008) 8 one obtains for the decay timescale where α 0.2 = α/0.2. In the thermal-viscous disk instability model (hereafter TVDIM) the critical temperatures depend only on the ionization state of the disk matter and are thus practically independent of radius, viscosity parameter etc. (Lasota 2001;Lasota, Dubus, & Kruk 2008). By definition, the viscous decay time depends on the parameter α. From observations of dwarf nova outbursts one deduces that α ≈ 0.2 (see Smak 1999;Kotko & Lasota 2012). Comparison of models with observations of X-ray transients suggests the same value of α for these systems too (Dubus, Hameury, & Lasota 2001;King, Pringle, & Livio 2007, see also Sec. 3).
Eliminating R between (2) and (5) gives the peak accretion rate through the disk at the start of the outburst asṀ = 4.9 × 10 17 m −3.
with t = 40 t 40 d. Assuming an efficiency of η of 10%, the corresponding luminosity is

SUB-EDDINGTON OUTBURSTS
The observed behaviour of outbursting systems differs significantly depending on whether they have sub-or super-Eddington accretion rates. The Eddington accretion rate isṀ where η = 0.1η 0.1 is the accretion efficiency we find the Eddington accretion ratiȯ This equation shows that the start of the outburst is sub-Eddington only if the outburst decay time is relatively short or the accretor (black hole) mass is high, i.e. the observed decay timescale is in good agreement with the decay timescale of the detailed outburst models of Dubus, Hameury, & Lasota (2001) and, more importantly, with the compilation of X-ray transients outburst durations by Yan & Yu (2014). This suggests that the standard value of η 0.1 ≃ 1, and the value α 0.2 ≃ 1 deduced from observations of dwarf novae, give the correct order of magnitude for the decay timescale in this type of system (from ≈ 3 days to ≈ 300 days, Fig. 5 in Yan & Yu 2014). This equation also implies that black hole transients have longer decay timescales than neutron star transients, all else being equal. Indeed, Yan & Yu (2014) find outbursts last on average ≈ 2.5× longer in black hole transients than in neutron star transients. For sub-Eddington outbursts Eq. (7) provides a straightforward relation between luminosity and outburst decay time. For a decay timescale t of 0.5 years (see Sec. 5), the expected luminosity is Equivalently, this gives a relationship between distance D, bolometric flux F and outburst decay time t, where D = D Mpc Mpc and F = 10 −12 F 12 erg s −1 cm −2 .

SUPER-EDDINGTON OUTBURSTS
If the condition (10) does not hold, the initial outburst accretion rate is super-Eddington. This has two consequences. First, because the accretion luminosity is at the radiation pressure maximum for a range of radii the bolometric luminosity is larger than the Eddington limit by a factor ∼ 1 + lnṁ (Shakura & Sunyaev 1973;Poutanen et al. 2007). Second, the outburst luminosity is likely to be beamed, and we adopt here the form deduced by King (2009). Whenṁ 8, an observer situated in the beam of this outbursting system (ULX) infers an apparent (spherical) X-ray luminosity with the beaming factor i.e.

SYSTEMS
We first use equations (11, 12) for extragalactic binary systems. We see that these are unlikely to be detectable if the outburst decay is short ( years), particularly if the accretor is a stellar-mass black hole (m 3). This independently supports the conclusion of Piro & Bildsten (2002) that the X-ray populations of elliptical galaxies probably consist largely of soft X-ray transients undergoing outbursts so long that that the ensemble shows little observed variation. They reached this conclusion since if the X-ray population were genuinely persistent, the observed accretion rates would long ago have exhausted the masses of the (necessarily low-mass) donor stars and extinguished the X-rays. If instead these systems are in reality transient, it follows that they must have very short duty cycles d. The total population must be larger by the factor 1/d ≫ 1, but almost all these systems are in quiescence at any given epoch. The required long outbursts tell us that the systems must have large disks, and so are wide, implying evolved donor stars. For such long periods the outburst morphology is too complex for the simple equations of Section 3 to hold. Accordingly we cannot use eqn (11) to argue from the fact that the known sources often have modest luminosities that they must in general have black hole accretors (m 3).
Equations (11,12) also show that at extragalactic distances, sub-Eddington transients with black hole masses above the normal stellar range (i.e. intermediate-mass or supermassive) must either be very faint, or have extremely long decay times. In other words such systems cannot correspond to observed rapidly-decaying transients unless these are within the Galaxy.
This argument is relevant for the source HLX-1 (Farrell et al. 2009). This shows a sequence of quasiregular outbursts lasting < 180 days. For the four outbursts between 2009 and 2012 the recurrence time was ∼ 370 days, but the 2013 outburst started about 1 month 'late' (Godet et al. 2013. Multiwavelength observations of HLX-1 during 2009-2013 reveal outburst properties similar in most respects to those of low-mass X-ray binaries (LMXBs: e.g. Remillard & McClintock 2006).
HLX-1 is positionally coincident with the outer regions of the edge-on spiral galaxy ESO 243-49 (Farrell et al. 2009) at a redshift of 0.0224. 9 At the distance (D = 95 Mpc) of this galaxy its unabsorbed 0.2-10 keV luminosity L max = 1.3×10 42 erg s −1 at maximum requires a black hole mass m > 10 4 , for the source to be sub-Eddington radiator. But from Eq. (11) this requires a decay time of order decades or centuries, in complete contrast to the observed 180 days. This supports the conclusion of Lasota et al. (2011), who found that a disk instability model could not explain the light curve of HLX-1 if the system was assumed to contain an intermediate-mass black hole (IMBH) and be at the 95 Mpc.
According to Eq. (9), an X-ray transient with outburst duration of ∼ 180 days is sub-Eddington if the black-hole mass m 4.5. This in turn corresponds to a distance < 2.3 Mpc. For D ∼ 1 Mpc, say, we have m ≃ 8 and R ∼ 2.2 × 10 11 cm and maximum outburst luminosities L max ∼ 1.1 × 10 38 erg s −1 . Such a system would have a period 1 day, so probably has an evolved donor star. Many low-mass X-ray binaries (LMXBs) like this are known, and almost all are transient. For HLX-1 to be a standard bright transient of this type the required distance D ∼ 1 Mpc places it outside the Milky Way but 9 A narrow Hα-line observed with the same redshift (Wiersema et al. 2010;Soria, Hau, & Pakull 2013) suggests that the positional coincidence corresponds to real membership. still well within the Local Group. The system must reside in a nearby dwarf galaxy. These are known to harbor transient LMXBs (Maccarone et al. 2005). There are probably far more dwarf galaxies in the Local Group than so far discovered (see e.g. Koposov et al. 2008). Because the escape velocities from them are far smaller than the typical natal kick velocities of LMXBs these can either escape them altogether or have orbits which put them well outside any visible host for most of their lives (Dehnen & King 2006). These considerations mean that HLX-1 could turn out to be hosted by a previously unrecognized Local Group dwarf galaxy, but might also have no apparent host. Were its association with ESO 243-49 to be challenged, HLX-1 could well be such a system. In summary, at least one of the three statements (a) HLX-1 is at 95 Mpc (b) its outbursts are driven by the thermal-viscous disc instability (c) it is sub-Eddington cannot be correct.
Adopting (a), we must drop at least one of (b) or (c). If this is (b) we must consider models where the outbursts of HLX-1 differ fundamentally from those of all other soft X-ray transients. This appears inherently unlikely, and worse, there is little room for plausible alternatives. In sub-Eddington stellar-mass binaries the only other outburst model seriously considered (e.g. for Be X-ray binaries) invokes periodic mass transfer from a companion on an eccentric orbit, filling its tidal lobe at pericenter. For HLX-1 the (assumed sub-Eddington) accretor must be an IMBH. Lasota et al. (2011) considered a model like this, but found that to account for the observed outburst timescales it required a stellar orbit perilously close to becoming unbound , and very nonstandard accretion disk structures (Webb et al. 2014b). Accordingly we retain (b) and consider instead the effect of dropping (c).

APPLICATION TO SUPER-EDDINGTON SYSTEMS
The view that most if not all ULXs are super-Eddington systems has been greatly encouraged by recent observations giving accretor masses in the stellar range. This requires that the observed apparent Xray luminosities exceed Eddington. Most spectacular is the case of M82 X-2, which was discovered to be an accretion-powered X-ray pulsar with an apparent X-ray luminosity of ∼ 100L Edd (Bachetti et al. 2012). Another ULX, the X-ray source P13 in the galaxy NGC 7793, was shown to have a 15 M ⊙ black hole (Motch et al. 2014). Finally, the observed properties of the source NGC 5907 ULX1 seem to be incompatible with the presence of an IMBH (Walton et al. 2014). All these three ULX show flux variations by factors ∼ 100, but the observational coverage is too sparse to determine the nature of the variability.
Nevertheless one needs to consider the origin of transient behavior for these systems also. The solid observational evidence for super-Eddington systems makes it sensible to apply the disk instability model to such objects. Here we will show that the well-observed outbursts of HLX-1 can be explained by the TVDIM if it is a super-Eddington system.
Observers within the radiation beam of super-Eddington transients see them as ULXs. A solution like this is possible for HLX-1 (King & Lasota 2014) if we disregard the outburst behaviour. King & Lasota suggested that the precession of the radiation beam might produce a similar light curve, and assumed a black hole mass m ≃ 10, determining an Eddington factorṁ ≃ 110.
But we see that combining (15, 17) allows a selfconsistent solution in which the X-ray light curve is given by disk instabilities instead of precession. This disk instability solution gives a lower accretor mass m ≃ 3 and a slightly higher Eddington factorṁ ≃ 170. It requires a mean binary mass transfer rate ∼ 10 −5 M ⊙ yr −1 , which is typical for systems undergoing thermal-timescale mass transfer, like SS433 (King et al. 2000). The companion star must be fairly cool to allow the the ionization instability. We note that the quasi-periodic recurrence of the outbursts would naturally appear if the outbursts are similar (as observed) and the disk is refilled at a roughly constant rate. A system like this would have a period ∼ 50 days.
If HLX-1 is subject to the thermal-viscous instability, only a stellar mass can account for the observed outburst timescales. These timescales are characteristic of such systems and no others.

CONCLUSION
We have shown that there is a simple relation between the accretor mass, and the peak outburst luminosity and decay timescale of X-ray outbursts. We used this to show that the observable X-ray population of elliptical galaxies probably consists largely of very long-lasting transients. We showed that the strongly-marked variations of the X-ray source HLX-1 cannot result from a disk instability if is the accretor is an intermediate-mass black hole.
Acceptable solutions for the disk instability picture are possible in two other ways. First, if the X-ray source is within the Local Group it may be bright sub-Eddington X-ray transient containing a stellar mass black hole. Alternatively if the source is in the galaxy ESO 243-49 it may be a strongly beamed stellar-mass system resembling SS433 undergoing outbursts driven by disk instabilities. We suggest that at least some of the variability of other, recently identified super-Eddington ULXs may result from the same process.