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

0.12 MB·English

by  Jean-Pierre Lasota

Draftversion February3,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
X–RAY TRANSIENTS: HYPER– OR HYPO–LUMINOUS?
Jean–Pierre Lasota1,2,3, Andrew R. King4,5 and Guillaume Dubus1,6,7
Draft versionFebruary 3, 2015
ABSTRACT
The disk instability picture gives a plausible explanation for the behavior of soft X–ray transient
5 systems if self–irradiation of the disk is included. We show that there is a simple relation between
1 the peak luminosity (at the start of an outburst) and the decay timescale. We use this relation to
0 placeconstraintsonsystemsassumedtoundergodiskinstabilities. TheobservableX–raypopulations
2 of elliptical galaxies must largely consist of long–lived transients, as deduced on different grounds by
Piro & Bildsten (2002). The strongly–varyingX–raysourceHLX–1 inthe galaxyESO243–49canbe
n
modeled as a disk instability of a highly super–Eddington stellar–massbinary similar to SS433. A fit
a
J 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.
1
3 Subject headings: black hole physics — accretion, accretion disks – X–rays: binaries

]
E 1. INTRODUCTION raypopulationsofellipticalgalaxies,andtothestrongly–
H Many bright X–ray sources are strongly variable. It is varying X–ray source HLX–1, whose nature remains un-
certain.
. nowlargelyacceptedthatmuchofthisvariabilityresults
h
from the thermal–viscous disk instability (see Lasota
p 2. OBSERVABLEPROPERTIESOFDISKINSTABILITIES
2001, for a review). The instability – originally discov-
-
o ered for dwarf novae, which are accreting white dwarf Two observable properties characterize the disk insta-
r systems – results from the presence of ionization zones bility picture for X–ray transients. First, the maximum
t of hydrogen in the accretion disk (helium in some some accretion rate (at the start of the outburst) is that of a
s
a ultracompact systems). The disk is forced to alternate (quasi)steadyX-rayirradiateddiskaccretingatconstant
[ between quiescence, when the disk is cool and faint and rateof∼3M˙ + (R ), where M˙ + (R ) is the value of the
crit d crit d
hydrogenpredominantlyneutral,andoutburstsinwhich minimum critical accretion for a hot, irradiated disk at
1
the disk is hot and hydrogen ionized. If the accretor is its outer radius R (see e.g. Fig. 31 in Lasota 2001).
v d
3 a neutron star or black hole, the X–rays produced by Thisfixesthe criticalaccretionrateM˙max throughthe
0 central accretion keep the disk in the hot state and only relation (Lasota, Dubus, & Kruk 2008)
1 allow a return to quiescence on a viscous timescale.
0 Although some of the properties of this model re- M˙ ≈3M˙ + =7.2×1017 C−0.36 α0.04+0.01logC−3
max crit −3 0.2
0 main to be worked out, in particular the duration of
2. the quiescent phase, its predictions for outburst be- Rd2.,3191−0.10logC−3 m−0.64+0.08logC−3gs−1
haviour are robust enough to allow quantitative tests
0 (1)
(Coriat, Fender, & Dubus 2012). We show here that
5
1 there is a simple connection between the accretor mass, whereC=10−3C−3isaconstantcharacterizingtheouter-
: the peak luminosity at outburst and the decay time diskirradiationby the point-like sourcecenteredatthey
v of the outburst, if this is well–defined by observations. accretor (Dubus et al. 1999), m is the accretor mass in
Xi If central irradiation is able to keep the whole disk solar units, α < s1 the standard viscosity parameter,
in the hot state the outburst indeed has a fast–rise, and R =R 1011cm is the disk outer radius. Taking
ar exponential decay (FRED) shape (King & Ritter 1998; C−3=d1(Dudb,1u1s, Hameury, & Lasota2001)andignoring
Dubus, Hameury, & Lasota 2001). the very weak dependence on α, one gets
The connection we consider is particularly useful for
uncoveringthepropertiesofvaryingX–raysourceswhich M˙ ≈7.0×1017 R2.39 m−0.64gs−1. (2)
max d,11
are too distant, or whose distance is too uncertain, to
study easily in other ways. Here we apply it the the X– FRED–type X–ray transients typically have disk radii
∼1011cm, corresponding to orbital periods of ∼10 hr.
1CNRS,UMR7095, Institutd’AstrophysiquedeParis,98bis The second observable property is the decay time for
BdArago,75014Paris,France;[email protected] the X–rays: in soft X–ray transients (unlike dwarf no-
2Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, vae), disk irradiation by the central X–rays traps the
00-716Warszawa,Poland
3Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7095, diskinthe hot, highstate,andonlyallowsadecayofM˙
98bisBdArago,75014Paris,France on the hot–state viscous timescale (King & Ritter 1998;
4TheoreticalAstrophysicsGroup,UniversityofLeicester,Le- Dubus, Hameury, & Lasota 2001). This is
icesterLE17RH,U.K.;[email protected]
5AstronomicalInstituteAntonPannekoek,UniversityofAm-
R2
ste6rdCaNmR,SS,cIiePnAcGe,PFar-3k8900040,G10r9en8oXblHe,AFmrasntceerdam,Netherlands t≃ 3ν (3)
7Univ. Grenoble Alpes, IPAG, F-38000 Grenoble, France,
[email protected] Herethe Shakura–Sunyaevviscosityis ν=αc2/Ω,where
s
2
c ∝T1/2 is the sound speed, T the disk midplane tem- decaytimescalesthanneutronstartransients,allelsebe-
s c c
perature, and Ω=(GM/R3)1/2. This gives ing equal. Indeed, Yan & Yu (2014) find outbursts last
on average ≈2.5× longer in black hole transients than
(GMR)1/2 inneutronstartransients. Forsub–Eddingtonoutbursts
t≃ . (4)
3αc2 Eq. (7) provides a straightforward relation between lu-
s
minosityandoutburstdecaytime. Foradecaytimescale
Taking the critical midplane temperature T+≈16300K t of 0.5 years (see Sec. 5), the expected luminosity is
c
corresponding to M˙ + (Lasota, Dubus, & Kruk 2008)8
crit L=6.2×1040η (α t )4.78m−3.03 ergs−1 (11)
one obtains for the decay timescale 0.1 0.2 0.5yr
t≈43 m1/2R1/2α−1days, (5) Equivalently, this gives a relationship between distance
d,11 0.2 D, bolometric flux F and outburst decay time t,
where α0.2=α/0.2. In the thermal-viscousdisk instabil- η 1/2
ity model (hereafter TVDIM) the critical temperatures D ≃23m−1.5 0.1 (α t )2.4 (12)
Mpc 0.2 0.5yr
depend only on the ionization state of the disk matter (cid:18)F12(cid:19)
and are thus practically independent of radius, viscos-
where D=D Mpc and F =10−12F ergs−1cm−2.
ityparameteretc. (Lasota2001;Lasota, Dubus, & Kruk Mpc 12
2008). By definition, the viscous decay time depends
4. SUPER–EDDINGTONOUTBURSTS
on the parameter α. From observations of dwarf nova
outbursts one deduces that α ≈ 0.2 (see Smak 1999; If the condition (10) does not hold, the initial out-
Kotko & Lasota 2012). Comparison of models with ob- burst accretion rate is super–Eddington. This has two
servations of X-ray transients suggests the same value consequences. First, because the accretion luminosity is
of α for these systems too (Dubus, Hameury, & Lasota at the radiation pressure maximum for a range of radii
2001; King, Pringle, & Livio 2007, see also Sec. 3). the bolometric luminosity is larger than the Eddington
Eliminating R between (2) and (5) gives the peak ac- limit by a factor ∼1+lnm˙ (Shakura & Sunyaev 1973;
cretionratethroughthedisk atthe startoftheoutburst Poutanen et al. 2007). Second, the outburst luminosity
as is likely to be beamed, and we adopt here the form de-
M˙ =4.9×1017 m−3.03(t α )4.78gs−1, (6) ducedbyKing(2009). Whenm˙ &8,anobserversituated
40 0.2
in the beam of this outbursting system (ULX) infers an
with t=40t40d. Assuming an efficiency ofη of10%, the apparent (spherical) X–ray luminosity
corresponding luminosity is
1
L=4.4×1037 η0.1m−3.03(t40α0.2)4.78ergs−1. (7) Lsph= bLE[1+ln(1+m˙ )] (13)
3. SUB–EDDINGTONOUTBURSTS with the beaming factor b
The observedbehaviour of outbursting systems differs 73
b≃ , (14)
significantly depending on whether they have sub– or m˙ 2
super–Eddington accretion rates. The Eddington accre-
i.e.
tion rate is
M˙ =1.3×1018η−1m gs−1 (8) Lsph=2.2×1036m˙ 2m[1+ln(1+m˙ )] ergs−1 (15)
E 0.1
(King 2009). Since the apparent luminosity scales ap-
where η=0.1η is the accretion efficiency we find the
Eddington accr0e.1tion ratio proximately as m˙ 2, and dL/dt=(dL/dM˙ )(dM˙ /dt), the
observed decay time is now
m˙ =0.34η (α t )4.78m−4.03. (9)
0.1 0.2 40
R2
This equation shows that the start of the outburst is t= (16)
6ν
sub–Eddington only if the outburst decay time is rela-
tively shortorthe accretor(black hole)massis high,i.e. leading to the modified form of (9) as
the observed decay timescale is
m˙ =1.3×104η (α t )4.78m−4.03. (17)
0.1 0.2 0.5yr
t.50η−0.21α−1m0.84 d, (10)
0.1 0.2 The X–ray light curve is now determined purely by
in good agreement with the decay timescale of the de- beaming, through Eq. (15). The outburst appears to
tailed outburst models of Dubus, Hameury, & Lasota decay twice as fast, as the beaming reduces simultane-
(2001) and, more importantly, with the compilation ously with the accretion rate. Equations (15, 17) deter-
of X–ray transients outburst durations by Yan & Yu mine the accretor’s mass m and the Eddington ratio m˙
(2014). Thissuggeststhatthestandardvalueofη ≃1, for any given case.
0.1
and the value α ≃ 1 deduced from observations of
dwarf novae, give0t.2he correct order of magnitude for the 5. APPLICATIONTOOBSERVEDSUB–EDDINGTON
decay timescale in this type of system (from ≈3 days SYSTEMS
to ≈300 days, Fig. 5 in Yan & Yu 2014). This equa- Wefirstuseequations(11,12)forextragalacticbinary
tion also implies that black hole transients have longer systems. We see that these are unlikely to be detectable
if the outburst decay is short (. years), particularly if
8 For irradiated disks, the value of Tc depends only weakly on theaccretorisastellar–massblackhole(m&3). Thisin-
viscosityandirradiationandisindependent ofmassandradius. dependently supports the conclusion of Piro & Bildsten
3
(2002) that the X–ray populations of elliptical galaxies still well within the Local Group. The system must re-
probablyconsistlargelyofsoftX–raytransientsundergo- side in a nearby dwarf galaxy. These are known to har-
ing outbursts so long thatthat the ensemble showslittle bor transient LMXBs (Maccarone et al. 2005). There
observed variation. They reached this conclusion since areprobablyfar moredwarfgalaxiesinthe LocalGroup
if the X–ray population were genuinely persistent, the thansofardiscovered(seee.g.Koposov et al.2008). Be-
observed accretion rates would long ago have exhausted causetheescapevelocitiesfromthemarefarsmallerthan
themassesofthe(necessarilylow–mass)donorstarsand the typical natal kick velocities of LMXBs these can ei-
extinguished the X–rays. If instead these systems are ther escape them altogether or have orbits which put
in reality transient, it follows that they must have very them well outside any visible host for most of their lives
shortduty cyclesd. Thetotalpopulationmustbe larger (Dehnen & King 2006). These considerationsmean that
by the factor 1/d≫1, but almost all these systems are HLX–1couldturnouttobehostedbyapreviouslyunrec-
inquiescenceatanygivenepoch. Therequiredlongout- ognized Local Group dwarf galaxy, but might also have
bursts tell us that the systems must have large disks, noapparenthost. Wereits associationwithESO243–49
and so are wide, implying evolved donor stars. For such tobechallenged,HLX–1couldwellbe suchasystem. In
longperiodsthe outburstmorphologyis toocomplex for summary, at least one of the three statements
the simple equations of Section 3 to hold. Accordingly (a) HLX–1 is at 95 Mpc
we cannot use eqn (11) to argue from the fact that the (b) its outbursts are driven by the thermal–viscous disc
known sources often have modest luminosities that they instability
must in general have black hole accretors (m&3). (c) it is sub–Eddington
Equations(11, 12) also show that at extragalacticdis- cannot be correct.
tances,sub–Eddingtontransientswithblackholemasses Adopting(a),wemustdropatleastoneof(b)or(c). If
above the normal stellar range (i.e. intermediate–mass this is (b) we must consider models where the outbursts
or supermassive) must either be very faint, or have ex- ofHLX–1differfundamentallyfromthoseofallothersoft
tremely long decay times. In other words such systems X-ray transients. This appears inherently unlikely, and
cannot correspond to observed rapidly–decaying tran- worse, there is little room for plausible alternatives. In
sients unless these are within the Galaxy. sub–Eddingtonstellar–mass binaries the only other out-
This argument is relevant for the source HLX–1 burst model seriously considered (e.g. for Be X–ray bi-
(Farrell et al. 2009). This shows a sequence of quasi– naries)invokesperiodic mass transfer froma companion
regular outbursts lasting <180 days. For the four out- on an eccentric orbit, filling its tidal lobe at pericenter.
bursts between 2009 and 2012 the recurrence time was For HLX–1 the (assumed sub–Eddington)accretormust
∼370days,butthe2013outburststartedabout1month be an IMBH. Lasota et al. (2011) considered a model
‘late’ (Godet et al. 2013, 2014). Multiwavelength ob- likethis, butfoundthattoaccountforthe observedout-
servations of HLX–1 during 2009–2013 reveal outburst bursttimescalesitrequiredastellarorbitperilouslyclose
properties similar in most respects to those of low–mass tobecomingunbound(Godet et al.2014),andverynon-
X–ray binaries (LMXBs: e.g. Remillard & McClintock standard accretion disk structures (Webb et al. 2014b).
2006). HLX–1 is positionally coincident with the Accordinglyweretain(b)andconsiderinsteadtheeffect
outer regions of the edge–on spiral galaxy ESO 243–49 of dropping (c).
(Farrell et al. 2009) at a redshift of 0.0224.9 At the dis-
tance (D=95 Mpc) of this galaxy its unabsorbed 0.2– 6. APPLICATIONTOSUPER–EDDINGTONSYSTEMS
10keVluminosityL =1.3×1042ergs−1 atmaximum The view that most if not all ULXs are super–
max
requires a black hole mass m>104, for the source to Eddington systems has been greatly encouraged by re-
be sub-Eddington radiator. But from Eq. (11) this cent observations giving accretor masses in the stellar
requires a decay time of order decades or centuries, in range. This requires that the observed apparent X–
completecontrasttotheobserved.180days. Thissup- ray luminosities exceed Eddington. Most spectacular is
ports the conclusion of Lasota et al. (2011), who found the case of M82 X–2, which was discovered to be an
that a disk instability model could not explain the light accretion–poweredX-ray pulsar with an apparent X-ray
curveofHLX–1ifthesystemwasassumedtocontainan luminosity of ∼100LEdd (Bachetti et al.2012). Another
intermediate-mass black hole (IMBH) and be at the 95 ULX,theX-raysourceP13inthegalaxyNGC7793,was
Mpc. showntohavea.15M⊙ blackhole (Motch et al.2014).
AccordingtoEq. (9),anX-raytransientwithoutburst Finally, the observedproperties of the source NGC 5907
durationof∼180daysissub-Eddingtoniftheblack-hole ULX1 seem to be incompatible with the presence of an
mass m&4.5. This in turn corresponds to a distance IMBH (Walton et al. 2014). All these three ULX show
<2.3 Mpc. For D∼1 Mpc, say, we have m≃8 and flux variations by factors ∼100, but the observational
R∼2.2×1011 cm and maximum outburst luminosities coverage is too sparse to determine the nature of the
L ∼1.1×1038ergs−1. Such a system would have a variability.
max
period &1 day, so probably has an evolved donor star. Nevertheless one needs to consider the origin of tran-
Many low–mass X–ray binaries (LMXBs) like this are sient behavior for these systems also. The solid obser-
known, and almost all are transient. For HLX–1 to be vational evidence for super–Eddington systems makes it
a standardbrighttransientof this type the requireddis- sensible to apply the disk instability model to such ob-
tance D∼1 Mpc places it outside the Milky Way but jects. Herewewillshowthatthewell-observedoutbursts
ofHLX-1canbeexplainedbytheTVDIMifitisasuper-
9 A narrow Hα–line observed with the same redshift Eddington system.
(Wiersemaetal. 2010; Soria,Hau,&Pakull 2013) suggests that Observers within the radiation beam of super–
thepositionalcoincidence correspondstorealmembership. Eddington transients see them as ULXs. A solution like
4
this is possible for HLX–1 (King & Lasota 2014) if we We are very grateful to the anonymous referee for the
disregard the outburst behaviour. King & Lasota sug- very helpful criticism of the first version of this paper.
gested that the precession of the radiation beam might We thank Chris Done, John Cannizzo and Chris Nixon
produce a similar light curve, and assumed a black hole for helpful conversations. JPL acknowledges support
mass m≃10,determining an Eddington factor m˙ ≃110. from the French Space Agency CNES and Polish NCN
But we see that combining (15, 17) allows a self– grant UMO-2013/08/A/ST9/00795. Theoretical astro-
consistentsolutioninwhichtheX–raylightcurveisgiven physics in Leicester is supported by an STFC Consoli-
by disk instabilities instead of precession. This disk in- datedGrant. GDalsoacknowledgessupportfromCNES.
stability solution gives a lower accretor mass m≃3 and
a slightly higherEddingtonfactor m˙ ≃170. It requiresa
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ACKNOWLEDGMENTS