On the Nature of Ultra-Luminous X-ray Sources from Optical/IR
  Measurements
Black Holes: from Stars to Galaxies – across the Range of Masses
Proceedings IAU Symposium No. 238, 2006
V. Karas & G. Matt, eds.
c© 2006 International Astronomical Union
DOI: 00.0000/X000000000000000X
On the Nature of Ultra-Luminous X-ray
Sources from Optical/IR Measurements
Mark Cropper1, Chris Copperwheat1, Roberto Soria2,1, Kinwah Wu1
1Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking,
Surrey RH5 6NT, UK
2Centre for Astrophysics, Harvard Smithsonian Astrophysical Observatory, 60 Garden St,
Cambridge, MA 02138, USA
Abstract. We present a model for the prediction of the optical/infra-red emission from ULXs. In
the model, ULXs are binary systems with accretion taking place through Roche lobe overflow.
We show that irradiation effects and presence of an accretion disk significantly modify the
optical/infrared flux compared to single stars, and also that the system orientation is important.
We include additional constraints from the mass transfer rate to constrain the parameters of the
donor star, and to a lesser extent the mass of the BH. We apply the model to fit photometric
data for several ULX counterparts. We find that most donor stars are of spectral type B and
are older and less massive than reported elsewhere, but that no late-type donors are admissable.
The degeneracy of the acceptable parameter space will be significantly reduced with observations
over a wider spectral range, and if time-resolved data become available.
Keywords. black hole physics – X-rays: galaxies – X-rays: stars – accretion, accretion discs –
binaries: general
1. Introduction
Ultra-luminous X-ray sources (ULXs) are non-nuclear X-ray sources in nearby galax-
ies with inferred luminosity >few×1039 ergs s−1. This luminosity exceeds the Edding-
ton luminosity of a 20M⊙ black hole (BH) (an observational overview is available in
Fabbiano, 2004). While these objects are generally agreed to be binary systems, the na-
ture of their constituents is still controversial. Their emission could be as a result of
sub-Eddington accretion rates onto intermediate mass black holes (IMBH) with masses
∼ 200− 1000M⊙, (Colbert & Mushotzky, 1999), super-Eddington accretion onto stellar-
mass BH (Begelmann 2002, King 2001) or Eddington accretion onto BH with masses in
the range ∼ 50− 200 M⊙ (Soria & Kuncic 2006).
Recently, reasonably secure optical counterparts for these systems have been identified,
mostly using HST observations. This has opened a new channel of investigation into
the nature of ULX. The optical/infrared emission is derived from the irradiated mass
donor star and disk, so it is essential to model these appropriately in both the spectral
and time domain if system parameters such as the mass and radius of the mass donor
star and the mass of the BH are to be constrained. This paper describes such a model
for the optical/infrared emission, and summarises some of the constraints that can be
derived from its application to optical/infrared data. The objectives of this work are (a)
to provide constraints on the possible optical counterparts of ULXs, eliminating those
candidates which are inconsistent with the predicted colours/variability; (b) to determine
the characteristics of the ULX constituent parts as accurately as possible; (c) to constrain
the origin of ULXs and (d) to make predictions for future observations. More detailed
expositions can be found in Copperwheat et al. (2005) and Copperwheat et al. (2006).
http://arxiv.org/abs/0704.1442v1
2 Cropper et al.
Figure 1. The variation in intensity B(τ ) with τ = 2/3 for (right) an irradiated O5V star and
(left) a disk for a BH mass of 150M⊙. The plot shows the view onto the orbital plane with the
labelled distances in units of R⊙. Note that the intensity scales are logarithmic for the disk and
linear for the star.
2. The model
The compact object in the model is a BH of mass in the range 10−1000M⊙. The mass
donor star fills its Roche lobe, and accretion takes place through Roche lobe overflow into
an accretion disk. We assume the disk to be a standard thin disk, tidally truncated at a
radius 0.6 of that of the distance to the L1 point. The mass donor star evolves according
to the isolated star evolutionary tracks of Lejeune & Schaerer (2001). We ignore the
effects of mass transfer on the star. We assume also that mass transfer is driven by the
nuclear evolution of the mass donor. The model includes the Roche geometry, gravity
and limb darkening, disk shadowing, radiation pressure according to the prescription of
Phillips & Podsiadlowski (2002), the evolution of the companion and system orientation
effects (inclination and binary phase). The X-ray irradiation is assumed to be isotropic.
The irradiation of the disk and star is handled according to a formulation byWu et al. (2001)
which is based originally on the grey stellar irradiation model of Milne (1926) and in-
corporates the different opacities of the irradiated surface to hard and soft X-rays (the
X-ray hardness ratio is an input parameter). The effective temperature of the irradiated
star or irrdiated disk is a superposition of the irradiated and natural temperatures i.e.
Teff =
Bx(2/3) + T
unirr
where Bx(τ) is derived in Copperwheat et al. (2005).
Figure 1 provides an example of the irradiated disk and star.
Using this model we can predict the different contributions of the constituents of the
ULX as a function of (for example) BH mass and donor star spectral type, as shown
in Figure 2. For high-mass BHs, the disk is large, and hence disk emission dominates.
In addition, irradiation effects are much larger for late-type stars. We make predictions
of the optical/infrared flux. We find that there is generally better system parameter
discrimination at infrared wavelengths. We also predict the variability timescale. Because
of the axial symmetry of our disks, these are dominated by the (modified) ellipsoidal
variations from the Roche-lobe-filling donor stars. The variability timescale is typically
days, dependent on BH mass.
The photometric predictions can be compared to observations of ULX counterparts in
different wavebands, and acceptable model parameter regimes determined from χ2 fitting
to the observations. If only single-epoch photometric observations are available in 2 or 3
bands the model fits are underconstrained, leading to degenerate solutions. An example
is shown in Figure 3(left). Nevertheless, even with limited photometric data much of the
possible parameter space can be eliminated, and with additional wavelength coverage
particularly in the infrared, degeneracies can be reduced further.
We add a further constraint for the χ2 fitting using the mass transfer rate, which is
The Nature of ULXs from Optical/IR data 3
 10  100  1000
BH Mass (Msun)
Irr. Star
Unirr. Star
Irr. Star + Disk
O5V star, disk model #2 (ξ=0.1)(c)
 10  100  1000
BH Mass (Msun)
Irr. Star
Unirr. Star
Irr. Star + Disk
G0I star, disk model #2 (ξ=0.1)(d)
Figure 2. The V band absolute magnitudes for an un-irradiated and irradiated O5V star and
accretion disk (left) and for a G0I supergiant with disk (right), shown as a function of BH mass.
Here Lx = 10
40 ergs s−1, cos i = 0.5 and the star is at superior conjunction.
determined by the evolution of the stellar radius (from the evolutionary tracks) compared
with the evolution of the Roche lobe radius (Wu, 1997, Ritter, 1988). We measure the
mass transfer rate from the X-ray luminosity assuming an accretion efficiency η = 0.1
appropriate for a BH, and select only those secondary stars which are evolving in radius
on nuclear timescales in such a way as to provide the measured mass transfer rate.
3. Fits to data
We have gathered HST and VLT photometric data available up to mid-2006 on the
most luminous ULX counterparts, where we can be reasonably certain that mass transfer
is driven by Roche lobe overflow. The input data for M81 X-6, NGC 4559 X-7, M101 ULX-
1, NGC 5408 ULX, Holmberg II ULX, NGC 1313 X-2 (C1) and NGC5204 ULX are given
in table 1 of Copperwheat et al. (2006) and for M51 X5/9 in Copperwheat (2007). We
fitted our model to these photometric data, using the additional mass transfer constraint
from X-ray measurements.
Figure 3 (right) shows an example of the allowed parameter space in the donor star
mass vs BH mass plane from the χ2 fitting. We also produced similar plots for the donor
star radius and donor star age, which we determined from the mass-radius relation from
the evolutionary tracks. More details can be found in Copperwheat et al. (2006).
These fits provide the current spectral type of the mass donor star. By tracing to earlier
times along the evolutionary tracks, the ZAMS spectral type can be predicted assuming
the mass loss has not significantly altered the evolution.
4. Main outcomes
The optical/infrared emission from our binary ULX model is significantly different from
models assuming unirradiated companion stars and no disks, hence it is not adequate to
assume standard colours from single stars to determine the mass donor characteristics in
ULXs.
The model fits to the currently available data do not provide strong constraints on
the BH mass, mainly because of the unknown orientation of the system. Depending on
inclination, upper or lower limits can, however, be set. For example, the BH mass in
NGC 5204 is < 240 M⊙ for cos i = 0.5, while that in NGC 1313 X-1 is < 100 M⊙. The
reason is that the signature of a disk can be almost entirely hidden for cos i = 0.0, in
which case little information can be obtained on the size of the primary Roche lobe.
The mass, radius and age of the donor star are, however, more tightly constrained.
4 Cropper et al.
3.02.01.00.80.60.4
Wavelength (µm)
M1=30Msun, M2=8Msun
Stellar age=30Myr, cos(i)=0.0
M1=50Msun, M2=16Msun
Stellar age=10Myr, cos(i)=0.5
M1=1000Msun, M2=70Msun
Stellar age=1Myr, cos(i)=0.5
M1=600Msun, M2=110Msun
Stellar age=1Myr, cos(i)=0.0
 10  100  1000
BH Mass (Msun)
Figure 3. (left) Absolute magnitude as a function of wavelength for different combinations of BH
(M1) and donor star (M2) and inclination i compared to photometric measurements for NGC5408
ULX, indicating the degeneracy of possible solutions when no mass transfer constraints are
applied. (right) Acceptable parameter space for the mass donor star projected onto the donor
mass/BH mass plane when the mass transfer constraint is included. Contours are at 68, 90 (solid
line), 95 and 99% confidence levels.
Typical ages range from 107 − 108 years, with typical ZAMS masses 5 − 10 M⊙, with
some up to 50 M⊙. In general we find that the mass donor stars are less massive and
older than generally quoted in the literature from less comprehensive modeling – this
is to be expected given the effects of irradiation. We find that none of the systems are
found to contain late-type mass donor stars, whatever disk component is admitted.
The preference for donor stars of spectral type B is interesting. The high mass transfer
rates and modest donor star masses require that ULX lifetimes are short (this is true
also for higher mass donors which in any case have short lifetimes). The duration that
the donor star has been in contact with its Roche lobe is an important parameter for
ULXs. If it has been in contact for some Myr, especially in the case of B-type ZAMS
stars, then binary evolution models will be required.
The diagnostic capability of our model for the BH mass and donor star characteristics
will improve significantly as more filter bands, and particularly time-resolved data become
available.
Acknowledgements
R. Soria acknowledges support from a Marie Curie Fellowship from the EC.
References
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	Introduction
	The model
	Fits to data
	Main outcomes
