Draft version August 8, 2021
Preprint typeset using LATEX style emulateapj v. 6/22/04
THE DEPENDENCE OF THE ESTIMATED LUMINOSITIES OF ULX ON SPECTRAL MODELS
A. Senorita Devi1, R. Misra2, V. K. Agrawal3 and K. Y. Singh1
Draft version August 8, 2021
ABSTRACT
Data from Chandra observations of thirty nearby galaxies were analyzed and 365 X-ray point sources
were chosen whose spectra were not contaminated by excessive diffuse emission and not affected by
photon pile up. The spectra of these sources were fitted using two spectral models (an absorbed
power-law and a disk blackbody) to ascertain the dependence of estimated parameters on the spectral
model used. It was found that the cumulative luminosity function depends on the choice of the
spectral model, especially for luminosities > 1040 ergs/s. In accordance with previous results, a large
number (∼ 80) of the sources have luminosities > 1039 ergs/s (Ultra-Luminous X-ray sources) with
indistinguishable average spectral parameters (inner disk temperature ∼ 1 keV and/or photon index
Γ ∼ 2) with those of the lower luminosities ones. After considering foreground stars and known
background AGN, we identify four sources whose minimum luminosity exceed 1040 ergs/s, and call
them Extremely Luminous X-ray sources (ELX). The spectra of these sources are in general better
represented by the disk black body model than the power-law one. These ELX can be grouped into
two distinct spectral classes. Two of them have an inner disk temperature of < 0.5 keV and hence
are called “supersoft” ELX, while the other two have temperatures & 1.3 keV and are called “hard”
ELX. The estimated inner disk temperatures of the supersoft ELX are compatible with the hypothesis
that they harbor intermediate size black holes, which are accreting at ∼ 0.5 times their Eddington
Luminosity. The radiative mechanism for hard ELX, seems to be Inverse Comptonization, which in
contrast to standard black holes systems, is probably saturated. Extensive variability analysis of these
ELX, will be able to distinguish whether these two spectral class represent different systems or they
are spectral states of the same kind of source.
Subject headings: Galaxies: general - X-rays: binaries
1. INTRODUCTION
In the last few years, Chandra observations of nearby
galaxies have detected many non-nuclear X-ray point
sources (Kaaret et al. 2001 ; Matsumoto et al. 2001;
Zezas & Fabbiano 2002), some of which have isotropic lu-
minosities> 1039 ergs/s and are called Ultra luminous X-
ray Sources (ULX). While some of these ULX are super-
nova remnants (e.g. Ryder et al. 1993; Fox et al. 2000),
it is believed that the majority of them are compact ac-
creting systems. Indeed, ASCA X-ray spectral studies of
many ULX have revealed that they display the charac-
teristics of accreting black holes (Makishima et al. 2000;
Mizuno et al. 2001). ULX have also been called Super-
Eddington Sources (Fabbiano 1989, 2004) and Intermedi-
ate luminosity X-ray objects (Roberts & Warwick 2000;
Colbert & Mushotzky 1999).
Since these ULX sources emit radiation at a rate
larger than the Eddington luminosity for a ten-solar mass
black hole, they are believed to harbor a black hole of
mass 10M⊙<M<10
5M⊙ (Colbert & Mushotzky 1999;
Makishima et al. 2000) where the upper limit is con-
strained by the fact that a more massive black hole would
have settled into the nucleus due to dynamical friction
(Kaaret et al. 2001 ). Black holes in this mass range are
called Intermediate Mass Black Holes (IMBH), since they
1 Department Of Physics, Manipur University, Canchipur,
Imphal-795003, Manipur, India; senorita@iucaa.ernet.in
2 Inter-University Center for Astronomy and Astrophysics, Post
Bag 4, Ganeshkhind, Pune-411007, India; rmisra@iucaa.ernet.in
3 Department of Astronomy and Astrophysics, Tata Institute of
Fundamental Research, Homi Bhabha Road, Mumbai-400 005,In-
seem to represent the missing component of the black
hole mass spectrum with masses prevailing in the gap be-
tween those of stellar mass black holes found in Galactic
X-ray binaries and those associated with Active Galac-
tic Nuclei, M ∼ 106 − 109 M⊙ (Richstone et al. 1998).
Miller & Colbert (2004) and Miller (2005) review the
present evidence for IMBH in ULX and Liu & Mirabel
(2005) have compiled a catalogue of some ULX and prop-
erties.
Alternate models for ULX are that their luminosi-
ties are super-Eddington (Begelman 2002) or that their
emission is beamed from a geometrically thick accre-
tion disk (King et al. 2001). However, it has been ar-
gued that in the latter case, such thick ”funnel” shaped
disks enhance the observed flux by just a factor of few
(Misra & Sriram 2003). For all of these models, the
creation of such sources (Portegies, Zwart & McMillian
2002; Taniguchi et al. 2000; Madau & Rees 2001) and
process by which they sustain high accretion rates
(King et al. 2001), are largely unknown.
Investigations on the nature of ULX have been un-
dertaken by studying the spectra and variability of in-
dividual sources. For example analysis of the spectra
of NGC 1313 X-1, X-2 (Miller et al. 2003) and M81 X-
9 (Miller, Fabian & Miller 2004), revealed the presence
of a cool accretion disk component (kTin ∼ 0.1 − 0.5
keV), suggesting that ULX indeed harbor IMBH. Tran-
sitions between two spectral states, similar to those
seen in Galactic black hole systems, have been reported
in NGC 1313 X-1(Colbert & Mushotzky 1999) and two
sources in IC342 (Kubota et al. 2001). Spectral transi-
tions have also been reported in two sources in NGC 1313
http://arxiv.org/abs/0704.1107v1
2 Senorita Devi et al.
(Feng & Kaaret 2006).
The large collecting area of XMM-Newton, allows for
detailed spectral fits to ULX, which often comprise of two
components (Wang et al. 2004; Feng & Kaaret 2005).
However, Gonçalves & Soria (2006), have argued that
such soft spectral components depend on the complex-
ity of the fitting model. An interesting object is the
brightest X-ray point source in M 82, whose intrinsic
luminosity has been measured to be as high as 1.6 ×
1041 ergs/s (Ptak and Griffiths 1999). The detection of
a 54 mHz quasi-periodic oscillation in its X-ray light
curve suggests that the source is a compact object and
not a background AGN (Strohmayer & Mushotzky 2003;
Dewangan et al. 2006a). The spectra of this source can
be fitted by a power-law with photon index, Γ ∼ 2
(Fiorito & Titarchuk 2004), but is more consistently fit-
ted with a flatter power-law with an high energy cut-
off around ∼ 6 keV, which can be interpreted as opti-
cally thick, saturated Comptonization (Agrawal & Misra
2006). A quasi-periodic oscillation has also been discov-
ered in the bright X-ray source of Holmberg IX, which
is similar to the source in M82 in having a flat spec-
trum (Γ ∼ 1) with a ∼ 9 keV cutoff (Dewangan et al.
2006b). Recently, Stobbart et al. (2006) found that the
XMM-Newton spectra of eleven of the eighteen ULX
studied by them, showed such high energy curvature.
Chandra observations of NGC 5204 X-1, also reveals the
presence of an optically thick Comptonized component
(Roberts et al. 2006). While these results of individual
ULX are intriguing, there does not seem to be any signif-
icantly distinguishable spectral property of ULX, and in
general their spectra can be described either by steep or
flat power-law indices, with and without soft components
(e.g. Dewangan et al. 2005).
Another line of investigation is to construct the cu-
mulative luminosity function and histograms of spec-
tral parameters of a large sample of X-ray sources (e.g.
Colbert & Ptak 2002). The hope here is that, in case
ULX are a distinct class of sources and/or they can be
classified into distinct subgroups, the luminosity func-
tion should exhibit a break and their spectral parame-
ters should show clustering. Swartz et al. (2004) ana-
lyzed data from 82 galaxies and estimated the luminos-
ity function and spectral parameters of the X-ray point
sources in these galaxies. They found that the average
photon index (as well as the distribution) of the ULX
and the less luminous sources is nearly same. Moreover,
their spatial and variability distributions are also similar.
While, their analysis revealed that the luminosity func-
tions of ULX depend on the host galaxy type and star
formation rate, they did not find any significant evidence
for breaks in them.
As emphasized by Swartz et al. (2004), the power-law
model they used to fit the data was chosen as an empir-
ical one. They attempted to fit all the sources with the
power-law model and only for those sources that did not
provide a reasonable fit, they used other models like disk
black body. They note that for many sources that are
well fitted by the power-law model, other spectral models
can also represent the spectra. In this work, we consider
a smaller sample of 30 galaxies but fit the spectra of the
points sources, with both a power-law and a disk black-
body model. In principle, the intrinsic (i.e. the absorp-
tion corrected) luminosity inferred for a source may be
different for the two spectral models. Our first motiva-
tion here is to make a qualitative estimate of this differ-
ence by noting the dependency of the luminosity function
on the spectral model used. A second motivation for this
work is based on the expectation that estimations of a
different spectral parameter like the inner disk tempera-
ture (as compared to the photon index), maybe better in
distinguishing ULX from other sources or they may re-
veal dependencies (like correlations between luminosity
and temperature) which could shed light on the nature
of these sources. As mentioned earlier, the spectra of
several ULX are complex requiring more than one com-
ponents. Thus, the two spectral models, an absorbed
power-law and and an absorbed disk blackbody, should
be considered as empirical ones, which can adequately
represent low count data and these models need not be
the correct physical representation of the actual source
spectrum.
It is clear that ULX are fairly common in nearby galax-
ies. For example, Swartz et al. (2004) identified 154 of
them in 82 galaxies. If these sources are Eddington lim-
ited, then black holes & 10M⊙ may indeed be quite com-
mon. However, only a few of these sources have luminosi-
ties greater than 1040 ergs/s. It is these sources, (the
best example being the bright source in M82 X-1), that
require black hole with masses, M ∼ 102−4M⊙. The de-
velopment of a self-consistent theory which explains the
process by which such black holes are created and un-
dergo high accretion, is theoretically challenging. Hence,
it is important to estimate the number of sources whose
minimum intrinsic luminosity exceeds 1040 ergs/s. Here
the minimum value of the luminosity should not only in-
clude the statistical spectral fitting error, but also the
variations in the luminosity estimation that may occur
upon using different viable spectral models. The third
motivation of this work is to identify such sources which
we call Extremely Luminous X-ray sources (ELX). To
avoid possible ambiguities in determining the luminos-
ity, we have chosen only those sources whose spectra are
not contaminated by excessive diffuse emission and which
are not affected by photon count pile up. Identification
of such relatively “clean” systems would allow for more
detailed studies of their properties to be undertaken and
would be the first step toward understanding their na-
ture.
A similar analysis has been undertaken recently by
Winter et al. (2006) for thirty galaxies observed by
XMM-Newton. Since their motivation was to check if
ULX also exhibit soft and hard spectral states like black
hole binaries, they limited their analysis to bright sources
where detailed spectral analysis could be done. They
found 16 sources as possible low-state ULX and 26 as
high state ones. For the high state ULX, the observed
range for the black body temperature was 0.1− 1.0 keV,
with the more luminous sources having lower temper-
ature. The Chandra analysis undertaken here, can be
compared with this contemporary work and as we discuss
later, the analysis are more or less consistent with each
other. This consistency is important, since although the
larger collecting area of XMM-Newton, allows for more
complex spectral analysis, the higher angular resolution
of Chandra ensures that a source spectrum is not contam-
inated by diffuse emission and flux from nearby sources.
Extremely luminous X-ray point sources 3
2. OBSERVATIONS AND DATA REDUCTION
The names of the thirty host galaxies and the details
of the Chandra ACIS observations are tabulated in Ta-
ble 1. Distances to the galaxies were obtained from
Swartz et al. (2004) and references therein. This sample
of galaxies is a subset of those analyzed by Swartz et al.
(2004). No particular criterion was imposed on the selec-
tion, since our motivation is limited to obtaining enough
sources and not to study dependency on galaxy type.
The data reduction and analysis were done using
CIAO3.2 and HEASOFT6.0.2. Using the CIAO source
detection tool wavdetect, X-ray point sources were ex-
tracted from the level 2 event list. It was found that at
least 60 counts are required to fit the spectral data with a
two parameter model and hence only those sources with
net counts ≥ 60 were chosen for the spectral analysis.
Choosing a lower threshold of 50 counts resulted in a
large number of sources for which spectral parameters
could not be constrained. To avoid photon pile up ef-
fects, a conservative threshold of the count rate being
> 0.05 counts/s was imposed which led to the rejec-
tion of fifteen sources which have been listed in Table
3 of the appendix. For some sources, typically near the
nucleus, it was difficult to find nearby source free back-
ground regions and hence these sources were also not
included in the analysis. Sources embedded in exces-
sive diffuse emission (i.e. when the background flux was
larger than 2 counts/arcsec2 ) were also rejected. Typi-
cally, this amounted to considering only those sources for
which the estimated background counts were less than
20. For each data set, observation-specific bad pixel lists
were set in the ardlib parameter file. Using a combina-
tion of CIAO tools and calibration data, the source and
background spectra were extracted.
These selection criteria makes the sample incomplete
both in low and high luminosity ends. Thus the results
obtained should not be used for quantitative analysis of
the luminosity functions. The motivation here is evaluate
dependency on spectral models and to identify sources
which have high intrinsic luminosity. Thus, care has been
taken to avoid possibly contaminated data, even if such
criteria result in a loss of sources.
Spectral analysis was done using XSPEC version 12.2
and the data was fitted in the energy range 0.3-8.0 keV.
All sources were fitted with two spectral models, the ab-
sorbed power-law and an absorbed disk blackbody. Ab-
sorption was taken into account using the XSPEC model
phabs. Since the number of counts in each spectrum was
typically low, the C-statistics was used for the analysis.
Technically, the C-statistics is not appropriate for high
counts and/or for background subtracted data. However,
it was ascertained that the model parameters obtained ei-
ther by C-statistics or χ2 statistics, were consistent with
each other for high count rate sources. This is reassuring,
because if the results depended on the statistics used, it
would be imperative to use the correct statistics for high
count sources (which need not be χ2) taking into account
the correct (possibly non-Gaussian) error profiles.
An important problem, when fitting low count data
with a two parameter (plus normalization) model, is
the possibility of many local minima in the discerning
statistic (in this case C-statistic) space. Hence, we take
a cautious approach and do not fit the data using the
Fig. 1.— The intrinsic luminosity (in 0.3-8.0 keV energy range)
estimated by fitting the power-law model versus the bolometric
intrinsic luminosity estimated using the disk black body model.
XSPEC minimization routine. Instead we compute the
C-statistic for a range of parameter values (using the
XSPEC command steppar) and find the global minimum.
Such a technique is numerically expensive, but it ensures
that the global minimum has been found and the correct
errors are obtained for the best fit parameters.
3. RESULTS
The 365 sources considered in this analysis were classi-
fied into three categories, depending on whether the data
was better fit by the disk black body model (23 sources)
or the power-law one (67 sources) or both (275 sources).
The criterion chosen to determine a better fit to the data
was that C-statistic difference between the models should
be larger than 2.7. If the difference was less, than both
model fits were considered to equally represent the data.
Although such a criterion is ad hoc (considering the un-
certainties in the actual error statistics) and count rate
dependent, it does serve as an qualitative guideline to
differentiate between those systems which can be repre-
sented by a power-law emission and/or a black body one.
The spectral parameters for all sources for the power-law
and disk blackbody models are tabulated in Tables 4 and
5 of the appendix.
For ULX, the physically relevant parameter is the in-
trinsic bolometric luminosity which should be used to de-
fine and identify them. However, given the limitations of
an instrument’s energy sensitivity range, the bolometric
luminosity is spectral model dependent. For a power-law
the bolometric luminosity cannot be estimated and only
a lower limit can be obtained using the observed energy
range. Since our motivation is to show how the bolomet-
ric luminosity is affected by the use of different spectral
models, we have plotted in Figure 1, the bolometric lu-
minosity for the disk black body model versus the lower
4 Senorita Devi et al.
TABLE 1
Sample Galaxy properties
Galaxy Distance (Mpc) ObsID Texp(ks) N(≥ 60cts)
NGC0253 2.6 969 13.98 13
NGC0628 9.7 2058 46.16 7
NGC0891 10.0 794 50.90 14
NGC1291 8.9 795 39.16 14
NGC1316 17.0 2022 29.85 9
NGC1399 18.3 319 55.94 36
NGC1569 2.2 782 96.75 16
NGC2403 3.1 2014 35.59 4
NGC3034 3.9 361 33.25 5
NGC3079 15.6 2038 26.57 5
NGC3379 11.1 1587 31.52 7
NGC3556 14.1 2025 59.36 15
NGC3628 10.0 2039 57.96 14
NGC4125 24.2 2071 64.23 8
NGC4365 20.9 2015 40.42 9
NGC4374 17.4 803 28.47 4
NGC4449 3.7 2031 26.59 12
NGC4485/90 7.8 1579 19.52 9
NGC4559 10.3 2027 10.70 1
NGC4579 21.0 807 33.90 3
NGC4594 9.6 1586 18.51 18
NGC4631 7.6 797 59.21 12
NGC4649 16.6 785 36.87 23
NGC4697 11.8 784 39.25 19
NGC5055 9.2 2197 27.99 16
NGC5128 4.0 962 36.50 22
NGC5194/5 8.4 1622 26.80 18
NGC5457 7.0 2065 9.63 4
NGC5775 26.7 2940 58.21 15
NGC6946 5.5 1043 58.28 16
Note. — (Texp)the exposure time in ks; (N) the number of point sources with total counts from the source≥ 60 as detected by
wavdetect with fluxscale= 1
limit to the luminosity using the power-law model. The
figure represents only those sources which can be rep-
resented by both models. The figure shows that while
for most sources the difference in luminosities is not sub-
stantial, there are sources with estimated luminosities
& 1039 erg/s, where the disk black body luminosity es-
timation is significantly smaller than the power-law one.
This happens for sources for which the spectral index is
large.
To show the dependence of the luminosity function on
the fitting model, we compute the cumulative luminos-
ity function in two ways. For the disk black body cu-
mulative luminosity function (DBCLF), the luminosity
obtained form fitting a black body is used, except for
those sources that are fitted better with a power-law
for which the power-law model estimated luminosity is
considered. Similarly, for the power-law cumulative lu-
minosity function, (PLCLF) the luminosity corresponds
to the power-law fit, except for those sources which are
better represented by a disk black body spectrum. In
Figure 2, the solid line represents the DBCLF while the
PLCLF is plotted as a dotted one. There are less num-
ber of sources with L > 1040 ergs/s for disk black body
preferred representation. Moreover, there is a significant
difference in the slope of the two luminosity function and
the presence of a faint break at L ∼ 1040 ergs/s for the
PLCLF, is not evident in the DBCLF. Of particular in-
terest is the number of sources whose minimum luminos-
ity (i.e. the minimum of the two lower limits obtained by
fitting the two spectral models) exceeds a certain value.
In Figure 2, the dashed line represents such a minimum
cumulative luminosity function, which reveals that there
are eight sources with minimum luminosity greater 1040
ergs/s (ELX) and ∼ 80 sources with minimum luminosity
greater 1039 ergs/s (ULX).
Figures 3 (a) shows the variation of the luminosity ver-
sus the disk black body temperature, While most of the
sources have an inner disk temperature ∼ 1 keV, as is
evident from the distribution (Figure 3 b), there is a pop-
ulation of high luminosity source with low (∼ 0.1 keV)
temperature. Although the number of sources is low,
there seems to be some evidence, that ELX (i.e. sources
with luminosities > 1040 ergs/s ) can be divided in two
groups, a “super-soft” group with temperature less than
0.2 keV and an harder group with temperature ∼ 2 keV.
Figure 3 may be compared with the results obtained by
Winter et al. (2006) using XMM-Newton data for a dif-
ferent sample and selection criteria. They also find that
sources with luminosities > 5 × 1039 ergs/s have have a
similar bimodal distribution in temperature as shown in
Figure 3. This supports the hypothesis that ELX can
be divided into two groups and this is not an artifact of
sample selection bias.
Figure 4 (a) shows the variation of luminosity with
power-law photon index for those sources which can be
fitted by a power-law model. There is a clear correla-
tion between the two. This correlation does not seem
to be due to overestimation of column density, since no
such correlation is seen in the luminosity versus NH
plot (Figure 5 b). Similar to the analysis using the
Extremely luminous X-ray point sources 5
Fig. 2.— The cumulative luminosity function using the disk
black body model (solid line), the power-law model (dotted line)
and the minimum cumulative luminosity function (dashed line).
0.1 1 10
Fig. 3.— (a) The luminosity versus inner disk temperature and
(b) the distribution of the inner disk temperature for sources whose
spectra can be modeled as disk black body emission. The triangles
represent sources which are better fitted by the disk black body
model as compared to the power-law one. The two solid lines
represent the expected luminosity versus maximum temperature
relations for accretion disks radiating at one and one-tenth of the
the Eddington Luminosity. Two sources which were identified as
foreground stars (see text) are not included in this plot.
0 2 4 6 8 10
Fig. 4.— (a) The luminosity versus power-law index and (b)
the distribution of the power-law index for sources whose spectra
can be modeled as a power-law emission. The triangles represent
sources which are better fitted by the power-law model as compared
to the disk black body one. Two sources which were identified as
background AGN (see text) are not included in this plot.
disk black body model, there is a group of “super-soft”
sources (i.e. photon spectral index > 3) which are also
highly luminous (L > 1040 ergs/s). The column den-
sity versus luminosity plots for both the power-law and
disk black body models (Figure 5), reveal an absence
of correlation, which is indicative that there may not
be a bias in the analysis, i.e. the luminosities are not
being over-estimated because of a NH overestimation.
In this analysis, there are eight sources which have an
apparent minimum luminosity greater than 1040 ergs/s.
However, two of these sources (NGC 5055, R.A: 13 15
30.18, Dec: +42 03 13.5 and NGC 4594, R.A: 12 39
45.22, Dec: -11 38 49.8) are foreground stars based
on the optical images of the galaxies. Optical spec-
troscopy of a source in NGC 5775 ( R.A: 14 53 55.8,
Dec: +3 33 28.02) reveals that it is a background AGN
(Gutiérrez & López-Corredoira 2005), while a source in
NGC 1399 ( R.A: 14 53 55.8, Dec: +3 33 28.02) is a
BLAGN (Green et al. 2004). The spectral properties of
the other four sources, which we call Extremely Lumi-
nous sources (ELX) are tabulated in Table 2. The NGC
0628 source reported in Table 2, is a different source than
the well studied ULX, CXOU J013651.1+154547. The
luminosity of this highly variable source (Krauss et al.
2005) is ∼ 1039 ergs/s and its spectral properties are
listed in Table 4. The source in NGC 6946 is a well known
variable source (Liu & Mirabel 2005) and has been called
X7 with L ∼ 1039.22 ergs/sec(Lira et al. 2000), IXO 85
(Colbert & Ptak 2002) and source no. 56 (Holt et al.
2003). Although, the best fit parameters for C-statistics
are shown, these results have been checked using χ2
statistics and by C-statistics fit for unbinned and back-
6 Senorita Devi et al.
36 38 40 42
Fig. 5.— The column density versus luminosity for sources fitted
with (a) the disk black body model and (b) the power-law model.
ground not subtracted data and it was found that the
parameters values are consistent within errors and the
errors on the estimated luminosities do not vary by more
than a factor two. In general, these sources are better
represented by disk black body emission than a power-
law model, except for the source in NGC 6946, which
however requires an exceptionally large power-law pho-
ton spectral index, (Γ > 5). The spectral properties of
these bright sources suggest that they may be divided
into two groups. The first group of four sources (Table
2), are represented by low inner disk temperatures (< 0.5
keV), and hence may be called “supersoft” sources. In
contrast the second group of three sources, have harder
spectra with inner disk temperatures & 1 keV or with
power-law photon index (Γ ∼ 2) and hence may be called
hard sources. For this group, the spectra are marginally
fitted better with a disk blackbody emission, although
considering the uncertainties in the spectral fitting, a
power-law representation may also be acceptable.
4. SUMMARY AND DISCUSSION
Chandra observations of thirty galaxies were analyzed
and the spectra of their points sources were fitted us-
ing both a power-law and a disk black body emission
model. Only those sources were chosen, which were
bright enough to allow a meaningful spectral fit, but
whose data was not contaminated by excessive diffuse
emission and/or effected by pile-up. It was found that
the shape of the luminosity function especially at the
high luminosity end, depends on the choice of the spec-
tral model.
In accordance with earlier results, a large number of
the sources (∼ 80 ) have a luminosity which exceeds 1039
ergs/s and hence satisfy the standard definition of be-
ing Ultra Luminous X-ray sources (ULX) and do not
seem to have any spectral distinction when compared
with sources having lower luminosity. In this sample of
365 sources, there are four source which we refer to as
Extremely luminous X-ray sources (ELX) since their lu-
minosities were estimated to exceed 1040 ergs/s. These
sources are in general better described by disk black-
body emission and can be distinctively grouped into two
classes. This is consistent with the results of an indepen-
dent analysis using XMM-Newton data (Winter et al.
2006). The members of the first class have soft spec-
tra with best fit inner disk temperature < 0.5 keV, while
for the other class the spectra is harder with inner disk
temperature & 1.3 keV.
If disk black body emission is indeed the correct radia-
tive process for the supersoft class then the inner disk
temperature should correspond to the maximum color
temperature of a disk, which can be estimated to be
Tcol ∼ 0.3 keV L
)−1/2 (1)
where L40 is the luminosity in 10
40 ergs/s, f is the color
factor and LEdd is the Eddington luminosity. In Figure
3 (a), the two solid lines represent this relationship for
L/LEdd = 1 and 0.1. Thus within the uncertainties, the
supersoft sources are compatible with having pure black
body disk emission, and have L ∼ 0.5LEdd.
ELX which are members of the hard class have inner
disk temperatures which are higher than that expected
from a Eddington limited black body accretion disks.
Hence, for these source the radiative mechanism is prob-
ably inverse Comptonization of soft photons. Detailed
spectral analysis, which included XMM observations, of
the bright X-ray source in M82 X-1 has revealed that its
spectrum is better fitted by a saturated Comptonization
model (Agrawal & Misra 2006), which is also the case for
the the bright X-ray source in Holmberg IX. Holmberg IX
is not part of the sample studied here and M82 X-1 has
been excluded because of pile-up effects and excess dif-
fuse emission. Thus, these sources, with estimated lumi-
nosities ∼ 1041 erg/s, could also be members of the hard
class of ELX. Thus it seems that like the the hard state
of standard black hole binaries, the hard class ELX also
have spectra which is due to thermal Comptonization,
however unlike black hole binaries, in ELX the Comp-
tonization seems to be saturated. Thus, it is tempting
to draw by analogy, that the two spectral classes of ELX
are actually two spectral states of the same kind of ob-
ject. This can be verified if spectral transition between
the two classes is observed.
With the identification of these ELX and other sources
from the literature, it is now possible to undertake a more
extensive study of their properties. Temporal variability
of these sources will shed more light on the nature of
these enigmatic sources.
The authors thank the referee for useful comments and
suggestions which have significantly improved the paper.
ASD thanks CSIR and IUCAA for support.
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Extremely luminous X-ray point sources 7
TABLE 2
Spectral properties of sources with minimum luminosity > 1040ergs/s
galaxy R.A. Dec. Counts Bins kTin (keV) log LDbb C-statDbb Γ log LPow C-statPow
NGC0628 01 36 47.45 +15 47 45.01 200 7 0.09
+0.04
−0.03
41.65
+2.49
−1.60
0.7 9.56
+0.44
−2.42
42.18
+0.36
−1.49
NGC6946 20 35 0.13 +60 9 7.97 1936 66 0.32
+0.02
−0.03
39.46
+0.08
−0.06
162.2 5.14
+0.34
−0.27
40.41
+0.21
−0.18
134.8
NGC4579 12 37 40.30 +11 47 27.48 1696 66 1.35
+0.10
−0.09
40.56
+0.02
−0.02
65.0 1.75
+0.11
−0.11
40.37
+0.00
−0.02
NGC5775 14 53 58.90 + 3 32 16.78 1358 60 1.97
+0.29
−0.22
41.11
+0.02
−0.02
55.8 1.86
+0.22
−0.11
40.95
+0.10
−0.06
Note. — Host Galaxy name; Right Ascension; Declination; Total counts; Number of energy bins after rebinning; Best fit inner disk
temperature; Bolometric luminosity estimate using disk black body model; C-statistic for disk black body model; Photon index Γ for
the power-law model; Luminosity estimate (0.3-8.0 keV) using the power-law model; C-statistic for power-law model;
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APPENDIX
8 Senorita Devi et al.
TABLE 3
List of sources with count rate greater than 0.05
counts/s
Galaxy R.A. Dec. Count rate s−1
NGC0253 0 47 32.97 -25 17 48.80 0.0845164
NGC0253 0 47 22.59 -25 20 50.87 0.0657110
NGC0253 0 47 17.55 -25 18 11.18 0.0569807
NGC1569 4 31 16.85 +64 49 50.13 0.0567468
NGC2403 7 36 55.61 +65 35 40.85 0.0746877
NGC2403 7 36 25.53 +65 35 40.02 0.1521207
NGC3628 11 20 15.75 +13 35 13.70 0.0530390
NGC4374 12 25 11.92 +12 51 53.53 0.0563400
NGC4449 12 28 17.83 +44 6 33.86 0.0525013
NGC4485 12 30 43.26 +41 38 18.36 0.0509909
NGC4485 12 30 30.56 +41 41 42.33 0.0758634
NGC4559 12 35 58.56 +27 57 41.91 0.1233310
NGC4559 12 35 51.71 +27 56 4.05 0.1984267
NGC4631 12 41 55.56 +32 32 16.90 0.0554584
NGC6946 20 35 0.74 +60 11 30.74 0.1448118
Note. — The spectra of these sources would be affected
by pile-up and hence have not been included in the sample
TABLE 4
Spectral Properties of point sources fitted with the Power-Law model
Galaxy R.A. Decl. nH(10
−2) Γ log(L) ergs/s Cstat d. o. f.
NGC0253 0 47 43.07 -25 15 29.28 0.15
+0.53
−0.15
+2.31
−1.21
37.70
+1.20
−0.18
9.43 4
NGC0253 0 47 42.80 -25 15 2.02 0.77
+0.51
−0.49
+0.66
−0.77
38.26
+0.27
−0.12
3.36 4
NGC0253 0 47 35.25 -25 15 11.53 0.48
+0.05
−0.13
+0.22
−0.33
38.65
+0.05
−0.08
38.94 19
NGC0253 0 47 34.28 -25 17 3.32 5.66
+5.98
−5.66
+4.62
−4.95
40.82
+3.28
−2.90
3.21 2
NGC0253 0 47 34.00 -25 16 36.51 1.04
+0.11
−0.10
+0.22
−0.22
39.01
+0.08
−0.07
10.93 27
NGC0253 0 47 33.55 -25 18 16.51 0.00
+0.18
−0.00
+0.99
−0.44
37.33
+0.15
−0.10
2.37 2
NGC0253 0 47 32.05 -25 17 21.43 3.17
+2.20
−2.46
+1.10
−1.10
38.61
+0.72
−0.32
1.63 3
NGC0253 0 47 30.98 -25 18 26.23 1.55
+1.46
−1.55
+1.21
−1.21
38.24
+0.65
−0.21
1.76 3
NGC0253 0 47 28.01 -25 18 20.21 0.93
+1.13
−0.92
+1.76
−1.54
38.02
+1.03
−0.23
2.13 1
NGC0253 0 47 25.20 -25 19 45.22 0.00
+0.15
−0.00
+0.66
−0.22
37.96
+0.09
−0.09
5.10 4
NGC0253 0 47 18.50 -25 19 13.94 0.00
+0.15
−0.00
+0.44
−0.22
37.97
+0.07
−0.05
3.94 5
NGC0253 0 47 40.66 -25 14 11.71 0.69
+0.72
−0.56
+1.98
−1.32
37.96
+1.11
−0.27
1.07 3
NGC0253 0 47 17.65 -25 18 26.45 0.11
+0.49
−0.11
+1.54
−0.77
38.12
+0.27
−0.12
3.13 3
NGC0628 1 36 51.06 +15 45 46.86 0.03
+0.05
−0.03
+0.22
−0.11
39.22
+0.04
−0.02
50.58 36
NGC0628 1 36 47.45 +15 47 45.01 0.89
+0.11
−0.33
+0.44
−2.42
42.18
+0.36
−1.49
8.56 4
. . . . . . . . .
Note. — Host galaxy name; Right Ascension; Declination; nH , equivalent hydrogen column density;
Γ, photon power-law index; L, X-ray luminosity in the energy range: 0.3-8.0 keV; C-statistics; degree
of freedom. The complete version of this table is in the electronic edition of the Journal. The printed
edition contains only a sample.
Extremely luminous X-ray point sources 9
TABLE 5
Spectral Properties of point sources fitted with the disk black body model
Galaxy R.A. Decl. nH(10
−2) kTin (keV) log(L) ergs/s Cstat d. o. f.
NGC0253 0 47 43.07 -25 15 29.28 0.00
+0.32
−0.00
+0.42
−0.25
37.69
+0.37
−0.00
9.41 4
NGC0253 0 47 42.80 -25 15 2.02 0.44
+0.36
−0.32
+1.95
−0.52
38.40
+0.26
−0.08
3.95 4
NGC0253 0 47 35.25 -25 15 11.53 0.24
+0.07
−0.07
+0.21
−0.15
38.71
+0.04
−0.03
35.79 19
NGC0253 0 47 34.28 -25 17 3.32 3.08
+5.36
−3.07
+9.38
−0.36
38.69
+2.04
−0.60
3.37 2
NGC0253 0 47 34.00 -25 16 36.51 0.64
+0.12
−0.10
+0.19
−0.16
39.06
+0.03
−0.03
8.60 27
NGC0253 0 47 33.55 -25 18 16.51 0.00
+0.08
−0.00
+0.69
−0.29
37.49
+0.20
−0.06
3.85 2
NGC0253 0 47 32.05 -25 17 21.43 2.04
+1.82
−1.62
+4.71
−0.80
38.68
+0.40
−0.09
1.37 3
NGC0253 0 47 30.98 -25 18 26.23 0.96
+0.96
−0.86
+8.00
−0.91
38.41
+0.73
−0.12
1.84 3
NGC0253 0 47 28.01 -25 18 20.21 0.62
+0.77
−0.56
+8.80
−0.55
38.08
+0.90
−0.12
2.51 1
NGC0253 0 47 25.20 -25 19 45.22 0.00
+0.06
−0.00
+0.86
−0.33
38.12
+0.21
−0.09
7.71 4
NGC0253 0 47 18.50 -25 19 13.94 0.00
+0.05
−0.00
+0.73
−0.41
38.22
+0.15
−0.09
6.36 5
NGC0253 0 47 40.66 -25 14 11.71 0.42
+0.47
−0.38
+2.76
−0.40
37.94
+0.38
−0.18
1.64 3
NGC0253 0 47 17.65 -25 18 26.45 0.08
+0.32
−0.07
+8.76
−0.65
38.23
+1.04
−0.13
2.85 3
NGC0628 1 36 51.06 +15 45 46.86 0.00
+0.00
−0.00
+0.08
−0.11
39.42
+0.02
−0.04
119.44 36
NGC0628 1 36 47.45 +15 47 45.01 0.75
+0.58
−0.39
+0.04
−0.03
41.65
+2.49
−1.60
0.66 4
. . . . . . . . .
Note. — Host galaxy name; Right Ascension; Declination; nH , equivalent hydrogen column density;
kTin, inner disk temperature; L, Bolometric X-ray luminosity; C-statistics; degree of freedom. The complete
version of this table is in the electronic edition of the Journal. The printed edition contains only a sample.

  Data from {\it Chandra} observations of thirty nearby galaxies were analyzed
and 365 X-ray point sources were chosen whose spectra were not contaminated by
excessive diffuse emission and not affected by photon pile up. The spectra of
these sources were fitted using two spectral models (an absorbed power-law and
a disk blackbody) to ascertain the dependence of estimated parameters on the
spectral model used. It was found that the cumulative luminosity function
depends on the choice of the spectral model, especially for luminosities $>
10^{40}$ ergs/s. In accordance with previous results, a large number ($\sim
80$) of the sources have luminosities $> 10^{39}$ ergs/s (Ultra-Luminous X-ray
sources) with indistinguishable average spectral parameters (inner disk
temperature $\sim 1$ keV and/or photon index $\Gamma \sim 2$) with those of the
lower luminosities ones. After considering foreground stars and known
background AGN,we identify four sources whose minimum luminosity exceed
$10^{40}$ ergs/s, and call them Extremely Luminous X-ray sources (ELX). The
spectra of these sources are in general better represented by the disk black
body model than the power-law one. These ELX can be grouped into two distinct
spectral classes. Two of them have an inner disk temperature of $< 0.5$ keV and
hence are called ``supersoft'' ELX, while the other two have temperatures
$\gtrsim 1.3$ keV and are called ``hard'' ELX. The estimated inner disk
temperatures of the supersoft ELX are compatible with the hypothesis that they
harbor intermediate size black holes, which are accreting at $\sim 0.5$ times
their Eddington Luminosity. The radiative mechanism for hard ELX, seems to be
Inverse Comptonization, which in contrast to standard black holes systems, is
probably saturated.

Draft version August 8, 2021
Preprint typeset using LATEX style emulateapj v. 6/22/04
THE DEPENDENCE OF THE ESTIMATED LUMINOSITIES OF ULX ON SPECTRAL MODELS
A. Senorita Devi1, R. Misra2, V. K. Agrawal3 and K. Y. Singh1
Draft version August 8, 2021
ABSTRACT
Data from Chandra observations of thirty nearby galaxies were analyzed and 365 X-ray point sources
were chosen whose spectra were not contaminated by excessive diffuse emission and not affected by
photon pile up. The spectra of these sources were fitted using two spectral models (an absorbed
power-law and a disk blackbody) to ascertain the dependence of estimated parameters on the spectral
model used. It was found that the cumulative luminosity function depends on the choice of the
spectral model, especially for luminosities > 1040 ergs/s. In accordance with previous results, a large
number (∼ 80) of the sources have luminosities > 1039 ergs/s (Ultra-Luminous X-ray sources) with
indistinguishable average spectral parameters (inner disk temperature ∼ 1 keV and/or photon index
Γ ∼ 2) with those of the lower luminosities ones. After considering foreground stars and known
background AGN, we identify four sources whose minimum luminosity exceed 1040 ergs/s, and call
them Extremely Luminous X-ray sources (ELX). The spectra of these sources are in general better
represented by the disk black body model than the power-law one. These ELX can be grouped into
two distinct spectral classes. Two of them have an inner disk temperature of < 0.5 keV and hence
are called “supersoft” ELX, while the other two have temperatures & 1.3 keV and are called “hard”
ELX. The estimated inner disk temperatures of the supersoft ELX are compatible with the hypothesis
that they harbor intermediate size black holes, which are accreting at ∼ 0.5 times their Eddington
Luminosity. The radiative mechanism for hard ELX, seems to be Inverse Comptonization, which in
contrast to standard black holes systems, is probably saturated. Extensive variability analysis of these
ELX, will be able to distinguish whether these two spectral class represent different systems or they
are spectral states of the same kind of source.
Subject headings: Galaxies: general - X-rays: binaries
1. INTRODUCTION
In the last few years, Chandra observations of nearby
galaxies have detected many non-nuclear X-ray point
sources (Kaaret et al. 2001 ; Matsumoto et al. 2001;
Zezas & Fabbiano 2002), some of which have isotropic lu-
minosities> 1039 ergs/s and are called Ultra luminous X-
ray Sources (ULX). While some of these ULX are super-
nova remnants (e.g. Ryder et al. 1993; Fox et al. 2000),
it is believed that the majority of them are compact ac-
creting systems. Indeed, ASCA X-ray spectral studies of
many ULX have revealed that they display the charac-
teristics of accreting black holes (Makishima et al. 2000;
Mizuno et al. 2001). ULX have also been called Super-
Eddington Sources (Fabbiano 1989, 2004) and Intermedi-
ate luminosity X-ray objects (Roberts & Warwick 2000;
Colbert & Mushotzky 1999).
Since these ULX sources emit radiation at a rate
larger than the Eddington luminosity for a ten-solar mass
black hole, they are believed to harbor a black hole of
mass 10M⊙<M<10
5M⊙ (Colbert & Mushotzky 1999;
Makishima et al. 2000) where the upper limit is con-
strained by the fact that a more massive black hole would
have settled into the nucleus due to dynamical friction
(Kaaret et al. 2001 ). Black holes in this mass range are
called Intermediate Mass Black Holes (IMBH), since they
1 Department Of Physics, Manipur University, Canchipur,
Imphal-795003, Manipur, India; senorita@iucaa.ernet.in
2 Inter-University Center for Astronomy and Astrophysics, Post
Bag 4, Ganeshkhind, Pune-411007, India; rmisra@iucaa.ernet.in
3 Department of Astronomy and Astrophysics, Tata Institute of
Fundamental Research, Homi Bhabha Road, Mumbai-400 005,In-
seem to represent the missing component of the black
hole mass spectrum with masses prevailing in the gap be-
tween those of stellar mass black holes found in Galactic
X-ray binaries and those associated with Active Galac-
tic Nuclei, M ∼ 106 − 109 M⊙ (Richstone et al. 1998).
Miller & Colbert (2004) and Miller (2005) review the
present evidence for IMBH in ULX and Liu & Mirabel
(2005) have compiled a catalogue of some ULX and prop-
erties.
Alternate models for ULX are that their luminosi-
ties are super-Eddington (Begelman 2002) or that their
emission is beamed from a geometrically thick accre-
tion disk (King et al. 2001). However, it has been ar-
gued that in the latter case, such thick ”funnel” shaped
disks enhance the observed flux by just a factor of few
(Misra & Sriram 2003). For all of these models, the
creation of such sources (Portegies, Zwart & McMillian
2002; Taniguchi et al. 2000; Madau & Rees 2001) and
process by which they sustain high accretion rates
(King et al. 2001), are largely unknown.
Investigations on the nature of ULX have been un-
dertaken by studying the spectra and variability of in-
dividual sources. For example analysis of the spectra
of NGC 1313 X-1, X-2 (Miller et al. 2003) and M81 X-
9 (Miller, Fabian & Miller 2004), revealed the presence
of a cool accretion disk component (kTin ∼ 0.1 − 0.5
keV), suggesting that ULX indeed harbor IMBH. Tran-
sitions between two spectral states, similar to those
seen in Galactic black hole systems, have been reported
in NGC 1313 X-1(Colbert & Mushotzky 1999) and two
sources in IC342 (Kubota et al. 2001). Spectral transi-
tions have also been reported in two sources in NGC 1313
http://arxiv.org/abs/0704.1107v1
2 Senorita Devi et al.
(Feng & Kaaret 2006).
The large collecting area of XMM-Newton, allows for
detailed spectral fits to ULX, which often comprise of two
components (Wang et al. 2004; Feng & Kaaret 2005).
However, Gonçalves & Soria (2006), have argued that
such soft spectral components depend on the complex-
ity of the fitting model. An interesting object is the
brightest X-ray point source in M 82, whose intrinsic
luminosity has been measured to be as high as 1.6 ×
1041 ergs/s (Ptak and Griffiths 1999). The detection of
a 54 mHz quasi-periodic oscillation in its X-ray light
curve suggests that the source is a compact object and
not a background AGN (Strohmayer & Mushotzky 2003;
Dewangan et al. 2006a). The spectra of this source can
be fitted by a power-law with photon index, Γ ∼ 2
(Fiorito & Titarchuk 2004), but is more consistently fit-
ted with a flatter power-law with an high energy cut-
off around ∼ 6 keV, which can be interpreted as opti-
cally thick, saturated Comptonization (Agrawal & Misra
2006). A quasi-periodic oscillation has also been discov-
ered in the bright X-ray source of Holmberg IX, which
is similar to the source in M82 in having a flat spec-
trum (Γ ∼ 1) with a ∼ 9 keV cutoff (Dewangan et al.
2006b). Recently, Stobbart et al. (2006) found that the
XMM-Newton spectra of eleven of the eighteen ULX
studied by them, showed such high energy curvature.
Chandra observations of NGC 5204 X-1, also reveals the
presence of an optically thick Comptonized component
(Roberts et al. 2006). While these results of individual
ULX are intriguing, there does not seem to be any signif-
icantly distinguishable spectral property of ULX, and in
general their spectra can be described either by steep or
flat power-law indices, with and without soft components
(e.g. Dewangan et al. 2005).
Another line of investigation is to construct the cu-
mulative luminosity function and histograms of spec-
tral parameters of a large sample of X-ray sources (e.g.
Colbert & Ptak 2002). The hope here is that, in case
ULX are a distinct class of sources and/or they can be
classified into distinct subgroups, the luminosity func-
tion should exhibit a break and their spectral parame-
ters should show clustering. Swartz et al. (2004) ana-
lyzed data from 82 galaxies and estimated the luminos-
ity function and spectral parameters of the X-ray point
sources in these galaxies. They found that the average
photon index (as well as the distribution) of the ULX
and the less luminous sources is nearly same. Moreover,
their spatial and variability distributions are also similar.
While, their analysis revealed that the luminosity func-
tions of ULX depend on the host galaxy type and star
formation rate, they did not find any significant evidence
for breaks in them.
As emphasized by Swartz et al. (2004), the power-law
model they used to fit the data was chosen as an empir-
ical one. They attempted to fit all the sources with the
power-law model and only for those sources that did not
provide a reasonable fit, they used other models like disk
black body. They note that for many sources that are
well fitted by the power-law model, other spectral models
can also represent the spectra. In this work, we consider
a smaller sample of 30 galaxies but fit the spectra of the
points sources, with both a power-law and a disk black-
body model. In principle, the intrinsic (i.e. the absorp-
tion corrected) luminosity inferred for a source may be
different for the two spectral models. Our first motiva-
tion here is to make a qualitative estimate of this differ-
ence by noting the dependency of the luminosity function
on the spectral model used. A second motivation for this
work is based on the expectation that estimations of a
different spectral parameter like the inner disk tempera-
ture (as compared to the photon index), maybe better in
distinguishing ULX from other sources or they may re-
veal dependencies (like correlations between luminosity
and temperature) which could shed light on the nature
of these sources. As mentioned earlier, the spectra of
several ULX are complex requiring more than one com-
ponents. Thus, the two spectral models, an absorbed
power-law and and an absorbed disk blackbody, should
be considered as empirical ones, which can adequately
represent low count data and these models need not be
the correct physical representation of the actual source
spectrum.
It is clear that ULX are fairly common in nearby galax-
ies. For example, Swartz et al. (2004) identified 154 of
them in 82 galaxies. If these sources are Eddington lim-
ited, then black holes & 10M⊙ may indeed be quite com-
mon. However, only a few of these sources have luminosi-
ties greater than 1040 ergs/s. It is these sources, (the
best example being the bright source in M82 X-1), that
require black hole with masses, M ∼ 102−4M⊙. The de-
velopment of a self-consistent theory which explains the
process by which such black holes are created and un-
dergo high accretion, is theoretically challenging. Hence,
it is important to estimate the number of sources whose
minimum intrinsic luminosity exceeds 1040 ergs/s. Here
the minimum value of the luminosity should not only in-
clude the statistical spectral fitting error, but also the
variations in the luminosity estimation that may occur
upon using different viable spectral models. The third
motivation of this work is to identify such sources which
we call Extremely Luminous X-ray sources (ELX). To
avoid possible ambiguities in determining the luminos-
ity, we have chosen only those sources whose spectra are
not contaminated by excessive diffuse emission and which
are not affected by photon count pile up. Identification
of such relatively “clean” systems would allow for more
detailed studies of their properties to be undertaken and
would be the first step toward understanding their na-
ture.
A similar analysis has been undertaken recently by
Winter et al. (2006) for thirty galaxies observed by
XMM-Newton. Since their motivation was to check if
ULX also exhibit soft and hard spectral states like black
hole binaries, they limited their analysis to bright sources
where detailed spectral analysis could be done. They
found 16 sources as possible low-state ULX and 26 as
high state ones. For the high state ULX, the observed
range for the black body temperature was 0.1− 1.0 keV,
with the more luminous sources having lower temper-
ature. The Chandra analysis undertaken here, can be
compared with this contemporary work and as we discuss
later, the analysis are more or less consistent with each
other. This consistency is important, since although the
larger collecting area of XMM-Newton, allows for more
complex spectral analysis, the higher angular resolution
of Chandra ensures that a source spectrum is not contam-
inated by diffuse emission and flux from nearby sources.
Extremely luminous X-ray point sources 3
2. OBSERVATIONS AND DATA REDUCTION
The names of the thirty host galaxies and the details
of the Chandra ACIS observations are tabulated in Ta-
ble 1. Distances to the galaxies were obtained from
Swartz et al. (2004) and references therein. This sample
of galaxies is a subset of those analyzed by Swartz et al.
(2004). No particular criterion was imposed on the selec-
tion, since our motivation is limited to obtaining enough
sources and not to study dependency on galaxy type.
The data reduction and analysis were done using
CIAO3.2 and HEASOFT6.0.2. Using the CIAO source
detection tool wavdetect, X-ray point sources were ex-
tracted from the level 2 event list. It was found that at
least 60 counts are required to fit the spectral data with a
two parameter model and hence only those sources with
net counts ≥ 60 were chosen for the spectral analysis.
Choosing a lower threshold of 50 counts resulted in a
large number of sources for which spectral parameters
could not be constrained. To avoid photon pile up ef-
fects, a conservative threshold of the count rate being
> 0.05 counts/s was imposed which led to the rejec-
tion of fifteen sources which have been listed in Table
3 of the appendix. For some sources, typically near the
nucleus, it was difficult to find nearby source free back-
ground regions and hence these sources were also not
included in the analysis. Sources embedded in exces-
sive diffuse emission (i.e. when the background flux was
larger than 2 counts/arcsec2 ) were also rejected. Typi-
cally, this amounted to considering only those sources for
which the estimated background counts were less than
20. For each data set, observation-specific bad pixel lists
were set in the ardlib parameter file. Using a combina-
tion of CIAO tools and calibration data, the source and
background spectra were extracted.
These selection criteria makes the sample incomplete
both in low and high luminosity ends. Thus the results
obtained should not be used for quantitative analysis of
the luminosity functions. The motivation here is evaluate
dependency on spectral models and to identify sources
which have high intrinsic luminosity. Thus, care has been
taken to avoid possibly contaminated data, even if such
criteria result in a loss of sources.
Spectral analysis was done using XSPEC version 12.2
and the data was fitted in the energy range 0.3-8.0 keV.
All sources were fitted with two spectral models, the ab-
sorbed power-law and an absorbed disk blackbody. Ab-
sorption was taken into account using the XSPEC model
phabs. Since the number of counts in each spectrum was
typically low, the C-statistics was used for the analysis.
Technically, the C-statistics is not appropriate for high
counts and/or for background subtracted data. However,
it was ascertained that the model parameters obtained ei-
ther by C-statistics or χ2 statistics, were consistent with
each other for high count rate sources. This is reassuring,
because if the results depended on the statistics used, it
would be imperative to use the correct statistics for high
count sources (which need not be χ2) taking into account
the correct (possibly non-Gaussian) error profiles.
An important problem, when fitting low count data
with a two parameter (plus normalization) model, is
the possibility of many local minima in the discerning
statistic (in this case C-statistic) space. Hence, we take
a cautious approach and do not fit the data using the
Fig. 1.— The intrinsic luminosity (in 0.3-8.0 keV energy range)
estimated by fitting the power-law model versus the bolometric
intrinsic luminosity estimated using the disk black body model.
XSPEC minimization routine. Instead we compute the
C-statistic for a range of parameter values (using the
XSPEC command steppar) and find the global minimum.
Such a technique is numerically expensive, but it ensures
that the global minimum has been found and the correct
errors are obtained for the best fit parameters.
3. RESULTS
The 365 sources considered in this analysis were classi-
fied into three categories, depending on whether the data
was better fit by the disk black body model (23 sources)
or the power-law one (67 sources) or both (275 sources).
The criterion chosen to determine a better fit to the data
was that C-statistic difference between the models should
be larger than 2.7. If the difference was less, than both
model fits were considered to equally represent the data.
Although such a criterion is ad hoc (considering the un-
certainties in the actual error statistics) and count rate
dependent, it does serve as an qualitative guideline to
differentiate between those systems which can be repre-
sented by a power-law emission and/or a black body one.
The spectral parameters for all sources for the power-law
and disk blackbody models are tabulated in Tables 4 and
5 of the appendix.
For ULX, the physically relevant parameter is the in-
trinsic bolometric luminosity which should be used to de-
fine and identify them. However, given the limitations of
an instrument’s energy sensitivity range, the bolometric
luminosity is spectral model dependent. For a power-law
the bolometric luminosity cannot be estimated and only
a lower limit can be obtained using the observed energy
range. Since our motivation is to show how the bolomet-
ric luminosity is affected by the use of different spectral
models, we have plotted in Figure 1, the bolometric lu-
minosity for the disk black body model versus the lower
4 Senorita Devi et al.
TABLE 1
Sample Galaxy properties
Galaxy Distance (Mpc) ObsID Texp(ks) N(≥ 60cts)
NGC0253 2.6 969 13.98 13
NGC0628 9.7 2058 46.16 7
NGC0891 10.0 794 50.90 14
NGC1291 8.9 795 39.16 14
NGC1316 17.0 2022 29.85 9
NGC1399 18.3 319 55.94 36
NGC1569 2.2 782 96.75 16
NGC2403 3.1 2014 35.59 4
NGC3034 3.9 361 33.25 5
NGC3079 15.6 2038 26.57 5
NGC3379 11.1 1587 31.52 7
NGC3556 14.1 2025 59.36 15
NGC3628 10.0 2039 57.96 14
NGC4125 24.2 2071 64.23 8
NGC4365 20.9 2015 40.42 9
NGC4374 17.4 803 28.47 4
NGC4449 3.7 2031 26.59 12
NGC4485/90 7.8 1579 19.52 9
NGC4559 10.3 2027 10.70 1
NGC4579 21.0 807 33.90 3
NGC4594 9.6 1586 18.51 18
NGC4631 7.6 797 59.21 12
NGC4649 16.6 785 36.87 23
NGC4697 11.8 784 39.25 19
NGC5055 9.2 2197 27.99 16
NGC5128 4.0 962 36.50 22
NGC5194/5 8.4 1622 26.80 18
NGC5457 7.0 2065 9.63 4
NGC5775 26.7 2940 58.21 15
NGC6946 5.5 1043 58.28 16
Note. — (Texp)the exposure time in ks; (N) the number of point sources with total counts from the source≥ 60 as detected by
wavdetect with fluxscale= 1
limit to the luminosity using the power-law model. The
figure represents only those sources which can be rep-
resented by both models. The figure shows that while
for most sources the difference in luminosities is not sub-
stantial, there are sources with estimated luminosities
& 1039 erg/s, where the disk black body luminosity es-
timation is significantly smaller than the power-law one.
This happens for sources for which the spectral index is
large.
To show the dependence of the luminosity function on
the fitting model, we compute the cumulative luminos-
ity function in two ways. For the disk black body cu-
mulative luminosity function (DBCLF), the luminosity
obtained form fitting a black body is used, except for
those sources that are fitted better with a power-law
for which the power-law model estimated luminosity is
considered. Similarly, for the power-law cumulative lu-
minosity function, (PLCLF) the luminosity corresponds
to the power-law fit, except for those sources which are
better represented by a disk black body spectrum. In
Figure 2, the solid line represents the DBCLF while the
PLCLF is plotted as a dotted one. There are less num-
ber of sources with L > 1040 ergs/s for disk black body
preferred representation. Moreover, there is a significant
difference in the slope of the two luminosity function and
the presence of a faint break at L ∼ 1040 ergs/s for the
PLCLF, is not evident in the DBCLF. Of particular in-
terest is the number of sources whose minimum luminos-
ity (i.e. the minimum of the two lower limits obtained by
fitting the two spectral models) exceeds a certain value.
In Figure 2, the dashed line represents such a minimum
cumulative luminosity function, which reveals that there
are eight sources with minimum luminosity greater 1040
ergs/s (ELX) and ∼ 80 sources with minimum luminosity
greater 1039 ergs/s (ULX).
Figures 3 (a) shows the variation of the luminosity ver-
sus the disk black body temperature, While most of the
sources have an inner disk temperature ∼ 1 keV, as is
evident from the distribution (Figure 3 b), there is a pop-
ulation of high luminosity source with low (∼ 0.1 keV)
temperature. Although the number of sources is low,
there seems to be some evidence, that ELX (i.e. sources
with luminosities > 1040 ergs/s ) can be divided in two
groups, a “super-soft” group with temperature less than
0.2 keV and an harder group with temperature ∼ 2 keV.
Figure 3 may be compared with the results obtained by
Winter et al. (2006) using XMM-Newton data for a dif-
ferent sample and selection criteria. They also find that
sources with luminosities > 5 × 1039 ergs/s have have a
similar bimodal distribution in temperature as shown in
Figure 3. This supports the hypothesis that ELX can
be divided into two groups and this is not an artifact of
sample selection bias.
Figure 4 (a) shows the variation of luminosity with
power-law photon index for those sources which can be
fitted by a power-law model. There is a clear correla-
tion between the two. This correlation does not seem
to be due to overestimation of column density, since no
such correlation is seen in the luminosity versus NH
plot (Figure 5 b). Similar to the analysis using the
Extremely luminous X-ray point sources 5
Fig. 2.— The cumulative luminosity function using the disk
black body model (solid line), the power-law model (dotted line)
and the minimum cumulative luminosity function (dashed line).
0.1 1 10
Fig. 3.— (a) The luminosity versus inner disk temperature and
(b) the distribution of the inner disk temperature for sources whose
spectra can be modeled as disk black body emission. The triangles
represent sources which are better fitted by the disk black body
model as compared to the power-law one. The two solid lines
represent the expected luminosity versus maximum temperature
relations for accretion disks radiating at one and one-tenth of the
the Eddington Luminosity. Two sources which were identified as
foreground stars (see text) are not included in this plot.
0 2 4 6 8 10
Fig. 4.— (a) The luminosity versus power-law index and (b)
the distribution of the power-law index for sources whose spectra
can be modeled as a power-law emission. The triangles represent
sources which are better fitted by the power-law model as compared
to the disk black body one. Two sources which were identified as
background AGN (see text) are not included in this plot.
disk black body model, there is a group of “super-soft”
sources (i.e. photon spectral index > 3) which are also
highly luminous (L > 1040 ergs/s). The column den-
sity versus luminosity plots for both the power-law and
disk black body models (Figure 5), reveal an absence
of correlation, which is indicative that there may not
be a bias in the analysis, i.e. the luminosities are not
being over-estimated because of a NH overestimation.
In this analysis, there are eight sources which have an
apparent minimum luminosity greater than 1040 ergs/s.
However, two of these sources (NGC 5055, R.A: 13 15
30.18, Dec: +42 03 13.5 and NGC 4594, R.A: 12 39
45.22, Dec: -11 38 49.8) are foreground stars based
on the optical images of the galaxies. Optical spec-
troscopy of a source in NGC 5775 ( R.A: 14 53 55.8,
Dec: +3 33 28.02) reveals that it is a background AGN
(Gutiérrez & López-Corredoira 2005), while a source in
NGC 1399 ( R.A: 14 53 55.8, Dec: +3 33 28.02) is a
BLAGN (Green et al. 2004). The spectral properties of
the other four sources, which we call Extremely Lumi-
nous sources (ELX) are tabulated in Table 2. The NGC
0628 source reported in Table 2, is a different source than
the well studied ULX, CXOU J013651.1+154547. The
luminosity of this highly variable source (Krauss et al.
2005) is ∼ 1039 ergs/s and its spectral properties are
listed in Table 4. The source in NGC 6946 is a well known
variable source (Liu & Mirabel 2005) and has been called
X7 with L ∼ 1039.22 ergs/sec(Lira et al. 2000), IXO 85
(Colbert & Ptak 2002) and source no. 56 (Holt et al.
2003). Although, the best fit parameters for C-statistics
are shown, these results have been checked using χ2
statistics and by C-statistics fit for unbinned and back-
6 Senorita Devi et al.
36 38 40 42
Fig. 5.— The column density versus luminosity for sources fitted
with (a) the disk black body model and (b) the power-law model.
ground not subtracted data and it was found that the
parameters values are consistent within errors and the
errors on the estimated luminosities do not vary by more
than a factor two. In general, these sources are better
represented by disk black body emission than a power-
law model, except for the source in NGC 6946, which
however requires an exceptionally large power-law pho-
ton spectral index, (Γ > 5). The spectral properties of
these bright sources suggest that they may be divided
into two groups. The first group of four sources (Table
2), are represented by low inner disk temperatures (< 0.5
keV), and hence may be called “supersoft” sources. In
contrast the second group of three sources, have harder
spectra with inner disk temperatures & 1 keV or with
power-law photon index (Γ ∼ 2) and hence may be called
hard sources. For this group, the spectra are marginally
fitted better with a disk blackbody emission, although
considering the uncertainties in the spectral fitting, a
power-law representation may also be acceptable.
4. SUMMARY AND DISCUSSION
Chandra observations of thirty galaxies were analyzed
and the spectra of their points sources were fitted us-
ing both a power-law and a disk black body emission
model. Only those sources were chosen, which were
bright enough to allow a meaningful spectral fit, but
whose data was not contaminated by excessive diffuse
emission and/or effected by pile-up. It was found that
the shape of the luminosity function especially at the
high luminosity end, depends on the choice of the spec-
tral model.
In accordance with earlier results, a large number of
the sources (∼ 80 ) have a luminosity which exceeds 1039
ergs/s and hence satisfy the standard definition of be-
ing Ultra Luminous X-ray sources (ULX) and do not
seem to have any spectral distinction when compared
with sources having lower luminosity. In this sample of
365 sources, there are four source which we refer to as
Extremely luminous X-ray sources (ELX) since their lu-
minosities were estimated to exceed 1040 ergs/s. These
sources are in general better described by disk black-
body emission and can be distinctively grouped into two
classes. This is consistent with the results of an indepen-
dent analysis using XMM-Newton data (Winter et al.
2006). The members of the first class have soft spec-
tra with best fit inner disk temperature < 0.5 keV, while
for the other class the spectra is harder with inner disk
temperature & 1.3 keV.
If disk black body emission is indeed the correct radia-
tive process for the supersoft class then the inner disk
temperature should correspond to the maximum color
temperature of a disk, which can be estimated to be
Tcol ∼ 0.3 keV L
)−1/2 (1)
where L40 is the luminosity in 10
40 ergs/s, f is the color
factor and LEdd is the Eddington luminosity. In Figure
3 (a), the two solid lines represent this relationship for
L/LEdd = 1 and 0.1. Thus within the uncertainties, the
supersoft sources are compatible with having pure black
body disk emission, and have L ∼ 0.5LEdd.
ELX which are members of the hard class have inner
disk temperatures which are higher than that expected
from a Eddington limited black body accretion disks.
Hence, for these source the radiative mechanism is prob-
ably inverse Comptonization of soft photons. Detailed
spectral analysis, which included XMM observations, of
the bright X-ray source in M82 X-1 has revealed that its
spectrum is better fitted by a saturated Comptonization
model (Agrawal & Misra 2006), which is also the case for
the the bright X-ray source in Holmberg IX. Holmberg IX
is not part of the sample studied here and M82 X-1 has
been excluded because of pile-up effects and excess dif-
fuse emission. Thus, these sources, with estimated lumi-
nosities ∼ 1041 erg/s, could also be members of the hard
class of ELX. Thus it seems that like the the hard state
of standard black hole binaries, the hard class ELX also
have spectra which is due to thermal Comptonization,
however unlike black hole binaries, in ELX the Comp-
tonization seems to be saturated. Thus, it is tempting
to draw by analogy, that the two spectral classes of ELX
are actually two spectral states of the same kind of ob-
ject. This can be verified if spectral transition between
the two classes is observed.
With the identification of these ELX and other sources
from the literature, it is now possible to undertake a more
extensive study of their properties. Temporal variability
of these sources will shed more light on the nature of
these enigmatic sources.
The authors thank the referee for useful comments and
suggestions which have significantly improved the paper.
ASD thanks CSIR and IUCAA for support.
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Extremely luminous X-ray point sources 7
TABLE 2
Spectral properties of sources with minimum luminosity > 1040ergs/s
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NGC0628 01 36 47.45 +15 47 45.01 200 7 0.09
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39.46
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162.2 5.14
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40.37
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Note. — Host Galaxy name; Right Ascension; Declination; Total counts; Number of energy bins after rebinning; Best fit inner disk
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APPENDIX
8 Senorita Devi et al.
TABLE 3
List of sources with count rate greater than 0.05
counts/s
Galaxy R.A. Dec. Count rate s−1
NGC0253 0 47 32.97 -25 17 48.80 0.0845164
NGC0253 0 47 22.59 -25 20 50.87 0.0657110
NGC0253 0 47 17.55 -25 18 11.18 0.0569807
NGC1569 4 31 16.85 +64 49 50.13 0.0567468
NGC2403 7 36 55.61 +65 35 40.85 0.0746877
NGC2403 7 36 25.53 +65 35 40.02 0.1521207
NGC3628 11 20 15.75 +13 35 13.70 0.0530390
NGC4374 12 25 11.92 +12 51 53.53 0.0563400
NGC4449 12 28 17.83 +44 6 33.86 0.0525013
NGC4485 12 30 43.26 +41 38 18.36 0.0509909
NGC4485 12 30 30.56 +41 41 42.33 0.0758634
NGC4559 12 35 58.56 +27 57 41.91 0.1233310
NGC4559 12 35 51.71 +27 56 4.05 0.1984267
NGC4631 12 41 55.56 +32 32 16.90 0.0554584
NGC6946 20 35 0.74 +60 11 30.74 0.1448118
Note. — The spectra of these sources would be affected
by pile-up and hence have not been included in the sample
TABLE 4
Spectral Properties of point sources fitted with the Power-Law model
Galaxy R.A. Decl. nH(10
−2) Γ log(L) ergs/s Cstat d. o. f.
NGC0253 0 47 43.07 -25 15 29.28 0.15
+0.53
−0.15
+2.31
−1.21
37.70
+1.20
−0.18
9.43 4
NGC0253 0 47 42.80 -25 15 2.02 0.77
+0.51
−0.49
+0.66
−0.77
38.26
+0.27
−0.12
3.36 4
NGC0253 0 47 35.25 -25 15 11.53 0.48
+0.05
−0.13
+0.22
−0.33
38.65
+0.05
−0.08
38.94 19
NGC0253 0 47 34.28 -25 17 3.32 5.66
+5.98
−5.66
+4.62
−4.95
40.82
+3.28
−2.90
3.21 2
NGC0253 0 47 34.00 -25 16 36.51 1.04
+0.11
−0.10
+0.22
−0.22
39.01
+0.08
−0.07
10.93 27
NGC0253 0 47 33.55 -25 18 16.51 0.00
+0.18
−0.00
+0.99
−0.44
37.33
+0.15
−0.10
2.37 2
NGC0253 0 47 32.05 -25 17 21.43 3.17
+2.20
−2.46
+1.10
−1.10
38.61
+0.72
−0.32
1.63 3
NGC0253 0 47 30.98 -25 18 26.23 1.55
+1.46
−1.55
+1.21
−1.21
38.24
+0.65
−0.21
1.76 3
NGC0253 0 47 28.01 -25 18 20.21 0.93
+1.13
−0.92
+1.76
−1.54
38.02
+1.03
−0.23
2.13 1
NGC0253 0 47 25.20 -25 19 45.22 0.00
+0.15
−0.00
+0.66
−0.22
37.96
+0.09
−0.09
5.10 4
NGC0253 0 47 18.50 -25 19 13.94 0.00
+0.15
−0.00
+0.44
−0.22
37.97
+0.07
−0.05
3.94 5
NGC0253 0 47 40.66 -25 14 11.71 0.69
+0.72
−0.56
+1.98
−1.32
37.96
+1.11
−0.27
1.07 3
NGC0253 0 47 17.65 -25 18 26.45 0.11
+0.49
−0.11
+1.54
−0.77
38.12
+0.27
−0.12
3.13 3
NGC0628 1 36 51.06 +15 45 46.86 0.03
+0.05
−0.03
+0.22
−0.11
39.22
+0.04
−0.02
50.58 36
NGC0628 1 36 47.45 +15 47 45.01 0.89
+0.11
−0.33
+0.44
−2.42
42.18
+0.36
−1.49
8.56 4
. . . . . . . . .
Note. — Host galaxy name; Right Ascension; Declination; nH , equivalent hydrogen column density;
Γ, photon power-law index; L, X-ray luminosity in the energy range: 0.3-8.0 keV; C-statistics; degree
of freedom. The complete version of this table is in the electronic edition of the Journal. The printed
edition contains only a sample.
Extremely luminous X-ray point sources 9
TABLE 5
Spectral Properties of point sources fitted with the disk black body model
Galaxy R.A. Decl. nH(10
−2) kTin (keV) log(L) ergs/s Cstat d. o. f.
NGC0253 0 47 43.07 -25 15 29.28 0.00
+0.32
−0.00
+0.42
−0.25
37.69
+0.37
−0.00
9.41 4
NGC0253 0 47 42.80 -25 15 2.02 0.44
+0.36
−0.32
+1.95
−0.52
38.40
+0.26
−0.08
3.95 4
NGC0253 0 47 35.25 -25 15 11.53 0.24
+0.07
−0.07
+0.21
−0.15
38.71
+0.04
−0.03
35.79 19
NGC0253 0 47 34.28 -25 17 3.32 3.08
+5.36
−3.07
+9.38
−0.36
38.69
+2.04
−0.60
3.37 2
NGC0253 0 47 34.00 -25 16 36.51 0.64
+0.12
−0.10
+0.19
−0.16
39.06
+0.03
−0.03
8.60 27
NGC0253 0 47 33.55 -25 18 16.51 0.00
+0.08
−0.00
+0.69
−0.29
37.49
+0.20
−0.06
3.85 2
NGC0253 0 47 32.05 -25 17 21.43 2.04
+1.82
−1.62
+4.71
−0.80
38.68
+0.40
−0.09
1.37 3
NGC0253 0 47 30.98 -25 18 26.23 0.96
+0.96
−0.86
+8.00
−0.91
38.41
+0.73
−0.12
1.84 3
NGC0253 0 47 28.01 -25 18 20.21 0.62
+0.77
−0.56
+8.80
−0.55
38.08
+0.90
−0.12
2.51 1
NGC0253 0 47 25.20 -25 19 45.22 0.00
+0.06
−0.00
+0.86
−0.33
38.12
+0.21
−0.09
7.71 4
NGC0253 0 47 18.50 -25 19 13.94 0.00
+0.05
−0.00
+0.73
−0.41
38.22
+0.15
−0.09
6.36 5
NGC0253 0 47 40.66 -25 14 11.71 0.42
+0.47
−0.38
+2.76
−0.40
37.94
+0.38
−0.18
1.64 3
NGC0253 0 47 17.65 -25 18 26.45 0.08
+0.32
−0.07
+8.76
−0.65
38.23
+1.04
−0.13
2.85 3
NGC0628 1 36 51.06 +15 45 46.86 0.00
+0.00
−0.00
+0.08
−0.11
39.42
+0.02
−0.04
119.44 36
NGC0628 1 36 47.45 +15 47 45.01 0.75
+0.58
−0.39
+0.04
−0.03
41.65
+2.49
−1.60
0.66 4
. . . . . . . . .
Note. — Host galaxy name; Right Ascension; Declination; nH , equivalent hydrogen column density;
kTin, inner disk temperature; L, Bolometric X-ray luminosity; C-statistics; degree of freedom. The complete
version of this table is in the electronic edition of the Journal. The printed edition contains only a sample.
