OPTICAL COUNTERPARTS OF THE NEAREST ULTRALUMINOUS X-RAY SOURCES

In the late 1970s and early 1980s the Einstein telescope was used to perform studies of normal galaxies, which revealed the presence of X-ray luminous non-nuclear objects that were brighter than those in our own Galaxy (Fabbiano 1989). These objects were later termed ultraluminous X-ray sources (ULXs; e.g., Makishima et al. 2000). Although studies of these luminous sources have continued for more than 30 yr, their nature is still unclear (e.g., Roberts 2007; Gladstone 2010; Feng & Soria 2011). It has been confirmed that many of these sources contain accreting black holes (Kubota et al. 2001), but currently the masses of the compact objects are still unknown. Their luminosities (L_X ≳ 10³⁹ erg s⁻¹) preclude the possibility that we are observing isotropic, sub-Eddington, accretion onto a stellar mass black hole (sMBH; comparable to the Galactic sMBHs, 3 ≲ M_BH ≲ 20 M_☉), which has led to the idea that we may be observing intermediate-mass black holes (IMBHs; 10²–10⁴ M_☉; Colbert & Mushotzky 1999). An alternative is that we may instead be observing massive stellar remnant black holes (MsBHs; Feng & Soria 2011; defined as the end product from the death of a single, current generation star; M_BH ≲ 100 M_☉; e.g., Fryer & Kalogera 2001; Heger et al. 2003; Belczynski et al. 2004) that are approaching, breaking, or circumventing the Eddington limit.

X-ray analysis has been exhaustive, with early XMM-Newton observations providing both spectral and timing evidence viewed as supporting IMBHs. Analysis of their X-ray spectra revealed the presence of cool disk emission, in combination with a power law, a combination used effectively to study Galactic sMBH systems. However, here the disk temperature appeared much cooler than that of sMBHs, suggesting IMBHs (e.g., Miller et al. 2003, 2004; Kaaret et al. 2003). Meanwhile, X-ray timing analysis revealed the presence of quasi-periodic oscillations (QPOs) in M82 X-1, M82 X42.3+59, and NGC 5408 X-1 (Casella et al. 2008; Feng et al. 2010; Strohmayer et al. 2007), something observed in both Galactic sMBH and SMBH systems, that seems to scale with black hole mass (e.g., McClintock & Remillard 2006; McHardy et al. 2006; van der Klis 2006). Combining both the spectral and timing analysis of these sources indicated that ULXs were hosts to IMBHs (e.g., Dheeraj & Strohmayer 2012). However, recent timing studies of ULXs show that many of these systems appear to have suppressed intra-observational variability (Heil et al. 2009), while spectral studies of higher quality data have indicated the presence of a break above 3 keV, a feature that would not be expected if we were viewing sub-Eddington accretion onto an IMBH (e.g., Stobbart et al. 2006; Gladstone et al. 2009). Instead, we have suggested that this combination of new X-ray spectral and timing features describes a new super-Eddington accretion state, the so-called ultraluminous state (Roberts 2007; Gladstone et al. 2009; Roberts et al. 2010). This is echoed in the re-analysis of NGC 5408 X-1, which shows that the spectra, power spectral density, and rms spectra of this source are better matched to models of super-Eddington accretion than sub-Eddington accretion onto an IMBH (Middleton et al. 2011a). In Middleton et al. (2011b), the authors reported on the analysis of XMM flux-binned data from M33 X-8, and suggested a similar two-component spectral fit. The spectral evolution and timing properties are unlike those of the standard sub-Eddington accretion states, leading the authors to invoke the onset of an extended photosphere and a wind to explain the observed data (photosphere and/or outflow dominated, as predicted in models of super-Eddington accretion; e.g., Begelman et al. 2006; Poutanen et al. 2007).

Although recent X-ray analysis seems to be pointing toward the presence of MsBHs, more direct evidence is required. An attractive method is that used to confirm the first known Galactic black hole, Cygnus X-1. Following Murdin & Webster (1971), we must first find the potential optical counterpart photometrically. Optical spectroscopic follow-up can then be performed to gain dynamical mass estimates for the system (Webster & Murdin 1972; Bolton 1972; Paczynski 1974). Such techniques have been used repeatedly with success in our Galaxy, e.g., van Paradijs & McClintock (1995) and Charles & Coe (2006), and more recently on the extra-galactic source IC 10 X-1 (Prestwich et al. 2007; Silverman & Filippenko 2008). If we could apply this method to ULXs, we could settle the debate over the mass of the black holes contained within these systems.

Here, we use optical observations to identify and classify the optical counterparts to ULXs. The identification of unique counterparts is not trivial, as many of these objects reside in crowded stellar fields (Liu et al. 2009), which is unsurprising given their apparent association with star-forming regions (Fabbiano et al. 2001; Lira et al. 2002; Gao et al. 2003; Swartz et al. 2009). This suggests that we may be looking for young companions, a theory supported by recent results finding a prevalence for blue companions to these ULXs indicative of OB-type stars (e.g., Liu et al. 2004; Grisé et al. 2006; Roberts et al. 2008), but it should be noted that such a blue color may be partly due to contamination by reprocessed X-rays from the accretion disk or stellar surface (e.g., Copperwheat et al. 2005, 2007; Madhusudhan et al. 2008; Patruno & Zampieri 2010; Grisé et al. 2012).

To date much of the analysis of potential counterparts has focused on individual source and/or their host galaxies (e.g., Ho II X-1, Kaaret et al. 2004; NGC 1313 X-2, Mucciarelli et al. 2005; Liu et al. 2007; Grisé et al. 2008; Impiombato et al. 2011; NGC 5408 X-1, Lang et al. 2007; M51 population, Terashima et al. 2006; Antennae galaxy, Zezas et al. 2002; Cartwheel galaxy, Gao et al. 2003), while only a small number of larger surveys have taken place (e.g., Ptak et al. 2006; Swartz et al. 2009; Tao et al. 2011).

Spectroscopic follow-up has begun for some of these sources, although only a small number have been published to date. Roberts et al. (2001) studied the counterpart of NGC 5204 X-1, finding a blue, almost featureless spectrum, with similar featureless spectra found for other sources (e.g., NGC 1313 X-2, Zampieri et al. 2004; Roberts et al. 2011; Ho IX X-1, Grisé et al. 2011; Roberts et al. 2011; NGC 5408 X-1, Kaaret & Corbel 2009; Cseh et al. 2011; Grisé et al. 2012). This suggests that the light is non-stellar in origin (see Figure 1 in Roberts et al. 2011; J. C. Gladstone et al., in preparation), indicating that the light may be dominated by emission from the accretion disk. Nevertheless, the search for dynamical mass constraints has continued, as a number of spectra contain the He ii 4686 Å high excitation line. This line has been associated with accretion disks in Galactic sources, and has been used successfully to gain such mass constraints in the past (e.g., GRO J1655−40; Soria et al. 1998). Initial results from the optical analysis of multi-epoch spectra of two ULXs (NGC 1313 X-2 and Ho IX X-1) have detected radial velocity variations; however, they may not be sinusoidal (Roberts et al. 2011; J. C. Gladstone et al., in preparation). Studies have also been performed on the optical counterpart to ULX P13, in NGC 7793 (Motch et al. 2011). Here variations in the He ii line are also present, but superimposed on a photospheric spectrum. This reveals the possible presence of a late B-type supergiant companion of between 10 and 20 M_☉ (Motch et al. 2011). Again, radial velocity variations were detected for this source, with further data and analysis required to confirm its period and nature.

To date the confirmation of black hole mass has proved elusive for known counterparts. This paper seeks to find more potential counterparts for further study. We focus our search on nearby galaxies, in order to have the best chance of finding unique optical counterparts, while maximizing the potential for photometric and spectroscopic follow-up of these systems.

This paper is organized as follows. First, we outline the sample selection, and the data reduction processes (Sections 2 and 3). We then go on to combine optical and X-ray imaging data to identify all possible counterparts in Section 4. Section 5 applies multiple techniques to classify these candidate counterparts, while Section 6 presents a discussion of our results, implications of the analysis, and routes for further study.

We compiled a complete list of the known ULXs, drawing from a number of ULX catalogs available in the public domain, including Roberts & Warwick (2000), Swartz et al. (2004), Liu & Mirabel (2005), Liu & Bregman (2005), Ptak et al. (2006), and Winter et al. (2006). A concise primary list was formed by merging duplicate identifications and removing any sources for which subsequent research has indicated that a ULX was not present (based on luminosity criteria, or the object later being identified as a non-ULX, e.g., a foreground star or background quasar).

Many of the optical counterparts identified to date are faint (≳24 mag; Roberts et al. 2008). Therefore, we place an additional distance constraint on our sample of 5 Mpc, to allow for potential photometric and spectroscopic follow-up. At this distance, a B0 V star would have an apparent magnitude of 24.4 (M_V = −4.1; Zombeck 1990), so more distant objects would be impractical for spectroscopic studies with current international ground-based facilities.

We retain the ULXs residing within NGC 3034 (M82) in our sample as some distance estimates have indicated that this galaxy may be located within 5 Mpc (e.g., ∼3.6 Mpc; Freedman et al. 1994). This provides a sample of 45 nearby ULXs that we list in Table 1, along with their published luminosities, distances, Galactic absorption, and extinction columns for both the optical and X-ray bands. We also include extra-galactic or total N_H columns for each source, as found via literature search (where available). It is not clear where the additional absorbing material is located, as it could be gas clouds in the host galaxy, or associated with the ULX itself (e.g., photosphere/wind).

Table 1. The ULX Sample Listed by Distance

Source	Alternative Names	R.A.	Decl.	d a	NHb	E(B − V)c	NHd	LXe
		(J2000)	(J2000)	(Mpc)				(1039 erg s−1)
NGC 598 ULX11	Source 37	01 33 50.9	+30 39 37	0.98	4.59	0.042	3.6 E9	2.5	αXI7
	Source 710
	M33-X-811
	CXOUJ013351.0+30393712
NGC 55 ULX12	NGC 55 613	00 15 28.9	−39 13 19	1.742	1.71	0.014	23.9 E9	1.3	αX2
	XMMU J001528.9−39131914
NGC 4190 X13		12 13 45.4	+36 37 55	2.83	1.54	0.030	12 T15	2.31	βRP3
NGC 253 ULX11	NGC 253 PSX-11	00 47 34.0	−25 16 37	3.03	1.42	0.019	N/A	1.2	C14
	CXOUJ004734.0−25163716
NGC 253 ULX21	NGC 253 PSX-21	00 47 33.0	−25 17 49	3.03	1.42	0.019	20 T4	5.7	αXI4
	NGC 253 X23
	NGC 253 XMM14
	CXOUJ004733.0
	−25174916
	S1021
NGC 253 ULX31	NGC 253 PSX-31	00 47 33.4	−25 17 22	3.03	1.42	0.019	N/A	1.74	βRP3
	NGC 253 X13
	CXOUJ004733.4−25172216
NGC 253X203*	NGC 253 ULX13	00 48 20.0	−25 10 10	3.03	1.52	0.019	N/A	2.37	βRP3
NGC 253XMM24*	NGC 253 X93	00 47 22.4	−25 20 55	3.03	1.41	0.019	39 T4	2.7	αXI4
NGC 253XMM44*		00 47 23.3	−25 19 07	3.03	1.42	0.019	1.2 T4	2.2	αXI4
NGC 253XMM54*	NGC 253 X73	00 47 17.6	−25 18 12	3.03	1.42	0.019	3.4 T4	2.2	αXI4
NGC 253XMM64	NGC 253 X63	00 47 42.8	−25 15 06	3.03	1.43	0.019	3.9 T4	3.1	αXI4
	RX J004742.5−25150117
M81-X-61	NGC 3031 X93	09 55 33.0	+69 00 33	3.43	4.16	0.080	19 E9	3.84	δC7
	NGC 3031 ULX13
	M81 XMM14
	Source 77
	CXOUJ095532.98
	+690033.47
Hol IX X-12	NGC 3031 ULX 21	09 57 54.1	+69 03 47	3.423	4.06	0.079	12.1 E9	13.4	γRP3
	M81-X-92
	Hol IX XMM14
	Source 177
	NGC 3031 1018
	H 4419
	IXO 3420
NGC 4395 ULX11	NGC 4395 X-13	12 26 01.9	+33 31 31	3.63	1.35	0.017	10.0 E22	1.73	γRP3
	NGC 4395 XMM14
	Source 127
	NGC 4395 X218
	IXO 5321
NGC 1313 X-11	NGC 1313 X23	03 18 20.0	−66 29 11	3.73	3.90	0.110	21.1 E9	1.3	αXI4
	NGC 1313 ULX13
	Source 47
	IXO 721
NGC 1313 X-21	NGC 1313 ULX21	03 18 22.3	−66 36 04	3.73	3.90	0.085	21 E9	4.2	αXI4
	NGC 1313 X73
	NGC 1313 ULX33
	Source 57
	IXO 821
XMM J031747.6		03 17 47.6	−66 30 10	3.73	3.83	0.109	23 T5	1.6	X5
−6630105*
IC 342 X-16	PGC13826-X63	03 45 55.17	+68 04 58.6	3.93	31.1	0.565	55 E9	12.77	γRP3
	PGC 13826 ULX33
	IC 342 XMM14
	Source 27
	IXO 2221
	CXOUJ034555.7
	+68045523
	Source 1924
IC 342 X-22	PGC13826-X73	03 46 15.0	+68 11 11.2	3.93	29.7	0.559	38 T4	8.43	αXI4
	IC 342 XMM24
	IC 342 X-36
	Source 2524
	IC 342 X-1325
IC 342 ULX21	PGC 13826 X13	03 46 48.6	+68 05 51.0	3.93	30.2	0.558	97 T4	2.57	γRP3
	IC 342 XMM34
	Source 3824
IC 342 X-46*	PGC13826-X33	03 46 45.54	+68 09 51.7	3.93	29.5	0.557	44 T24	1.49	γRP3
	PGC 13826 ULX23
	Source 3624
IC 342 X-66	PGC13826-X23	03 46 57.17	+68 06 22.4	3.93	30.0	0.558	21 T24	1.21	γRP3
	PGC 13826 ULX13
	IC 342 XMM44
	Source 4424
Circinus l ULX11	CG-X-11	14 13 12.3	−65 20 13.0	45	55.6	1.488	24 E28	24 3.72	δC7
	ULX 4226
	CXOUJ141312.3
	−65201327
	U4328
Circinus ULX31	CXOUJ141310.3	14 13 10.3	−65 20 17.0	45	55.6	1.468	<487 T27	1.4	βCI22
	−65201727
Circinus ULX41	CXOUJ141310.4	14 13 10.4	−65 20 22.0	45	55.7	1.464	91 T27	2.09	βC22
	−65202227
Circinus XMM14*	Source 17	14 12 54.2	−65 22 55.3	45	55.2	1.028	101 T4	23	αXI4
Circinus XMM24*		14 12 39.2	−65 23 34.3	45	55.1	0.891	112 T4	10.7	αXI4
Circinus XMM34*		14 13 28.3	−65 18 08.3	45	56.0	1.363	135 T4	14.5	αXI4
NGC 2403 X-11	NGC 2403 X23	07 36 25.55	+65 35 40.0	4.22	4.17	0.040	23.4 E9	1.73	δC8
	NGC 2403 ULX13
	NGC 2403 XMM14
	Source 68
	Source 2129
	CXOUJ073625.5
	+65354030
NGC 2403 XMM24*	CXOUJ073650.0	07 36 50.2	+65 36 02.1	4.22	4.13	0.040	18 T4	1.6	αXI4
	+65360331
NGC 5128 ULX13	NGC 5128 X43	13 25 19.9	−43 03 17.0	4.213	8.37	0.115	9.5 E28	9.27	γRP6
	IXO-7621
	ULX 4026
	U3528
	CXOUJ132519.9
	−43031732
NGC 5128 X373*		13 26 26.16	−43 17 15.6	4.213	8.71	0.109	N/A	1.96	γRP3
NGC 5128 X383*		13 26 56.81	−42 49 53.6	4.213	8.41	0.095	N/A	1.97	γRP3
CXOUJ132518.3		1325 18.3	−43 03 03	4.213	8.63	0.110	10E18	1.4	αC7
−4303038
NGC 4736 XMM14	NGC 4736 X-16	12 50 50.2	+41 07 12.0	4.34	1.44	0.018	20 T28	17.9	γXI4
	NGC 4736 X-433
	CXOUJ125050.3
	+41071234
Holmberg II X-11, 2	PGC 23324 ULX13	08 19 30.2	+70 42 18.0	4.52	3.41	0.032	7.9 E9	17	αX2
	Hol II XMM14
	Source 287
	IXO-3121
	CXOUJ081928.99
	+704219.430
M83 XMM14	NGC 5236 X113	13 37 19.8	−29 53 49.8	4.73	3.78	0.066	6.5 E22	2.8	αXI4
	NGC 5236 ULX13
	Source 247
	IXO-8221
	CXOUJ133719.8
	−29534934
M83 XMM24	NGC 5236 X63	13 36 59.4	−29 49 57.2	4.73	3.96	0.066	N/A	3.4	αXI5
	CXOUJ133659.5
	−29495934
NGC 5204 X-16	Source 237	13 29 38.6	+58 25 06.0	4.82	1.39	0.013	3.6 E9	4.4	αX2
	IXO 7721
	CXOUJ132938.61
	+582505.630
NGC 5408 X-12	NGC 5408 ULX11	14 03 19.61	−41 22 59.6	4.84	5.67	0.069	2.9 E9	10.9	αXI4
	NGC 5408 XMM14
	Source 257
	J140319.606
	−412259.57235
NGC 3034 ULX31	CXOUJ095551.2	09 55 51.4	+69 40 44.0	5.23	3.98	0.159	1300 T36	12	βCI36
	+69404436
NGC 3034 ULX41	ULX 1425	09 55 51.1	+69 40 45.0	5.23	3.98	0.159	320 T36	17	βCI36
	CXOUJ095551.07
	+69404536
NGC 3034 ULX51	ULX 1326	09 55 50.2	+69 40 47.0	5.23	3.98	0.159	113 T38	100	ζX38
	M82 X-137
NGC 3034 ULX61	NGC 3034 X13	09 55 47.5	+69 40 36.0	5.23	3.99	0.160	67.1 T3	11.6	βCI36
	CXOUJ095546.6
	69403734
	CXOM82 J095547.5
	69403639
CXOUJ095550.6		0. 55 50.6	+69 40 44	5.23	3.98	0.159	260 T37	11.6	βCI37
+69404437

Notes. ^aDistance to host galaxy collated from literature search, with cut applied at 5 Mpc. NGC 3034 has been included due to uncertainties in this measurement. ^bGalactic absorption column (in units of 10²⁰ cm⁻²) from Dickey & Lockman (1990) using the NASA HEASARC tool (this can be found at http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl). ^cGalactic extinction values found using Schlegel et al. (1998) via NED extinction calculator (located at http://ned.ipac.caltech.edu/forms/calculator.html). Each is calculated at the position of the ULX. ^dTotal (T) or extra-galactic (E) absorption column (in units of 10²⁰ cm⁻²) found via literature search. In cases where no value was found we list it as not available (N/A). ^eLuminosity of ULX, energy band, telescope, and comments relating to its calculation. Energy bands are noted as follows: α = 0.3–10.0 keV, β = 0.5–10.0 keV, γ = 0.3–8.0 keV, δ = 0.5–8.0 keV, = 0.3–7.0 keV, and ζ = bolometric luminosity. Telescope notation—C: Chandra; R: ROSAT; X: XMM-Newton. Luminosity annotation: I—intrinsic/unabsorbed luminosity; P—derived using webpimms. * Removed from sample due to lack of Chandra and/or HST data, see Section 3 for further details. References.¹Liu & Mirabel 2005; ²Stobbart et al. 2006; ³Liu & Bregman 2005; ⁴Winter et al. 2006; ⁵Trudolyubov 2008; ⁶Roberts & Warwick 2000; ⁷Feng & Kaaret 2005; ⁸Sivakoff et al. 2008; ⁹Gladstone et al. 2009; ¹⁰Schlegel et al. 1998; ¹¹Trinchieri et al. 1988; ¹²Grimm et al. 2005; ¹³Read et al. 1997; ¹⁴Stobbart et al. 2004; ¹⁵T. P. Roberts et al. (in preparation); ¹⁶Humphrey et al. 2003; ¹⁷Barnard et al. 2008; ¹⁸Vogler & Pietsch 1999; ¹⁹Radecke 1997; ²⁰Immler & Wang 2001; ²¹Colbert & Ptak 2002; ²²Stobbart et al. 2006; ²³Roberts et al. 2004; ²⁴Mak et al. 2011; ²⁵Kong 2003; ²⁶Ptak et al. 2006; ²⁷Bauer et al. 2001; ²⁸Berghea et al. 2008; ²⁹Schlegel & Pannuti 2003; ³⁰Swartz et al. 2004; ³¹Yukita et al. 2007; ³²Kraft et al. 2001; ³³Eracleous et al. 2002; ³⁴Colbert et al. 2004; ³⁵Kaaret et al. 2003; ³⁶Kong et al. 2007; ³⁷Strohmayer & Mushotzky 2003; ³⁸Kaaret et al. 2006; ³⁹Griffiths et al. 2000.

Download table as:  ASCIITypeset images: 1 2 3

Table 1 also indicates that the sources residing within 5 Mpc cover the majority of ULXs' X-ray luminosity range (L_X ∼ 10³⁹ to ∼10⁴¹ erg s⁻¹, only excluding the new hyperluminous X-ray sources; e.g., Matsumoto et al. 2004; Farrell et al. 2009; Sutton et al. 2012). The X-ray luminosities listed within this table are taken from the references denoted in superscript. As the data are collated from published results we highlight inconsistencies in their calculation. Many are the observed X-ray luminosities, although some are intrinsic/de-absorbed (identified by "I"). The luminosities listed in Table 1 include values derived from observations using three separate X-ray telescopes (ROSAT: R, Chandra: C, and XMM-Newton: X), with detectors that are sensitive to differing energy ranges.

Liu & Bregman (2005) used the ROSAT archive in combination with the online tool webpimms⁷ to extrapolate a luminosity over the 0.3–8.0 keV energy range. In each case they used a photon index of 1.7 and Galactic N_H. Luminosities calculated using webpimms are marked with a "P." The authors Swartz et al. (2004), Humphrey et al. (2003), and Bauer et al. (2001) each used data from the Chandra X-ray telescope to provide luminosities over the ranges 0.5–8.0, 0.3–7.0, and 0.5–10.0 keV ranges, respectively. Some authors provide 0.3–10 keV luminosities calculated using observations from the XMM-Newton telescope including Winter et al. (2006), Stobbart et al. (2006), and Feng & Kaaret (2005). Trudolyubov (2008) also used XMM-Newton, but considered only the 0.3–7.0 keV bandpass, while Strohmayer & Mushotzky (2003) calculated the bolometric luminosity for each source. Finally, Liu & Mirabel (2005) collated information from published works and so provide details of the observed peak luminosity over an identified range specific to each source (all luminosities taken from this work were calculated over the 0.5–10.0 keV energy range).

We searched the Chandra archive and Hubble Legacy Archive (HLA) for publicly available observations of each of the 45 sources (using data available in 2011 November). Twelve objects which lack Chandra and/or Hubble Space Telescope (HST) data are marked with an "*" in Column 1 of Table 1, and we do not discuss them further in this paper. We are left with a sample of 33 ULXs residing within 5 Mpc.

With the inception of the HLA,⁸ designed to optimize the science from HST, we are able to collate pre-processed data. These data sets are produced using the standard HST pipeline products, which combine the individual exposures using the iraf task MultiDrizzle.⁹ Each field is astrometrically corrected (whenever possible), by matching sources in the field to one or more of three catalogs: Sloan Digital Sky Survey (SDSS), Guide Star Catalogue 2 (GSC2), and Two Micron All Sky Survey (2MASS), in order of preference. Information provided on the HLA pages states that this is only possible in ∼80% of the ACS–WFC fields, due to crowding or lack of matching sources, or sources that are unresolved from the ground (and therefore not present in the catalogs). As a result, we check and improve on these to produce the best possible astrometry.

To astrometrically correct these fields, it is important to have a number of sources in the field. We therefore opt to use observations with large fields of view wherever possible, and so select the HST instrument and detector based on these criteria. In order of preference, we select observations in available bands from the Advanced Camera for Surveys (ACS) Wide Field Camera (WFC), the Wide Field Planetary Camera 2 (WFPC2), and ACS High Resolution Camera (HRC).

Another consideration is the variability that occurs within these systems, which would affect the emission observed in the optical and UV bands. From the X-ray spectra of these systems, we see variability on longer inter-observational timescales of days to years (e.g., Fabbiano 2004). Such variability is likely to affect the optical and UV emission, as seen in Galactic X-ray binary systems (e.g., Charles & Coe 2006). However, the X-ray variability appears to be suppressed on shorter, intra-observational, timescales (Heil et al. 2009). Thus, we expect that near-simultaneous (≲24 hr) observations in multiple bands are unlikely to be significantly impacted by variability.

We fold these considerations into our observation selection criteria, awarding observations of multiple bands, over short timescales, higher priority. Where these were not available, different bands were selected from multiple observations, in order to give a fuller view of the source. In these cases we must seriously consider the potential impact of optical variability, as observations could have been made months, or even years apart (see Section 5.2). The observation IDs, instrument, date of observations and mode selection, filter band information, and exposure times for selected observations are listed in Table 2.

We also collated and downloaded Chandra observations for each of our ULX sample. Wherever more than one X-ray observation was available in the public archive, we chose the longest appropriate observation containing that source. In the case of transient ULXs this was not always the most recent observation of the field. The observation IDs, instrument setup, and exposure times for each of these X-ray observations are also listed in Table 2.

We attempt to improve the astrometry in order to maximize the chance of obtaining unique optical counterparts to these sources. We approach the optical data first, by checking and improving the astrometric corrections of each field using the iraf tools CCFIND, CCMAP, and CCSETWCS, in combination with either the 2MASS or USNO 2.0 catalogs (depending on the number of sources available in the field). This process also provides the average astrometric error (3σ) across the field.

We find that 14 of the 98 HST observations used in our analysis do not contain enough cataloged objects in the optical/ultraviolet fields of view to allow for accurate astrometry corrections. In these cases we compare the field to an alternative corrected observation in a similar waveband. We match sources in these observations and perform relative astrometry corrections using the iraf tools IMEXAM and GEOMAP. The tool GEOXYTRAN is then used to translate the position of the ULX to the relative field coordinates.

In the case of NGC 4190, we find that we are unable to correct the astrometry of any field by matching to known catalogs. We therefore opt to take advantage of the increased field of view afforded us by SDSS, collecting an image of this region from their archive. The astrometry of this image is corrected using the 2MASS catalog, and relative astrometry performed on each of the HST images. We note that where relative astrometry is required, the additional errors arising from this are also folded into our calculations.

The astrometry of the X-ray observations must also be checked. We chose to use the reduced primary data provided by the Chandra X-Ray Center (CXC). Each observation was checked for any known aspect offset.¹⁰ There is a small intrinsic astrometric uncertainty in Chandra observations, an error of 06 for ACIS-S, 08 in ACIS-I, 06 for HRC-S, and 05 for HRC-I fields (90% confidence region for absolute positional accuracy¹¹). This known error is folded into the initial positional error calculation.

The X-ray astrometry can be further improved by cross-matching sources to the same catalogs used in the optical. The tool WAVDETECT was used to identify sources in the 0.3–7.0 keV energy band, within 6' of the target (in some cases we were forced to use a smaller region, details can be found in Table 3). We cross-correlated the positions of sources with >20 counts with the 2MASS or USNO catalogs (choice depending on which was used for the respective HST fields). Care was taken in the selection of sources, for example, galactic centers were considered unsuitable as it can be difficult to get accurate centroiding for such sources in the optical (e.g., NGC 4736; Eracleous et al. 2002).

Another concern was the limited number of sources available for cross-matching. In cases where no suitable sources were found, we revert to the 90% confidence region for absolute positional accuracy of Chandra. In some cases only one object was available for cross-matching in the region of the sky surrounding the ULX. Some previous works have used this single source to perform relative astrometry, but we suggest caution in doing so, as corrections can only be made in the xy plane, with no consideration for rotational error. In these cases we show both the corrected position and the unimproved 90% confidence error region. All sources falling within the larger 90% error region are considered, but the corrected position can be used to help identify the more likely ULX counterpart candidate.

If multiple sources are present in both the Chandra and HST fields, we used a weighted average to cross-correlate the positions of these sources, and find the required shift. When applying corrections with few sources, it is only possible to correct by shifting in the xy plane, which does not account for all rotational error in the telescope, but the impact is minimized. As a result, errors may be underestimated. We still attempt such corrections but apply them with care, using them only as guidance in selection of "most likely" when multiple counterparts lie within the larger error circle.

When considering transient sources, the object is not always visible in the deepest X-ray observations. In these cases we were able to match the position of this source to the position of other X-ray sources in another observation.

Finally, the accurate source positions were found using WAVDETECT, and any calculated shifts applied. The positions of each ULX are listed in Table 3, along with their associated errors. These errors are found by combining in quadrature the astrometry errors from both fields with the source's individual positional error to provide the resulting error regions for each individual ULX.

The derived positions and their respective error regions are applied to each field in order to search for potential counterparts to these sources. Figure 1 contains a 25'' × 25'' color image (tricolor wherever possible), and a finding chart (6'' × 6'') for each ULX. Error regions are plotted in each case, with blue representing the standard 90% confidence ellipse, while the error derived from relative astrometry corrections is plotted in magenta.

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Tarball of figure set images

To construct the color images, we select available wavebands for each part of the optical/UV spectrum. We use filter bands ranging from F656N to F814W to represent the red end of our range, filter bands F475W to F606W for the green band, while F220W–F450W are blue. In each case where more than one band is available, we opt for a band that gives the clearest view of any potential counterparts. If this is not required, we opt for the band with the smallest error region. In some cases we have no data in one or more of the color bands, in which case the images are presented in one or two color bands only.

The positions of all potential counterparts are also marked in each field. One of these is NGC 598 ULX1, which was identified as the nucleus of the galaxy by Dubus et al. (2004), as is clearly seen in Figure 1. The revised Chandra position of IC 342 ULX2 shows that this source is also nuclear. As a ULX is non-nuclear by definition, we remove both of these sources from our catalog. Nine of the remaining ULXs have no optical counterparts in their error regions. Of the 22 remaining sources, 13 have a unique candidate counterpart, and the rest have up to 5 objects within their error ellipse.

In the nine error circles which lack optical counterparts, limits are obtained for the approximate V-band observation of each ULX field (listed in Table 4), given the observed background within the positional error circle for each ULX. We compare these values to the expected V magnitude of each stellar type (Zombeck 1990) at the distance of the galaxy (converted to m₅₅₅ Vega-mag using synphot), with Galactic extinction corrections applied using the E(B − V) values in Table 1. O stars appear to be ruled out for five of these ULXs. However, it is possible for the companion star to be a main-sequence B star in all cases (some only valid for later-type B stars). We are unable to obtain a ∼ V-band image for M83 XMM2, as the error region for this source lies on the ACS-WFC chip gap in the F555W band. We thus compare limits for the (only) available image, a WFPC2 F336W image, to the expected m₃₃₆ values for O5 V, B0 V, and B5V stars (derived using stellar templates for the Bruzual–Persson–Gunn–Stryker (BPGS) catalog using the synphot tool CALCPHOT). O stars are ruled out by this comparison, but B stars are acceptable. We should note, however, that this does not take into account any extinction from the host galaxy or that is intrinsic to the system itself. If this extinction is high, as is seen for those sources in NGC 3034, this may be masking a brighter blue object.

In those fields where potential counterparts are identified, we collate Vega magnitude zero points (Zpt) to allow for the derivation of HST filter-dependent Vega magnitudes of each source. For observations made using the ACS instruments, we are able to take these values directly from Sirianni et al. (2005). For WFPC2 data, the HLA pipeline converts the units contained within the science field to electrons s⁻¹ (like ACS) rather than DN (Data Number), and hence the tabulated zero points given in the HST Data Handbook for WFPC2¹² must also be converted, by applying a correction for the gain,¹³ using Zpt = tabulated zero point +2.5 × log (gain).

Aperture photometry is performed on all potential counterparts using Gaia.¹⁴ Aperture corrections are applied to all fields, irrespective of instrument and detector, following the procedures laid down by Sirianni et al. (2005), with values of corrections for WFPC2 observations taken from the HST WFPC2 cookbook¹⁵).

Galactic extinction corrections are also applied, using E(B − V) values listed in Table 1. These are used in combination with the filter-specific extinction ratios depending on the instrument. Extinction ratios for WFPC2 data were taken from Schlegel et al. (1998) where available, or calculated using synphot when this was not possible. The calculated extinction ratios are found by folding a template spectrum through the instrumental response allowing for foreground extinction using Cardelli laws (chosen for consistency with Schlegel et al. 1998). Although this correction is spectrum-dependent, we find that this dependence is small, and we choose a 10,000 K blackbody as a first-order estimate for these corrections, since the observed candidate counterparts are of unknown type. For magnitudes calculated using ACS fields, filter-dependent extinction ratios are given by Sirianni et al. (2005). Again, since the extinction ratios are also dependent on stellar type (and no blackbody is available), we choose to use the corrections for an O5 V star, following the example of Roberts et al. (2008). Although this choice will affect the calculated magnitudes of our sources, the impact will be minimal in most bands, with a larger (although still marginal) impact in the bluest bands (F435W and bluer). The aperture and Galactic extinction-corrected Vega magnitudes are given in Table 4.

If we wish to get a clear view of the binary system, we must obtain intrinsic magnitudes for these sources. To do this we must also take into account any absorption from either the host galaxy or that is intrinsic to the ULX itself. One method that has been used previously to correct for this extinction is to use the measured absorption from X-ray spectral fitting (e.g., Roberts et al. 2008), which will give an upper limit to the extinction of the optical light from the binary.

To calculate the maximal optical extinction column, we use the relation for X-ray-to-optical dust-to-gas ratios published by Güver & Özel (2009; N_H = (2.21 ± 0.18) × 10²⁰A_V, with 2σ errors). However, X-ray spectral fitting can be degenerate, and the N_H columns derived can vary substantially depending on the author's model choice. We minimize the impact of model choices by using the highest quality X-ray spectra available, and fitting these spectra with current physical models used to describe ULXs. We begin by collating N_H values from published results along with their respective errors, preferring long observations, physical models, and statistically good fits. When physically motivated models have not been applied to an object, we use values from publications of the deepest X-ray observation of these sources which show statistically good fits based on phenomenological models. Our adopted N_H values can be found in Table 1. Using the standard Galactic extinction curve (R_V = A_VE(B − V) = 3.1; Cardelli et al. 1989), we estimate the intrinsic optical magnitudes of these sources. The relevant errors are calculated by combining the error on N_H, obtained from the literature, with that of Güver & Özel (2009). The intrinsic Vega magnitudes for each potential counterpart are listed in Table 4.

We also compile details of previous identifications of potential counterparts, in order to compare our results and search for the most likely candidates. Hereafter in the text, bracketed values refer to the candidate counterpart ID (e.g., IC 342 X-1 (1) for candidate counterpart 1). Details of each potential counterpart are listed in Table 4, along with any previous identifications of potential counterparts. We compare our findings to previous work in Section 5.3.

In our sample, we find 40 potential counterparts to the 22 ULXs. Thirteen of these have previously been reported in the literature (ignoring NGC 598 ULX1), with the remaining 27 potential counterparts identified here for the first time. Up to 22 of these potential counterparts may be the true counterparts, but it is possible that all the potential counterparts in some error circles are chance coincidences. Therefore, we calculate the likelihood of chance coincidences given the density of the local stellar population of each ULX. We search for stellar objects within an annulus around each object with an inner radius of 1'' and an outer radius of 3''. For Circinus ULX1, we use a rectangle of size 3'' × 8'' instead, due to the chip geometry. We expect an average of 27 ± 5 objects to be present within the positional error regions of our ULX sample, yet we have observed a total of 40 potential counterparts. This indicates an overpopulation of 13 ± 5, which is our best estimate of the number of true counterparts identified in all ULX fields. There is a greater likelihood of foreground object contamination when considering those ULXs in Circinus, as it lies in the Galactic plane, so we temporarily remove these sources from our calculations. If we also removed NGC 3034 (M82) from our likelihood calculations, because the sources lie in an extremely obscured region of the galaxy, such that it is very unlikely that any optical emission would be detected from any real counterparts, this results in an excess of 15 ± 4 for 36 ULXs, with 19 of these having detected candidate counterparts. Thus we believe that for ∼83% of the ULXs with candidate counterparts, the true counterpart lies among our candidate counterparts. However, we note the caveat that if the ULX is located in a star-forming region with higher stellar density than areas ∼1'' away, our number of true counterparts could be overestimated.

In this section, we compare each candidate to stellar models to constrain the nature of the donor star in these ULX binary systems. In Section 5.1, we consider the spectral energy distribution (SED) and the apparent magnitude of each candidate to characterize the star (assuming the light is stellar in origin). In Section 5.2, we check whether variability may impact our characterization, which is relevant when we are incorporating optical data from multiple epochs. In Section 5.3, we compare our findings to previous works. In Section 5.4, we introduce an additional component in the form of an accretion disk, and also consider the effects of irradiative heating of the star and disk.

5.1. Spectral Typing from Stellar Templates and Magnitudes

We initially consider the case where the donor star contributes 100% of the optical light, and it has a luminosity and spectrum which is consistent with a single star. For these preliminary fits, we use only Galactic corrected magnitudes, ignoring any intrinsic extinction. We attempt to classify the donor stars by comparing the candidates with template SEDs. Previously, authors have done this by converting the filter band magnitudes to UBVRI magnitudes to compare with typical values for different stellar types (e.g., Soria et al. 2005; Ramsey et al. 2006; Roberts et al. 2008; Tao et al. 2011). The HST filters are not an exact match to other photometric systems, which can lead to large errors in typing stars using the HST filter bands (see Sirianni et al. 2005 for more detailed discussion).

Here, we perform typing by folding standard stellar spectra through the synphot tool CALCPHOT, a package that allows the user to calculate the photometric magnitudes observed for a given stellar type. In order to simplify our comparisons, we choose to normalize all spectra to a V-band magnitude of zero. We use the BPGS standard stellar templates associated with the synphot package. Although the atlas has the broadband coverage required for our analysis, it contains few giants/bright giants/supergiants, which could affect our results.

The conversion is performed for all instrument/detector/filter combinations used in the analysis of our ULX fields, with the resulting values plotted in Figure 2. Our templates range from O to M, varying in size from main sequence to supergiant. The templates are grouped by color, according to type (listed in figure caption).

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Simple χ² minimization is performed to determine the best-fitting stellar type, whenever more than one filter band is available, with some examples of resulting fits shown in Figure 3. This fitting requires that an offset be calculated in each instance (the shift required between its current magnitude in F555W and zero, for the best-fitting model). This offset can also be considered to be the m₅₅₅ of the source (which will be similar in value to m_V).

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SED fitting is only possible when more than one filter band is available, however, of the 40 candidate counterparts identified, 15 are observed in only a single filter band (due to chip gaps, or depth of exposures in other filters; see Ptak et al. 2006). Of the 25 remaining potential counterparts, we note that in 10 instances fitting is performed where only two bands are available; five of our sample have three data points available for fitting, seven contain four HST bands and three contain five data bins for comparison to standard stellar types. The resultant types and offsets are displayed in Table 5, with sample fits shown in Figure 3.

Table 5. Typing of Potential ULX Counterparts

Source	C/P	Typeb	Type	Distance	m555e	Offsetf	Δm555g	Types from	M555i	Types from	Previous
	IDa		MVc	Modulusd				Colorh		M555j	IDk
NGC 598 ULX1	Nucleus	...	...	24.771	...	...	...	...	...	...	Nucleus3
NGC 55 ULX1	1	A1 V	+0.7*1	26.203	26.898	23.179	−3.719	O, B, A,	−3.0	Late B V,	...
								early F		IV, III, A II
	2	M0V	+9.01	26.203	35.208	24.704	−10.499	Late K, M	−1.499	B V, IV,	...
								early F		and late III,
								early F		F-K II
NGC 4190 X-1	1	B2 V	−2.6412	27.236	24.595	24.114	0.481	O, B, A,	−3.1	Mid B III,	...
								F, G, early		late A or
								to mid F		later II
NGC 253 ULX1	1	...	...	27.386	...	...	...	...	...	...	...
	2	M2 III	−0.61	27.386	29.930	24.099	−2.831	All	−3.3	B V, late	...
										B III, A II
	3	K0 III	+0.51	27.386	27.886	25.234	−2.652	All	−2.152	Late B	...
										all B III,
										all II
	4	G8 III	+0.61	27.386	28.006	25.073	−2.933	All	−2.313	Late B	...
										all B III,
										all II
NGC 253 ULX2	1	M0 V	+9.01	27.386	36.478	21.165	−15.313	M, late K	−6.2	All Ib	...
NGC 253 ULX3	1	K8 V	+6.7*1	27.386	34.126	22.518	−11.608	Late B, A,	−4.868	OB V and III,	...
								F, G, K,		A II,
								early M		A–M Ib
NGC 253 XMM6	1	M0 V	+9.01	27.386	36.478	25.601	−10.877	all	−1.8	Late B V	...
										and IV, F–M II
	2	M0 III	−0.21	27.386	27.304	25.782	−1.522	M	−1.4	Late B V	...
										and IV, F–M II
	3	...	...	27.386	...	...	...	...	...	...	...
	4	...	...	27.386	...	...	...	...	...	...	...
	5	...	...	27.386	...	...	...	...	...	...	...
M81 X-6	1	B2 III	−2.632	27.657	25.027	23.795	−1.232	O, B, A,	−3.682	B V, IV,	O8 V4, 5
								F,		Late B II,
								early G		A II
Hol IX X-1	1	B4 V	−1.222	27.670	26.429	22.253	−4.176	B	−5.4	O, early	OB5, 6
										B V, BII,
										all Ib
	2	...	...	27.670	...	...	...	...	...	...	...
	3	B6 V	−0.812	27.670	26.860	26.123	−0.737	O, B, A,	−1.574	Late B V	...
								F, mid G		and II, F–K II
NGC 4395 ULX1	1	...	...	27.782	...	...	...	...	...	...	...
NGC 1313 X-1	1	B2 III	−2.632	27.841	25.180	23.707	−1.473	O, B	−4.1	Late O V,	K5–M0 II7
								F, mid G		IV, III, B, Ib
NGC 1313 X-2	1	B2 III	−2.632	27.841	25.180	23.359	−1.821	O, early B	−4.5	OB, all Ib	OB5, 8
	2	...	...	27.841	...	...	...	...	...	...	...
IC 342 X-1	1	K0 IV	+3.21	27.955	31.221	22.227	−8.994	K, G	−5.7	OB, all I	F8–G0 Ib9,
											F0–F5 I10
	2	F6 V	+3.4*1	27.955	31.378	24.045	−7.333	O, B, A,	−3.9	OB and A II	...
								F, G, K,		F Ib
								early M		or later
IC 342 X-2	1	...	...	27.955	...	...	...	...	...	...	Y10
	2	...	...	27.955	...	...	...	...	...	...	...
	3	...	...	27.955	...	...	...	...	...	...	...
IC 342 ULX2	Nucleus	...	...	27.955	...	...	...	...	...	...
IC 342 X-6	1	B6V	−0.812	27.955	27.145	24.407	−2.738	O, B, A,	−3.548	B V, IV,	...
								F, G, K,		III, A II,
								early M		K Ib
										or later
	2	...	...	27.955	...	...	...	...	...	...	...
	3	...	...	27.955	...	...	...	...	...	...	...
Circinus ULX1	1	...	...	28.010	...	...	...	...	...	...	K5 or
											later11
NGC 2403 X-1	1	B8 Ia	−5.672	28.116	22.444	24.538	+2.095	O, B, A,	−3.6	B V, IV,	OB giant/
								F,		III, A II,	supergiant10
								early K		K Ib
										or later
NGC 5128 ULX1	0	...	...	28.121	...	...	...	...	...	...	OB12
Hol II X-1	1	A3 III	−0.2*1	28.266	28.756	21.490	−7.266	B, A	−6.8	All Ia	O4 V /
											B3 Ib13
M83 XMM1	1	A3 V	+2.0*1	28.360	30.358	25.486	−4.872	All	−2.9	Late B,	...
										A II
										or later
NGC 5204 X-1	1	O5 V	−5.002	28.406	23.370	22.743	−0.627	O	−5.3	O, B II	O5 V,
											O7III or
											B0 Ib14
	2	F8 V	+3.4*1	28.406	31.840	20.184	−11.656	None	−8.2	Late	Star cluster15
										A Ia,	O5 V +
										FG Ia or	cluster14
										early
										M Ia
NGC 5408 X-1	1	O8 f	−4.83*2	28.406	23.539	22.198	−1.341	O, B, A,	−6.2	O,	B/A I16
								F, G, K,		B II and I
								early M
NGC 3034 ULX5	1	M2 III	−0.61	28.580	28.108	21.610	−6.498	B, A, F, G,	6.9	All Ia
								K, M
	2	...	...	28.580	...	...	...	...	...	...	...
NGC 3034 ULX6	1	...	...	28.580	...	...	...	...	...	...	...

Notes. ^aCandidate counterpart ID taken from Table 4. We remove those ULXs for which there are no candidate counterparts detected from the list. The only exception to this is NGC 5128 ULX1, as a candidate counterpart has been published elsewhere. ^bStellar type derived from χ² fitting of HST band stellar templates, created using synphot. ^cAbsolute magnitude of identified stellar type in the V band (taken from similar type if particular M_V is unavailable, sources are indicated by *). ^dCalculated distance modulus using values in Table 1. ^eDerived Vega magnitude in the F555W band, assuming stellar type classification is correct. ^fOffset required to fit observed data to stellar types, this can also be considered to be the apparent magnitude in the F555W band (∼ m₅₅₅). This is found by χ² fitting. ^gValue Δm₅₅₅ = offset − m₅₅₅. ^hAll possible types allowed from SED fitting, within errors. ⁱGalactic extinction corrected absolute magnitude in the HST band F555W, calculated using offset value. ^jAll possible types allowed from absolute magnitude fitting, within errors. ^kStellar types collated from the work of other authors, where Y refers to identification without typing. Figures shown in brackets relate to the following references: ¹Zombeck 1990; ²Wegner 2006; ³Dubus et al. 2004; ⁴Liu et al. 2002; ⁵Ramsey et al. 2006; ⁶Grisé et al. 2006; ⁷Yang et al. 2011; ⁸Liu et al. 2007; ⁹Feng & Kaaret 2008; ¹⁰Roberts et al. 2008; ¹¹Weisskopf et al. 2004; ¹²Ghosh et al. 2006; ¹³Kaaret et al. 2004; ¹⁴Liu et al. 2004; ¹⁵Goad et al. 2002; ¹⁶Lang et al. 2007.

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The best fits achieved by this process, given in Column 3 of Table 5, suggest that the majority of these 25 objects are not best fit by OB stars, as was previously suggested (e.g., Liu et al. 2007; Copperwheat et al. 2007). Only two are best fit with O-type stars, while eight prefer B-type stars, and six are best fit by M stars. The best-fit luminosity classes are typically not supergiants (only 2), but main sequence (14) or giants (9).

We list all types that can explain the observed SEDs within their errors in Column 9 of Table 5. These allow for more blue companions, with 20 now consistent with OB stars. Five of our sample appear to require later-type sources (NGC 55 ULX1 (2), NGC 253 ULX2 (1), NGC 253 XMM6 (2), IC 342 X-1 (1), and NGC 5204 X-1 (2)). However, the redder nature of these candidates could also be a function of reddening, as a result of the host galaxy or their local environment. For example, IC 342 X-1 and NGC 3034 ULX5 have been shown to be heavily absorbed in X-rays on many occasions, which is evident from the high values of N_H listed in Table 1. Holmberg II X-1 may not show as high an absorption column, but this source resides in an excited He ii region (Pakull & Mirioni 2002; Kaaret et al. 2004). Although X-rays appear not to be heavily obscured by this nebula, it may be affecting the optical emission from the star. Nebulae have also been associated with other ULXs, including NGC 5204 X-1 (Roberts et al. 2001) and IC 342 X-1 (Pakull & Mirioni 2002). Thus, it is possible that the typing of these objects is incorrect, but this evidence for possible later-type companions to some ULXs is intriguing, and worth further study.

We also consider the absolute magnitude that would be observed from each of these stellar types (Zombeck 1990; Wegner 2006). These are combined with the distance modulus for each source (in Table 1) to derive the apparent magnitude for a star of that class at the required distance.¹⁶ We use the absolute magnitude for the V band to allow for easy comparison to our fits, and fold this through CALCPHOT to derive the value for the HST band F555W (i.e., m₅₅₅ for that stellar type). As all templates are normalized to a V-band magnitude of zero, this means that the choice of instrument and detector will have minimal impact on the derived apparent magnitude in this HST filter band. Since more than half of our observations were taken by ACS using the WFC, we choose this combination to derive the apparent magnitudes that would be observed. The absolute magnitude, distance modulus, and derived apparent F555W magnitudes are given in Table 5.

As we do not have a F555W observation for every source, we use the offset value to derive the observed absolute F555W band magnitude. To calculate the value of M₅₅₅ for each candidate counterpart, we combine the offset from fitting with the distance modulus for each potential counterpart, listing the resultant value in Column 10 of Table 5. These calculations provide us with absolute magnitudes over the range −1.4 < M₅₅₅ < −8.2. We use this information in combination with the absolute magnitudes listed in Zombeck (1990) to list all possible stellar types that can be observed at approximately this absolute magnitude (see Column 11 of Table 5). As Zombeck (1990) only lists those classified with subtypes 0 or 5 for each stellar type (e.g., O5, B0, B5, etc.), we classify some stars as being early (≲5) or late (≳5) within a stellar type.

We compare the observed apparent magnitudes of candidate counterparts with the calculated magnitudes (using the offsets gained from χ² fitting). To do this we group our sources into four categories for ease of comparison; those that differ by ≳ 10 mag (extreme difference), 5 ≲ Δm₅₅₅ ≲ 10 mag (large difference), those that differ by ≲ 2 mag (comparable), and those that lie in the range of 2 ≲ Δm₅₅₅ ≲ 5 mag (other). The ranges are designed to allow for magnitude and stellar template fitting errors, and for slight variations on tabulated absolute magnitudes while clearly identifying those that show striking differences. We find that five exhibit "extreme" differences, four display "large" differences, nine show "comparable" values, and seven are classified as "other."

The sources with an "extreme" value of Δm₅₅₅ are generally best fit by later-type main-sequence stars. However, in most cases we would be unable to see such an object, as it would be too faint to be observed at that distance. The first is NGC 5204 X-1 (2) and is discussed in depth in Section 5.2, so we will not consider it further here. The SED of NGC 253 XMM6 (1) allows for any spectral type, while M₅₅₅ limits the range to OB or later II. We will also return to this source in Section 5.3. The SEDs of the three remaining candidate counterparts only allow later types within their errors, while in each case the M₅₅₅ value indicates a need for bright giants or supergiants. This potential misclassification is probably due to a lack of bright giants/supergiants in the chosen catalog.

Those sources that have a "large" value of Δm₅₅₅ also appear to be late-type sources. These sources are IC 342 X-1 (1) and (2), Ho II X-1 (1), and NGC 3034 ULX5 (1). If we again consider the types allowed within errors, we find that two appear fairly well constrained (IC 342 X-1 (1) and Ho II X-1 (1)). The difference in observed and derived m₅₅₅ may be largely because of mistyping due to the catalog used. It may also be the case that this mistyping is due to reddening, which must be considered as we are using Galactic corrected magnitudes, but given the increase in errors, no fits would be achievable.

Of the remaining 16 sources, 9 display similar apparent magnitudes to their offsets (Δm₅₅₅ ≲ 2) and so are "comparable," while the 7 remaining sources display a greater divergence. In four of these cases we were unable to collate the exact value of M_V for the specified source type, which could induce 1–2 mag of errors. So these candidate counterparts can also be considered as "comparable" within the increased errors. Thus, we have consistent stellar typing and magnitudes for 13 of our sources. Of these 13 sources, we find that 8 are likely OB-type stars. The other five sources are a mixture of mid- to late-type stars. The two potential counterparts classified as A-like stars are less well constrained, although in both cases any errors veer more toward the blue. Of the three later-type classifications (G to M), NGC 253 XMM6 (2) seems well constrained. This is very interesting, as it is unlike many previous classifications of ULX counterparts and as such, deserves further study. Such a find is also supported by the recent discovery of two nearby low-mass X-ray binary (LMXB) ULXs (e.g., Middleton et al. 2012; Soria et al. 2012). Two of our ULXs (NGC 253 ULX1 and XMM6) had multiple XMM-Newton observations in early 2006, eight months before the HST observations we used, which did not show X-ray activity. If X-ray activity did not restart during these eight months, then these HST observations may be given an unprecedented view of the ULX companion stars, potentially lending more support to the LMXB hypothesis as other LMXB ULXs are also transients (e.g., Middleton et al. 2012).

Previous studies have shown that many ULXs appear to have blue counterparts (e.g., Roberts et al. 2008). Many of our potential counterparts appear to agree with this, when using simple stellar templates. If we now consider this on a ULX-by-ULX basis (instead of each candidate counterpart in turn), we find that OB companions are possible in all but one instance—NGC 253 ULX2. This makes this a key source for further study. While B-type companions are viable for all but one other ULX (NGC 5204 X-1), we can rule out O-type companions in 20 cases. However, the apparent blue color of these ULX optical counterparts may be due to the presence of a strong, blue, accretion disk component (e.g., Copperwheat et al. 2005, 2007). Since we did not include an accretion disk in these stellar template fits, finding possible red counterparts is of interest. If these classifications are correct, it would suggest that the star is dominant in these filters, as any disk emission would be intrinsically blue. This implies that either the ULX was dim in X-rays during these optical observations, or that these red objects are not the true counterparts to these ULXs.