MULTIWAVELENGTH OBSERVATIONS OF Swift J1753.5−0127

We observed Swift J1753.5−0127 with COS on 2012 October 2. Information about the design and on-orbit performance of COS can be found in Osterman et al. (2011), Green et al. (2012), and in the COS Instrument Handbook (Holland et al. 2012). We used the G130M and G160M gratings to obtain the FUV (1150–1800 Å) spectrum at moderate spectral resolution (R ≃ 18,000). We stepped each grating through four central wavelength positions to minimize the effects of fixed pattern noise. We also obtained NUV spectra using the G230L grating taken in two grating tilt positions (the 2950 Å and 3360 Å settings). Each G230L exposure covers three non-contiguous spectral regions, so the two tilt positions together subtend 1650–3560 Å with some gaps. The spectral resolution of the G230L data is R ≃ 3000.

We retrieved the COS data from the Multi-Mission Archive at STScI (MAST). The data had been processed with V. 2.18.5 of CALCOS. For the FUV data, we coadded the output one-dimensional spectral data products using a custom IDL code described in Danforth et al. (2010).⁹ The code combines different wavelength settings and creates a weighted mean spectrum (with lower weight given to regions of uncertain flux calibration near detector edges). For the NUV spectra, we used the X1D files as delivered by CALCOS.

Swift acquired pointed observations of Swift J1753.5−0127 for 2100 s on 2012 October 2, simultaneous with the HST/COS observations. We retrieved and calibrated the X-Ray Telescope (XRT; Burrows et al. 2005) and UV/Optical Telescope (UVOT; Roming et al. 2005) data. The XRT was in windowed timing mode for the observation. A total of 12,355 X-ray counts were detected. The background is ≃20 photons, so a background subtraction in the spectrum was neglected during the analysis. For the UVOT data, we used the Swift FTOOL¹⁰ uvotsource to extract the background-subtracted flux from the UVOT observations in the U filter. The U-band magnitude is given in Table 2.

For the XRT observation, we fit the data with an absorbed power-law model (phabs^*powerlaw in XSPEC version 12.0; Arnaud 1996). If the foreground absorption is allowed to float freely, we find N_H = 2.66 ± 0.14 × 10²¹ cm⁻² and Γ = 2.00 ± 0.04, with the errors assumed to be purely statistical and the uncertainties given at the 90% confidence level. The fit has $\chi ^2_\nu = 1.01$ (with 769 dof). The absorbed flux in the 0.3–8 keV band is 2.37 × 10⁻¹⁰ erg cm⁻² s⁻¹, and the unabsorbed flux in the same band is 3.8 × 10⁻¹⁰ erg cm⁻² s⁻¹. If we fix the interstellar hydrogen absorption at the value found by our fits to the Lyα absorption line profile (N_H = 2.0 × 10²¹ cm⁻²; see Section 3.2), we obtain Γ = 1.81 ± 0.02 and $\chi ^2_\nu = 1.11$ (768 dof). The 0.3–8.0 keV unabsorbed flux is 2.45 × 10⁻¹⁰ erg cm⁻² s⁻¹ for this model. There was no significant improvement to the X-ray fits if we added additional components such as a thermal accretion disk component or a Gaussian emission component in the 6–7 keV range.

We obtained optical and NIR photometry of Swift J1753.5−0127 using SPIcam and NIC-FPS (Hearty et al. 2004) on the 3.5 m telescope at Apache Point Observatory, taking exposures in the B, V, R, I, J, H, and K filters. Weather conditions were clear with moderate, variable seeing (FWHM ≃ 09–15). We reduced the data using IRAF¹¹ for standard calibration tasks (e.g., bias subtraction, sky subtraction, and flat-fielding) and aperture photometry. We calibrated the photometry in the optical using the in-field standards given in Zurita et al. (2008). For the NIR, we acquired separate standards from the ARNICA catalog (Hunt et al. 1998). We averaged the results for multiple exposures for the target and standard star fields. The results are tabulated in Table 2. The uncertainties on the magnitudes are the propagated statistical errors for our exposures; because Swift J1753.5−0127 is variable, the observed magnitudes fluctuate at levels that are larger than the statistical errors.

The FUV spectrum of Swift J1753.5−0127 is shown in Figure 1. The observed spectrum has a FUV continuum flux of 2 × 10⁻¹⁵ erg cm⁻² s⁻¹ Å⁻¹ at 1450 Å. Spectral features include broad emission lines of C iv λλ1548,1551 and He ii λ1640 and interstellar absorption features (Morton 1978). In Figure 1, we labeled the locations of other FUV lines that are often seen in the spectra of XRBs; however, only C iv and He ii are clearly detected in Swift J1753.5−0127. There is an enhancement in the spectrum around 1240 Å that suggests the presence of the N v λλ1238,1242 doublet, but most of the line, if present, is lost in the broad interstellar Lyα absorption.

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We dereddened the spectrum using E(B − V) = 0.45 (see Section 3.2). The dereddened spectrum shows a smooth continuum increasing to short wavelengths. The NUV spectrum extends the continuum to the red and shows no spectral features (see Figure 2). We fit single Gaussian profiles to the two emission lines in the dereddened spectrum using Specfit (Kriss 1994). The fit to C iv also included coincident interstellar lines to correct for their effects on the line flux. The C iv and He ii line fluxes are 5.5 ± 0.8 × 10⁻¹³ erg cm⁻² s⁻¹ and 2.6 ± 0.6 × 10⁻¹³ erg cm⁻² s⁻¹, respectively. Both lines have FWHM ≃ 3500 km s⁻¹; the widths are not constrained to better than approximately 500 km s⁻¹. We do not have the signal to noise to determine if the emission lines are single- or double-peaked. Using the observed flux density in the region of the N v doublet and correcting for the interstellar absorption, we set an upper limit on the N v line flux of ≲ 2.5 × 10⁻¹⁴ erg cm⁻² s⁻¹.

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Using the COS time-tagged photon event list, we searched for variability in the continuum and emission lines during the observations. We identified regions of interest in the two-dimensional (wavelength versus cross-dispersion position) corrected time-tag spectral images and summed the counts in each image for selected time bins, subtracting a background region of the same size but offset from the target spectrum in the cross-dispersion direction for each bin. We selected several line-free continuum regions and the C iv and He ii emission lines, examining the data in 50 s and 200 s time intervals. We used different grating tilt settings during the observation, so we restricted our analysis to the time intervals when our chosen wavebands were fully on the detector. We were insensitive to low-level variability because of the faintness of the target: we could not detect fluctuations (at >3σ) below 10% on 50 s time scales. Above that limit, the COS data were steady over the course of the observations. There were no trends in the FUV light curves, and all fluctuations were consistent with statistical noise.

Finally, we examined the C iv line profile over time to see if we could identify radial velocity variations in the line over the orbital period. The orbital period of Swift J1753.5−0127 is unknown: a 3.24 hr photometric periodicity has been observed and was interpreted as a superhump modulation that occurs in low-mass ratio systems when a 3:1 orbital resonance is established within the accretion disk, which causes the disk to precess and exhibit a periodic emission modulation (Zurita et al. 2008; Haswell et al. 2001; Whitehurst 1988). Using an empirical relation between the orbital and superhump periods determined by Patterson et al. (2005), Zurita et al. found an orbital period range for Swift J1753.5−0127 between 3.18 < P_orb < 3.24 hr. We examined spectra extracted in time subintervals from 100 to 800 s. Unfortunately, the combination of low signal to noise in the individual spectra, the relatively low contrast between the line and continuum (the peak line flux is only 50% above the continuum flux), and the contamination of the line center by the interstellar absorption precluded obtaining reliable velocity shifts from C iv. The He ii line was also too faint to yield significant results.

There have been various estimates for the interstellar absorption and reddening along the line of sight to Swift J1753.5−0127. Fits to X-ray spectra in which hydrogen column density, N_H, was allowed to vary have resulted in values of N_H = 1.7–2.3 × 10²¹ cm⁻² (Hiemstra et al. 2009; Miller et al. 2006; Morris et al. 2005). Cadolle Bel et al. (2007) and Durant et al. (2008) determined reddening values from the equivalent widths of the optical Na i D lines using the prescription of Munari & Zwitter (1997) and converted these to N_H after Bohlin et al. (1978). Using this method, Cadolle Bel et al. (2007) found E(B − V) = 0.34 ± 0.04 and N_H = 2.0 × 10²¹ cm⁻², while Durant et al. (2008) obtained E(B − V) = 0.42 ± 0.02 and N_H = 2.45 × 10²¹ cm⁻². Durant et al. speculated that the absorption internal to the system may vary over time, given the difference in their results from those of Cadolle Bel et al. Although there is some variation in determinations of N_H, all of the derived values are comparable to the average total Galactic absorption along this line of sight (Morris et al. 2005; Durant et al. 2009).

We obtained values for both E(B − V) and N_H from our UV spectra by fitting 2175 Å dust feature and the damping wings of the interstellar Lyα absorption line profile, respectively. To determine the reddening, we fit the 2175 Å feature in the NUV. Figure 2 shows the UV spectrum of Swift J1753.5−0127 in the region of the 2175 Å dust feature. The upper panel shows the observed spectrum normalized to a mean value of 1.0. Using the ccm_unred task from the IDL Astronomy User's Library¹², we dereddened the spectrum, stepping E(B − V) from 0.00 to 1.00 in steps of 0.01 to find the reddening value that minimized the χ² deviation about a power-law fit to the residual. R_V was held fixed at 3.1. The best fit was E(B − V) = 0.45 with $\chi ^{2}_{\nu } = 1.55$ (566 dof) for a 1400–3100 Å fit range. The reddening is consistent with the value found by Durant et al. (2008). Following the lead of Fitzpatrick (1999), who noted the large scatter about the mean in the amplitude of the 2175 Å feature in Galactic sight lines, we assume 20% uncertainty on our derived reddening and adopt E(B − V) = 0.45 ± 0.09.

Figure 3 shows the Lyα absorption line and the best fit to the line profile. We fit the interstellar H i column density using a linear approximation of the observed (reddened) FUV continuum of Swift J1753.5−0127 and a Voigt profile for the Lyα resonance line. First, the geocoronal airglow emission (1213.5–1218.3 Å) was removed from the core of the interstellar absorption trough. A linear fit was then made across the Lyα region (1174–1270 Å), anchored on the blue end by the average continuum flux from 1175–1186 Å and on the red end by the average continuum flux from 1254–1258 Å. The Lyα absorber is characterized by a column density, N_H (in units of cm⁻²), a Doppler-b parameter (in units of km s⁻¹), and a velocity offset relative to the rest wavelength of the Lyα transition (in units of km s⁻¹ relative to λ_rest = 1215.67 Å). The velocity was fit by eye to produce a profile that evenly filled in the red and blue edges of the Lyα absorption trough (v_Lyα = −10 km s⁻¹). The b-value was chosen to be typical of the local interstellar medium (10 km s⁻¹; Redfield & Linsky 2004), although the b-value does not have a large influence on the heavily damped line profile observed for Swift J1753.5−0127. The interstellar column density was then varied until a best-fit value was found, with error bars defined as values of N_H that produce fits consistent with the 1σ photometric error bars in the line-core and wings. This procedure yielded N_H = 2.0 ± 0.3 × 10²¹ cm⁻².

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If we use the reddening to infer N_H from the relation of Bohlin et al. (1978), we obtain a value larger than the one directly found from the Lyα line profile fitting, although they agree within the uncertainties on N_H and E(B − V). Relating gas and dust absorption is subject to a number of uncertainties that could cause a slight discrepancy: we do not know the value of R_V for this sight line, and there is considerable scatter in the relationships between reddening and the size of 2175 Å feature (as noted above) and between gas and dust for individual sight lines (∼30% scatter about the Bohlin et al. relation). The gas along the line of sight to Swift J1753.5−0127 may also be more metal-rich than the average Galactic value, resulting in a larger reddening and a higher N_H found from the X-ray fitting compared to the fit to the Lyα line profile (whereas the Lyα interstellar line directly traces the neutral hydrogen along the line of sight, the N_H from the X-ray model fits includes absorption from helium and metals). Ultimately, the various methods for determining N_H and E(B − V) for the sight line to Swift J1753.5−0127 have proven satisfactorily consistent within the uncertainties.

If we assume that the UV emission is dominated by the accretion disk, we can use disk model fits to the dereddened spectrum to determine black hole masses and accretion rates as a function of the distance to Swift J1753.5−0127. Most parameters are unknown or poorly constrained for this system, however, so our fits will be more instructive in placing limits on interesting values than in providing precise determinations. We fit the dereddened UV continuum with a grid of steady-state accretion disk model spectra constructed from summed, area-weighted blackbody spectra. The blackbody spectrum for each disk annulus was chosen to correspond to the theoretical, steady-state thin accretion disk temperature for that annulus. The models did not include disk irradiation.

Following Cheng et al. (1992), we can describe the observed flux density from a thin, steady-state, viscously heated accretion disk as:

$$\begin{equation} f_{\nu } = f_{0} \frac{\cos i}{d^{2}} (m\dot{m})^{2/3} \nu _{15}^{1/3} \int _{x_{{\rm in}}(\nu)}^{x_{{\rm out}}(\nu)} \frac{x^{5/3}dx}{e^{x} - 1} , \end{equation} \tag{ 1 }$$

where f₀ ≃ 2.9 × 10⁻²⁶ erg cm² s⁻¹ Hz⁻¹, d is the distance in kiloparsecs, i is the binary inclination, m (=M_BH/M_☉) is the mass of the black hole, $\dot{m}$ is the mass accretion rate in units of 10⁻⁹ M_☉ yr⁻¹, ν₁₅ = ν/10¹⁵ Hz, and x = hν/kT(r) where T(r) denotes the blackbody temperature (K) and radius (in units of 10¹¹ cm) of each annulus.

The disk temperature at each annulus is a function of M_BH, $\dot{m}$, and the radius. The overall temperature distribution in the disk depends on the inner and outer disk radii adopted. For the inner disk radius, r_in, we examined models between two extreme values: r_in = 1.23 r_g and 500 r_g, where r_g is the gravitational radius for a given black hole mass. The values represent differing predictions of the inner radius of the thin disk as extending to the ISCO for a maximally rotating Kerr black hole or truncated at larger radii under the ADAF model paradigm (Reynolds et al. 2010; Zhang et al. 2010). We set the outer disk radius, r_out, to 60% of the Roche lobe radius. Following Zurita et al., we fixed P_orb = 3.23 hr and the donor star mass to M₂ = 0.3 M_☉, which we used in conjunction with the black hole mass to set the binary geometry and r_out.¹³ Because the UV flux is dominated by emission from the inner disk annuli, the exact value of the r_out does not affect our fit results.

For these model parameters, the accretion disk model spectra for Swift J1753.5−0127 follow a ν^1/3 power-law profile in the FUV spectral region. Therefore, we can use the normalization of the disk models to the observed FUV flux to constrain the black hole mass as a function of accretion rate, distance, and inclination. For the continuum region centered on 1470 Å (1425–1520 Å; ν = 2.04 × 10¹⁵), we measure an average flux density of f_λ = 6.48 × 10⁻¹⁴ erg cm² s⁻¹ Å⁻¹. Converting to the frequency domain and substituting into Equation (6) of Cheng et al., we can express the mass of the black hole in Swift J1753.5−0127 as:

$$\begin{equation} \frac{M_{{\rm BH}}}{M_{\odot }} = 0.546 [\cos i]^{-3/2} \left[\frac{d}{1\ {\rm kpc}}\right]^{3} \left[\frac{\dot{m}}{10^{-9}\ M_{\odot }\ {\rm yr}^{-1}}\right]^{-1}. \end{equation} \tag{ 2 }$$

The binary inclination, distance, and mass accretion rate for Swift J1753.5−0127 are not known. The system does not show eclipses, which restricts inclinations to i ≲ 80°. Reis et al. (2009) found $i = 55^{\circ +2}_{ -7}$ based on model fits to X-ray reflection features. We adopt this as our default inclination but also examine how varying the inclination affects the other model parameters. (Note that the reflection fits assume that the disk extended to the ISCO at the time of the observations, which may not have been the case; see Section 4.)

Swift J1753.5−0127 has remained in the low/hard state throughout its outburst. Maccarone (2003) found that XRBs transition from the soft to the hard state between 1%–4% of the Eddington luminosity. The transition from hard state to soft can occur over a somewhat larger range of luminosities due to hysteresis effects (Maccarone & Coppi 2003). Here, we adopt an upper limit on the mass accretion rate of $\dot{m} \le 0.05 \dot{m}_{{\rm Edd}}$, where $\dot{m}_{{\rm Edd}} = L_{{\rm Edd}} / (0.1 c^{2})$, assuming a radiative efficiency of 10%. For the units in Equation (2), this corresponds to $\dot{m} \le 1.097 \times m$. Since our data were taken at an X-ray luminosity several times smaller than the peak value (when the system remained in the low state), this upper limit is conservative.

Based on these parameter assumptions, we have generated upper limits on the distance to Swift J1753.5−0127 for given black hole masses based on fits to the dereddened UV continuum. These are given in Table 3. For the upper limits, we also assumed that the disk radius extends to the ISCO to maximize the potential disk emission. The distance could be higher for a lower inclination disk so we also present the upper limit on the distance for the extreme case of a face-on disk with i = 0°.

Figure 4 shows the 12 M_☉ disk model compared to the data. The accretion disk models with viscous heating and no irradiation provide qualitatively good fits to the shape of the FUV continuum. The observed spectrum may be somewhat more blue than the model at the shortest FUV wavelengths, but we do not make a quantitative conclusion on this point because a small error in the adopted dereddening and/or the presence of unidentified emission features (such as C iii 1175 Å and N v 1238, 1242 Å) could bias the continuum shape in this region. We are unable to distinguish between an accretion disk extending to the ISCO or one truncated at larger radii from the UV data alone (although see Section 4 for comparisons with the broadband SED). In either scenario, the UV is on the ν^1/3 power-law portion of the disk SED, with peak emission occurring in the EUV for the truncated disk or in soft X-rays for the ISCO disk. The two radii give different results when fit to the data, however, since the ISCO model generates more UV flux; for example, for a 9 M_☉ black hole at a 6 kpc distance, the inferred mass accretion rate must be 25% higher for the truncated disk compared to the ISCO radius to match the observed UV flux.

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In Figure 5, we plot the broadband SED for Swift J1753.5−0127 at the time of our observations. Table 4 gives the data we used for the SED for future reference. The NIR/optical/UV data were dereddened assuming E(B − V) = 0.45. For the X-ray data, we plot the power-law component of the model fit to the data and its uncertainties. In the figure, we also plot previous SEDs acquired in 2005 (three months after outburst start) and in 2007, with the optical/NIR points dereddened using our E(B − V) value for a consistent comparison (Cadolle Bel et al. 2007; Durant et al. 2009).

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A comparison of the X-ray SED from the three epochs shows that the X-ray fluxes have declined. The system has also faded in the optical/NIR. The NIR fluxes we observed are ≃90%, and the optical fluxes are ≃65% of those observed in 2005. The 2012 data are also fainter than the 2007 observations, with fluxes that are ≃75% of the 2007 data in the optical. However, the shape of the optical/NIR SED has not changed significantly as it has faded: all three epochs show approximately power-law shapes, although a single power law cannot fit all of the optical/NIR data in any epoch. The new FUV observations show that the power-law shape extends at least to ≃1150 Å. The spectral break between the X-rays and lower energy data occurs at higher energies than the FUV.

In this manuscript, we have presented the first UV spectrum of Swift J1753.5−0127, which is accompanied by contemporaneous X-ray, optical, and NIR observations. The dereddened UV spectrum is characterized by a continuum that smoothly increases to the blue and broad line emission from C iv, He ii, and possibly N v. There are now high-quality FUV observations of three black hole XRBs in outburst: Swift J1753.5−0127, XTE J1118+480, and XTE J1859+226 (Haswell et al. 2002). The emission line spectra are different in each case. In XTE J1859+226, the UV spectrum has strong lines of C iii, C iv, N v, O v, He ii, and Si iv. That spectrum is richer in emission lines than Swift J1753.5−0127, and the N v line flux is nearly equal to that of C iv, whereas we do not confidently detect N v here. As noted by Haswell et al., the N v line can be suppressed relative to C iv by either photoionization by a harder X-ray ionizing spectrum or by relatively metal-poor abundances.

On the other hand, XTE J1118+480 shows the opposite effect: a much stronger N v emission and no C iv that has also been observed in A0620−00 (Froning et al. 2011) and is attributed to CNO processing in the accreted material. If Swift J1753.5−0127 had followed the evolutionary path proposed by Haswell et al. for XTE J1118+480 and A0620−00, wherein mass transfer was initiated after the donor star had already begun to move off the main sequence, their model would predict a current C/N abundance ratio for Swift J1753.5−0127 of log (C/N) ⩽ −2.3, lower than in XTE J1118+480, where C iv is undetectable (Haswell et al. Figure 3; see also their discussion of why the low C v to N v ratio is unlikely to be caused by photoionization effects). Instead, the UV line spectrum of Swift J1753.5−0127 suggests little CNO processing, which is consistent with a system that initiated mass transfer at a shorter orbital period when the lower-mass donor star was still on the main sequence. More generally, the comparison of the three black hole XRB spectra in the UV shows that the complicated interplay of evolutionary history, metallicity, and photoionization leads to diverse spectroscopic signatures; observations of more systems will be valuable to constrain the physical processes underlying the line emission.

Swift J1753.5−0127 was stable during our observations to <10%, showing neither secular variability nor any evidence of the 3.24 hr orbital modulation seen in the optical light curves (Zurita et al. 2008), though the orbital modulation may have been below our detection threshold. Our longest continuous light curve in a single waveband was 5538 s, or about half of the 3.24 hr modulation. The Zurita et al. R-band light curves typically showed a 0.1 mag or smaller variation over those time scales, which is at the level of our sensitivity, assuming a similar amplitude in the FUV. Our NUV spectra show hints of variability on the ∼8% level but the 1400 s baseline in each spectrum is too short to determine if the orbital modulation is present. It is also unclear whether the modulation, believed to be due to superhumps, will still be present in Swift J1753.5−0127 several years after the initial outburst, although superhumps were seen in the light curve of XTE J1118+480 near quiescence (Zurita et al. 2002). The expected amplitude of the superhumps will likely be lower in the UV than in the optical, as the effect occurs in the cooler outer disk. Haswell et al. (2001) attributed superhumps in XRBs as an effect of changing disk area rather than changes in viscous dissipation in the disk, which might be more visible in the UV; however, this effect was in play for XRB disks dominated by irradiation, which may not be the case here (see below).

In Section 3.3, we fit the dereddened UV continuum spectrum with models of emission from a steady-state thin accretion disk. The models provide qualitatively acceptable fits to the spectral shape. The assumption that the UV emission is dominated by the thin disk is consistent with observations at other wavelengths and with system models. Reynolds et al. (2010) showed that a power law with a slope consistent with optically thin emission from a jet extended from the X-ray regime to longer wavelengths would have a negligible contribution to the optical/NIR flux. Their notional power-law component falls roughly an order of magnitude below our dereddened FUV fluxes. Similarly, an ADAF model fit to Swift J1753.5−0127 also predicts UV emission dominated by the thin disk (Zhang et al. 2010). Finally, Soleri et al. (2010) found that the jet is fainter in Swift J1753.5−0127 than in other hard state XRBs based on a comparison of its radio/X-ray flux ratio with the standard empirical relation. They too attribute the NIR/optical emission to the accretion disk.

Our disk models fit the UV continuum well given vicious dissipation in the disk as the only emission source. Disk models which include irradiation predict a flattening in the SED in the FUV that is inconsistent with our observed spectrum (see, e.g., Figures 7 and 9 of Chiang et al. 2010). This places Swift J1753.5−0127 in the category of "UV-hard" sources as defined by Hynes (2005), who compiled the UV/optical SEDs of several black hole XRBs in outburst and found that the systems either showed rising fluxes in the FUV (the UV-hard sources) or a peak in the NUV with a drop off in flux to shorter wavelengths (the "UV-soft") systems. The UV-hard sources were fit with viscously heated accretion disks while the UV-soft sources were dominated by emission from reprocessing of X-ray irradiation in the disk. (The UV-hard spectra can also be fit by irradiation models if the irradiating source is vertically extended above the disk plane, but the characteristic spectrum in that case remains different from the UV-soft profile; Hynes 2005; Dubus et al. 1999). One system, XTE J1859+226, has shown a transition during the outburst decline from being best fit with irradiation-dominated model spectra to models dominated by viscous heating (Hynes et al. 2002). The X-ray/optical cross-correlation function in Swift J1753.5−0127 also evolved from a clear signature of thermal reprocessing near outburst peak to an unusual profile at later times in which the optical and X-ray emission are anti-correlated, with the optical leading the X-rays (Hynes et al. 2009; Durant et al. 2008). A similar cross-correlation function was seen in XTE J1118+480, another XRB that remained in the low/hard state during its outburst (Kanbach et al. 2001). These correlations indicate a link between optical and X-ray emission, but not one that is explained by simple reprocessing of X-rays in the outer accretion disk.

Because the system parameters for Swift J1753.5−0127 are not well constrained, we could not use our disk model fits to directly determine the mass accretion rate in the disk. However, by setting upper limits on the accretion rate as a fraction of the Eddington luminosity based on the fact that the system did not transition from the hard state to the soft state during the outburst, we were able to place limits on the mass of the black hole and the distance to the system based on the dereddened FUV continuum fluxes. We presented upper limits on the distance to Swift J1753.5−0127 for a range of black hole masses. These values are consistent with those found by Cadolle Bel et al. (2007, note that they present the minimum black hole mass for a given distance while we give the maximum distance for a given mass).

We are in closest agreement with the X-ray predictions for our models in which the disk is face-on rather than inclined. The Cadolle Bel et al. observations were conducted near outburst peak while ours were taken during the ongoing state in which Swift J1753.5−0127 has declined from its peak level but has not returned to quiescence. Accordingly, we expect that the disk accretion rate is lower now than in 2005, which is why our low inclination models (which produce more observable UV flux) are in closer agreement with the earlier black hole mass-distance relation. For a higher inclination, our more recent observations place tighter limits on the distance for a given black hole mass. Our limits are also conservative, since the mass accretion rate should be well below the 5% of Eddington transition luminosity seven years after the initial outburst. The hysteresis effect that can boost the transition luminosity for the hard to soft transition relative to the soft to hard one is a phenomenon of early outburst and will be seen near the peak rather than during the outburst decline (Maccarone & Coppi 2003). Moreover, Soleri et al. (2013) found that the X-ray spectrum of Swift J1753.5−0127 began to soften, but did not fully transition to the soft state, at an X-ray flux that was ≃5 times larger than our observed fluxes.

Although we cannot directly determine the black hole mass from our observations, our black hole mass/distance limits can be compared to current estimates of the distance to Swift J1753.5−0127, which lie roughly in the d = 1–10 kpc range. Zurita et al. (2008) used the non-detection of Swift J1753.5−0127 in optical catalogs prior to outburst to set the quiescent magnitude V_quies > 21 and a distance d > 1 kpc for a M2 main sequence donor star. Their comparison of the outburst luminosities to various empirical relations for XRBs gave a distance range of ≃2.5–8 kpc. The interstellar hydrogen absorption column density in the spectrum, N_H, of Swift J1753.5−0127 is comparable to the total Galactic column density in this direction, also suggesting a distance of d ∼6–7 kpc (Morris et al. 2005; Cadolle Bel et al. 2007; Durant et al. 2009). A 6 kpc distance would correspond to a black hole mass of ⩾10.4 M_☉.

We compared our disk model results to the system parameters adopted by Zurita et al. (2008): M_BH = 12.0 M_☉ and d = 5.5 kpc. If we adopt those values, we must set $\dot{m} \simeq 2 \times 10^{-8}$ M_☉ yr⁻¹, or $0.08 \, \dot{m}_{{\rm Edd}}$, to match the UV flux (for an i = 55° disk). Some of the ADAF models of XRBs have predicted that the accretion rate could be as high as $\dot{m} = 0.08\hbox{--}0.1\, \dot{m}_{{\rm Edd}}$ in the hard state (Esin et al. 1997; Zhang et al. 2010). If the accretion rate is <8% Eddington, the Zurita et al. parameters would require an adjustment to a higher black hole mass or a lower distance to be consistent with the UV fluxes. Once Swift J1753.5−0127 has returned to quiescence, there may be opportunities to place better constraints on the dynamical parameters of the binary system if the donor star can be observed. In that event, it will be of interest to revisit disk model fits to the UV spectrum to place tighter limits on the mass accretion rate through the thin disk during the outburst.

Swift J1753.5−0127 has faded at all wavelengths since 2007, when previous broadband data were acquired (Durant et al. 2009; Soleri et al. 2010). The X-ray spectrum has dropped in luminosity by ≃60%. The optical/NIR data continue the slow decline seen since the 2005 outburst (Shaw et al. 2013). The shape of the SED has not changed dramatically, although the flux decline has been larger in the optical than in the NIR. The thin disk component fit to the UV also fits the optical fluxes reasonably well. There is a slight excess in the NIR compared to the model. Some of the excess NIR flux can be recovered by increasing the outer disk radius above the $0.6 R_{L_{1}}$ value we used, but even disks extending to 90% of the Roche lobe radius don't recover all of the NIR emission. The excess may indicate an additional contribution from either the jet, the hot flow component of an ADAF, or synchrotron emission by non-thermal electrons in the hot corona (Zhang et al. 2010; Veledina et al. 2013).

As noted in Section 3.3, we could not distinguish between accretion disks whose inner radii extend to the ISCO versus those that are truncated at a larger radius from the UV data alone. However, if we compare the disk models to the broadband SED, we find a discrepancy between the observed UV and X-ray fluxes if the accretion disk extends to the ISCO. This is illustrated in Figure 6, where we plot our 12 M_☉ model on the SED. The model that fits the UV fluxes well exceeds the X-ray component by two orders of magnitude.

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There are two ways to resolve this discrepancy. First, if the UV is not dominated by the steady-state thin disk, a disk that extends to the ISCO can be present. The models of Miller et al. (2006) and Reynolds et al. (2010), for example, include a thermal component from a thin disk extending to the ISCO. Their disk components (assuming a 10 M_☉ black hole and 8.5 kpc distance) will not match the UV: they fall a factor of five below our 2011 observed fluxes, which moreover will be fainter than the 2006/2007 data fit by these groups. In this event, the NIR/optical/UV data would need a substantial contribution from an additional component with a power-law shape. In some XRBs, the UV emission is dominated by a single temperature blackbody component with a small emitting area, attributed either to the hotspot where the in falling accretion stream impacts the outer disk or to emission at the transition radius between the thin disk and the ADAF (Froning et al. 2011; McClintock et al. 1995; Hynes & Robinson 2012). These systems were in quiescence, however, not the active state observed in Swift J1753.5−0127, and a single temperature blackbody does not fit the slope of the UV data. Given that Swift J1753.5−0127 is in outburst, has a UV SED consistent with steady-state accretion disk models, and, as discussed above, other emission components (such as the jet or the X-ray hot flow) are unlikely to contribute substantially at these wavelengths, we believe that the UV emission is dominated by the thin disk.

Second, the disk could be truncated at a larger radius than the ISCO. In Figure 6, we show that a disk model whose inner radius is truncated at r_in = 100r_g fits the optical/UV data without exceeding the X-ray flux. The inner radius is larger than the r_in = 10 − 50r_g radii cited by Reynolds et al. (2010) but not as large as the 250r_s (500r_g) radius adopted by Zhang et al. (2010) for their ADAF model fits. The low luminosity in the X-ray band relative to the UV underscores the importance of understanding the energy balance in the low state of XRBs near the black hole: significant mass loss from the system and/or enormous energy loss via advection is required to reconcile the observational discrepancy.

Chiang et al. (2010) also noted that the X-ray data in Swift J1753.5−0127 are under-luminous relative to optical/UV fluxes, with accretion disk model fits to the X-rays under predicting the longer wavelength data. The deviation between the extrapolated X-ray model fits and the optical/UV data increased with time further from outburst peak. They were able to fit the SED with a truncated, irradiated disk to fit the optical/UV and invoked a separate soft component to fit the X-rays. They did not favor that model because the irradiated area of the disk was implausibly small and instead attributed the optical/UV data to synchrotron radiation from the jet. As we noted above, however, the FUV data are inconsistent with the irradiated disk models. Given that the jet in Swift J1753.5−0127 is under-luminous compared to other hard state XRBs, and the radio to optical spectral indices are inconsistent with the compact steady jet extending to the NIR/optical waveband, the evidence argues against jet-dominated emission in the optical/UV (Soleri et al. 2010).