A STRONGLY HEATED NEUTRON STAR IN THE TRANSIENT Z SOURCE MAXI J0556–332

We used data from MAXI/Gas Slit Cameras (GSC) (Mihara et al. 2011) to create a long-term light curve for MAXI J0556–332. The light curve was constructed from 1 day averages in the 2–4 keV band (which had the highest signal-to-noise ratio). Data points with errors on the count rate larger than 0.025 counts s⁻¹ were removed and data were further rebinned to 3 day averages to increase the signal-to-noise. The resulting light curve is shown in Figure 1(a).

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The outburst and (early) quiescent phases of MAXI J0556–332 were monitored densely with the X-Ray Telescope (XRT) on board Swift (Burrows et al. 2005). In total 177 XRT observations were made. A long-term 0.3–10 keV light curve was constructed using the online Swift/XRT data products generator⁸ (Evans et al. 2009); it is shown in Figure 1(b). We performed a spectral analysis of XRT observations that cover the last few weeks of the decay and the first week of quiescence (see Table 1 for details of the four quiescent observations).

The XRT observations were made in Windowed Timing and Photon Counting modes and they were analyzed with HEASOFT v6.12. For the Photon Counting mode observations, the source location was determined with ximage. Source spectra were extracted from a circle with a 40'' radius; background spectra were extracted from an annulus with inner/outer radii of 50''/80'', centered on the source. For the Windowed Timing mode observations, source spectra were extracted from a one-dimensional region with a width of 60'', centered on the pixel with the highest count rate. The background region had a width of 40'' and was located at the end of the one-dimensional image farthest from the source. Exposure maps were created with xrtexpomap and these were used with xrtmkarf to produce ancillary response matrices. We used the same RMF files from the Swift calibration database as were selected by the xrtmkarf task. The AREASCAL keyword in the background spectra was updated to account for vignetting, bad pixels, and hot columns. The spectra were rebinned to a minimum of 20 counts per bin. However, given the low number of source counts in the Photon Counting mode spectra from the quiescent phase (∼75 for each of the four Swift observations listed in Table 1), these spectra were grouped to at least one photon per spectral bin, and we used the C statistic (Cash 1979), modified to account for the subtraction of background counts (the so-called W statistic; Wachter et al. 1979), when fitting them. The spectra were fitted in the 0.3–10 keV band, although for the quiescent spectra there typically were no counts above ∼6 keV.

The RXTE Proportional Counter Array (PCA; Jahoda et al. 2006) was used to monitor the outburst of MAXI J0556–332 in detail as well, until the end of the mission in early 2012 January. A total of 264 pointed observations were made, 262 of which yielded useful data; the other two did not have PCA data.

We extracted background-corrected light curves in five energy bands from standard-2 data from all active proportional counter units (PCUs). The count rates were corrected for changes in the PCA response, using long-term light curves of the Crab for each individual PCU, and then normalized to those of PCU 2. The data were adaptively rebinned in time to achieve a minimum of 16,000 counts per bin in the 2–60 keV band, to obtain a more uniform size in the error bars across different values in count rate; data in other energy bands were rebinned accordingly. We also created a CD and color–intensity diagrams, using the same rebinned data. We define soft color as the net counts in the 4.0–7.3 keV band divided by those in the 2.4–4.0 keV band and hard color (hardness) as net counts in the 9.8–18.2 keV band divided by those in the 7.3–9.8 keV band. The intensity we use for the color–intensity diagrams is the net count rate per PCU in the 2–60 keV band. An RXTE outburst light curve is shown in Figure 1(c), while the corresponding HID is shown in Figure 2(a).

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MAXI J0556–332 was observed seven times with the back-illuminated S3 CCD chip of the Advanced CCD Imaging Spectrometer (ACIS; Garmire et al. 2003) on board Chandra. All observations were made in FAINT mode, with a 1/8 subarray and a frame time of 0.4 s. The data were analyzed using CIAO 4.5 (CALDB 4.5.6) and ACIS Extract version 2012 November 1 (Broos et al. 2010). As a first step, the chandra$\_$repro script was run to reprocess the data from all the observations. The data were checked for periods of enhanced background; only 0.35 ks from observation 14434 had to be removed. Further analysis was performed with the help of ACIS Extract.

An improved X-ray position was obtained (J2000): $\alpha =05^{\rm h}56^{\rm m}46\buildrel{\mathrm{s}}\over{.}27$, δ = −33°10'265, with an estimated 90% uncertainty less than 03. This is consistent with the positions of the optical (Halpern 2011) and radio counterparts (Coriat et al. 2011), as well as the less accurate Swift/XRT X-ray position reported by Kennea et al. (2011).

Source spectra were extracted from near-circular polygon-shaped regions modeled on the Chandra /ACIS point-spread-function (PSF). The source extraction regions had a PSF enclosed energy fraction of ∼0.97 (for a photon energy of ∼1.5 keV) and a radius of ∼19. For all observations except 14227 and 14429 the background was extracted from an annulus with inner radius 59 and outer radius of 133–135. For ObsID 14227 we additionally masked out the readout streak with a 85''×7'' rectangle surrounding the streak, and in this case the outer radius of the background annulus was 148 (same inner radius as for the other ObsIDs). For ObsID 14429 we masked out the readout streak in the same way, but used an inner/outer radius of 10''/166 for the background annulus. Response files were created using the mkacisrmf and mkarf tools in CIAO. The spectra were grouped to a minimum signal-to-noise ratio of 4.5 with the ACIS Extract task ae_group_spectrum and cover the range 0.3–10 keV.

We observed MAXI J0556–332 three times with XMM-Newton, using the EPIC-pn (Strüder et al. 2001) and EPIC-MOS detectors (Turner et al. 2001). The detectors were operated in Extended-Full-Frame and Full-Frame modes, respectively, with the thin filter in front of them. The XMM-Newton data were analyzed with the SAS data analysis package, version 12.0.1. The tasks epproc and emproc were run to produce event files for the pn and MOS observations. All files were inspected for background flares by producing light curves for the entire detectors and only selecting events with PATTERN = 0 (single events) and energies between 10 keV and 12 keV. Data from time intervals with count rates higher than 0.4 counts s⁻¹ (pn) and 0.15 counts s⁻¹ (MOS) were discarded. For the first, second, and third XMM-Newton observations, ∼0%–1%, 30%–40%, and ∼4%–7% of the data was removed, respectively. The resulting exposure times are given in Table 1. To extract spectra we used evselect, with optimal source extraction regions (radii of 20''–45'') having been determined by eregionanalyse. Background spectra were extracted from rectangular regions (pn) or from circular regions (MOS) on the same chips that the source was located on. The SAS tasks arfgen and rmfgen were used to create (ancillary) response files. The resulting source spectra were rebinned using the task specgroup to obtain a signal-to-noise ratio of 4.5 and the energy range was constrained to 0.3–10 keV.

There were strong indications that the spectra of observations 4 and 6 (third and fifth Chandra observations) were affected by residual accretion (see Sections 3.3 and 4). For this reason these two observations were fitted together and separately from the main fit. Given the low number of counts in the Swift spectra, a different fit statistic was used (see Section 2.2), and observations 1a–d were therefore fitted separately as well. The spectra of the remaining observations (2, 3, 5, and 7–11) were fitted simultaneously. All spectral fits were made with XSPEC v12.8.0 (Arnaud 1996). For the absorption component in our spectral models we used tbnew (Wilms et al. 2000)⁹; the abund and xsect parameters were set to "wilm" and "vern" (Verner et al. 1996), respectively. Note that the use of "wilm" abundances typically results in N_H values that are ∼50% higher than with "angr" abundances, as used by Maitra et al. (2011).

In addition, we used the pile-up model of Davis (2001) to correct the Chandra spectra; pile-up fractions in the Chandra spectra were as high as ∼10% in the brightest observations. Note that pile-up in the XMM-Newton and quiescent Swift spectra was negligible (<0.1%). The grade morphing parameter α of the pile-up model could not be constrained very well and was set to 0.6 for all spectra. The actual value of this parameter (0–1) only had minor effects on the resulting fit parameters. For the XMM-Newton spectra in the simultaneous fit the frame-time parameter (i.e., the exposure time for each frame) was set to 10⁻⁶ s to disable the pile-up correction. For the highest-flux Chandra observation (obs. 4; 0.15 counts per frame) the temperature shifted upward by ∼6% due to the addition of the pile-up model; for the lowest-flux Chandra observation (obs. 10; 0.013 counts per frame) the temperature was not affected significantly. The pile-up model was removed before fluxes were calculated. No further mention will be made of the pile-up model in Section 3, where we present our results.

For the simultaneous fits to the XMM-Newton and Chandra spectra, the parameters for the pn and MOS1/MOS2 spectra were tied for each XMM-Newton observation. We further tied the value of N_H between all observations and this was done for the distance parameter of the neutron-star atmosphere model and, when applicable, the index Γ of the power-law component as well. The best-fit values of these parameters were later used for fits to the spectra of observations 1, 4, and 6, with the exception of the power-law index, which was allowed to vary in the fits to the spectra of observations 4 and 6. Quoted errors on the fit parameters correspond to 68.3% confidence limits. The N_H, distance and power-law index were fixed to their best-fit values prior to determining the errors on the temperatures and power-law normalizations. Fixing these parameters allows for more accurate relative temperature measurements, so that the course of the cooling can be followed in more detail, even if the absolute temperatures are not known precisely. We note that the uncertainty on the absolute temperatures is dominated by our poor knowledge of the distance, with the uncertainties in the N_H and power-law index having much smaller contributions.

In Figure 1(b) we show the Swift/XRT 0.3–10 keV light curve of MAXI J0556–332, with each data point representing a single Swift observation. It covers the ∼16 month outburst, from the end of the rising phase until the source had returned to quiescence. In Figure 1(c) we show the RXTE/PCA light curve of MAXI J0556–332, which covers only part of the outburst. The RXTE data points represent averages over periods of 48 s to a few hundred seconds. Strong short-term variations (dips and flares) were present during the early stages of the outburst (first ∼50 days). During the later stages of the outburst moderate flaring was present. The MAXI (Figure 1(a)), Swift and RXTE light curves show an initial decline that resulted in a minimum around day 105. This was followed by a rebrightening of the source by a factor of ∼2.5. After a broad secondary maximum the source showed a prolonged slow decline, with the Swift/XRT count rate decreasing by a factor of ∼4 during a period of ∼250 days. This slow decline was followed by a very rapid decay into quiescence, which will be discussed in more detail in Section 3.2.

To estimate the fluence of the outburst we used the Swift/XRT light curve shown in Figure1(b). We integrated the 0.3–10 keV count rate over the outburst, up to day 480 (see gray vertical line in Figure 1(b)), which we define as the end of the outburst (see Section 3.2). Count rates were converted to unabsorbed 0.01–100 keV fluxes using a conversion factor that we derived from fits to Swift/XRT 0.5–10 keV spectra near the peak of the outburst and during the secondary maximum. Fits were made with a model consisting of a black body (bbody) and a multi-color disk blackbody (diskbb), modified by absorption (tbnew, with N_H set to 4 × 10²⁰ atoms cm⁻², a value close to what we obtain from our fits to the quiescent spectra). This model provides good fits to the spectra and results in conversion factors around 3.5 × 10⁻¹¹ erg s⁻¹ cm⁻² counts⁻¹. While the above spectral model may not be suitable for the harder spectra at low luminosities, for which the conversion factor would likely be larger, the low-luminosity phase of the outburst is short and the effects on our fluence estimate are expected to be very small. Using our conversion factor we obtain a fluence of 2.9× 10⁻² erg cm⁻² and an integrated luminosity (or total radiated energy) of 7.1× 10⁴⁵(d₄₅)² erg, where d₄₅ is the distance to the source in units of 45 kpc (see end of this section and Section 3.3 for various distance estimates). The time-averaged luminosity is 1.7× 10³⁸(d₄₅)² erg s⁻¹, using an outburst duration of ∼480 days. This is close to the Eddington luminosity for a 1.4 M_☉ neutron star (1.8× 10³⁸ erg s⁻¹).

In Figure 2(a) we show the complete HID of the RXTE data (which do not cover the entire outburst). The HID reveals a large patch of data points with no clearly identifiable tracks or branches. However, by first inspecting tracks from single observations and later combining data from subsets of consecutive observations, we were able to identify and construct tracks whose shapes are strongly reminiscent of those of the Z sources. In panels (b)–(e) of Figure 2 we show four examples of such relatively complete tracks, in order of decreasing overall count rates. The time ranges covered by these subsets and the corresponding ObsIDs are listed in Table 2. For two of the subset tracks (b and d) we have labeled the Z source branches. We note that the first and second XMM-Newton observations analyzed by Maitra et al. (2011) were made during the time intervals used for the HID tracks shown in panels (2b) and (2c), respectively.

The shapes of the HID tracks of MAXI J0556–332 gradually evolved as the overall intensity changed. As part of this evolution, the two vertices between the Z source branches showed systematic shifts along paths that could be approximated by straight lines (see gray diagonal lines in Figure 2), except during the brief initial rising phase of the outburst (for which we show no separate tracks). This is similar to what was observed for the HID tracks in the transient Z source XTE J1701–462 (Lin et al. 2009b; Homan et al. 2010). At the highest count rates we observe so-called Cyg-like Z tracks (b and c), in which the flaring branch is a "dipping" flaring branch (although the specific shapes of the tracks shown in panels (2 b) and (c) are not seen in all Cyg-like Z sources), while at lower count rates we observe Sco-like Z tracks, with the flaring branch showing higher count rates than the normal/flaring-branch vertex. In the soft-color/intensity diagram (not shown) the Cyg-like tracks show a strong upturn at the end of the horizontal branch, indications of which can also be seen in the HID track shown in panel (2 c). At the lowest count rates (track e) the horizontal branch has disappeared and the normal branch has become very short. All these types of behavior are very similar to what was seen in XTE J1701–462, and strongly suggest that MAXI J0556–332 is a transient Z source.

Quasi-periodic oscillations (QPOs) have also been detected in MAXI J0556–332 (Belloni et al. 2011). A preliminary timing analysis performed by Homan et al. (2011) revealed low-frequency QPOs between ∼1.5 Hz and ∼35 Hz on the horizontal branch of one of the Cyg-like Z tracks. These QPOs increased in frequency from the horizontal branch upturn towards the horizontal/normal branch vertex, similar to what is seen in other Z sources (see, e.g., Kuulkers et al. 1994; Jonker et al. 2002).

If we assume that similarly shaped Z tracks occur at similar X-ray luminosities in different sources, the HID tracks of MAXI J0556–332 can be used to obtain a rough estimate of the distance to the source. To do this, we compare the count rate levels at which certain track shapes are observed in MAXI J0556–332 to the count rate levels at which similarly shaped tracks are seen in other Z sources. Specifically, we are using the count rates of the normal/flaring-branch vertex, which is present in all four of the subset HID tracks of MAXI J0556–332 shown in Figure 2, as a benchmark. The resulting estimates are by no means exact; for example, the effects of interstellar absorption and binary viewing angle are not corrected for, and the method is based on a simple visual comparison. However, the obtained distances should give us an indication of what distance range needs to be explored for our fits to the quiescent spectra. In Table 3 we list the three Z sources that we use for our distance estimate. We also list the methods that were used to obtain the distances to these three sources. The HID tracks we used for these sources were taken from Fridriksson (2011). Of the four tracks, the one shown in Figure 2(d) is most similar to the tracks of Sco X-1 and LMC X-2, so we used that track for our comparison with those two sources. For XTE J1701–462 we used the tracks from Figures 2(b), (d), and (e), since, like MAXI J0556–332, it showed a variety of track shapes. From our comparison we find a wide range of distances, 28–66 kpc, and this takes into account the distance uncertainties for the comparison sources. We take the average of the three mid-range values in Table 3, 46 kpc, as our best distance estimate and we assume an uncertainty of 15 kpc. While not very constraining, this range rules out the short distance of 1 kpc used by Maitra et al. (2011), which they chose to keep the source well within the Galactic plane. Our distance estimate puts the source well into the Galactic halo, with a distance from the Galactic center of more than 33 kpc and a distance below the plane of more than 12 kpc.

As can be seen from Figure 1(b), after a long, slow decline that started around day 200, the decay of MAXI J0556–332 started to accelerate around day 460 of the outburst. Between days 466 and 480 the Swift/XRT count rate dropped by a factor of ∼60 with an exponential decay timescale of ∼3.3 days. On day 482 the decay had become considerably slower, which we interpret as the source having reached quiescence (see Fridriksson et al. 2010, for similar behavior in XTE J1701–462). The change in decay rate appears to have occurred close to the previous Swift observation (on day 480) and we therefore tentatively set the time of the end of the outburst, t₀, to be MJD 56052.11 (indicated by the gray vertical line in Figure 1(b)), which is the start time of Swift/XRT observation 00032452003.

The early quiescent phase of MAXI J0556–332 was well covered with Swift; considerable variability can be seen in Figure 1(b) in the form of small "flares", lasting several days, on top of a steady, slow decline. During these flares the Swift/XRT count rate typically went up by factors of two to three. Indications of similar variability can still be seen around ∼280 days into quiescence. A much stronger reflare started ∼170 days into quiescence. During this event the Swift/XRT count rate increased by a factor of more than 600 and from the MAXI light curve in Figure 1(a) we estimate the duration to have been ∼55–60 days. Judging from the MAXI light curve, the Swift/XRT observations were done around the peak of the reflare; using the same spectral model as in Section 3.1, we estimate the peak luminosity (0.01–100 keV) to have been ∼8.0 × 10³⁷(d₄₅)² erg s⁻¹. Given the sparse Swift coverage of the large reflare it is hard to obtain an accurate measurement of its fluence. Using the average MAXI count rate during the reflare, a MAXI-to-Swift/XRT count rate conversion factor of 2.9× 10², and the same Swift/XRT-to-flux conversion factor as used earlier, we estimate the fluence to be 8.7 × 10⁻³ erg cm⁻², which is a factor of ∼33 smaller than the fluence of the main outburst. We note that the duration and the time-averaged luminosity (∼4.4× 10³⁷(d₄₅)² erg s⁻¹) of the reflare are similar to those of the strongest outbursts of ordinary transient NS-LMXBs, such as Aql X-1 and 4U 1608–52. We also note that the time-averaged luminosity of the reflare is about ∼65% of that of the 11 week outburst of IGR J17480–2446 (∼6× 10³⁷ erg s⁻¹; Linares et al. 2012), during which moderate crustal heating occurred (Degenaar et al. 2011a, 2013).

We started modeling the quiescent spectra of MAXI J0556–332 by simultaneously fitting our main set of spectra (i.e., those from observations 2, 3, 5, and 7–11) with single-component models. An absorbed power law (pileup*tbnew*pegpwrlw) with Γ tied between observations results in a poor fit, $\chi ^2_{\rm red}$(degrees of freedom (dof)) = 2.75 (433), with N_H = (5.1 ± 0.1)× 10²¹ atoms cm⁻² and Γ = 3.17 ± 0.03. Allowing the power-law index to vary between observations results in a small improvement, $\chi ^2_{\rm red}$ (dof) = 1.99 (426), with a similar N_H and indices between 2.4 and 3.6.

Next, we tried several absorbed neutron-star atmosphere models. We only considered hydrogen atmosphere models; this is justified by the presence of strong hydrogen lines in the optical spectra (Cornelisse et al. 2012), which ensures that hydrogen was present in the accreted material. For these models we always assumed a neutron-star mass M_ns of 1.4 M_☉ and a neutron-star radius R_ns of 10 km, similar to what we used in our previous works. These values were used to convert the obtained unredshifted effective temperatures, T_eff, to redshifted effective temperatures as measured by an observer at infinity, $T_\mathrm{eff}^\infty =T_\mathrm{eff}/(1+z)$. Here, 1 + z = (1 − R_S/R_ns)^−1/2 is the gravitational redshift factor, with R_S = 2 GM_ns/c² being the Schwarzschild radius. For the mass and radius we used this factor is ∼1.306.

First we performed fits with the neutron-star atmosphere model nsatmos of Heinke et al. (2006), pileup*tbnew* nsatmos, with the temperatures allowed to vary between observations and the distance left free. This resulted in a poor fit as well, $\chi ^2_{\rm red}$ (dof) = 2.32 (433), with the temperatures of observations 2, 3, and 5 pegging at their maximum allowed value, log (kT) = 6.5, which is set by the omission of Comptonization in the nsatmos model. For this fit we find a distance of 21.6$^{+0.2}_{-0.6}$ kpc. The distance has to be reduced to ∼18.8 kpc to avoid the pegging of the temperatures, but this results in a worse fit: $\chi ^2_{\rm red}$ (dof) = 2.48 (434). Leaving the distance free and including a power law improves the fit ($\chi ^2_{\rm red}$ (dof) = 1.37 (424); distance is 27.2$^{+0.8}_{-0.5}$ kpc), but it does not resolve the pegging issue for observations 2, 3, and 5. We therefore switched from nsatmos to the neutron-star atmosphere model of Zavlin et al. (1996), nsa, which does take into account the effects of Comptonization and allows for higher temperature values. This model, pileup*tbnew*nsa (hereafter model I), resulted in a greatly improved fit compared to the nsatmos model, with $\chi ^2_{\rm red}$ (dof) = 1.04 (433) and a χ² probability, P_χ, of 0.29. For this fit we obtain N_H = (3.5 ± 0.6)× 10²⁰ atoms cm⁻², a distance of 46.5$^{+1.0}_{-1.6}$ kpc, and a $T_\mathrm{eff}^\infty$ range of 190–329 eV.

Adding a power-law component (with indices tied and all normalizations allowed to vary) to the model, pileup*tbnew*(nsa+pegpwrlw), as was necessary to obtain good fits for the quiescent spectra of XTE J1701–462 (Fridriksson et al. 2010), leads to $\chi ^2_{\rm red}$ (dof) = 0.99 (424) and P_χ = 0.58. To test the significance of this small improvement we performed a posterior predictive p-value (ppp) test (Protassov et al. 2002; Hurkett et al. 2008; Cackett et al. 2013a). We simulated 1000 sets of spectra, based on the best fit with model I. These sets of spectra were then fit with model I and with the above model that included the power-law component. For none of the 1000 simulated sets of spectra, the latter model yielded an improvement in χ² as large as for the observed set of spectra. This suggest that the minor improvement in $\chi ^2_{\rm red}$, as the result of adding a power law, is statistically highly significant. However, the obtained power-law index of 0.3 ± 0.4 is extremely low and likely unphysical. Fixing the power-law index to a more reasonable value of 1.0 results in $\chi ^2_{\rm red}$ (dof) = 1.00 (425) and P_χ = 0.52; a ppp test indicates that this is still a significant improvement with respect to the fits with model I, with again none of the 1000 simulated sets of spectra yielding a χ² improvement as large as the actual set of spectra. We refer to the model with Γ fixed to a value of 1.0 as model II. For this model we obtain N_H = (4.4$^{+0.7}_{-0.4})\times 10^{20}$ atoms cm⁻², a distance of 43.6$^{+0.5}_{-1.5}$ kpc, and a $T_\mathrm{eff}^\infty$ range of 184–307 eV. We note that fits with power-law indices fixed to values closer to those measured in other quiescent NS-LMXBs (e.g., Wijnands et al. 2005; Fridriksson et al. 2010) no longer result in improvements compared to model I (i.e., without a power-law component); fits with Γ = 1.5 and Γ = 2.0 give $\chi ^2_{\rm red}$ (dof) = 1.04 (425) and $\chi ^2_{\rm red}$ (dof) =  1.05 (425), respectively.

The N_H values obtained with models I and II are only slightly higher than the N_H values in the direction of MAXI J0556–332 obtained from the H i surveys of Dickey & Lockman (1990) and Kalberla et al. (2005; ∼2.6× 10²⁰ atoms cm⁻² and ∼2.9× 10²⁰ atoms cm⁻²) and fall in the range obtained by Maitra et al. (2011) from fits to XMM-Newton /RGS spectra, (∼2.1–4.6× 10²⁰ atoms cm⁻², using angr abundances). In Table 4 we show how N_H and other fit parameters vary as we fix the distance to several different values. For this we used nsa models with and without a power-law component; for comparison, results from models I and II are shown as well. As can be seen, there is a strong dependence of most parameters on the distance; as the distance increases, the column density decreases, the temperatures increase, and (for model II) the power-law component becomes less steep and its flux decreases. The quality of the fits becomes very poor when moving away from the best-fit distances of models I and II.

Table 4. Spectral Fit Results for Different Distances

Model	d	NH	Γ	$kT_{\rm eff}^{\infty }$	FPLb	$\chi ^2_{\rm red}$	Pχ
	(kpc)	(1020 atoms cm−2)		(eV)a		(dof)
nsa	10c	35.4$^{+0.6}_{-1.0}$	⋅⋅⋅	105–161	⋅⋅⋅	4.34 (434)	4× 10−179
nsa	20c	19.2$^{+0.4}_{-0.6}$	⋅⋅⋅	134–218	⋅⋅⋅	2.41 (434)	2× 10−52
nsa	30c	10.8$^{+0.3}_{-0.6}$	⋅⋅⋅	156–264	⋅⋅⋅	1.51 (434)	4× 10−11
nsa	40c	5.9 ± 0.4	⋅⋅⋅	178–306	⋅⋅⋅	1.10 (434)	8.3× 10−2
nsa (I)	46.5$^{+1.0}_{-1.6}$	3.5 ± 0.6	⋅⋅⋅	190–329	⋅⋅⋅	1.04 (433)	0.29
nsa	50c	2.3 ± 0.4	⋅⋅⋅	196–342	⋅⋅⋅	1.05 (434)	0.21
nsa	60c	0.0$^{+0.6}_{-0.0}$	⋅⋅⋅	213–377	⋅⋅⋅	1.27 (434)	1× 10−4
nsa + pegpwrlw	10c	37.5 ± 0.5	2.58$^{+0.01}_{-0.05}$	<118d	0.7–15.6	2.33 (425)	3× 10−47
nsa + pegpwrlw	20c	18.0$^{+0.7}_{-0.3}$	1.48 ± 0.10	131–195	0.22–7.2	1.68 (425)	5× 10−17
nsa + pegpwrlw	30c	9.8 ± 0.3	0.94 ± 0.17	156–249	0.13–5.2	1.20 (425)	2.5× 10−3
nsa + pegpwrlw	40c	5.6 ± 0.4	0.4 ± 0.3	177–297	0.0–3.7	1.00 (425)	0.52
nsa + pegpwrlw	43.6$^{+1.0}_{-1.7}$	4.3 ± 0.5	0.3 ± 0.4	185–312	0.0–3.3	0.98 (424)	0.58
nsa + pegpwrlw (II)	43.6$^{+0.5}_{-1.5}$	4.4$^{+0.7}_{-0.4}$	1.0c	184–307	0.0–3.2	1.00 (425)	0.52
nsa + pegpwrlw	50c	2.2 ± 0.4	0c	196–337	0.0–2.6	1.04 (426)	0.31
nsa + pegpwrlw	60c	0.0$^{+0.6}_{-0.0}$	0c	213–374	0.0–1.3	1.29 (426)	5× 10−5

Notes. Observations 1, 4, and 6 were excluded from the fits. All fits used a neutron-star mass M_ns of 1.4 M_☉ and a neutron-star radius R_ns of 10 km. ^aTemperature range. ^bPower-law flux range (0.5–10 keV, 10⁻¹³ erg s⁻¹ cm⁻²). ^cParameter was fixed during fit. ^dThe temperatures of several observations peg at the lowest allowed value of ∼7 eV. The reported maximum value is for obs. 8.

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While fits with model I yield acceptable fits for our main set of spectra (and the spectra of observation 1), this is not the case for the two flare observations (obs. 4 and 6). Fitting the spectra of these two observations simultaneously with model I and keeping N_H and distance fixed to the values obtained from our main set of spectra, we obtain $\chi ^2_{\rm red}$ (dof) = 2.06 (248). Adding a power law with the indices tied leads to a large improvement, $\chi ^2_{\rm red}$ (dof) = 1.11 (245) and P_χ = 0.10, with Γ = 1.34 ± 0.05. For fits with model II we obtain Γ = 1.26 ± 0.05 for these two observations ($\chi ^2_{\rm red}$ (dof) = 1.17 (245)). In Figure 3 we show example fits to a flare (obs. 4) and non-flare spectrum (obs. 5) with model II. As can be seen, the relative contribution of the power-law component is much larger in the flare observation.

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The full fit results of models I and II, including those of observations 1, 4, and 6, are reported in Tables 5 and 6, respectively. The $\chi ^2_{\rm red}$ (dof) for the fits to the spectra of observation 1 were 1.03 (262) for model I and 0.99 (261) for model II. The evolution of the unabsorbed 0.5–10 keV flux, the neutron-star temperature, the 0.5–10 keV power-law flux, and fractional power-law contribution in the 0.5–10 keV band are shown in Figure 4. As can be seen from Tables 5 and 6 and Figure 4, there is an overall monotonic decay of the 0.5–10 keV luminosity and the temperature that is interrupted during observations 4 and 6. In those two observations there is a clear increase in both the thermal and power-law fluxes. As we discuss in Section 4, these two observations were likely affected by increases in the quiescent accretion rate. The fractional contribution of the power-law component as obtained from model II was quite high in the first few observations, with values in the range ∼10%–50%, but after day ∼100 it has remained below 10%. The power-law and nsa fluxes are strongly correlated for model II, as can be seen from the values in Table 6.

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Table 5. Detailed Spectral Fit Results for Model I (pileup*tbnew*nsa)

Obs.	Days Since t0	$kT_{\rm eff}^{\infty }$	FTota	FPLa
		(eV)
1	5.5	336 ± 6	12.7 ± 1.6	⋅⋅⋅
2	16.1	329 ± 3	9.6 ± 0.3	⋅⋅⋅
3	23.3	311 ± 3	7.6 ± 0.3	⋅⋅⋅
4b	31.9	386$^{+4}_{-10}$	34.4 ± 0.9	16.3$^{+2.7}_{-1.3}$
5b	51.1	292 ± 2	5.81 ± 0.15	⋅⋅⋅
6	85.4	327 ± 5	23.4 ± 0.6	14.1 ± 1.1
7	104.5	260.4 ± 0.9	3.66 ± 0.05	⋅⋅⋅
8	134.9	250.7 ± 1.0	3.12 ± 0.05	⋅⋅⋅
9	150.9	250 ± 2	3.08 ± 0.10	⋅⋅⋅
10	291.8	216 ± 2	1.67 ± 0.06	⋅⋅⋅
11	497.1	190.3 ± 1.0	0.99 ± 0.02	⋅⋅⋅

Notes. ^aUnabsorbed 0.5–10 keV flux (10⁻¹³ erg s⁻¹ cm⁻²). ^bFor these observations an additional power law was added to the fit model (pileup*tbnew*(nsa+pegpwrlw)).

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Table 6. Detailed Spectral Fit Results for Model II (pileup*tbnew*(nsa+pegpwrlw))

Obs.	Days Since t0	$kT_{\rm eff}^{\infty }$	FTota	FPLa
		(eV)
1	5.5	308 ± 11	12.7 ± 0.2	5 ± 3
2	16.1	307 ± 4	11.3 ± 0.6	3.2 ± 0.6
3	23.3	298 ± 3	8.0 ± 0.4	0.8 ± 0.4
4	31.9	365$^{+5}_{-9}$	35.7 ± 1.0	19.2$^{+2.5}_{-1.5}$
5	51.1	276 ± 3	6.5 ± 0.3	1.3 ± 0.3
6	85.4	320 ± 5	23.6 ± 0.7	13.9 ± 1.1
7	104.5	252.6 ± 1.0	3.70$^{+0.11}_{-0.03}$	0.04$^{+0.10}_{-0.04}$
8	134.9	243.6 ± 1.0	3.14$^{+0.11}_{-0.01}$	0.0$^{+0.05}_{-0.00}$
9	150.9	241 ± 2	3.2 ± 0.2	0.2 ± 0.2
10	291.8	208 ± 2	1.71$^{+0.13}_{-0.05}$	0.06$^{+0.12}_{-0.06}$
11	497.1	184.3 ± 1.1	1.02 ± 0.03	0.04 ± 0.04

Note. ^aUnabsorbed 0.5–10 keV flux (10⁻¹³ erg s⁻¹ cm⁻²).

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In Figure 5 we compare the temperature evolution seen in MAXI J0556–332 with that of other cooling-neutron-star systems. We also show fits to the data with an exponential decay to a constant. We stress that these are simply phenomenological fits to extract some basic characteristics for a comparison of the different cooling curves; fits with theoretical models are beyond the scope of the current paper. Fit values are given in Table 7 and were taken from the literature (see references in table); for MAXI J0556–332 we performed fits to the temperatures obtained with models I and II (excluding observations 4 and 6). The timescales measured for MAXI J0556–332 are among the shortest seen, while the temperature drop it has shown is by far the largest of the sources in our sample. There are no clear indications in the cooling curve of MAXI J0556–332 that the source is close to reaching a plateau, so the high baseline level from the fit should be treated more as an upper limit. To investigate the effect of a change in distance on the fit parameters, we also fitted the temperature data from spectral fits with the nsa model and the distance fixed to 20 kpc. For this case we find an exponential decay timescale τ of 180 ± 7 days, decay amplitude A of 92.0 ± 1.2 eV, and constant level B of 129.3 ± 1.1 eV. Compared to the model I cooling curve the decay timescale is slightly longer, while the normalization and constant level are both significantly lower.

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