X-Ray Reflection and an Exceptionally Long Thermonuclear Helium Burst from IGR J17062-6143

MAXI (Matsuoka et al. 2009) was installed on the International Space Station (ISS) in 2009. We employ data from the Gas Slit Camera (GSC; Mihara et al. 2011; Sugizaki et al. 2011), which consists of 12 xenon-filled proportional counters that are sensitive in the 2–30 keV energy range and have a combined collecting area of 5350 cm². A slit and slat collimator restricts the field of view to a narrow elongated region of 3° × 80°. 85% of the sky is scanned each 92 minute orbit of the ISS. At the time of the burst, IGR J17062-6143 dominated the X-ray flux near the source position, and no other nearby transients were active. We extract source spectra for the triggering GSC scan on 2015 November 3 10:29 UT as well as the subsequent scan (Table 1).⁶ A scan preceding the trigger by 92 minutes had not detected the burst. The source is visible for 1 minute during each scan, and the effective area peaks at 3 cm² in the middle of the scans. The first spectrum has 893 counts, whereas the second consists of only 90 counts. The background and instrument response are modeled with tools provided by the instrument team (Sugizaki et al. 2011).

The Swift observatory was launched in 2004 (Gehrels et al. 2004). Its main pointed X-ray instrument is the X-Ray Telescope (XRT; Burrows et al. 2005). The XRT is a CCD imager sensitive in the 0.2–10 keV band with an effective area of 120 cm² at 1.5 keV. Starting 3 hr after the first MAXI/GSC scan, Swift performed a series of pointed observations of IGR J17062-6143 (Iwakiri et al. 2015). A total of 75.3 ks were collected over 11.7 days (Table 1; Figure 1). The XRT observations were performed in either Photon Counting (PC) mode or Windowed Timing (WT) mode. Whereas in PC mode the full CCD image is stored, in WT mode a reduced 1D image is read out to increase the time resolution. We use xrtpipeline to extract spectra in the 0.5–10 keV band and light curves from a circular region with a radius of 70.8 arcsec (30 pixels) centered on the source, and from an off-source region of the same size as the background. The standard selection of event grades are used: 0–12 for PC mode and 0–2 for WT mode. The PC mode data suffer from pile-up. We exclude the piled-up center of the point-spread-function. The size of this region is determined by comparing the observed spatial distribution of events to a King profile that describes the expected point-spread-function (Moretti et al. 2005): the excluded regions have a radius ranging from 20 arcsec at the highest flux to 9 arcsec at the lowest flux. The detector light curves are inspected for background flares. The ancillary response is generated by xrtpipeline, and we employ the appropriate response matrices provided by the instrument team: swxpc0to12s6_20130101v014.rmf for PC mode and swxwt0to2s6_20131212v015.rmf for WT mode. The data are labeled with an Observation Identifier (ObsID), and each ObsID represents several consecutive satellite orbits. For the first two ObsIDs, which cover the initial burst decay, we create separate spectra for each orbit. For the rest, one spectrum per ObsID is generated. The resulting XRT spectra each have between 840 and 13,175 counts, with a median value of 5003 counts. In Section 4.3 we demonstrate that these spectra provide sufficient time resolution to resolve the cooling trend of the burst.

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Swift's other pointed instrument is the Ultraviolet/Optical Telescope (UVOT; Roming et al. 2005), which records CCD images in the 170–650 nm wavelength range. UVOT has seven filters to select a narrow wavelength interval from this range, four of which were used in the different pointings (Figure 1 bottom). UVOT magnitudes are extracted using the uvotmaghist tool from the same source and background locations as employed for the XRT. A standard aperture size of 5 arcsec is used, and approximate aperture corrections are applied by the uvotsource tool.

Swift's Burst Alert Telescope (BAT; Barthelmy et al. 2005) is a coded-mask imager with a wide field of view of 1.4 sr and a 15–150 keV band pass. We employ BAT in combination with MAXI to illustrate the long term evolution of the persistent flux (Figure 2).⁷ The source was first detected at the onset of its outburst in 2006, and it has been accreting continuously at a low rate. MAXI operations started in 2009. We are especially interested in the period between the burst observed in 2012 (Degenaar et al. 2013) and the one in 2015 (studied in this paper). To quantify the variability in that time interval, we take the root mean squared of the photon flux at a 70 day resolution: it is 38% of the mean for BAT and 22% for MAXI. The corresponding hardness ratio from the 4–20 keV and 2–4 keV MAXI bands does not exhibit significant variability. We take this as an indication that the spectral shape did not change substantially, and we extract one MAXI/GSC spectrum from all observations in that interval combined (Table 2). We restrict the energy range to 2–10 keV where the source is detected most clearly, collecting a total of 5.5 × 10³ net source counts. In the same period, the source was also observed with the following instruments.

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The Chandra X-ray Observatory (Weisskopf et al. 2000) was launched in 1999. Chandra observed the source on 2014 October 25 and 27 for a total of 93 ks with the High Energy Transmission Grating Spectrometer (HETGS; Canizares et al. 2005), which includes the High Energy Grating (HEG) and the Medium Energy Grating (MEG). We use the spectra and response matrices provided in the Chandra Grating-Data Archive and Catalog (TGCat; Huenemoerder et al. 2011).⁸ The data products were extracted using a narrow mask for better flux correction of the HEG below 6.9 keV. The background was extracted from an off-source position. No significant variability is apparent during the pointings. We will analyze the 0.5–10 keV spectra of the +1, −1 orders of the MEG and HEG for both pointings, which have a total of 1.8 × 10⁵ counts (91% of the counts in all orders). The MEG and HEG spectra of both orders for each pointing will be fit jointly.

The Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al. 2013) has observed the hard X-ray sky since 2012 with its focusing optics and two imaging Focal-Plane Modules: FPMA and FPMB. NuSTAR observed IGR J17062-6143 on 2015 May 06 for 70.1 ks. The data is reprocessed with nupipeline version 0.4.5 using calibration data with the time stamp 2016 July 31, creating spectra for both modules in the 3–50 keV band from a circular extraction region with a radius of 65 arcsec. The combined FPMA and FPMB spectra have 1.5 × 10⁵ counts. Background spectra are extracted from an off-source position, and we find that the background dominates the signal at energies in excess of ≳50 keV. During the pointing, the count rate is consistent with being constant.

As part of our spectral model, interstellar absorption is described by the Tübingen–Boulder model with abundances from Wilms et al. (2000). The tool NHtot ⁹ calculates the Galactic absorption column of atomic (Kalberla et al. 2005) and molecular (Schlegel et al. 1998) hydrogen using radio and infrared maps, respectively (Willingale et al. 2013). In the direction of IGR J17062-6143, within 1° from the source, we find a mean value of N_H = 1.58 × 10²¹ cm⁻².

For bright low-mass X-ray binaries (LMXBs), absorption lines and edges have been used to quantify the interstellar absorption column (e.g., Pinto et al. 2010). A study of the Chandra gratings spectra of the persistent emission did not find significant absorption features that could be used for this purpose (Degenaar et al. 2017). Alternatively, N_H may be determined as part of the fit to the continuum spectrum. Indeed, N_H measured from XRT spectra of the 2012 burst from IGR J17062-6143 is consistent with NHtot (Degenaar et al. 2013). The best-fitting value is, however, dependent on the model for the continuum spectrum, because a model that adds more flux at low energies (E ≲ 2 keV) requires a larger N_H to compensate (see, e.g., the fits by Degenaar et al. 2017). Because N_H cannot be robustly constrained by the X-ray spectra, we fix N_H to the value from NHtot, under the assumption that there is no substantial contribution from a local absorber (e.g., Degenaar et al. 2017).

We employ models of reflection off a photoionized accretion disk that is illuminated by either a power law or a blackbody spectrum. Both models implement the disk as a slab of constant number density n and with ionization parameter $\xi \equiv 4\pi F/n$, where F is the irradiating flux. We will report $\mathrm{log}\xi$, with ξ in units of erg s⁻¹ cm.

The reflection spectrum has a dependence on the composition of the reflecting material. For the ultra-compact X-ray binary (UCXB) 4U 1820–30, Ballantyne (2004) calculated models of a reflected blackbody assuming a helium-rich composition with metals at solar abundance. The accretion composition of IGR J17062-6143 is unknown at present, but intermediate duration bursts and accretion at a constant low rate have been associated with UCXBs (e.g., in't Zand et al. 2007). It is, therefore, plausible that IGR J17062-6143 is of a similar nature as 4U 1820–30, and the same reflection models are also applicable here. The models assume a density of n = 10¹⁵ cm⁻³, although n = 10²⁰ cm⁻³ may be more realistic for the inner disk. The density dependence is most pronounced for E ≲ 3 keV (Figure 3; Ballantyne 2004). It is unimportant when fitting, e.g., RXTE/PCA data (Ballantyne & Strohmayer 2004; Keek et al. 2014b) or MAXI data, and we use the Ballantyne (2004) models for the latter. For the XRT spectra, however, we calculate a new grid of models with n = 10²⁰ cm⁻³, using the same procedure as Ballantyne (2004). The new grid covers a range of blackbody temperatures 0.2 keV ≤ kT ≤ 1.2 keV as well as $1.5\leqslant \mathrm{log}\xi \leqslant 3.0$.

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For reflection of a power law we employ version 0.4c of the relxill model (Dauser et al. 2014; García et al. 2014). relxill provides the illuminating power law with photon index Γ and a high energy cutoff as well as the xillver model of reflection off a photoionized accretion disk (García et al. 2013). The flux ratio of the reflection and illumination components is given by the reflection fraction, f_refl. xillver assumes a density of n = 10¹⁵ cm⁻³ and a composition based on solar with a variable iron abundance. Unfortunately, the composition and density do not match the values that we preferred for blackbody reflection. Therefore, we only apply this model to E > 3 keV, where the effect of these parameters is minimal (see Figure 3 for an illustration using blackbody reflection).

relxill further takes into account relativistic effects that smooth the reflection spectrum using the relline code (Dauser et al. 2010), depending on the inclination angle of the disk with respect to the line of sight and the emissivity profile of the disk. We apply the same smoothing to the blackbody reflection models using the relconv convolution model, which is also based on the relline code.

All persistent MAXI, Chandra, and NuSTAR spectra are fit jointly, allowing for multiplication factors between MAXI, NuSTAR FPMA, NuSTAR FPMB, Chandra observation 15749, and Chandra observation 17543 (using XSPEC model constant). The factor for the latter is fixed to unity. We first fit a model that includes a blackbody with temperature kT and normalization K_bb, as well as a power law with photon index Γ. Instead of the power law normalization, we report the 0.5–10 keV unabsorbed flux of the power law provided by a cflux component in XSPEC. Interstellar absorption is implemented as described in Section 2.3. The complete XSPEC model is constant∗TBabs(bbodyrad + cflux∗powerlaw). It provides a reasonable fit to the data (Figure 4 top). The residuals of the Chandra/MEG data show some features near 1 keV, but the HEG is less sensitive at those energies and its spectra do not exhibit them. The residuals for the NuSTAR data show an emission line near 6.4 keV and a broad excess at E > 20 keV, which may be the Fe Kα line complex and the Compton hump, respectively (second panel of Figure 4), that are known to be produced by photoionized reflection. For NuSTAR we exclude the parts of the spectra where reflection features appear: 6.0 keV < E < 7.5 keV and 20.0 keV < E < 50 keV. In principle the reprocessing of the spectrum by reflection can also influence the measured continuum parameters such as Γ, but we find this not to be an important effect in this case (see also the discussion in Keek & Ballantyne 2016). The best-fitting parameter values are presented in Table 3. The scaling factor for Chandra pointing 15749 is consistent with the ratio of the count rates in the two Chandra pointings of 0.981. The ratio of the factors for NuSTAR FPMA and FPMB is 1.02 ± 0.02: the two spectra are consistent. The scaling factor for MAXI indicates that the long-term average flux was a bit lower than at the times of the Chandra and NuSTAR pointings. Furthermore, the spectrum is dominated by the power law: the ratio of the 0.5–10 keV power law flux and the bolometric blackbody flux is 4.6 ± 0.3.

Table 3.  Fit of the Persistent Spectra with a Blackbody and Power Law

bbodyrad
kT(keV)	0.456 ± 0.005
${K}_{\mathrm{bb}}{(\mathrm{km}/10\mathrm{kpc})}^{2}$	48 ± 3
powerlaw
Γ	2.159 ± 0.008
${F}_{\mathrm{po}}({10}^{-10}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2})$ a	1.03 ± 0.02
constant	scaling relative to Chandra 17543
Chandra 15749	0.974 ± 0.007
NuSTAR/FPMA	0.923 ± 0.010
NuSTAR/FPMB	0.907 ± 0.010
MAXI	0.54 ± 0.04
${\chi }_{\nu }^{2}(\mathrm{degrees}\,\mathrm{of}\,\mathrm{freedom})$	0.58(9455)

Note.

^aUnabsorbed flux in the 0.5–10 keV band for Chandra ObsID 17543.

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To measure the bolometric flux, the model needs to be extrapolated outside of the combined instrument bands. The power law component poses a problem, as it strongly increases toward lower energies. A power law component from accreting compact objects is often explained as the result of inverse Compton scattering in an accretion disk corona. In our case, flux from the blackbody component could be Comptonized by hot electrons in a corona. In the spectral model we replace the power law by the simpl model (Steiner et al. 2009) convolved with the blackbody. This is an empirical Comptonization model that takes a "scattering fraction" f_sc of the blackbody flux, and produces a power law with photon index Γ toward higher energies from Compton upscattering. Toward lower energies, the downscattered flux falls off quickly with energy. A cflux component is used to measure the total unabsorbed bolometric flux in the 0.01–100 keV range. The complete XSPEC model becomes constant∗TBabs∗cflux∗simpl∗bbodyrad. The quality of the fit is similar to the previous fit (Table 4). The largest difference is a lower kT: simpl rolls off at the lower energies, and the blackbody moves to lower energies to compensate. In turn, the flux is now underpredicted around ∼3 keV (third panel of Figure 4). If Comptonization of the blackbody is the correct interpretation of the power law at higher energies, the excess at lower energies must be produced by another process. Photoionized reflection off the accretion disk could produce this in combination with the Fe Kα line near 6.4 keV and the Compton hump.

Table 4.  Fit of the Persistent Spectra with a Blackbody and Simpl

bbodyrad
kT(keV)	0.298 ± 0.006
simpl
Γ	2.250 ± 0.007
fsc	0.664 ± 0.013
constant	scaling relative to Chandra 17543
Chandra 15749	0.973 ± 0.007
NuSTAR FPMA	0.882 ± 0.010
NuSTAR FPMB	0.865 ± 0.010
MAXI	0.54 ± 0.04
Fbol(10−10 erg s−1 cm−2)a	1.70 ± 0.02
${\chi }_{\nu }^{2}(\mathrm{degrees}\,\mathrm{of}\,\mathrm{freedom})$	0.62(9455)

Note.

^aUnabsorbed bolometric flux in the 0.01–100 keV band for Chandra spectrum 17543.

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We test the reflection interpretation using the relxill model (Section 2.4), with the complete XSPEC model being constant∗TBabs(bbodyrad + cflux∗relxill). It is a complex model that, when fit to data of modest quality, presents multiple degenerate solutions. For example, there are eight parameters that shape the Fe Kα line. Moreover, several potentially important effects are not taken into account, such as the dependence on the density of the disk and the low-energy turn-off of the illuminating power law (fixed at 0.1 keV; García et al. 2013). In fitting this model, one runs the risk of certain parameters taking on unphysical values in order to compensate for these deficiencies. Indeed, when left unconstrained, the fit prefers a maximally spinning neutron star (a = 1) and an iron abundance of the disk of 10 times solar (the maximal value provided by the model; see also Degenaar et al. 2017). Therefore, we fix several parameters to reasonable values. We assume a solar iron abundance. The disk emissivity is taken to decrease with the third power of the radius, and the disk's outer radius is fixed at a large value of 400 R_g. As no eclipses or dipping are apparent in the light curves, the disk's inclination is likely less than ∼60°: we choose a value of 30°. Similarly, the fastest spinning neutron star known in an LMXB has spin a ≃ 0.3 (e.g., Degenaar et al. 2015): we choose a value of a = 0.15. During the fits, the high energy cutoff pegs at the domain boundary of 1000 keV. Therefore, we fix the cutoff energy to this value. Furthermore, the mentioned dependencies of the reflection spectrum on density and low-energy turn-off are strongest at E ≲ 3 keV (Section 2.4). We therefore limit the fit to the NuSTAR spectra in their full 3.0–50.0 keV band.

We perform a fit with these constraints (Table 5), which is largely consistent with the results from Degenaar et al. (2017). The blackbody parameters are consistent within 1σ with the fit of the blackbody + power law model (Table 3), whereas the power law's Γ is 5% smaller. The inner disk radius is large: R_in ≃ 210 R_g. The width of the Fe Kα line is influenced by R_in as well as the neutron star spin and the disk's inclination. Repeating the fit for spin 0 < a < 0.3 and for inclination angles up to 60° always leads to similarly large R_in ≳ 10² R_g. A local minimum in χ² is present at $\mathrm{log}\xi \simeq 1.6$ and a global minimum at $\mathrm{log}\xi =3.28\pm 0.08$. The latter indicates that the reflecting material is highly ionized. The reflection model provides a good description of the Fe Kα line (Figure 4 bottom), but a minor part of the Compton hump remains visible in the residuals; its precise peak energy depends on the density of the reflector (García et al. 2016). Although we only fit to the NuSTAR spectra, we also show the residuals of a Chandra spectrum with respect to the best-fitting model (Figure 4 bottom). The features near 1 keV remain visible. This part of the spectrum is most sensitive to density, or alternatively these features could be produced by a local warm absorber. We refer to Degenaar et al. (2017) for an in-depth discussion of the line features.

Table 5.  Fit of the NuSTAR Persistent Spectra with a Blackbody and a Reflected Power Law

bbodyrad
kT(keV)	0.48 ± 0.02
Kbb(km/10 kpc)2	44 ± 14
relxill
Γ	2.060 ± 0.013
$\mathrm{log}\xi$	3.28 ± 0.08
frefl	0.31 ± 0.04
Rin(102 Rg)	${2.1}_{-1.3}^{+1.9p}$
${F}_{3-50\mathrm{keV}}({10}^{-10}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2})$ a	0.716 ± 0.004
constant	scaling relative to FPMA
NuSTAR FPMB	0.980 ± 0.006
${\chi }_{\nu }^{2}(\mathrm{degrees}\,\mathrm{of}\,\mathrm{freedom})$	0.97(974)

Note.

^aUnabsorbed bolometric flux in the 3.0–50 keV NuSTAR band of the relxill component of the FPMA spectrum.

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We illustrate our choice of spectral model using the first XRT spectrum (Figure 5). The spectrum is dominated by a blackbody (Iwakiri et al. 2015; Negoro et al. 2015), but excesses are visible at both low and high energy (second panel of Figure 5). Adding a power law provides a reasonable description, although some structure remains in the residuals (third panel of Figure 5). The strongest is an emission feature around 1 keV (also present in the 2012 burst and the persistent spectrum; Degenaar et al. 2013, 2017) which can be fit with a Gaussian profile (fourth panel of Figure 5). The complete model is, therefore, similar to the persistent model in Section 3.1 with the addition of the Gaussian: TBabs(bbodyrad + cflux∗powerlaw + Gaussian), where interstellar absorption is again implemented with a fixed N_H (Section 2.3).

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This model is fit to all XRT spectra. The MAXI spectra, however, do not cover the 1 keV line and do not require the power law. Those two spectra are fit with only an absorbed blackbody (Figure 6).

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Both the power law and the blackbody are detected in all XRT spectra. Even though the count rate is substantially lower at later times, the spectra have similar statistics, as subsequent pointings were combined (Table 1). The blackbody temperature decreases from kT = 1.47 ± 0.05 keV in the first (MAXI) data point to a mean value of kT = 0.291 ± 0.005 keV at the end in a week of XRT pointings (Figure 7). The first data point indicates photospheric radius expansion (PRE), as the blackbody normalization is an order of magnitude larger (K_bb = (1.2 ± 0.2) × 10³ (km/10 kpc)²) than the mean value for the subsequent seven spectra (K_bb = (1.69 ± 0.08) × 10² (km/10 kpc)²). PRE is often observed around the peak of the brightest bursts, when the flux reaches the Eddington limit (e.g., Kuulkers et al. 2003). We further calculate the bolometric unabsorbed blackbody flux using its proportionality to the temperature, F_bb ∝ σT⁴, and taking into account K_bb (Figure 8 top).

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The power law index evolves over time: the first six XRT spectra yield a weighted mean of Γ = 1.31 ± 0.05, and we find Γ = 1.72 ± 0.06 for the last eight spectra. In between, Γ displays some variability. We determine the unabsorbed in-band (0.5–10 keV) power law flux, F_po, and take the ratio to the blackbody flux (on average 95% of the bolometric blackbody flux falls in the 0.5–10 keV band; Figure 8 bottom). In the first six XRT spectra the weighted mean is 0.66 ± 0.04. The ratio increases over time: for the last eight spectra it is 1.01 ± 0.09. No power law component is detected in the first MAXI scan, but including a power law with the persistent value for Γ (Table 3) one finds a 90% upper limit of F_po ≲ 1.0 × 10⁻⁸ erg s⁻¹ cm⁻², which places an upper limit on F_po/F_bb ≲ 0.17 ± 0.02.

The Gaussian emission feature near 1 keV is outside of the MAXI/GSC band, but it is a significant component for the first seven XRT spectra. The weighted mean of the centroid energy is 1.035 ± 0.009 keV. The width of the Gaussian is small: typically ∼10⁻² keV, which is consistent with being unresolved. We investigate the significance of the line by comparing the normalization, K_Gauss, to its 1σ error: for the first seven XRT spectra the mean value is K_Gauss = 3.3σ. Furthermore, K_Gauss decreases at the same rate as the blackbody flux.

The phenomenological fits suggest that the burst flux, as represented by the blackbody that dominates the spectrum, is reprocessed into the power law and Gaussian components, whose fluxes follow the blackbody flux. The flux fraction (Figure 8) and the power law's photon index (Figure 7) are different in the early and the later observations. This may indicate that two reprocessing regions are active, and their relative contributions to the flux change with time. Similar to our model of the persistent emission, we replace the power law by a simpl component for Comptonization of the blackbody emission (Section 3.2) and a reflection component. Because the burst emission is dominated by the blackbody, we use a model of a reflected blackbody, which has the same temperature as the blackbody component (2.4). The full model is: TBabs(simpl∗bbodyrad+cflux∗relconv∗reflection).

After we replace the power law with these two components, competition between them during the fit yields large uncertainties in the model parameters. We therefore fit all burst spectra simultaneously and constrain certain parameters to be the same for each spectrum, similar to the procedure followed by, e.g., Keek et al. (2014b). Specifically, each spectrum has its own value of the blackbody parameters kT and K_bb and the unabsorbed bolometric reflection flux F_refl (determined in the 0.01–100 keV band), whereas the spectra share the ionization parameter $\mathrm{log}\xi$, the inner radius of the reflection site R_in, as well as Γ and f_sc of the simpl component. Parameters of the relconv component (other than R_in) are the same as for the persistent emission (Section 3.3).

We fit the model to the XRT spectra, and find that after the first six spectra, the reflection component can no longer be distinguished. Therefore, we perform a simultaneous fit to the first six XRT spectra, which cover the initial 9 hr of the burst. We obtain a good fit with ${\chi }_{\nu }^{2}=1.04$ (Table 6 and Figure 9). The fit residuals are similar to those for the phenomenological model (Figure 6 bottom).

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Table 6.  Fit of the Burst Spectra with a Comptonized Blackbody and Reflection^a

	MAXI/GSC	Swift/XRT
blackbody reflection
$\mathrm{log}\xi$	${2.7}_{-0.2}^{+0.4}$	${3.0}_{-0.2}^{+0{\rm{p}}}$
relconv
Rin(Rg)	$({4.0}_{-3.0}^{+0{\rm{p}}})\times {10}^{2}$	${14}_{-7}^{+25}$
simpl
Γ	⋯	${2.3}_{-0.3}^{+0.2}$
fsc	⋯	${0.56}_{-0.10}^{+0.12}$
${\chi }_{\nu }^{2}(\mathrm{degrees}\,\mathrm{of}\,\mathrm{freedom})$	0.86(61)	1.04(1296)

Note.

^aA subsection of the fit parameters is listed here for the first MAXI scan and the first six XRT spectra, where reflection is detected. The XRT spectra are fit simultaneously, and the listed values are shared between the spectra. The fit parameters that are allowed to vary for each spectrum are shown in Figure 9. "p" indicates where a fit parameter was pegged to the domain boundary.

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Of the MAXI spectra, only the first has sufficient counts to distinguish deviations from a pure blackbody. No power law component was found with the phenomenological spectral model (Figure 6 second panel), and a fit with the reflection model finds a vanishingly small f_sc. Therefore, we fit the first MAXI spectrum without the simpl component (Table 6 and Figure 9). The modeled energy response of MAXI/GSC was tested in-orbit with observations of the Crab Nebula (Sugizaki et al. 2011). The Crab spectra indicate unmodeled features in the energy response, but these deviations are smaller than the statistical error of our spectra, and they are at different energies than the residuals of a blackbody fit to the burst spectrum (Figure 6 second panel). Those residuals are successfully described by a reflection component (Figure 6 bottom).

Compared to the phenomenological fits, kT is on average 6% smaller. K_bb is 55% larger, but part of the blackbody flux is Comptonized by simpl. The pure blackbody normalization is $(1-{f}_{\mathrm{sc}}){K}_{\mathrm{bb}}$, which is 32% smaller than the phenomenological K_bb. The changes in kT and K_bb partially compensate each other, such that the blackbody flux is lower by a factor $(1-{f}_{\mathrm{sc}})$ (Figure 10). The reflection fraction, F_refl/F_bb, has a weighted mean of 0.39 ± 0.05 for the XRT spectra. Interestingly, the flux of the first MAXI spectrum is also consistent with being lower by a factor $(1-{f}_{\mathrm{sc}})$. Its reflection fraction may, however, be substantially larger: F_refl/F_bb = 3 ± 2.

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To determine the properties of the burst, we consider the first 10.5 hr, because for later spectra the power law flux does not show smooth behavior (Figure 7), indicating that other effects besides cooling start playing a role. This time interval includes the two MAXI spectra and the first seven XRT spectra. We use the blackbody flux from the phenomenological fits to determine the burst properties (see also discussion in Section 5.6).

The unabsorbed bolometric peak blackbody flux is (6.0 ± 0.9) × 10⁻⁸ erg cm⁻² s⁻¹ in the first MAXI scan, and the blackbody normalization is substantially larger than in subsequent measurements. It is likely an episode of PRE where the Eddington limit is reached. Because of the PRE phase, we expect that the burst had a fast rise to the Eddington limit (≲1 s; e.g., in't Zand et al. 2014c), and that the flux stayed at this value until the end of PRE at time t_PRE, followed by a power law decay with index α produced by the cooling neutron star envelope. This leads to the following simple model of the burst flux as a function of time:

$$\begin{eqnarray}F(t\lt {t}_{\mathrm{PRE}}) & = & {F}_{\mathrm{Edd}}\\ F(t\gt {t}_{\mathrm{PRE}}) & = & {F}_{\mathrm{Edd}}\,{\left(\displaystyle \frac{t}{{t}_{\mathrm{PRE}}}\right)}^{-\alpha }.\end{eqnarray} \tag{ 1 }$$

We fit this model to the burst flux. Because the first MAXI scan exhibits PRE and the second does not, we constrain t_PRE to lie between those two. The start time of the burst is unknown. We therefore take a time offset, t₀, into account with respect to the center of the first MAXI scan. t₀ = 30 s places the burst start at the beginning of the MAXI scan, and t₀ = 92 minutes places it at the start of the data gap preceding the scan. We perform the fit for a linear grid of 1000 values for t₀ in this range. The effect of t₀ is largest for the first data point: the fit is worse for increasing t₀, because for large t₀ the first data point lies above the power law implied by the other points. For each value of t₀ we determine the likelihood of the fit by calculating the probability of obtaining the measured χ² or larger for six degrees of freedom. Fits with t₀ > 6.1 × 10² s are disfavored at a 95% confidence level: the burst start was likely at most 10 minutes before the first MAXI scan.

For each fit we determine the optimal values of the parameters and their 1σ positive and negative errors. We represent these by distributions that peak at the optimal value and have Gaussian "wings" to lower and higher values as appropriate for the asymmetric errors. The distributions are scaled by the likelihood of each fit, and then summed for a given parameter over all fits. This produces a distribution that includes the uncertainty in t₀ as well as the likelihood of each value of t₀. It typically has a bell shape with asymmetric wings. We report the value where the distribution peaks as the optimal value, and integrate the wings outwards to locate the 68% confidence regions. We find $\alpha ={1.15}_{-0.12}^{+0.14}$, ${F}_{\mathrm{Edd}}=({5.7}_{-0.7}^{+1.0})$ $\times {10}^{-8}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$, and ${t}_{\mathrm{PRE}}=({1.7}_{-1.1{\rm{p}}}^{+1.7})\times {10}^{2}\,{\rm{s}}$, where "p" indicates for t_PRE that the lower error is pegged to the end of the first MAXI scan. F_Edd is slightly lower than the flux value of the first data point, because a lower F_Edd is preferred for larger values of t₀. The difference is, however, only 0.3σ. For each fit we calculate the burst fluence, ${{ \mathcal F }}_{\mathrm{burst}}$, and the ratio of the fluence and peak flux, τ, and combine the results in the same way as the fit parameters: ${{ \mathcal F }}_{\mathrm{burst}}=({7.2}_{-1.3}^{+2.2})\times {10}^{-5}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}$ and $\tau =({1.3}_{-0.3}^{+0.4})\times {10}^{3}\,{\rm{s}}$, where the fluence is calculated from t = 0 to the end of the ninth data point where we ended the fit.

Now that we have a description of the flux decay, we check whether the time resolution that we employ is sufficient. During the exposure interval of each spectrum, we compare the expected change in the blackbody temperature from the central value (half of the total change), ΔkT, to the uncertainty, σ, in the measured kT for the respective spectrum. For the majority of spectra, ΔkT ≲ 1σ, and for one spectrum ΔkT = 3.7σ. Therefore, for all but the latter case the change in kT is small enough to allow for fitting with a single temperature blackbody. The worst case is the spectrum just before t = 10⁵ s, which spans a substantially longer time interval than the other spectra. Because this spectrum was taken after the first 10.5 hr where we determine the burst properties, and because the spectral parameters do not exhibit especially deviant behavior, we forego splitting the spectrum in shorter time intervals.

A comparison of the 2012 and 2015 bursts from IGR J17062-6143 is challenging because of the different coverage and data quality of the two bursts. The 2012 burst was first detected by Swift/BAT, and the BAT spectrum yields a blackbody flux of ${4.8}_{-1.6}^{+2.8}\times {10}^{-8}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ (Degenaar et al. 2013), which is 0.4σ smaller than the peak flux that we derive for the 2015 burst (Section 4.3). For the 2015 burst we find evidence of PRE, and one expects the same for the 2012 burst, because the flux variations in its tail are thought to be associated with strong expansion at the onset (Degenaar et al. 2013). Nevertheless, PRE was not detected for the 2012 burst, likely because of the limited data quality. The BAT count rate peaked halfway through the exposure, and Degenaar et al. (2013) interpreted this as the true maximum in the burst flux, arguing that the peak flux was larger than the time-averaged BAT flux. However, because of the BAT's energy band (>15 keV), it is less sensitive to the PRE phase, where the blackbody temperature is reduced. The BAT spectrum was, therefore, dominated by the post-PRE phase, and the peak in the BAT count rate may coincide with the end of the PRE phase ("touchdown"; e.g., compare the count rate in different bands for a burst from SLX 1735-269 in Molkov et al. 2005). We suggest that the flux measured from the BAT spectrum was close to the Eddington limit, and both the 2012 and 2015 bursts reached this limit.

If the peak in the BAT count rate coincides with the end of the PRE phase, the 2012 burst had a PRE duration of at least t_PRE ≳ 80 s (the time from the burst start up to the BAT trigger is not included), which is compatible with the ${t}_{\mathrm{PRE}}=({1.7}_{-1.1{\rm{p}}}^{+1.7})\times {10}^{2}\,{\rm{s}}$ that we infer for the 2015 burst (Section 4.3). t_PRE is typically proportional to the burst duration (e.g., in't Zand & Weinberg 2010), and based on t_PRE the 2015 burst is of similar or substantially longer duration than the 2012 burst. Only the early part of the 2012 burst was observed, and the presence of strong flux variability makes it challenging to constrain the cooling trend. Degenaar et al. (2013) suggest a linear trend, which implies a much faster flux decay than the expected power law (e.g., in't Zand et al. 2014b). Interestingly, robotic optical telescopes detected a declining R-band flux in the 2 hr following the Swift/BAT trigger (Ivarsen et al. 2012; Meehan et al. 2012), and from 1.1 × 10³ s to the end of the observations at 7.0 × 10³ s the flux decay follows a power-law trend. Perhaps the burst tail continued longer than the previously inferred duration of 1.1 × 10³ s (Degenaar et al. 2013). Furthermore, the reported burst fluence is ∼1/4 of the 2015 burst (Degenaar et al. 2013), but it may have been underestimated as well, if the unobserved tail continued for longer than previously assumed.

Comparing the 2015 burst to bursts from other sources, it is observable for hours, similar to superbursts (e.g., Keek & in't Zand 2008). Therefore, the burst was initially tentatively classified as a superburst (Negoro et al. 2015; Iwakiri et al. 2015). However, the day-long duration is in part due to the low persistent flux, which allows the burst to be detectable for many hours (see Degenaar et al. 2011, for a similar event lasting 3 hr). A better quantity for comparison is the decay timescale τ, which is derived from the burst fluence (Section 4.3). We find τ = 21 ± 7 minutes for the 2015 burst, whereas superbursts typically have τ ≳ 69 minutes (Strohmayer & Brown 2002; Keek & in't Zand 2008). It is, therefore, more likely to be a long helium burst, i.e., an intermediate duration burst. It is among the most energetic helium flashes observed thus far (e.g., Linares et al. 2012). Some of the longer specimens from other sources have τ ≃ 4 minutes (XMMU J174716.1-281048; Degenaar et al. 2011), τ ≃ 7 minutes (SLX 1735-269; Molkov et al. 2005), τ ≃ 8 minutes (SLX1737-282; in't Zand et al. 2002), and τ ≃ 16 minutes and τ ≃ 43 minutes (4U 1850-086; in't Zand et al. 2014a; Serino et al. 2016, based on the reported exponential decay timescales). A common issue for these bursts is again sparse coverage and modest data quality, which makes the precise measurement of the burst properties challenging. Nevertheless, one long burst from 4U 1850-086 exhibited t_PRE = (4.8 ± 0.5) × 10² s (in't Zand et al. 2014a), suggesting that it was a more energetic event than the 2015 burst from IGR J17062-6143. Furthermore, for several superbursts from other sources with low mass accretion rates, there remains ambiguity as to whether the fuel consists of carbon or helium, although their interpretation as carbon flashes remains preferred (e.g., Kuulkers et al. 2010; Altamirano et al. 2012; Serino et al. 2016).

We regard the flux of the first MAXI scan as the Eddington limited flux. Equating the luminosity to the empirical Eddington luminosity of L_Edd = 3.8 × 10³⁸ erg s⁻¹ (Kuulkers et al. 2003), we find a distance of d = 7.3 ± 0.5 kpc. Degenaar et al. (2013) derived a distance of 5 kpc by extrapolating the peak flux of the 2012 burst, but we suggested that this may not be the correct measure of the Eddington flux (Section 5.1).

Using the above distance, we find the burst energy of ${E}_{{\rm{b}}}=({4.5}_{-1.0}^{+1.6})\times {10}^{41}\,\mathrm{erg}$ in the observer frame. Part of the burst energy may escape the neutron star as a neutrino flux. We neglect it here, as it is expected to be minor for columns of y ≲ 10¹¹ g cm⁻² (Keek & Heger 2011). During PRE, a substantial part of the burst energy may power a radiative wind (e.g., Weinberg et al. 2006). The fraction of the fluence during the PRE phase is ${t}_{\mathrm{PRE}}{F}_{\mathrm{Edd}}/{{ \mathcal F }}_{\mathrm{burst}}={0.13}_{-0.10}^{+0.14}$. The total burst energy could, therefore, be larger by ∼10%. To calculate the ignition column depth, we take an energy release of burning He to Ni of E_nuc ≃ 10¹⁸ erg g⁻¹, and assume a neutron star mass of 1.4 M_⊙ and radius of R = 10 km, which give a gravitational redshift of $1+z=1.31$. We find

$$\begin{eqnarray*}&&{y}_{\mathrm{ign}}=\displaystyle \frac{(1+z){E}_{{\rm{b}}}}{4\pi {R}^{2}{E}_{\mathrm{nuc}}}=({4.7}_{-1.0}^{+1.6})\times {10}^{10}\,{\rm{g}}\,{\mathrm{cm}}^{-2}.\end{eqnarray*}$$

We have fit several models to the persistent flux (Section 3). When extrapolating the model to lower energies, a power law gives an unphysically large bolometric flux. The reflection model has a low-energy turn-over of the power law at 0.1 keV, but the turn-over is likely near the peak of the blackbody at an order of magnitude higher energy. Therefore, we prefer the bolometric flux obtained with the simpl model (Table 4). Multiplying the flux measured for Chandra spectrum 17543 by the MAXI scaling factor, we find a bolometric unabsorbed flux of F_pers = (0.92 ± 0.07) × 10⁻¹⁰ erg s⁻¹ cm⁻². This is the time-averaged persistent flux between the bursts in 2012 and 2015. Using the flux of the first MAXI burst observation as a measure of the Eddington limit, we find F_pers/F_Edd = (1.5 ± 0.3) × 10⁻³.

Only a few LMXBs have shown bursts at such low persistent flux (e.g., Kaptein et al. 2000; Degenaar et al. 2010; Chenevez et al. 2012), and IGR J17062-6143 presents a rare instance of recurring bursts at low mass accretion rate (1RXS J171824.2-402934 is another example; in't Zand et al. 2009). The time between the triggers of the bursts in 2012 and 2015 is 3.3552 year, and the ratio of the persistent and burst fluences is $\alpha ={{ \mathcal F }}_{\mathrm{pers}}/{{ \mathcal F }}_{\mathrm{burst}}=(1.4\pm 0.4)\times {10}^{2}$. Assuming 100% efficiency of converting gravitational energy to X-rays, a column of ${y}_{\mathrm{acc}}=(2.7\pm 0.4)\times {10}^{10}\,{\rm{g}}\,{\mathrm{cm}}^{-2}\,\left(\tfrac{1.4\,{M}_{\odot }}{M}\right)\,\left(\tfrac{10\,\mathrm{km}}{R}\right)$ was accreted. This includes the uncertainty in the distance. When comparing y_acc to y_ign, we can avoid this uncertainty by simply taking

$$\begin{eqnarray*}&&\displaystyle \frac{{y}_{\mathrm{acc}}}{{y}_{\mathrm{ign}}}=\displaystyle \frac{{{ \mathcal F }}_{\mathrm{pers}}}{{{ \mathcal F }}_{\mathrm{burst}}}\displaystyle \frac{{E}_{\mathrm{nuc}}}{{GM}/R}={0.73}_{-0.14}^{+0.23}\,\left(\displaystyle \frac{1.4\,{M}_{\odot }}{M}\right)\,\left(\displaystyle \frac{R}{10\,\mathrm{km}}\right),\end{eqnarray*}$$

which means that the two columns are consistent within 1.2σ. This confirms that X-ray luminosity is indeed a good measure of the mass accretion rate in this system. Unfortunately, there were many instances when the source was not observed by any X-ray instrument for several hours, and we cannot verify that indeed no other burst occurred between 2012 and 2015. MAXI covered the source with at least one scan per 3 hours for 63% of the time, and similar gaps are present in the coverage by Swift/BAT.

y_ign is substantially smaller than typical for superbursts (Cumming et al. 2006), especially at low mass accretion rates (e.g., Kuulkers et al. 2010; Altamirano et al. 2012), where carbon ignition is expected to occur much deeper (Cumming et al. 2006; Keek & Heger 2011). This comfirms our classification of the event as due to deep helium ignition (Section 5.1). Models of pure helium accretors, however, predict y_ign to be much larger at the observed mass accretion rate (Cumming et al. 2006). These models consider heating of the neutron star envelope by nuclear processes in the crust and neutrino cooling in the core. The maximum heating that this provides is insufficient to explain the observed y_ign, and additional "shallow" heating would be required to ignite helium at the observed depth (Brown & Cumming 2009; Deibel et al. 2015, 2016). This burst from IGR J17062-6143 could indicate that shallow heating is active even at very low mass accretion rates. Alternatively, the accretion composition could include some hydrogen, the burning of which could heat the envelope and lower y_ign to the observed value. At low mass accretion rates, hydrogen may burn at a small depth, producing a deep layer of helium (e.g., Fujimoto et al. 1981; Peng et al. 2007), and intermediate duration bursts have been observed from such sources (e.g., Falanga et al. 2009). Optical spectroscopic observations of the companion star could determine the presence of hydrogen.

The 2012 burst spectrum exhibited a strong emission line near 1 keV, which was suggested to be a fluorescent Fe L line originating at a distance of ∼10² R_g from the neutron star (Degenaar et al. 2013). We find an emission feature with similar energy and width in the XRT spectra of the 2015 burst. The normalization of the line decreases at the same rate as the blackbody flux, and the line during the 2012 burst roughly follows the same trend. This is a strong indication that the line is produced by reprocessed burst emission. High resolution Chandra spectra of the persistent emission also exhibit emission features near 1 keV. Furthermore, the NuSTAR persistent spectra clearly exhibit a broadened Fe Kα line and a Compton hump: the tell-tale signs of photoionized reflection (Degenaar et al. 2017). Therefore, we argue that the 1 keV feature is similarly produced by reflection, and we have assumed reflection to be dominated by a single reflection component at each moment in time. During the bursts, the feature is accompanied by a soft excess, which may be the Bremsstrahlung continuum from reflection (e.g., Ballantyne 2004). Reflection models can describe the soft excess and part of the 1 keV line, but residuals remain around the line both for the 2015 burst (Figure 5 bottom) and the persistent spectra (Figure 4 bottom; see also Degenaar et al. 2017). The strength of the lines in the reflection spectrum is highly dependent on the composition (e.g., Madej et al. 2014) and the density of the reflecting material (Ballantyne 2004). Current reflection models are limited in this respect, which may be the cause of the imperfect description of the observed feature.

The reflection models suggest that the disk is highly ionized ($\mathrm{log}\xi \simeq 3$) both during the burst and the persistent spectrum, even though the illuminating flux changes by orders of magnitude. During two superbursts, $\mathrm{log}\xi$ was observed to decrease over time (Ballantyne & Strohmayer 2004; Keek et al. 2014b), but for several other sources the persistent $\mathrm{log}\xi$ is similarly large (e.g., Cackett et al. 2010; Degenaar et al. 2015; Iaria et al. 2016). As ξ depends on both flux and density (Section 2.4), one explanation could be an increase in the density of the reflection site during the burst, for example if the burst strips the low-density upper layer from the disk. Low density material could also be present near the inner edge of a disk that is truncated by the neutron star's magnetic field (Ballantyne et al. 2012). The persistent flux could reflect off this material, whereas the burst flux may reflect off the inner disk. Another possibility is that the inner disk is overionized, such that it does not produce emission lines. Instead of the inner radius of the disk, R_in would correspond to a location further out in the disk, where ξ is sufficiently reduced to produce the reflection features. For stronger illumination, R_in would then increase, whereas we see it decrease during the burst. Furthermore, overionization has not been inferred for other LMXBs where the inner disk is similarly highly ionized (e.g., Cackett et al. 2010).

Care must be taken, however, not to overinterpret the present results, because the uncertainties in R_in are large, at least in part due to the limitations of the reflection models (Section 2.4). Moreover, the fit parameters may be subject to small systematic changes if we had employed reflection models for a hydrogen-rich accretion disk, instead of a helium-rich disk (Section 2.4). More importantly, the soft reflection spectrum (≲2 keV) depends strongly on the density of the reflector (Figure 3), and fits with models assuming, e.g., a lower density would likely yield a larger reflection fraction.

Both the persistent and burst spectra are well-described by a blackbody and a power law. The blackbody likely originates at the neutron star surface, which is heated by persistent accretion and by thermonuclear burning during the burst. The blackbody temperature demonstrates cooling in the burst tail, which is often cited as a defining characteristic of a Type I X-ray burst of thermonuclear origin. Over the course of a day, the blackbody flux decreases with time as ${F}_{\mathrm{bb}}\propto {t}^{-1.15\pm 0.14}$. The power is just 1.1σ smaller than the expected ≃1.3 for bursts that ignite at large column depths where cooling is dominated by ions (in't Zand et al. 2014b).

During the burst and the subsequent 11 days, the power law flux traces changes in the blackbody flux. The power law is likely produced by reprocessing of the blackbody emission. We speculate that this is Comptonization in an optically thin plasma near the neutron star. We refer to it as a "corona," but it may be a boundary layer or accretion flow between a truncated disk and the neutron star. As no high-energy cut-off is detected in the NuSTAR band, the electrons in the plasma must be hot: kT_e ≳ 10² keV. During the PRE phase at the start of the burst, the MAXI spectrum shows no sign of the power law, suggesting disruption of the corona by the burst, reducing its scattering fraction by at least a factor four (Section 4.1). In the burst tail the corona may have reformed, since the power law returns with a similar Γ and a slightly lower scattering fraction than in the persistent spectrum.

Fits with reflection models find an inner disk radius of R_in ∼ 10² R_g for persistent emission, which suggests that the disk is truncated far from the neutron star (Degenaar et al. 2017), whereas in the burst tail the disk may have moved inwards to R_in ∼ 10¹ R_g. Possibly, in the tail Poynting–Robertson drag brings the inner disk closer to the neutron star (Walker 1992; Ballantyne & Everett 2005; Worpel et al. 2013, 2015). At the burst start a large R_in is favored, and the effect of Poynting–Robertson drag may have been temporarily kept at bay by radiation pressure or an outflowing wind. However, the quality of the burst spectra is modest, and the uncertainty in R_in is large.

Another quantity to consider is the reflection fraction, which at all times is substantial. For the persistent emission, a large R_in and reflection fraction may be consistent if the disk is illuminated by a corona that extends at least to R_in, such that a substantial part of the power law flux is intercepted by the disk. In the burst, the blackbody dominates the reflection signal instead of the power law. In the tail, the measured reflection fraction meets the expectations for a flat disk that extends to the neutron star (Lapidus & Sunyaev 1985; Fujimoto 1988; He & Keek 2016), and R_in at this time is indeed consistent with no or a small gap between star and disk. At the burst start, however, the reflection fraction is substantially larger than unity (with a large error). This may require a steeply inclined reflection surface close to the star (He & Keek 2016), but the measured R_in is large. However, the large uncertainty of R_in allows for a value of similar size as in the tail. Therefore, we favor the scenario where the disk is truncated at R_in ∼ 10² R_g during persistent accretion, whereas the impact of the burst brings the inner disk close to the neutron star, both at the burst start and in the tail.

During the burst, the behavior of the source is dominated by the cooling of the blackbody, until the total bolometric flux is reduced to the pre-burst persistent level. Over the course of a week, the spectrum returns to being dominated by the power law. At the end of the XRT observations, both Γ and the scattering fraction are lower than the persistent values. Perhaps the corona has not fully recovered from the burst, which may take longer than for other bursting LMXBs, because of the low mass accretion rate. The influence of a burst on the hard tail has previously been inferred for a superburst (Keek et al. 2014a) and by stacking short bursts (Maccarone & Coppi 2003; Chen et al. 2013; Ji et al. 2014; Kajava et al. 2016). Interestingly, at t ≃ 2 × 10⁵ s the spectrum suddenly changes, and it takes several days to return to its previous behavior. The blackbody, which we attribute to the cooling neutron star, is strongly suppressed at this time, and the overall source flux is reduced. The flux reduction could be the result of an inner disk depleted by Poynting–Robertson drag. The restoration of the inner disk and the accretion flow might briefly block our view of the neutron star.

The limitations posed by the modest quality of the burst spectra and by the reflection models make it challenging to put firm constraints on the interaction of the burst and the accretion environment. It is however, clear that the burst has a strong influence on both the "corona" and the disk (for further discussion, see Ballantyne & Everett 2005).

We have derived the burst properties under the assumption of isotropic emission, which is not the case in LMXBs (Lapidus & Sunyaev 1985; Fujimoto 1988; He & Keek 2016). Now that we have a picture of the different emission and reprocessing sites in IGR J17062-6143, we investigate how this affects the observed burst flux. Anisotropy factors for burst emission have only been calculated for disks that extend to the neutron star surface. The burst tail may be the closest to this situation. The measured reflection fraction of 0.39 ± 0.05 corresponds to a geometrically thin disk with an inclination angle of 39° ± 7° (He & Keek 2016), which is consistent with the absence of eclipses and dips, and is 1.3σ larger than the 30° that we assumed in Section 3.3. It implies an anisotropy factor of ${\xi }_{{\rm{d}}}^{-1}=0.92\pm 0.03$ for the direct blackbody emission (He & Keek 2016), and the intrinsic direct neutron star flux is larger by 9% than observed. For truncated disks, blocking of the line of sight by the disk is smaller, and ${\xi }_{{\rm{d}}}^{-1}$ is even closer to unity.

We find that a scattering fraction f_sc of the blackbody emission is reprocessed by a Comptonizing corona. If the corona has a spherical geometry that envelops the neutron star, its anisotropy is similarly small as for the blackbody itself. Part of the blackbody is scattered from the line of sight, and the intrinsic neutron star emission is the sum of the observed blackbody and the Comptonized part. Indeed, the burst fit that includes the simpl model returns a blackbody flux that is lower by a factor $(1-{f}_{\mathrm{sc}})$ than the blackbody flux from the phenomenological fit (Section 4.2).¹⁰ The latter is, therefore, a good measure of the intrinsic isotropic burst emission. The anisotropy correction for the persistent flux may be similarly small.

At the start of the burst, we suspect that the disk may not be flat. The anisotropy is strongly dependent on the disk geometry (He & Keek 2016), and in principle a large correction could be needed: ${\xi }_{{\rm{d}}}^{-1}\sim 0.1$. This would have important consequences for the derived quantities such as the distance and y_ign. Fortunately, the Comptonizing corona is absent at the burst start, and we can regard all flux to be from the blackbody and its reflection, the sum of which may underestimate the intrinsic burst emission by at most tens of percent (He & Keek 2016).