NuSTAR and Swift Observations of Swift J1357.2–0933 During an Early Phase of Its 2017 Outburst

We analyzed the NuSTAR (Harrison et al. 2013) data taken on April 28 (obsid: 90201057002; exposure: 34.5 ks) using the NuSTARDAS tools nupipeline and nuproducts. To extract source photons, we used a circular region with a radius of 30'' located at the known position of Swift J1357.2–0933. Photons for the background spectra were extracted from a region of the same shape and size located close to the source on the same detector that was free of source photons. To investigate short-term variability we derived cospectra in the 3–30 keV band using MaLTPyNT (Bachetti 2015). The energy range from 3 to 30 keV comprises about 97.3% of the source photons detected with NuSTAR in the 3–78 keV band. The cospectrum is the cross-power density spectrum (PDS) derived from data of the two completely independent focal planes and represents a good proxy of the white-noise-subtracted PDS (Bachetti et al. 2015).

We analyzed Swift/XRT (Burrows et al. 2005) monitoring data, using the online data analysis tools provided by the Leicester Swift data center,³ including single pixel events only (Evans et al. 2009). Two observations were taken simultaneously to our NuSTAR ToO observation: the first observation (obsid: 00088094002; PI: Stiele) was taken in photon counting mode, while the second observation (obsid: 00031918053; PI: Sivakoff) was taken in windowed timing mode. In the first observation, the exposure was split into two parts of 196 and 765 s, with a gap of 5615 s in between. The exposure of the second observation was 524 s.

For the Swift/UVOT (Roming et al. 2005) data, we used the task uvot2pha to extract spectral information. In the first observation images in the U and UVW1 filter are taken, while in the second observation B, V, U, UVW1, UVW2, and UVM2 images are available.

The Swift/XRT longterm light curve is shown in Figure 1. The NuSTAR observation was taken near the outburst peak.

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For the NuSTAR data, light curves in three energy bands with a binning of 240 s, and corresponding hardness ratios are shown in Figure 2. We derived cospectra in the 3–30 keV range, using time bins of ${2}^{-8}$ s and of 0.5 s and stretches of 512 s, corresponding to frequencies between ∼2⁻³ Hz and 128 or 1 Hz, respectively (Figure 3). The cospectra can be fitted with two zero-centered Lorentzians, modeling band-limited noise (BLN) components, and one Lorentzian to fit a peaked noise (PN) component. The BLN components have an rms variability of ${18.9}_{-1.4}^{+1.6} \%$ and ${23.0}_{-1.0}^{+0.9} \%$, respectively, and a characteristic frequency of $\nu ={6.0}_{-1.1}^{+1.6}$ mHz and $\nu ={0.31}_{-0.05}^{+0.06}$ Hz, respectively. The PN component has a centroid frequency of ${\nu }_{0}=20.3\pm 1.8$ mHz, a half width at half maximum of ${\rm{\Delta }}={10.3}_{-2.8}^{+2.7}$ mHz, an rms variability of ${14.8}_{-2.2}^{+1.8} \%$, and a significance of 3.3σ. The parameters are almost identical in both bands.

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We fit the averaged energy spectra of the NuSTAR and Swift ToO observations within isis (V. 1.6.2; Houck & Denicola 2000) in the 0.3–78 keV range, where the Swift/XRT data cover the 0.3–10 keV range and the NuSTAR data cover the 3–78 keV range. We grouped the Swift/XRT data to a signal-to-noise ratio of 3 and the NuSTAR data to a signal-to-noise ratio of 5, with at least five channels per bin, both for Swift/XRT and NuSTAR. The Swift/XRT and NuSTAR spectra can be well fitted with an absorbed power-law model (${\chi }^{2}/\mathrm{dof}$: 539.7/525; Figure 4), where the absorption, modeled with TBabs (Wilms et al. 2000), is fixed at ${N}_{{\rm{H}}}=3\times {10}^{20}$ cm⁻². We use the abundances of Wilms et al. (2000) and the cross sections given in Verner et al. (1996). The obtained photon index is ${\rm{\Gamma }}=1.679\pm 0.006$. The spectral parameters are given in Table 1. We also add a floating cross-normalization parameter, which is fixed to one for NuSTAR FPMA, to take uncertainties in the cross-calibration between the different telescopes into account. The absorbed flux in the 0.3–78 keV band is $2.08\,\pm 0.08\times {10}^{-9}$ erg cm⁻² s⁻¹, and the unabsorbed flux in the 0.5–10 keV band is $2.75\pm 0.11\times {10}^{-10}$ erg cm⁻² s⁻¹, a factor ∼2.6 bigger that the unabsorbed flux observed on April 21 (Sivakoff et al. 2017). The uncertainties on the flux are obtained following the approach presented in Wijnands et al. (2004).

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Table 1.  Averaged Swift and NuSTAR Spectra of Swift J1357.2–0933 Fitted with Different Phenomenological Models

	Swift/XRT and NuSTAR				+Swift/UVOT
Parameter	powerlaw	cutoffpl	bknpower	diskbb+nthcomp	diskbb+nthcomp	diskir
Γ	1.679 ± 0.006	1.656 ± 0.006	${1.678}_{-0.000}^{+0.005}$	${1.703}_{-0.005}^{+0.004}$	1.702 ± 0.005	1.697 ± 0.005
${{\rm{\Gamma }}}_{2}$	⋯	⋯	${2.46}_{-0.26}^{+1.83}$	⋯	⋯	⋯
norma × 10−2	2.47 ± 0.03	2.40 ± 0.03	${2.01}_{-1.60}^{+0.30}$	${2.21}_{-1.62}^{+0.22}$	2.51 ± 0.02	⋯
${E}_{\mathrm{cut}/\mathrm{break}/{\rm{e}}}$ (keV)	⋯	≳427.7	${0.77}_{-0.27}^{+0.12}$	${47.2}_{-12.7}^{+40.5}$	${46.0}_{-11.3}^{+41.1}$	${32.9}_{-4.5}^{+9.1}$
${R}_{\mathrm{in}}$ b(km)	⋯	⋯	⋯	${367.67}_{-266.53}^{+1191.87}$	${1395.33}_{-108.65}^{+103.37}$	${108.87}_{-25.81}^{+188.65}$
${T}_{\mathrm{in}}$ (eV)	⋯	⋯	⋯	${47.2}_{-12.7}^{+40.5}$	${43.5}_{-1.9}^{+2.1}$	${97.5}_{-14.7}^{+10.8}$
${L}_{{\rm{c}}}/{L}_{{\rm{d}}}$	⋯	⋯	⋯	⋯	⋯	${3.02}_{-1.01}^{+0.86}$
${R}_{\mathrm{irr}}$ (${R}_{\mathrm{in}}$)	⋯	⋯	⋯	⋯	⋯	1.003 ± 0.001
${f}_{\mathrm{out}}$	⋯	⋯	⋯	⋯	⋯	${0.0122}_{-0.0022}^{+0.0055}$
${R}_{\mathrm{out}}$ (log10${R}_{\mathrm{in}}$)	⋯	⋯	⋯	⋯	⋯	${3.48}_{-0.21}^{+0.04}$
$E(B-V)$ (mag)	⋯	⋯	⋯	⋯	0.075 ± 0.010	$\lt 0.042$
${\mathrm{const}}_{\mathrm{FPMB}}$	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006
${\mathrm{const}}_{\mathrm{XRT}}$	${0.541}_{-0.029}^{+0.030}$	0.584 ± 0.029	${0.541}_{-0.029}^{+0.030}$	${0.539}_{-0.028}^{+0.029}$	${0.545}_{-0.029}^{+0.028}$	${0.417}_{-0.025}^{+0.024}$
${\mathrm{const}}_{\mathrm{XRT}2}$	${0.627}_{-0.028}^{+0.032}$	${0.660}_{-0.028}^{+0.029}$	${0.627}_{-0.028}^{+0.032}$	${0.625}_{-0.026}^{+0.028}$	0.631 ± 0.027	0.455 ± 0.023
${\chi }^{2}/\mathrm{dof}$	539.7/525	541.3/524	526.1/523	520.3/522	557.3/521	526.4/518
Fc	2.08 ± 0.08	2.14 ± 0.04	${2.54}_{-0.12}^{+0.28}$	2.07 ± 0.08	⋯	⋯

Notes.

^aIn units of photons keV⁻¹ cm⁻² s⁻¹ at 1 keV. ^bAssuming an inclination of 70° and a distance of 2.3 kpc. ^cAbsorbed flux in the 0.3–78 keV band in units of 10⁻⁹ erg cm⁻² s⁻¹.

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We also try to fit a cut-off power law to the Swift and NuSTAR spectra. This model gives a cut-off energy ≳428 keV, outside the energy range covered by the data. The values of all other parameters are similar to the one found using the power-law model (see Table 1). The cut-off power law is not statistically required compared with the simple power-law model (${\chi }^{2}$/dof: 541.3/524).

Using a broken power law (bknpower), we obtain a statistically improved fit (${\chi }^{2}/\mathrm{dof}$: 526.1/523). According to the sample-corrected Akaike Information Criterion (AIC; Akaike 1974), this is an improvement of ΔAIC = 9.5, i.e., a 115 times better model (Burnham et al. 2011). The spectral parameters and the flux is given in Table 1.

As the broken power law provides a much better fit than the simple power law, we also fit the spectra with an absorbed disk blackbody (diskbb) plus thermal Comptonization model (nthcomp; Zdziarski et al. 1996; Życki et al. 1999). This results in a further improved fit of ${\chi }^{2}/\mathrm{dof}$: 520.3/522. The spectral parameters and the flux can be found in Table 1. To investigate a possible dependency of the disk parameters on the absorption, which is low (Armas Padilla et al. 2014; Plotkin et al. 2016), we fit the spectra with rather extreme absorptions of ${N}_{{\rm{H}}}=0$ and 1 × 10²¹ cm⁻², and find that the disk temperature increases, while the disk radius decreases, with increasing absorption, but that the obtained parameters are consistent within errors.

While the phenomenological models presented above provide a statistically very good fit, they do not contain information about the geometry of the X-ray producing region. To obtain information about the geometry, we need to study the strong relativistic effects close to the black hole. We model the relativistic effects using the relxill model (Dauser et al. 2014; García et al. 2014). We use an emissivity index of 3, which is appropriate for a standard Shakura–Sunyaev accretion disk and an extended corona (Reynolds & Begelman 1997). Due to the low count rates and the degeneracy of different spectral parameters of the model, we need to fix some values. Because the cut-off power-law model gives a high cut-off energy, we keep the cut-off energy in the relxill model at 300 keV. We also set the outer disk radius to ${r}_{\mathrm{out}}=400\,{R}_{g}$. We try two different inclinations of 30° and 70°, where the higher inclination is motivated by dip-like features observed in optical light curves. As there are no measurements of the spin available from the literature, we try values of zero (Schwarzschild black hole), 0.8, 0.9, and 0.95 for the spin.

Using the higher inclination, we obtain a photon index of ${\rm{\Gamma }}\sim 1.70$, an inner disk temperature of ${T}_{\mathrm{in}}\sim 56\,\mathrm{eV}$ and a low reflection of ${{ \mathcal R }}_{\mathrm{refl}}\sim 0.16$. The iron abundance (${A}_{\mathrm{Fe}}\lt 0.8$), and the ionization parameter (log($\xi /$(erg cm s⁻¹)) ∼ 1.0) are not well constrained. That the presence of a disk component hampers constraining the ionization parameter has already been noticed in previous studies (Basak & Zdziarski 2016; Stiele & Kong 2017). The values of the spectral parameters are consistent for the different spin values (see Table 2). The inner radius of the reflection disk (measured in ${R}_{\mathrm{ISCO}}$) increases with increasing spin, but the data prefer an accretion disk truncated close (within $\lesssim 5\,{R}_{\mathrm{ISCO}}$) to the black hole. We show in Figure 5 how ${\chi }^{2}$ changes with the inner disk radius compared to the best-fit ${\chi }^{2}$ value. These relations confirm that a disk truncated close to the black hole is preferred, independent of the spin value. The flux of the direct disk component contributes about one-third of the total flux in the 0.3–1 keV band. For the lower inclination of 30°, which gives statistically slightly worse fits with ${\rm{\Delta }}\chi \sim +1-2$ (for the same dof), we obtain a photon index of ${\rm{\Gamma }}\sim 1.68$, an inner disk temperature of ${T}_{\mathrm{in}}\sim 59\,\mathrm{eV}$ and an even lower reflection fraction of ${{ \mathcal R }}_{\mathrm{refl}}\sim 0.11$, independent of the spin. The iron abundance (${A}_{\mathrm{Fe}}\lt 0.9$) and the ionization parameter (log($\xi /$(erg cm s⁻¹)) ∼2.0) are not well constrained. The inner disk radius is also not well constrained, but now the fits prefer a bigger inner disk radius with a disk truncated above $\sim 3\,{R}_{\mathrm{ISCO}}$.

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Table 2.  Averaged Swift/XRT and NuSTAR Spectra of Swift J1357.2–0933 Fitted with an Absorbed Relxill Model Assuming Different Inclination and Spin

Parameter	a = 0	a = 0.8	a = 0.9	a = 0.95
	Inclination: 70°
${R}_{\mathrm{in}}$ a (km)	${452.64}_{-357.10}^{+2482.27}$	${461.33}_{-366.55}^{+2262.94}$	${464.98}_{-370.53}^{+2140.77}$	${441.37}_{-346.39}^{+2232.74}$
${T}_{\mathrm{in}}$ (eV)	${56.0}_{-18.7}^{+29.8}$	${55.8}_{-18.0}^{+30.0}$	${55.7}_{-17.4}^{+30.1}$	${56.4}_{-18.4}^{+29.4}$
Γ	1.70 ± 0.02	${1.70}_{-0.03}^{+0.02}$	1.70 ± 0.02	1.70 ± 0.02
norm × 10−2	${2.55}_{-0.14}^{+0.08}$	2.55 ± 0.08	${2.55}_{-0.18}^{+0.08}$	${2.55}_{-0.18}^{+0.08}$
${R}_{\mathrm{refl}}({R}_{\mathrm{ISCO}})$	$\lt 2.75$	$\lt 2.26$	$\lt 3.49$	$\lt 5.72$
logξ (erg cm s−1)	${0.92}_{-0.92}^{+1.61}$	${0.95}_{-0.95}^{+1.79}$	${0.99}_{-0.99}^{+1.74}$	${1.00}_{-1.00}^{+1.74}$
${A}_{\mathrm{Fe}}$	$\lt 0.81$	$\lt 0.81$	$\lt 0.79$	$\lt 0.80$
${{ \mathcal R }}_{\mathrm{refl}}$	0.17 ± 0.06	0.17 ± 0.06	${0.16}_{-0.05}^{+0.06}$	0.16 ± 0.06
${\mathrm{const}}_{\mathrm{FPMB}}$	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006
${\mathrm{const}}_{\mathrm{XRT}/\mathrm{PC}}$	${0.533}_{-0.030}^{+0.031}$	${0.532}_{-0.030}^{+0.031}$	${0.533}_{-0.031}^{+0.030}$	${0.533}_{-0.031}^{+0.030}$
${\mathrm{const}}_{\mathrm{XRT}/\mathrm{WT}}$	0.617 ± 0.030	${0.616}_{-0.033}^{+0.030}$	${0.617}_{-0.031}^{+0.030}$	${0.617}_{-0.035}^{+0.030}$
${\chi }^{2}/\mathrm{dof}$	517.7/519	517.2/519	517.4/519	517.5/519
Fb	2.08 ± 0.06	2.08 ± 0.06	2.07 ± 0.06	2.07 ± 0.06
	Inclination: 30°
${R}_{\mathrm{in}}$ a (km)	${235.84}_{-171.07}^{+253.62}$	${238.48}_{-174.05}^{+1149.38}$	${233.67}_{-169.22}^{+160.65}$	${220.49}_{-156.28}^{+1176.39}$
${T}_{\mathrm{in}}$ (eV)	${58.9}_{-17.5}^{+23.1}$	${58.7}_{-17.3}^{+28.2}$	${59.0}_{-19.4}^{+27.9}$	${59.9}_{-20.4}^{+27.2}$
Γ	${1.68}_{-0.08}^{+0.02}$	1.68 ± 0.02	1.68 ± 0.02	1.68 ± 0.02
norm ×10−2	2.48 ± 0.06	${2.48}_{-0.04}^{+0.06}$	${2.48}_{-0.04}^{+0.06}$	${2.48}_{-0.06}^{+0.05}$
${R}_{\mathrm{refl}}({R}_{\mathrm{ISCO}})$	$\gt 1.00$	$\gt 1.73$	$\gt 2.16$	$\gt 2.66$
logξ (erg cm s−1)	${1.98}_{-1.98}^{+0.43}$	${2.00}_{-2.00}^{+0.42}$	${2.00}_{-2.00}^{+0.42}$	${1.99}_{-1.99}^{+0.43}$
${A}_{\mathrm{Fe}}$	$\lt 0.94$	$\lt 0.94$	$\lt 0.93$	$\lt 0.92$
${{ \mathcal R }}_{\mathrm{refl}}$	0.11 ± 0.04	0.11 ± 0.04	0.11 ± 0.04	0.11 ± 0.04
${\mathrm{const}}_{\mathrm{FPMB}}$	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006	0.992 ± 0.006
${\mathrm{const}}_{\mathrm{XRT}/\mathrm{PC}}$	${0.538}_{-0.029}^{+0.031}$	${0.538}_{-0.029}^{+0.030}$	${0.537}_{-0.029}^{+0.031}$	${0.537}_{-0.029}^{+0.030}$
${\mathrm{const}}_{\mathrm{XRT}/\mathrm{WT}}$	${0.624}_{-0.028}^{+0.030}$	${0.624}_{-0.020}^{+0.030}$	${0.623}_{-0.028}^{+0.030}$	${0.623}_{-0.020}^{+0.029}$
${\chi }^{2}/\mathrm{dof}$	519.0/519	519.0/519	519.0/519	519.0/519
Fb	${2.06}_{-0.08}^{+0.06}$	${2.06}_{-0.09}^{+0.06}$	${2.06}_{-0.08}^{+0.06}$	${2.06}_{-0.08}^{+0.06}$

Notes.

^aAssuming a distance of 2.3 kpc. ^bAbsorbed flux in the 0.3–78 keV band in units of 10⁻⁹ erg cm⁻² s⁻¹.

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Assuming a lamp-post geometry and an inclination of 70°, the obtained spectral parameters are in agreement with those given in Table 2 for the relxill model. For the disk height, we find upper limits of 20.01, 15.47, 18.53, and 19.47 R_g for spin values of 0, 0.8, 0.9, and 0.95, respectively. For an inclination of 30°, the inner disk radius is unconstrained and we obtain lower limits on the height of the accretion disk of 5.78, 6.18, and 6.34 R_g for spin values of 0.8, 0.9, and 0.95, respectively. For a Schwarzschild black hole the disk height is unconstrained.

Adding the Swift/UVOT data points and using the absorbed power-law and broken power-law models, we obtain photon indices and a break energy consistent with those of the Swift/XRT and NuSTAR fit with the same model given in Table 1. Fitting just the Swift/UVOT data points with a power-law model results in a statistically unacceptable fit with a photon index inconsistent with ${\rm{\Gamma }}\sim 1.6\mbox{--}1.7$, which confirms a change of the spectral shape at soft energies. Fitting the combined Swift/UVOT, XRT, and NuSTAR spectra with an absorbed disk blackbody plus thermal Comptonization model, where we used the redden component (Cardelli et al. 1989) for the interstellar extinction in the UVOT filters, we obtain spectral parameters consistent within errors with those of the Swift/XRT and NuSTAR fit with the same model (see Table 1). We also fit the spectra with the diskir model (Gierliński et al. 2008, 2009), which takes irradiation of the accretion disk into account. The obtained parameters can be found in Table 1. Including disk irradiation gives a higher disk temperature and a smaller disk radius, but the obtained parameters are consistent within errors with those of the Swift/XRT and NuSTAR fit with the absorbed disk blackbody plus thermal Comptonization model. Armas Padilla et al. (2013) found that the correlation between Swift/UVOT v-band and XRT data is consistent with a non-irradiated accretion disk. The data point obtained from the 2017 outburst lies below the correlation shown in Armas Padilla et al. (2013). Because we only have this data point, the correlation between v-band and XRT flux does not help us to decide if disk irradiation plays a role in the 2017 outburst. The obtained interstellar extinction is at least as big as the Galactic reddening in the direction of Swift J1357.2–0933 ($E(B-V)=0.04$ mag; Schlegel et al. 1998).