NUSTAR AND XMM-NEWTON OBSERVATIONS OF THE NEUTRON STAR X-RAY BINARY 1RXS J180408.9-34205

NuSTAR (Harrison et al. 2013) observed the target for $\simeq 80$ ks between 9:21 UT on 2015 March 5 and 7:36 UT March 6 (Obs ID 80001040002). Light curves and spectra were created using a ${120}^{\prime\prime }$ circular extraction region centered around the source and another region of the same dimensions away from the source as a background using the nuproducts tool from nustardas v1.3.1 with caldb 20150123. There were a total of five Type 1 X-ray bursts present in the light curves. We will report on the bursts in a separate paper. We created good time intervals (GTIs) to remove 100–170 s after the initial fast rise (depending on the duration of the individual burst) to separate these from the steady emission. These GTIs were applied during the generation of the spectra for both the FPMA and FPMB. Initial modeling of the steady spectra with a constant fixed to 1 for the FPMA and allowed to float for the FPMB was found to be within 0.95–1.05. We proceeded to combine the two source spectra, background spectra, and ancillary response matrices via addascaspec. We use addrmf to create a single redistribution matrix file. The spectra were grouped using grppha to have a minimum of 25 counts per bin (Cash 1979). The net count rate was 39.9 counts s⁻¹.

XMM-Newton observed the target on 2015 March 6 (Obs ID 0741620101) on revolution 2791 for 57 ks. The EPIC-pn camera was operated in "timing" (∼41.1 ks) and "burst" (∼9.5 ks) mode during this time with a medium optical blocking filter. The RGS cameras were also operational for $\simeq 55.8$ ks. The data were reduced using SAS ver. 13.5. We are primarily interested in the spectra obtained from RGS due to the high resolution. Moreover, the Epic-pn "timing" mode and "burst" mode spectra suffer from pileup and calibration issues (Walton et al. 2012). The net count rate was 210 and 167 counts s⁻¹ for the "timing" and "burst" mode, respectively. Even when eliminating the centralmost columns from the observation, the spectra obtained in the different modes did not agree with NuSTAR or even each other. NuSTAR does not suffer from photon pileup, so we chose to characterize the spectrum through the Fe K band using only NuSTAR. During the observation, there were seven Type 1 X-ray bursts that were filtered from the data by GTIs that removed 125–225 s after the initial fast rise depending on the duration of each burst. We then created spectra through rgsproc that were grouped using grppha to have a minimum of 25 counts per bin to allow the use of χ² statistics. There was an average of 2.6 counts s⁻¹ for RGS1 and 3.3 counts s⁻¹ for RGS2.

We start with investigating the NuSTAR data alone. Initial fits were performed with an absorbed power law with two Gaussian lines at 10.1 and 11.5 keV to account for instrumental response features (Harrison et al. 2013). These Gaussians will be present in all NuSTAR fits hereafter. This gives a particularly poor fit (χ²/dof = 9545/1159). The addition of a blackbody to account for the thermal component in the spectrum did not improve the goodness of fit (χ²/dof = 9545/1157). The absence of a thermal component is consistent with previous investigations of 1RXS J1804 in the hard state (Deller et al. 2015; Krimm et al. 2015a; Negoro et al. 2015).

A prominent Fe ${{\rm{K}}}_{\alpha }$ line centered at ∼6.4 keV with a red wing extending to lower energies and Fe edges can be seen rising above the continuum in Figure 1. There is also a prominent reflection hump in the higher energies above 10 keV. These reflection features not being properly described lend to the poor goodness of fit. Since a thermal component is not necessary to describe the spectrum, the only source of emission is a power law. This means that the disk is being illuminated by a source of hard X-ray photons and likely follows a radial dependence ${R}^{-3}$ profile.

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To properly describe the reflection features and relativistic effects present in the data, we employ the model relxill (García et al. 2014). This model self-consistently models for X-ray reflection and relativistic ray tracing for a power law irradiating an accretion disk. The parameters of this model are as follows: inner emissivity (q_in), outer emissivity (q_out), break radius (R_break) between the two emissivities, spin parameter (a_*), inclination of the disk (i), inner radius of the disk (R_in), outer radius of the disk (R_out), redshift (z), photon index of the power law (Γ), log of the ionization parameter ($\mathrm{log}(\xi )$), iron abundance (A_Fe), cutoff energy of the power law (E_cut), reflection fraction (f_refl), angleon, and normalization.

A few reasonable conditions were enforced when making fits with relxill. First, we tie the outer emissivity index, q_out, to the inner emissivity index, q_in, to create a constant emissivity index that is allowed to vary between 1 and 3. Next, we fix the spin parameter, a_* (where ${a}_{\ast }={cJ}/{{GM}}^{2}$), in the model relxill to 0 in the subsequent fits since NSs in LMXBs have ${a}_{\ast }\leqslant 0.3$ (Galloway et al. 2008; Miller et al. 2011). This does not hinder our estimate of the inner radius since the position of the innermost stable circular orbit (ISCO) is relatively constant for low spin parameters. In fact, Miller et al. (1998) found that corrections for frame-dragging for ${a}_{\ast }\lt 0.3$ give errors $\ll 10 \%$. Further, the outer disk radius has been fixed to 400R_g (where ${R}_{g}={GM}/{c}^{2}$). Lastly, to ensure that the inclination is properly taken into account in the reflection from the disk, we set angleon = 1 rather than 0 (angle averaged).

Fits with tbnew∗relxill and two Gaussian components, again accounting for instrument response features, provide a significantly better fit (χ²/dof = 1213/1151). This is well over a 20σ improvement. Values for model parameters are given in Table 1. Figure 2 shows the modeled spectrum and the ratio of the model to the data. The absorption column density is $(2.0\pm 2.0)\times {10}^{21}$ cm⁻². The large uncertainties are due to the lack of data in the low-energy range, where X-ray absorption is prevalent. The photon index is consistent with the hard limit of 1.4 at the 90% confidence level. The power-law cutoff energy is ${45}_{-1}^{+2}$ keV. The inclination of the disk is $25^\circ \pm 4^\circ$. The parameter of most interest is the inner radius, R_in, which was found to be ${1.9}_{-0.8}^{+1.4}$ ISCO.

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Table 1.  Relxill Fitting of NuSTAR and RGS

Component	Parameter	NuSTAR	RGS	NuSTAR + RGS
tbnew	NH (1022)	0.2 ± 0.2	0.360 ± 0.002	0.345 ± 0.001
	AO	...	1.77 ± 0.01	1.71 ± 0.01
relxill	${q}_{\mathrm{in}}={q}_{\mathrm{out}}$	${2.4}_{-0.4}^{+0.5}$	$\lt 1.9$	1.3 ± 0.2
	${a}_{\ast }^{\prime }$	0	0	0
	$i{(}^{\circ })$	25 ± 4	${18.4}_{-0.2}^{+0.5}$	18.3 ± 0.2
	${R}_{\mathrm{in}}(\mathrm{ISCO})$	${1.9}_{-0.8}^{+1.4}$	${1.2}_{-0.2}^{+3.3}$	$\leqslant 1.85$
	${R}_{\mathrm{out}}{({R}_{g})}^{\prime }$	400	400	400
	${z}^{\prime }$	0	0	0
	Γ	$\lt 1.424$	$\lt 1.402$	1.402 ± 0.001
	$\mathrm{log}(\xi )$	${2.4}_{-0.1}^{+0.4}$	3.14 ± 0.03	2.75 ± 0.01
	${A}_{\mathrm{Fe}}$	${0.83}_{-0.3}^{+0.4}$	$\lt 0.51$	$\lt 0.51$
	${E}_{\mathrm{cut}}(\mathrm{keV})$	${45}_{-1}^{+2}$	30 ± 3	47.3 ± 0.3
	${f}_{\mathrm{refl}}$	0.15 ± 0.02	0.21 ± 0.01	0.15 ± 0.01
	angleon'	1	1	1
	norm $({10}^{-2})$	${9.5}_{-0.6}^{+0.3}$	9.81 ± 0.04	9.35 ± 0.01
relline	${E}_{\mathrm{line}}$	...	0.569 ± 0.001	0.569 ± 0.001
	norm $({10}^{-3})$	...	6.7 ± 0.8	3.9 ± 0.6
	${\chi }_{\nu }^{2}$(dof)	1.05 (1151)	1.48 (2804)	1.34 (3963)

' = fixed

Note. Errors are quoted at ≥90% confidence level. Setting angleon =1 takes the inclination into account when modeling reflection. A constant was allowed to float between NuSTAR and the RGS data. The NuSTAR was frozen at the value of 1.0, RGS1 was fit at 1.234 ± 0.006, and RGS2 was fit at 1.182 ± 0.005. The emissivity index, inclination, and inner radius in relline were tied to the values in relxill. The unabsorbed flux from the combined NuSTAR+RGS fit from 0.45 to 50.0 keV is ${F}_{\mathrm{unabs},(0.45\mbox{--}50.0\mathrm{keV})}=1.71\times {10}^{-9}$ erg cm⁻² s⁻¹. This gives a luminosity of ${L}_{(0.45\mbox{--}50.0\mathrm{keV})}=6.8\times {10}^{36}$ erg s⁻¹ (∼3%–4% L_Edd).

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The RGS spectra showed prominent broad features rising above the continuum emission (modeled with an absorbed power law) at ∼0.50, ∼0.57, and ∼0.65 keV corresponding to H-like N vii, He-like O vii, and H-like O viii, respectively (see Figure 3). Applying simple Gaussian lines places their centroid energy at 0.501 ± 0.002 keV, 0.568 ± 0.002 keV, and 0.655 ± 0.001 keV detected at the 3.2σ, 5.9σ, and 9σ confidence level. To test the robustness of these lines to different assumptions about the interstellar medium, we applied ismabs (Gatuzz et al. 2014) with the same power-law continuum. The abundance of each element is left as a free parameter so that the photoelectric absorption edges in ismabs have the greatest possible opportunity to model the data in a way that would remove line-like features. The lines are still present in the spectra, though their significance has decreased slightly, with the N vii line only being marginally significant. We believe the N vii to be a real feature, but due to its location at the edge of the effective area of the detector, we are unable to model it properly in subsequent fits. See Table 2 for the values obtained for the Gaussian lines with each absorption model.

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Table 2.  Emission Line in RGS Spectra

Abs Model	Ion	Lab E (keV)	Ecentroid (keV)	σ (keV) (${10}^{-2}$)	Norm (${10}^{-4}$)	Significance (σ)
tbnew	N vii	0.5003	0.501 ± 0.002	0.6 ± 0.2	1.6 ± 0.5	3.2
	O vii	0.574	0.568 ± 0.002	1.1 ± 0.2	2.9 ± 0.5	5.9
	O viii	0.654	0.655 ± 0.001	1.2 ± 0.2	4.5 ± 0.5	9
ismabs	N vii	0.5003	0.501 ± 0.002	0.6 ± 0.3	1.3 ± 0.5	2.6
	O vii	0.574	0.571 ± 0.001	0.8 ± 0.2	2.2 ± 0.5	4.4
	O viii	0.654	0.654 ± 0.001	1.0 ± 0.2	3.4 ± 0.6	5.7

Note. In tbnew, all abundances were set to solar with ${N}_{{\rm{H}}}=2.0\times {10}^{21}$ cm⁻² (Dickey & Lockman 1990). Normalization is given in units of photons cm⁻² s⁻¹. An absorbed power law was used to model the continuum. In ismabs, elemental abundances were allowed to vary. The continuum was modeled with a power law of photon index 1.4.

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We then applied the self-consistent reflection model relxill in combination with tbnew to describe the lines simultaneously. We allowed the abundance of O to be a free parameter in tbnew to fully account for the O viii K edge at 0.53 keV, which can be seen in Figure 3. The model was not able to account for the He-like O vii line with the other two H-like lines, likely due to the lower ionization parameter needed to create the line. We employ the relativistic line model relline to describe this feature. The emissivity index, inclination, and inner radius were tied to the parameters in relxill. The limb parameter was set to 2 for consistency with relxill, which assumes limb brightening. We only allowed the normalization and line energy to be free. The addition of the relline component to relxill improves the overall fit by ${\rm{\Delta }}{\chi }^{2}=147$ (for 2 dof). The resulting best fit can be seen in Table 1. The probability of the additional component improving the fit by chance was found to be negligibly small ($3.19\times {10}^{-24}$) via an F-test. This is a 9.6σ improvement. The unfolded model can be seen in Figure 4. Figure 5 shows the relxill-only model decomposed into the continuum and reflection components that are comprised in the model.

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The cut energy and emissivity are not well constrained, likely due to limited bandwidth. Again, the photon index is consistent with the hard limit of 1.4 at the 90% confidence level. The absorption column is better constrained than in the previous fit with ${N}_{{\rm{H}}}=3.60(\pm )0.02\times {10}^{21}$ cm⁻² with an oxygen abundance 1.77 ± 0.01 solar. The reflection fraction is higher than that of the NuSTAR spectrum, meaning that it is dominated by more reflection. The high reflection fraction reaffirms that the emission lines are reflection features. The inclination is several degrees lower than the inclination found in the higher energy range, but is generally consistent. The location of the inner disk (${1.2}_{-0.2}^{+3.3}$ ISCO) is compatible with the iron line region.

Due to the limited energy bandwidth of the RGS, we fit the NuSTAR and RGS together in order to obtain better estimates of the spectral parameters of interest. Tying the RGS data with the NuSTAR data provides an opportunity to fit multiple relativistic reflection features over a wide energy range (∼0.45–50.0 keV) and from different ionized regions in the disk. A constant was allowed to float between the two observations, but all other model parameters were tied. The constant was frozen at the value of 1.0 for NuSTAR and free to vary for RGS1 and RGS2. The constant for RGS1 was found to be $c=1.234\pm 0.006$ and $c=1.182\pm 0.005$ for RGS2. The model we first use is tbnew∗(relxill+relline+Gauss+Gauss) to model the relativistic reflection features with X-ray absorption along the line of sight. The Gaussian lines are to account for instrumental response features. See Table 1 and Figure 6.

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Simultaneous fits return a neutral absorption column density ${N}_{{\rm{H}}}=(3.45\pm 0.01)\times {10}^{21}$ cm⁻² with a slight overabundance in oxygen, ${\rm{O}}=1.71\pm 0.01$ solar. The emissivity index, $q=1.3\pm 0.2$, suggests that a large area of the disk is being illuminated by a hard X-ray source. The ionization parameter being $\mathrm{log}(\xi )=2.75\pm 0.01$ is within reason for an accreting source in the low/hard state (LHS; Cackett et al. 2010), although there are a number of cases where lower ionizations are found for an NS in the LHS (SAX J1808.4-3658: Papitto et al. 2009; Cackett et al. 2009; 4U 1705-44: D'Aì et al. 2010; Di Salvo et al. 2015). The iron abundance was allowed to be a free parameter and is consistent with the hard limit of 0.5 at the 90% confidence level. The photon index of the power-law component that is responsible for producing the reflection spectrum is on the harder side with ${\rm{\Gamma }}=1.402\pm 0.001$. The reflection fraction, ${f}_{\mathrm{refl}}$, is 0.15 ± 0.01. The inclination agrees with the previous individual fit to the RGS data alone. The inner radius, ${R}_{\mathrm{in}}\leqslant 1.85$ ISCO, is consistent within uncertainties with the individual fits to NuSTAR and RGS alone. Figure 7 shows the change in χ² when stepping the inner disk radius parameter out to 5 ISCO using the "steppar" command in XSPEC.

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To explore the multiple ionization parameters that seem prevalent in the RGS data, we remove the relline component and apply a double relxill model to the joint spectra. The idea is to be able to map the X-ray interactions with accretion disk radii. We tie the emissivity index, inclination, inner radius, photon index, and iron abundance between the two relxill components and allow the ionization, reflection fraction, and normalization to change between them. Parameter values can be seen in Table 3.

Table 3.  Double Relxill Fitting of NuSTAR and RGS

Component	Parameter	Values
tbnew	${N}_{{\rm{H}}}({10}^{22})$	0.340 ± 0.003
	AO	1.689 ± 0.03
relxill	${q}_{\mathrm{in}}={q}_{\mathrm{out}}$	$\lt 1.2$
	${a}_{\ast }^{\prime }$	0
	$i{(}^{\circ })$	${18.11}_{-0.2}^{+0.3}$
	${R}_{\mathrm{in}}(\mathrm{ISCO})$	${1.13}_{-0.13}^{+2.98}$
	${R}_{\mathrm{out}}{({R}_{g})}^{\prime }$	400
	${z}^{\prime }$	0
	Γ	$\lt 1.41$
	$\mathrm{log}{(\xi )}_{1}$	2.9 ± 0.1
	$\mathrm{log}{(\xi )}_{2}$	1.5 ± 0.2
	${A}_{\mathrm{Fe}}$	$\lt 0.54$
	${E}_{\mathrm{cut}}(\mathrm{keV})$	$45.1\pm 0$
	${f}_{\mathrm{refl},1}$	0.2 ± 0.1
	${f}_{\mathrm{refl},2}$	0.22 ± 0.02
	angleon'	1
	norm1 $({10}^{-2})$	${4.73}_{-1.3}^{+2.2}$
	norm2 $({10}^{-2})$	${4.68}_{-1.0}^{+4.7}$
	${\chi }_{\nu }^{2}$(dof)	1.36 (3962)

' = fixed

Note. Errors are quoted at ≥90% confidence level. Setting angleon = 1 takes the inclination into account when modeling reflection. A constant was allowed to float between NuSTAR and the RGS data. The NuSTAR was frozen at the value of 1.0, RGS1 was fit at 1.25 ± 0.01, and RGS2 was fit at 1.19 ± 0.01.

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The higher ionization parameter agrees with the values obtained in the previous fits. The lower ionization value accounts for the production of the O vii line. The inner radius, ${R}_{\mathrm{in}}\lt 4.1$ ISCO, agrees with the value obtained in the previous model when using relline to describe the O vii line, which does not make assumptions about the underlying gas physics like relxill does. The reflection fractions for each component are consistent with one another, though the normalization is not well constrained. We do not expect these two different ionization states to occur at the same radii, and as such, we tried to free the inner radius in each of the relxill components to map the radius at which the X-ray interactions with the disk occurred. We were unable to obtain radii that were statistically distinct. The goodness of fit of the double relxill model is comparable to the simpler fit with just one relxill component and relline. We chose to use the parameter values from the simpler model fits in subsequent calculations.

If the inner disk is truncated substantially above the NS surface itself, as allowed by our upper limits on R_in, then the disk may instead be truncated by a boundary layer extending from the stellar surface. The upper limit on R_in would require a boundary layer that is a few times the stellar radius in size. Alternatively, the disk could be truncated by magnetic pressure. We can place an upper limit on the strength of the field using the upper limit of ${R}_{\mathrm{in}}=1.85$ ISCO. Assuming a mass of 1.4 ${M}_{\odot }$, taking the distance to be 5.8 kpc (Krimm et al. 2015b), and using the unabsorbed flux from 0.45 to 50.0 keV of $1.71\times {10}^{-9}$ erg cm⁻² s⁻¹ as the bolometric flux, we can determine the magnetic dipole moment, μ, from Equation (1) taken from Cackett et al. (2009):

$$\begin{eqnarray}\mu & = & 3.5\times {10}^{23}\ {k}_{A}^{-7/4}\ {x}^{7/4}{\left(\displaystyle \frac{M}{1.4{M}_{\odot }}\right)}^{2}\\ & & \times {\left(\displaystyle \frac{{f}_{\mathrm{ang}}}{\eta }\displaystyle \frac{{F}_{\mathrm{bol}}}{{10}^{-9}\mathrm{erg}{\mathrm{cm}}^{-2}{{\rm{s}}}^{-1}}\right)}^{1/2}\displaystyle \frac{D}{3.5\;\mathrm{kpc}}\ {\rm{G}}\;{\mathrm{cm}}^{3}.\end{eqnarray} \tag{ 1 }$$

If we make the same assumptions about geometry and accretion efficiency (i.e., ${k}_{A}=1,{f}_{\mathrm{ang}}=1$, and $\eta =0.1$), then $\mu \simeq 1.62\times {10}^{26}$ G cm³. This corresponds to a magnetic field strength of $B\simeq 3.2\times {10}^{8}$ G at the magnetic poles for an NS of 10 km. Moreover, if we assume a different conversion factor ${k}_{A}=0.5$ (Long et al. 2005), then the magnetic field strength at the poles would be $B\simeq 1.0\times {10}^{9}$ G. We note, however, that coherent pulsations have not been detected in 1RXS J1804, and the source is not identified as a pulsar.

However, if the disk does extend closer to the ISCO, then we can place a lower limit on the gravitational redshift from the NS surface, z_NS. Gravitational redshift is given by $z+1=1/\sqrt{1-2{GM}/{R}_{\mathrm{in}}{c}^{2}}$. For ${R}_{\mathrm{in}}=1.1$ ISCO, assuming a 1.4 ${M}_{\odot }$ NS and ${a}_{\ast }=0$, ${z}_{\mathrm{NS}}\geqslant 0.2$ given that the NS is smaller than the radius of the disk. Our measurement for R_in does extend down to 1 ISCO. If this were the case, then ${z}_{\mathrm{NS}}\geqslant 0.22$ for a 12 km NS.

To be thorough, we fix the spin to 0.12 and 0.24 to test our assumption that the position of the inner disk radius changes slowly for low spin parameters as per Miller et al. (2013). The inner radius changes only marginally for the highest spin of ${a}_{\ast }=0.24$, confirming that our fits are not highly dependent on the choice of spin parameter.