THE TRANSIENT ACCRETING X-RAY PULSAR XTE J1946+274: STABILITY OF X-RAY PROPERTIES AT LOW FLUX AND UPDATED ORBITAL SOLUTION

Figures 2(a) and (b) show the background-subtracted light curves for the summed count rates of XIS 0, 1, and 3 (0.5–10 keV) and for the PIN count rate (10–70 keV), respectively. According to the Swift-BAT light curve in Figure 1, the Suzaku observation was performed at the end of a decreasing long-term flux trend. This appears to be consistent with the PIN light curve, which might show a moderate decline from 1.06 ± 0.03 counts s⁻¹ in the first satellite orbit of the observation to 0.86 ± 0.03 counts s⁻¹ in the last one. There are no significant flares or dips observed. The XIS light curve displays jumps between two count rate levels for most Suzaku orbits. The effect can be observed in all three XIS units individually, and it is consistent with the systematic attitude instability mentioned in Section 2. This is aggravated by the HXD aim-point used for this observation, since it is slightly off-center on the XIS chips.

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Figures 2(c) and (d) show hardness ratio evolutions for count rates in the energy bands 5–10 keV and 0.5–5 keV and for count rates in the energy bands 10–20 keV and 0.5–5 keV, respectively. We observe little structure related to the systematic attitude instability in the XIS-PIN band ratios, and no structure in the XIS-XIS band ratios. Since there are no significant source related flux or hardness changes over the observation, we do not perform a time-resolved spectral analysis, but model the observation averaged spectra in Section 4.

The XIS has a time resolution of 2 s when in 1/4 window mode, while the PIN has a resolution of 61 μs (ISAS/JAXA & X-ray Astrophysics Laboratory NASA/Goddard Space Flight Center 2015). Therefore, only the PIN data were used for the pulse period determination. Applying epoch folding (Leahy et al. 1983; Schwarzenberg-Czerny 1989) to the screened, barycenter-corrected, non-background-subtracted PIN events, in the 10–40 keV range, we determined a local pulse period of 15.750025(27) s. The uncertainty was estimated using Monte Carlo light curve simulations as described in Section 3.3.

Based on this period and a reference time of MJD 55481.714 for phase 0, we obtained pulse profiles in several energy bands by folding the screened, barycenter-corrected events using 8 phase bins for XIS (0.5–5 keV and 5–10 keV; note that the Suzaku-XIS pulse profiles presented by Maitra & Paul (2013) are oversampled) and 128 phase bins for PIN (10–20 keV, 20–40 keV and 40–70 keV). Figure 3 shows that up to 40 keV the pulse profiles are consistent in general structure: they are double-peaked, with a deep (ϕ ∼ 0.35) and a shallow minimum (ϕ ∼ 0.9). In the 10–20 keV range an additional narrow peak feature is visible (ϕ ∼ 0.2) before the deep minimum. The shallow minimum is deeper at energies ≲5 keV than at higher energies. Similar behavior was found by Wilson et al. (2003) during two outbursts observed with RXTE-PCA in 1998 and 2001. We determined the pulse fractions measured with PIN as the difference between the maximum and minimum count rates of the profiles normalized by mean count rate, and obtained values of 1.02 ± 0.09 and 1.04 ± 0.12 for the 10–20 keV and 20–40 keV energy ranges, respectively. Wilson et al. (2003) found pulsed fractions as high as 0.74 in the 2–30 keV range during low-flux outbursts in 2001. No pulsations are visible in the 40–70 keV Suzaku profile.

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Figures 3(c) and (d) include a comparison for the 10–20 keV and 20–40 keV energy bands between the Suzaku-PIN pulse profiles from 2010 October 12 (end of the second outburst) and the RXTE-PCA pulse profiles from 2010 June 26 (ObsID 95032-12-02-00, peak of the first outburst). The latter were obtained using the same light curve extraction criteria as Müller et al. (2012) used for the full PCA energy band and applying epoch folding with the local period of 15.764 s determined by their analysis. This comparison emphasizes that the shapes of the profiles obtained from the two instruments are very similar, especially at higher energies, despite the large difference in flux:

$$\begin{eqnarray*}{\rm{10\mbox{--}20}}\;\mathrm{keV}\;\mathrm{flux} & : & \left\{\begin{array}{ll}1.57\;\times \;{10}^{-9}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2} & \mathrm{PCA},\\ 2.10\;\times \;{10}^{-10}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2} & {Suzaku},\end{array}\right.\\ {\rm{20\mbox{--}40}}\;\mathrm{keV}\;\mathrm{flux} & : & \left\{\begin{array}{ll}1.12\;\times \;{10}^{-9}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2} & \mathrm{PCA},\\ 1.30\;\times \;{10}^{-10}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2} & {Suzaku}.\end{array}\right.\end{eqnarray*}$$

The Suzaku fluxes were derived from the spectral best-fit model presented in Section 4.1 and the RXTE-PCA fluxes from the spectral best fit of the averaged observations during the peak of the first outburst (epoch 1 fit of Müller et al. 2012).

The observed pulse period over time as measured by an observer is due to the intrinsic spin-up or spin-down of the neutron star, caused, e.g., by accretion torques, and on due to the Doppler shift by orbital motion. Usually the Doppler shift dominates changes in the measured pulse period. For XTE J1946+274, however, the neutron star undergoes a strong spin-up during outbursts such that the orbital parameters of the system could not be constrained well in the past.

Wilson et al. (2003) were able to describe the pulse frequencies as measured by CGRO-BATSE and RXTE-PCA during the outburst series between 1998 and 2001 using a piecewise linear approximation of the intrinsic spin-up. Their best fit with a ${\chi }_{\mathrm{red}}^{2}=5.94$ for 37 degrees of freedom (dof) shows that this simplified approximation cannot give a good description of the measured period evolution.

In the most simple model for the angular momentum transfer of the infalling material onto the neutron star (Ghosh & Lamb 1979), the period change of the neutron star is connected to the luminosity L via

$$\begin{eqnarray}&&-\dot{P}\propto {P}^{2}{L}^{\alpha }\end{eqnarray} \tag{ 2 }$$

where α = 1 for wind and α = 6/7 for disk accretion. Assuming that the luminosity of the source is proportional to the measured flux F, the pulse period at the time t is then given by

$$\begin{eqnarray}&&P(t)={P}_{0}+a(t-{t}_{0})-b{\displaystyle \int }_{{t}_{0}}^{t}{\left(\displaystyle \frac{P(t^{\prime} )}{{P}_{0}}\right)}^{2}{\left(\displaystyle \frac{F(t^{\prime} )}{{F}_{\mathrm{ref}}}\right)}^{\alpha }{dt}^{\prime} ,\end{eqnarray} \tag{ 3 }$$

where P₀ is the pulse period at the reference time, t₀, b is the torque strength, and F_ref is a reference flux. The model also takes a constant spin change, a, into account, which could be caused by, e.g., the propeller effect (Illarionov & Sunyaev 1975). We obtain the observed pulse period P_obs(t) by applying the Doppler shift caused by the orbital motion to P(t) as defined in Equation (3):

$$\begin{eqnarray}&&{P}_{\mathrm{obs}}=P(t)(1+v(t)/c),\end{eqnarray} \tag{ 4 }$$

where $v(t)$ is the orbital velocity of the neutron star projected on the line of sight and c is the speed of light. The orbital parameters needed to calculate v(t) are the orbital period, P_orb, the time of periastron passage, τ, the projected semimajor axis, ${a}_{\mathrm{sm}}\mathrm{sin}i,$ where i is the inclination, the eccentricity e, and the longitude of periastron ω, such that

$$\begin{eqnarray}&&v(t)=\displaystyle \frac{2\pi {a}_{\mathrm{sm}}\mathrm{sin}i}{{P}_{\mathrm{orb}}{(1-{e}^{2})}^{1/2}}\left(\mathrm{cos}(\theta (t)+\omega )+e\mathrm{cos}\omega \right),\end{eqnarray} \tag{ 5 }$$

where θ(t) is the true anomaly found by solving Kepler's equation, which itself depends on the orbital parameters listed above.

During the activity of XTE J1946+274 in 2010 and 2011, various X-ray and gamma-ray missions observed the source (see Section 2 and Table 1 for details), such that the pulse period evolution is known in great detail especially from Fermi-GBM. We searched for pulsations near the GBM period for Suzaku-PIN, RXTE-PCA, and Swift-XRT using the epoch folding technique. For the PIN we determined a pulse period of 15.750025(27) s, see Section 3.2. For PCA, we used PCU2 top-layer light curves, extracted in GoodXenon mode with a time resolution of 0.125 s. The XRT data were taken in Windowed Timing mode. The XRT light curves were obtained from a ∼05 region centered on the source position and rebinned to a 1 s time resolution. The initial uncertainties of the measured pulse periods were estimated by Monte Carlo simulations, where synthetic light curves of the source based on the observed pulse profile were searched for the pulse period. The uncertainties of the periods measured by Fermi-GBM were provided by the GBM Pulsar Project. The measured pulse periods of XTE J1946+274 are shown in Figure 4.

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In order to compute the pulse periods via Equation (3), we used the 1 day binned 15–50 keV Swift-BAT light curve of the source as the bolometric flux evolution F(t) and chose F_ref = 1 count s⁻¹ cm⁻². Using the hard BAT flux as a proxy for the bolometric flux is justified since the source does not show strong spectral changes over and between outbursts (Müller et al. 2012, this work). The main source of uncertainty in the predicted pulse period therefore does not come from changes in the spectral shape, but from the overall uncertainty in the BAT flux measurements, which can have uncertainties of up to 15%. In order to take these uncertainties into account, we use a Monte Carlo approach in which 10,000 BAT light curves are simulated. For each time with a BAT measurement, t_i, we draw a simulated BAT count rate from a Gaussian distribution with mean and standard deviation given by the measured BAT rate and uncertainty, respectively. For each of the light curve realizations we then derive the best-fit pulse period evolution using Equation (4). The standard deviation of the resulting simulated pulse periods, ${\sigma }_{M({t}_{i})},$ at each t_i is then taken to be representative of the uncertainty of the modeled pulse period evolution.

In order to obtain the final orbit and pulse period model, based on an initial estimate for ${\sigma }_{M({t}_{i})}$ we minimize the fit statistics

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}\displaystyle \frac{{({P}_{i}-{P}_{\mathrm{obs}}({t}_{i}))}^{2}}{{\sigma }_{{P}_{i}}^{2}+{\sigma }_{M({t}_{i})}^{2}},\end{eqnarray} \tag{ 6 }$$

where P_i is the measured pulse period at time t_i, ${P}_{\mathrm{obs}}({t}_{i})$ is the model period (Equation (4)), and ${\sigma }_{{P}_{i}}$ and ${\sigma }_{M({t}_{i})}$ are the uncertainties of the data and the model as described above. We then iteratively apply the Monte Carlo approach above to refine the estimated model uncertainties. Usually three iterations are sufficient to obtain convergence. Figure 4(d) displays the final estimate for the uncertainty of the pulse period model.

Fits to Equation (4) are shown in Figure 4. The modeled intrinsic spin period P(t) of the neutron star (shown in purple) dominates the period evolution (black) compared to the effect of the orbital motion (orange). The two residual panels show different assumptions for the exponent α of Equation (2). In order to check the dependency of the orbital parameters on the assumed torque model, we model the data for both, α = 6/7 (the DISK model) and for α = 1 (the WIND model). As illustrated by Figure 4, both models result in a successful description of the measured pulse period evolution and yield orbital parameters that are consistent with each other (Table 2).

Table 2.  Orbital Parameters and Spin Period Evolution; Uncertainties Are on the 90% Confidence Level

	DISK	WIND
${a}_{\mathrm{sm}}\mathrm{sin}i$ (lt-s)	${471.2}_{-4.3}^{+2.6}$	${471.1}_{-2.8}^{+2.7}$
Porb (days)	${172.7}_{-0.6}^{+0.6}$	${171.4}_{-0.4}^{+0.4}$
τ (MJD)	${55514.8}_{-1.1}^{+0.8}$	${55515.5}_{-0.7}^{+0.8}$
e	${0.246}_{-0.009}^{+0.009}$	${0.266}_{-0.007}^{+0.007}$
ω (°)	$-{87.4}_{-1.7}^{+1.5}$	$-{87.1}_{-1.0}^{+1.2}$
t0	55550 (fixed)	55550 (fixed)
P0 (s)	${15.749742}_{-0.000014}^{+0.000023}$	${15.749753}_{-0.000013}^{+0.000013}$
a (s s−1)	${1.67}_{-0.18}^{+0.16}\times {10}^{-10}$	${0.47}_{-0.10}^{+0.20}\times {10}^{-10}$
b (s s−1)	${6.52}_{-0.08}^{+0.06}\times {10}^{-8}$	${10.76}_{-0.04}^{+0.05}\times {10}^{-8}$
α	6/7 (fixed)	1 (fixed)
${\chi }_{\mathrm{red}}^{2}/\mathrm{dof}$	1.05/89	1.06/89

Note. Listed are the projected semimajor axis, ${a}_{\mathrm{sm}}\mathrm{sin}i,$ the orbital period, P_orb, the time of periastron passage, τ, the eccentricity, e, the longitude of periastron, ω, the reference time, t₀, the spin period at t₀, P₀, the constant spin change, a, the torque strength, b, and the luminosity exponent, α.

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We stress again that for each of the two models the additional uncertainties due to the BAT data have to be calculated separately by the iterative Monte Carlo approach described above. The resulting uncertainties of the model vary between 0.02 and 0.38 ms with a mean of 0.09 ms (see Figure 4(d)). Within the model uncertainties, however, the model pulse periods agree with the measured data. For example, the pulse period predicted by the DISK model for the time of the Suzaku observation is 15.750300(380) s, while the observed period is 15.750025(27) s. Unfortunately, the model uncertainty is large enough that it is not possible for us to distinguish between the different torquing models, with both model fits yielding almost the same χ². Thankfully, as shown in Table 2, the orbital parameters are insensitive to the details of modeling $\dot{P}(t).$ It is only the best-fit values for the spin change, a, and the torque strength, b, that differ significantly. Numerical experimenting revealed that this is due to a strong parameter degeneracy of the luminosity exponent α with a and b. Based on the pulse period evolution alone it is therefore not possible to distinguish between the two torquing scenarios.

We modeled the 1–9.4 keV XIS and the 17–38 keV PIN spectra using xspec12 (Arnaud 1996). The 1.8–2.4 keV range was excluded due to known calibration uncertainties (ISAS/JAXA & X-ray Astrophysics Laboratory NASA/Goddard Space Flight Center 2013). We applied the normalization constants ${c}_{\mathrm{XIS}\;1},\;$ ${c}_{\mathrm{XIS}\;3},$ and c_PIN to account for the flux cross-calibration between the respective instruments relative to XIS 0, where ${c}_{\mathrm{XIS}\;0}$ was fixed at 1 (xspec model constant). The absorption was modeled with tbnew, an updated version of tbabs, ²⁰ using cross sections by Verner & Yakovlev (1995) and abundances by Wilms et al. (2000). Extending the fit down to 0.8 keV, Maitra & Paul (2013) included an additional partial covering absorption component. Since they found that its parameters are model dependent and since the hardness ratio evolution over the observation (Figures 2(c) and (d)) does not indicate any variability due to partial covering, we used one fully covering absorber alone sufficient which is to model the data down to 1 keV well.

Following the spectral analysis of Müller et al. (2012), we first fitted a Fermi–Dirac cut-off model (power×fdcut, Tanaka 1986), described by:

$$\begin{eqnarray}&&{M}_{\mathrm{FDCUT}}(E)\propto {E}^{-{\rm{\Gamma }}}\times {\left[1+\mathrm{exp}\left(\displaystyle \frac{E-{E}_{\mathrm{cut}}}{{E}_{\mathrm{fold}}}\right)\right]}^{-1},\end{eqnarray} \tag{ 7 }$$

where the photon flux at energy E is described by a power law with a photon index Γ, multiplied by an exponential cut off at energy E_cut with a folding energy E_fold. The soft Galactic ridge emission seen in the 6–7 keV range, which needed to be taken into account for PCA data modeling by Müller et al. (2012), is not required for Suzaku due to XIS being an imaging instrument. The results of this fit are listed in Table 3 in the column labeled FDCUT I. Figure 5(b) shows the residuals from fitting the continuum model only.

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Table 3.  Spectral Fit Parameters

	FDCUT I	FDCUT II	FDCUT III	CUTOFFPL	HIGHECUT	NPEXb
NH (×1022 cm−2)	${1.14}_{-0.02}^{+0.01}$	${1.66}_{-0.03}^{+0.02}$	1.67(3)	${1.59}_{-0.04}^{+0.02}$	${1.59}_{-0.04}^{+0.02}$	${1.58}_{-0.05}^{+0.03}$
AΓ(×10−2 keV−1 cm−2 s−1)	${2.04}_{-0.05}^{+0.03}$	${2.02}_{-0.05}^{+0.03}$	${2.05}_{-0.05}^{+0.04}$	0.97(2)	0.97(2)	${0.96}_{-0.04}^{+0.02}$
Γ	${0.55}_{-0.02}^{+0.01}$	${0.55}_{-0.02}^{+0.01}$	0.57(2)	${0.41}_{-0.04}^{+0.02}$	${0.41}_{-0.04}^{+0.02}$	${0.39}_{-0.08}^{+0.04}$
Efold (keV)	${8.6}_{-0.3}^{+0.2}$	${8.5}_{-0.3}^{+0.2}$	${8.9}_{-0.4}^{+0.4}$	${9.6}_{-0.6}^{+0.4}$	${9.6}_{-0.6}^{+0.4}$	${9.1}_{-1.4}^{+0.8}$
Ecut (×10−2 keV)	${0.09}_{-0.09}^{+0.04}$	${0.01}_{-0.01}^{+0.00}$	${0.05}_{-0.05}^{+0.03}$	⋯	${0.01}_{-0.01}^{+0.00}$	⋯
Γ2	⋯	⋯	⋯	⋯	⋯	−2a
α(×10−2) (keV/keV)	⋯	⋯	⋯	⋯	⋯	${0.020}_{-0.020}^{0.003}$
EFe (keV)	⋯	6.41(3)	6.41(3)	6.41(3)	6.41(3)	6.41(3)
σFe (keV)	⋯	0.1a	0.1a	0.1a	0.1a	0.1a
AFe (×10−5 photons cm−2 s−1)	⋯	${8.6}_{-1.4}^{+1.3}$	${8.6}_{-1.3}^{+1.3}$	${8.7}_{-1.4}^{+1.3}$	${8.7}_{-1.4}^{+1.3}$	${8.7}_{-1.0}^{+1.1}$
ECRSF (keV)	⋯	⋯	${35.2}_{-1.3}^{+1.5}$	${34.8}_{-1.0}^{+1.2}$	${34.8}_{-1.0}^{+1.2}$	${34.8}_{-1.0}^{+1.1}$
σCRSF (keV)	⋯	⋯	2a	2a	2a	2a
DCRSF (keV)	⋯	⋯	${2.4}_{-1.3}^{+1.5}$	${3.5}_{-1.5}^{+1.5}$	${3.5}_{-1.5}^{+1.5}$	${3.8}_{-1.5}^{+1.6}$
${c}_{\mathrm{XIS}\;0}$	1a	1a	1a	1a	1a	1a
${c}_{\mathrm{XIS}\;1}$	1.07(1)	1.07(1)	1.07(1)	1.07(1)	1.07(1)	1.07(1)
${c}_{\mathrm{XIS}\;3}$	0.95(1)	0.95(1)	0.95(1)	0.95(1)	0.95(1)	0.95(1)
cPIN	${1.32}_{-0.05}^{+0.07}$	${1.35}_{-0.05}^{+0.07}$	${1.29}_{-0.06}^{+0.07}$	${1.29}_{-0.05}^{+0.07}$	${1.29}_{-0.05}^{+0.08}$	${1.31}_{-0.06}^{+0.07}$
${\chi }_{\mathrm{red}}^{2}/\mathrm{dof}$	1.38/470	1.19/468	1.17/466	1.12/467	1.12/466	1.12/466

Notes. The XIS and PIN spectra were fitted simultaneously with the models described in Section 4.1. The columns are labeled according to the continuum that was used. The uncertainties are given on a 90% confidence level.

^aThese parameters were frozen while fitting. ^bFor the model ${M}_{\mathrm{NPEX}}(E)\propto ({E}^{-{\rm{\Gamma }}}+\alpha {E}^{+{{\rm{\Gamma }}}_{2}}){e}^{-E/{E}_{\mathrm{fold}}}$ the parameters Γ and Γ₂ are the indices of the falling and rising power-law components and α is the normalization of the rising relative to the falling component.

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The strongest residuals are seen at 6.41 keV. We interpreted this as a narrow Fe Kα fluorescence line that we proceeded to describe with a Gaussian line model (Gaussian). The width is unresolved and we fixed it at σ_Fe = 0. 1 keV, slightly below the XIS detector resolution. The results of this fit are listed in Table 3 in the column labeled FDCUT II and Figure 5(c) shows the fit residuals.

Residuals are still visible in the PIN energy range, especially around 35 keV. We included an absorption-like line with a Gaussian optical depth profile (gabs) often used to describe cyclotron lines:

$$\begin{eqnarray}&&{M}_{\mathrm{CRSF}}(E)=\mathrm{exp}(-\tau (E))\end{eqnarray} \tag{ 8 }$$

with

$$\begin{eqnarray}&&\tau (E)={\tau }_{\mathrm{CRSF}}\mathrm{exp}\left[-\displaystyle \frac{1}{2}{\left(\displaystyle \frac{E-{E}_{\mathrm{CRSF}}}{{\sigma }_{\mathrm{CRSF}}}\right)}^{2}\right]\end{eqnarray} \tag{ 9 }$$

where E_CRSF is the cyclotron line energy, σ_CRSF is the line width, and τ_CRSF is the optical depth. Note that the gabs implementation provides the line depth ${D}_{\mathrm{CRSF}}\;={\tau }_{\mathrm{CRSF}}{\sigma }_{\mathrm{CRSF}}\sqrt{2\pi }$ instead of τ_CRSF. The CRSF width was unresolved and we fixed it at σ_CRSF = 2 keV, close to PIN's detector resolution. The results of this fit are listed in Table 3 in the column labeled FDCUT III. Figure 5(a) shows the spectra and fitted model and Figure 5(e) shows the fit residuals. The latter do not show any further strong features. In order to illustrate the contribution of the CRSF feature to the best fit, Figure 5(d) shows the residuals of the best fit with the CRSF depth set to 0. We tried fixing the PIN cross normalization constant to its canonical value of 1.181 for an HXD-nominal pointing position (Maeda et al. 2008). This resulted in a worse fit with ${\chi }_{\mathrm{red}}^{2}=1.35,$ therefore, we left c_PIN free.

We then checked whether the presence of a "10 keV feature" is consistent with the data. This is a broad residual that has been observed in the spectra of several accreting pulsars thought to be caused by imperfect modeling of the continuum shape using empirical models (see, e.g., Coburn et al. 2002). It is generally detected as a positive residual (e.g., in Cen X-3, see Suchy et al. 2008) but in some sources, including XTE J1946+274, it appears as a negative one (e.g., in Vela X-1, see Fürst et al. 2014). We applied the deeper of the two detections reported for XTE J1946+274 by Müller et al. (2012) to our model, i.e., following them, we included a gauabs component (another parameterization of the gabs shape) with ${E}_{10\;\mathrm{keV}}=9.85\;{\rm{keV}},$ ${\sigma }_{10\;\mathrm{keV}}=2.2\;{\rm{keV}},$ and ${\tau }_{10\;\mathrm{keV}}=0.069.$ This approach did not significantly change the quality of the fit and fitting ${\tau }_{10\;\mathrm{keV}}$ resulted in a value consistent with 0. We conclude that such a component could be present in the spectrum but is not detected, probably in part due to the lack of data between 9.4 and 17 keV.

Our fdcut based best-fit model (FDCUT III) thus consists of absorption in the interstellar medium as well as intrinsic to the system, a power-law continuum with a rollover, a Gaussian emission line for Fe Kα fluorescence, and an absorption-like line with a Gaussian optical depth profile for the cyclotron line:

$$\begin{eqnarray}{M}_{\mathrm{best}}(E) & = & {\mathtt{const}}\times {\mathtt{tbnew}}\\ & & \times ({\mathtt{power}}\times {\mathtt{fdcut}}+{\mathtt{Gauss}})\times {\mathtt{gabs}}\end{eqnarray} \tag{ 10 }$$

in xspec notation. We obtain an unabsorbed 3–60 keV flux of 4.40 ± 0.01 × 10⁻¹⁰ erg s⁻¹ cm⁻².

In the following we present results replacing the power×fdcut continuum with other continuum models commonly applied to accreting X-ray pulsars (see, e.g., Müller et al. 2013b, for the equations describing these models): a power law with an exponential cut off (cutoffpl), a power law with a high energy cut off (power×highecut, sometimes also called plcut), and the sum of a negative and a positive power law with an exponential cut off (npex, Mihara 1995). The last three columns of Table 3 show the best-fit spectral parameters using these continuum models. Since the fitted values of the cut-off energy of highecut and the normalization of the positive power law of npex are consistent with 0 these three models are degenerate and result in the same fit quality and in the same values of their common parameters. The fdcut fit has a slightly different rollover shape, but its parameters are also qualitatively, and often quantitatively within errors, the same. We note that the npex parameters reported by Heindl et al. (2001) for the bright outburst of 1998, which were obtained fitting averaged RXTE monitoring spectra above 8 keV, can also describe the PIN spectrum, but they do not provide a good description of the XIS spectrum (below 8 keV the spectra were variable between individual monitoring pointings).

Maitra & Paul (2013) reported highecut and npex fit of the same Suzaku data set. Their best-fit parameters are generally not consistent with ours. For example, their highecut cut-off energy of ${7.02}_{-0.29}^{+0.69}\;\mathrm{keV}$ and their npex positive power-law normalization are not consistent with 0. A possible explanation for this discrepancy is that the highecut model has a break at the cut-off energy, which here is located at the energy of the Fe K edge. In part this approach therefore could be modeling imperfections of the fit in the region of the iron line and edge. No edge component was required in our fits. Using the approach of Maitra & Paul (2013) by extending the spectrum to 70 keV, i.e., beyond where the source is detected (see next section), and allowing for a 9 keV wide cyclotron line using the cyclabs model we were able to reproduce their continuum parameters. Maitra & Paul (2013) do not quote flux calibration constants. We found a PIN/XIS ratio similar to our other fits. We also assumed that their unitless CRSF width values W_CRSF were given in keV. As mentioned in Section 1 a 9 keV wide cyclotron line can be expected to in part model the continuum (Müller et al. 2013b). Similar to Maitra & Paul (2013) we found that thermal Comptonization of soft photons in a hot plasma (comptt, Titarchuk 1994) cannot explain the Suzaku spectra, particularly in the PIN range (${\chi }_{\mathrm{red}}^{2}/$dof = 5.86/464, unconstrained parameters).

The cyclotron line we found in the Suzaku spectrum from the end of the second outburst of the 2010 series has an energy of ${E}_{\mathrm{CRSF}}={35.16}_{-1.3}^{+1.5}\;\mathrm{keV}$, a line depth of ${D}_{\mathrm{CRSF}}={2.42}_{-1.3}^{+1.5}\;\mathrm{keV}$ and a fixed width of σ_CRSF = 2 keV. Heindl et al. (2001) found a CRSF with similar parameters at ${E}_{\mathrm{CRSF}}={36.2}_{-0.7}^{+0.5}\;\mathrm{keV}$ with ${D}_{\mathrm{CRSF}}={2.79}_{-1.77}^{+2.14}\;\mathrm{keV}$ (${\tau }_{\mathrm{CRSF}}={0.33}_{-0.06}^{+0.07}$) and ${\sigma }_{\mathrm{CRSF}}\;={3.37}_{-0.75}^{+0.92}\;\mathrm{keV}$ for the bright outburst in 1998, from RXTE data. The CRSF energy obtained with RXTE is consistent with the one obtained with Suzaku. Müller et al. (2012) did not find a line at 35 keV, but found marginal evidence (1.8σ) for a CRSF at ∼25 keV in the first and third outbursts of the 2010 series.

In order to check the robustness of the Suzaku detection of an unresolved cyclotron line at 35 keV with respect to changes of the continuum model parameters we calculated confidence contours for two parameters of interest, the CRSF depth D_CRSF and one continuum parameter at a time. We found no strong correlations. Not unexpectedly, moderate correlations are present with the folding energy E_fold and with the flux cross-calibration constant of the PIN spectrum c_PIN, see Figure 6. The confidence contours indicate that the CRSF feature is present independently of the continuum modeling on a ∼3σ level. We further confirmed this picture by determining a significance of 2.81σ for a cyclotron line feature at 35 keV using Monte Carlo simulations. This significance value was obtained by simulating 5000 spectra based on the best-fit model parameters without the CRSF (column FDCUT II of Table 3) and fitting them with and without including the CRSF (width fixed at 2 keV in the former case). In 25 cases we found a bigger improvement in χ² than in the real data, resulting in the quoted significance. For an unresolved line at 25 keV we determined a 3σ upper limit of D_CRSF ∼ 0.9 for the line depth, based on Monte Carlo simulations including a 25 keV line with different depths and for each depth comparing the χ² values obtained from fitting the line to the data and the simulations.

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We also investigated the modeled PIN background spectrum and the effect of its uncertainty on the fit parameters, particularly of the cyclotron line. To this end we first included the background normalization as a fit parameter in the FDCUT III model using recorn. The uncertainty of the fitted background normalization ranged from a decrease of 20% to an increase of 3%. Repeating the fit fixing the background normalization at either of these values or at the default and adding the expected systematic uncertainty of 3% to the PIN background spectrum (ISAS/JAXA & X-ray Astrophysics Laboratory NASA/Goddard Space Flight Center 2013, node10) did not significantly change the resulting cyclotron line parameters. We confirm Maitra & Paul (2013)'s report that the normalization of the background spectrum observed when the source was occulted by the Earth (obtained by setting ${\mathtt{ELV}}\lt -5^\circ$ in aepipeline) was about 20% below that of the modeled background spectrum. This result can qualitatively be explained with the anticorrelation between the magnetic field strength and the background flux at a given satellite location (ISAS/JAXA & X-ray Astrophysics Laboratory NASA/Goddard Space Flight Center 2015, node12): A measure for the strength of the Earth's magnetic field—the time-resolved magnetic cut-off rigidity of the Earth at the satellite position during the observation—can be obtained from the observation's filter file and we found that it was on average lower during the on-source time (${\mathtt{ELV}}\gt 5$) than during the Earth-occultation time (${\mathtt{ELV}}\lt -5$) for the XTE J1946+274 observation.

In Section 3.2 we showed that there is no broadband detection of the pulsar above 40 keV. The background-subtracted spectrum generally confirms this. It is consistent with 0 above 38 keV with the exception of two independent spectral bins in the 43–47 keV range that show a marginal source detection (see also Figure 4 of Maitra & Paul 2013). The picture stays the same when taking the 3% background uncertainty into account. Using non-background-subtracted events we detected no pulsations in the 38–45 keV range and marginal ones in the 43–47 keV range, confirming again that the background model is sufficiently accurate. The background spectrum dominates over the source contribution above ∼33 keV and declines smoothly with energy with no systematic features around 35 or 40 keV. Above 38 keV the source spectrum might thus show some structure but it is mostly below the detection limit and was therefore excluded from our analysis.

We successfully applied the accretion torque theory of Ghosh & Lamb (1979) to XTE J1946+274 and updated the orbital solution for this source (Table 2). Previously Wilson et al. (2003) used three different approaches to model the observed pulse period evolution obtained by RXTE-PCA and CGRO-BATSE in 1998, which was dominated by a strong spin-up as well. Comparing the resulting orbital parameters to ours we find that the semimajor axis, ${a}_{\mathrm{sm}}\mathrm{sin}i,$ agrees best with their 10th-order polynomial model. Extrapolating our derived time of periastron passage, τ, back to 1998, gives times which agree to within 2σ with the result of their model as well. The orbital period, P_orb, and eccentricity, e, are consistent with their linear model, while the longitude of periastron, ω, is the same as in their piecewise approximation within the uncertainties. As noted by Wilson et al., however, the χ² of all three different approaches is not acceptable because the models do "not completely describe the intrinsic torques."

In contrast to other methods such as, e.g., a Fourier series approach (e.g., Kühnel et al. 2013), calculating the spin-up of accreting pulsars using the theory of Ghosh & Lamb (1979) allows us to model the possibly complex, intrinsic spin period evolution of the neutron star with better accuracy (see also Galloway et al. 2004; Sugizaki et al. 2015). As a result the orbital motion can be properly disentangled from the overall observed pulse period evolution and the derived orbital parameters are generally more reliable. We caution, however, that assuming P(t') is a constant on the right side of Equation (3) in order to simplify the calculation of this differential equation (see, e.g., Sugizaki et al. 2015) might lead to additional uncertainties when fitting longer time series. If we set $P(t^{\prime} )={P}_{0},$ for example, the modeled pulse period evolution differs up to 0.01 ms, which is of the same order as the uncertainties of the Fermi-GBM period measurements. As soon as more precise flux measurements are used for F(t) or the measured spin-up is even stronger than for XTE J1946+274 the differential equation should thus be solved properly.

This kind of timing analysis would not be possible without regular flux monitoring by all-sky observatories, such as Fermi-GBM, Swift-BAT, or MAXI.

The accurately determined orbital parameters allow us to derive the value of the mass function of XTE J1946+274 following the same approach as in, e.g., Wilson et al. (2003). The mass function of a binary,

$$\begin{eqnarray}&&f(M)=\displaystyle \frac{{({M}_{\mathrm{opt}}\mathrm{sin}i)}^{3}}{{({M}_{\mathrm{NS}}+{M}_{\mathrm{opt}})}^{2}}=\displaystyle \frac{4{\pi }^{2}}{G}\displaystyle \frac{{({a}_{\mathrm{sm}}\mathrm{sin}i)}^{3}}{{P}_{\mathrm{orb}}^{2}}\end{eqnarray} \tag{ 11 }$$

depends on the masses, M_opt and M_NS, of the optical companion and neutron star, respectively, and on the orbital inclination angle, i. However, the mass function can also be calculated using the orbital period, P_orb, and the projected semimajor axis, ${a}_{\mathrm{sm}}\mathrm{sin}i.$ Using the orbital parameters listed in Table 2 we derive consistent values of $f(M)={3.77}_{-0.07}^{+0.11}\;{M}_{\odot }$ for disk accretion and $f(M)={3.82}_{-0.07}^{+0.07}\;{M}_{\odot }$ for wind accretion. Assuming the same mass range for the companion star of $10\;{M}_{\odot }\leqslant {M}_{\mathrm{opt}}\leqslant 16\;{M}_{\odot }$ as used by Wilson et al. (2003) and the canonical neutron star mass ${M}_{\mathrm{NS}}=1.4\;{M}_{\odot },$ we can solve Equation (11) for the inclination angle, i. Using the widest possible range for the mass function as calculated above, $3.70\;{M}_{\odot }\leqslant f(M)\leqslant 3.89\;{M}_{\odot },$ we derive an orbital inclination angle of $41^\circ \leqslant i\leqslant 52^\circ .$ This is in good agreement with the value of i ≳ 46° as found by Wilson et al. (2003).

As already argued by Wilson et al. (2003), the inclination angle of the Be disk, i_disk, with respect to the observer is not necessarily aligned with the inclination angle of the orbit, i. From measurements of the width of the single-peaked Hα line in an optical spectrum, Wilson et al. (2003) concluded that the Be star is seen nearly pole-on. Thus, the Be disk and orbital plane might indeed be misaligned in XTE J1946+274. Özbey Arabacı et al. (2014) recently analyzed optical spectra of the system and noted, however, that deriving the Be-disk inclination from the Hα line profile is highly uncertain based on theoretical investigations by Silaj et al. (2010). Assuming that the orbital plane and the Be disk are aligned (i_disk = i), Özbey Arabacı et al. (2014) derived the rotational velocity of the Be star. They concluded that the Be companion of XTE J1946+274 is rotating with 0.50–0.72 times the critical break-up velocity of a typical Be-type star (${v}_{\mathrm{crit}}\sim 618\;\mathrm{km}\;{{\rm{s}}}^{-1}$). Using their initial value of the projected velocity, $v\mathrm{sin}i=323\;\mathrm{km}\;{{\rm{s}}}^{-1}$ and our determined inclination angle, i, we find a velocity of 0.66–0.80 times the break-up velocity.

Two outburst series of XTE J1946+274 have been observed, one in 1998 (Wilson et al. 2003) and one in 2010 (Figure 1) with two to three outbursts per orbit. In order to explain this X-ray activity the companion of XTE J1946+274 has been studied in the optical and IR. Based on observations of permanent Hα emission, Özbey Arabacı et al. (2014) conclude that during X-ray quiescence a large Be disk is present. They observed a brightening in the optical/IR indicating that the Be star experienced a long mass-ejection event from 2006 to 2012, reaching its maximum intensity in 2010, around the time of the outburst series. Özbey Arabacı et al. postulate that this ejection caused an increase in size, perturbations, and warping of the Be disk. They also state that the X-ray activity is triggered by the neutron star coming into contact with the warped areas in the tilted Be disk. This could explain why we observe two to three outbursts per orbit. The presence of Hα and optical/IR emissions after the X-ray activity indicates that once the material was consumed through accretion, the Be disk quickly and steadily recovered and the system returned to quiescence (Özbey Arabacı et al. 2014).

We described the spectral shape of XTE J1946+274 with a Fermi–Dirac cut-off power law together with an Fe Kα fluorescence line and a CRSF at 35 keV. We find E_fold = 8.89(4) keV and a hydrogen column density of ${N}_{{\rm{H}}}=1.67(3)\times {10}^{22}\;{\mathrm{cm}}^{-2}.$ These parameters are roughly consistent with the ones found by Müller et al. (2012) in PCA data taken during earlier outbursts, namely ${E}_{\mathrm{fold}}\;={6.0}_{-1.6}^{+2.6}\mbox{--}{8.1}_{-0.6}^{+0.7}\;\mathrm{keV}$, and ${N}_{{\rm{H}}}={1.77}_{-0.29}^{+0.25}\mbox{--}{5.1}_{-3.3}^{+2.5}\times {10}^{22}\;{\mathrm{cm}}^{-2}.$ Their measured ${\rm{\Gamma }}={0.74}_{-0.17}^{+0.12}\mbox{--}{1.04}_{-0.18}^{+0.13}$ is slightly softer than ours, Γ = 0.57(2). The cut-off energy is different as well: it is found here to be zero, while Müller et al. (2012) found ${E}_{\mathrm{cut}}=14\pm 4\mbox{--}{19.4}_{-9.7}^{+2.1}\;\mathrm{keV}.$

In order to study the changes in the spectral shape at different times and luminosities during the outburst series we compared our best-fit model and the models fitted in Müller et al. (2012) by eye. The Suzaku spectrum is harder at high energies (>12 keV) than the spectra from Müller et al. (2012). This hardness change could be an indication of a higher temperature of the plasma in the accretion column, despite the lower luminosity. At first glance this may seem inconsistent, however, the electron temperature and mass accretion rate cannot be clearly determined without a physical continuum model. The implementation and testing of such a physical model is a work in progress (Marcu et al. 2014).

We and Müller et al. (2012) both find N_H values that are almost twice as large as the Galactic N_H in the direction of XTE J1946+274 (${N}_{{\rm{H}}}=9.4\times {10}^{21}\;{\mathrm{cm}}^{-2};\;$Kalberla et al. 2005). This excess indicates the presence of absorbing material intrinsic to the X-ray binary system. The excitation of such neutral to moderately ionized material surrounding the neutron star by the X-rays emitted from the accretion column can produce fluorescent lines from iron and other elements. These lines are a very useful tool for analyzing the properties of the material (e.g., Inoue 1985; Leahy & Creighton 1993; Torrejón et al. 2010; Reig & Nespoli 2013).

We find a narrow (σ_Fe = 0.1 keV) Fe Kα fluorescent emission line at E_Fe = 6.41(3) keV, confirming the presence of this neutral to moderately ionized material. The flux was ${A}_{\mathrm{Fe}}\sim 8.6\times {10}^{-5}\;\mathrm{photons}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$ (see Table 3). The equivalent width is 32.2 eV for the Suzaku observation, consistent with the ∼29 eV found by Maitra & Paul (2013) in the same data set, but lower than the measured 49–69 eV found in earlier data taken at different fluxes (Heindl et al. 2001; Müller et al. 2012). As shown, e.g., by Inoue (1985), one expects the flux in the flourescence line to be correlated with the continuum flux above 7 keV. Figure 7 shows this relationship using data of all published observations of XTE J1946+274, extending a similar figure by Müller et al. (2012) to lower fluxes. The figure also shows the correlation predicted by Equation (4a) of Nagase et al. (1986), which is an estimate for the fluorescent line flux as a function of N_H and continuum flux. The hashed region in Figure 7 illustrates the range of the expected Fe Kα flux values according to Nagase et al. (1986), taking into account the variation in N_H between all published spectral fits. This range is an upper limit to the absorption column of the system. For the values with the lowest uncertainties the observed Fe Kα flux is slightly higher than the one predicted by Nagase et al. (1986). This is especially the case for the high-flux data points and is qualitatively consistent with their higher equivalent width compared to the Suzaku measurement. A possible reason for this slight excess could be an overabundance of iron in the emitting medium. Alternatively, the excess could also be due to the fact that the ionization structure of the material is more complicated than the purely neutral Fe absorber assumed by Nagase et al. (1986). Finally, it is also likely that the emission is not purely from the line of sight, but from other areas such as fluorescence from a tilted and/or warped Be disk around the neutron star.

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Evidence of a ∼35 keV cyclotron line line was first seen by Heindl et al. (2001) in RXTE data obtained during a time when the source was much brighter than in the observations analyzed here. Our Suzaku observation supports the presence of this line: the χ² slightly improved from 557 to 545, corresponding to a significance of 2.81σ (obtained using Monte Carlo simulations), between the FDCUT II and FDCUT III fits. Including this line improved the fits with the other continuum models as well. The centroid energy of ${35.2}_{-1.3}^{+1.5}\;\mathrm{keV}$ implies a surface magnetic field of ${B}_{\mathrm{NS}}={3.1}_{-0.1}^{+0.1}(1+z)\times {10}^{12}\;{\rm{G}}.$

The CRSF parameters are independent of the continuum model. Furthermore, describing the PIN data only with the npex model, we obtain a good fit with ${\chi }_{\mathrm{red}}^{2}=0.92$ for 50 dof, for continuum parameters consistent with Heindl et al. (2001). Both the energy of the cyclotron line and its optical depth measured with Suzaku are within 1σ of those measured with RXTE. Note, however, that due to spectral complexity below 10 keV the RXTE based npex values do not describe the broad band (XIS and PIN) Suzaku data.

We find a lower centroid energy for the CRSF than the effectively ∼40 keV previously reported for this data set by Maitra & Paul (2013). As explained in Section 4.2, their higher value could be due to in part modeling an artificial feature, as these authors include PIN data above 40 keV, where the source is mostly not detected.

Our spectrum is not consistent with the 25 keV feature discussed by Müller et al. (2012). We tried including a feature with their parameters and the ${\chi }_{\mathrm{red}}^{2}$ increased to 1.92. When the depth of this 25 keV feature was left free it became consistent with zero.

It has recently been recognized that different types of correlations between the energy of the CRSF E_CRSF and the X-ray luminosity L_X are observed for accreting pulsars, probably reflecting different accretion states (Staubert et al. 2007). Studying these correlations allows us to derive constraints on the physical conditions in the accretion column. Becker et al. (2012) presented a model of the different accretion regimes and of how the height (i.e., the B-field and therefore E_CRSF) of the region in the accretion column where the CRSF is produced changes with luminosity for the different regimes (see also Mushtukov et al. 2015): for supercritical sources (${L}_{{\rm{X}}}\gtrsim {L}_{\mathrm{crit}}$) radiation pressure in a radiative shock in the accretion column is the dominant decelerator for the material inside the accretion column. A source in this regime is expected to show a negative E_CRSF–L_X correlation, as observed for V 0332+53 (Mowlavi et al. 2006). For moderately subcritical sources (L_X ≲ L_crit) the radiation-dominated shock causes the initial deceleration, followed by Coulomb interactions below the shock, which bring the matter to a stop on the neutron star surface. Subcritical sources in this regime are expected to show a positive E_CRSF–L_X correlation, as observed for Her X-1 or GX 304−1 (Staubert et al. 2007; Klochkov et al. 2012). The expected relationship at even lower luminosities (L_X ≲ L_Coul), where the radiative shock and Coulomb interactions disappear, and the matter falls through a gas-mediated shock before hitting the stellar surface, is less clear. A 0535+26, for example, is a low-luminosity source that does not show any changes of E_CRSF in pulse averaged spectra with luminosity (Caballero et al. 2007, but see Müller et al. 2013a and Sartore et al. 2015).

Where does XTE J1946+274 fit into this picture? In Figure 8 we show the Coulomb luminosity L_Coul and the critical luminosity L_crit for a range of B-fields, i.e., cyclotron line energies (after Becker et al. 2012), separating the different accretion regimes. These luminosities depend, among other things, on the accretion geometry outside of the Afvén sphere where two cases are presented: disk and wind accretion. Overplotted are the gravitational redshift-corrected cyclotron line energies and 3–60 keV luminosities from Heindl et al. (2001) and our Suzaku analysis. We calculated the Suzaku luminosity using the unabsorbed flux measurement from the FDCUT III spectral fit. The CRSF energy is consistent within errors between 1998 and 2010, implying that the height of the CRSF emission region is similar for both observations. The luminosities, while both moderate, span a range larger than observed for any other moderate luminosity pulsar (e.g., Her X-1 or GX 304−1) and fall in the transition region between low and high luminosity pulsars. In the case of disk accretion, i.e., the default assumption for Be systems, both luminosities are consistent with subcritical accretion, with the 1998 RXTE measurement at L_X ≲ L_crit and the Suzaku measurement at L_X ≲ L_Coul. Taking the uncertainties of the distance measurement into account, the similarity of the cyclotron line energy measurements is not inconsistent with the Becker et al. (2012) picture. In the case of wind accretion XTE J1946+274 would have been supercritical during both measurements and a negative E_CRSF–L_X correlation would be expected. Calculating the difference in emission heights for supercritical accretion following Equation (40) of Becker et al. (2012) and assuming a dipole magnetic field, Δ E_CRSF ≲ 1. 4 keV is expected for the two luminosities. This is comparable to the uncertainties of the two E_CRSF measurements, i.e., though unlikely, we cannot rule out the presence of such a change. We note that wind accretion has so far only been discussed as a possibility for explaining the E_CRSF–L_X relationship of persistent, non-Be, low-luminosity sources like Vela X-1 and 4U 1538−522 (Fürst et al. 2014; Hemphill et al. 2014). We did not include the data from Müller et al. (2012) because the presence of a CRSF at 25 keV at fluxes between the 1998 and 2010 extremes is only marginally supported (see Section 4.2). However, a higher emission region at intermediate fluxes in the Coulomb braking regime (disk accretion) is again consistent with the Becker et al. (2012) picture, while it is not consistent in the supercritical regime (wind accretion). Using the more precise treatment of the critical luminosity by Mushtukov et al. (2015) is qualitatively in agreement with this picture.

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We can calculate the CRSF emission region height for a subcritical source at which the Coulomb interactions start decelerating the plasma using Equation (51) of Becker et al. (2012):

$$\begin{eqnarray}{h}_{{\rm{c}}} & = & 1.48\times {10}^{5}\;\mathrm{cm}{\left(\displaystyle \frac{\lambda }{0.1}\right)}^{-1}\left(\displaystyle \frac{{\tau }_{*}}{20}\right)\\ & & \times {\left(\displaystyle \frac{{M}_{\mathrm{NS}}}{1.4\;{M}_{\odot }}\right)}^{19/14}{\left(\displaystyle \frac{{R}_{\mathrm{NS}}}{10\;\mathrm{km}}\right)}^{1/14}\\ & & \cdot {\left(\displaystyle \frac{{B}_{\mathrm{NS}}}{{10}^{12}\;{\rm{G}}}\right)}^{-4/7}{\left(\displaystyle \frac{{L}_{{\rm{X}}}}{{10}^{37}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)}^{-5/7}\end{eqnarray} \tag{ 12 }$$

where the following parameters are as defined in Becker et al. (2012): λ = 0.1 describes the disk accretion case, ${\tau }_{*}\sim 20$ is the Thomson optical depth in the Coulomb regime, ${M}_{\mathrm{NS}}=1.4\;{M}_{\odot }$ and R_NS = 10 km are typical values for the neutron star mass and radius. We obtained h_c = 211 m for the emission height using ${B}_{\mathrm{NS}}=3.1(1+z)\times {10}^{12}\;{\rm{G}}$ with z = 0.3 and ${L}_{{\rm{X}}}=5\times {10}^{37}\;\mathrm{erg}\;{{\rm{s}}}^{-1}$ (Heindl et al. 2001).

The similarity of the observed pulse profiles at low and high fluxes supports a scenario where no strong changes in the emission geometry happen over and between outbursts. The 2010 RXTE and Suzaku pulse profiles of XTE J1946+274 are double-peaked with a deep and a shallow minimum that show weak energy dependence of the depths (Figure 3). This structure is strongly similar to what has been observed by Wilson et al. (2003) and Paul et al. (2001) during the 1998 outburst with other instruments at different luminosities. The source even shows a double-peaked profile during quiescence as observed by Chandra (Özbey Arabacı et al. 2014). Interestingly, the ∼20–40 keV pulse profile of A 0535+26 is very similar to that of XTE J1946+274 (Caballero et al. 2007; Sartore et al. 2015). Modeling the profiles of the 2005 August/September outburst of A 0535+26, Caballero et al. (2011) determined a possible emission pattern by taking into account the contribution of each of the two magnetic poles. They assumed a dipole magnetic field with axisymmetric emission regions. The asymmetry of the pulse profile minima is explained by a small offset of one of the emission regions from being antipodal. The profiles for A 0535+26 were obtained when the source had a luminosity of ${L}_{3-50\;\mathrm{keV}}\sim 0.8\times {10}^{37}$ erg s⁻¹ (Caballero et al. 2011), i.e., not unlike the lower range observed for XTE J1946+274.

In summary, for XTE J1946+274 the stability of the pulse profile shape, the lack of strong changes of the spectral shape (Section 5.4), and the possibly constant CRSF energy with luminosity all indicate that there have been no major changes in the accretion column structure and emission geometry over the broad range of moderate luminosities covered by observations.