MULTI-WAVELENGTH OBSERVATIONS OF THE BLACK WIDOW PULSAR 2FGL J2339.6-0532 WITH OISTER AND SUZAKU

2FGL J2339.6-0532 was observed from 22 September to 2011 October 7 utilizing the global telescope network Optical and Infrared Synergetic Telescopes for Education and Research (OISTER).²² OISTER consists of 14 independent observatories that are funded by Japanese universities and research associations. For this work, we also asked for photometry observations from the Kottamia Astronomical observatory, which has a 188 cm reflector. Thanks to the locations of the observatories distributed across the globe, we can continuously trace the variability all day long. Moreover, the telescopes cover a wide range of wavelengths from Ks to B band which can provide the phase-resolved SED of the target. The photometric observations conducted are summarized in Table 1. The locations of the reference stars and the target are shown in Figure 1.

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In the case of PSR B1957+20, the binary system is surrounded by an Hα bow shock due to its super-sonic proper motion with respect to the surrounding ISM (Kulkarni & Hester 1988). To search for a similar feature around 2FGL J2339.6-0532, we took Hα images with the Kiso Schmidt telescope at the minimum phase to prevent contamination from the companion star. Figure 1 shows the obtained Hα image in the vicinity of 2FGL J2339.6-0532 utilizing an Hα narrow-band filter (${\Delta }\lambda =9$ nm) in which we could not find the evidence of bow-shock nebula.

To evaluate the detection limit, we calculated the standard deviation of the 33'' $\;\times \;67^{\prime\prime}$ (50 × 100 pixel) rectangular region near the target and obtained STDEV = 7.82 ADU. The sky background of the CCD image shows a weak striped pattern running in the southeast-to-northwest direction with a peak-to-peak value of ∼8 ADU, which seems to be the dominant noise component restricting the detection limit. Regardless, if we adopt a conservative threshold with a 3σ confidence level, the detection limit becomes 23.5 ADU. Based on the flux calibrations of the reference stars listed in Table 2, the conversion coefficient of ADU to energy flux, $(8.3\pm 0.1)\times {{10}^{-18}}$ erg s⁻¹ cm⁻² ADU⁻¹, was observed for the Hα filter with a bandwidth of 9 nm. Finally, we obtained a 3σ detection limit of $\lt 1.9\times {{10}^{-16}}$ erg s⁻¹ cm⁻² pixel⁻¹, which corresponds to a surface brightness of $\lt 8.7\times {{10}^{-17}}$ erg s⁻¹ cm⁻² arcsec⁻².²³

Table 2.  Summary of Field Photometry

	Reference-1	Reference-2	Aλ†
Name(USNO-2.0A)	U0825_19993817	U0825_19993871
Coordinate(J2000.0)	(23:39:39.487, −05:32:40.56)	(23:39:40.366, −05:31:51.89)
B	18.435 ± 0.014	17.603 ± 0.008	0.120
V	17.834 ± 0.018	16.828 ± 0.008	0.091
R	17.484 ± 0.016	16.388 ± 0.007	0.072
I	17.296 ± 0.020	16.105 ± 0.008	0.050
g'	18.098 ± 0.011a	17.177 ± 0.006a	0.110
J	16.47 ± 0.10b	15.19 ± 0.04b	0.024
H	16.45 ± 0.23b	14.87 ± 0.05b	0.015
Ks	16.12b,c	14.55 ± 0.08b	0.011
Hα (656 nm)	314 ± 46 μJyd	854 ± 170 μJyd	...

Note. Errors are with 1σ confidence level.

^†Galactic extinction at the target coordinate (Cardelli et al. 1989; Schlafly & Finkbeiner 2011). ^aSDSS magnitudes were calculated from B-band and V-band magnitudes based on Smith et al. (2002). ^bFor the flux calibrations of J, H, and Ks, we referred to the 2MASS catalog (Skrutskie et al. 2006). ^cThe catalog error of the Reference-1 for the Ks band was not available. ^dThe flux density was evaluated from the absorption-corrected SED assuming a simple balckbody model. The estimated temperature of the reference stars were ${{T}_{{\rm BB},{\rm ref}1}}=7320\pm 160$ K, ${{T}_{{\rm BB},{\rm ref}1}}=6300\pm 180$ K.

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The prototype black widow PSR B1957+20, residing at a distance of 1.6 kpc from the earth, has a bow shock nebula extending over ∼30'' × 30'' with an Hα flux of $3.3\;\times \;{{10}^{-14}}$ erg s⁻¹ integrated over the entire nebula (Kulkarni & Hester 1988). If our target is accompanied by an equivalent bow-shock nebula, then the Hα flux and the size should be $6.1\times {{10}^{-14}}$ erg s⁻¹ cm⁻² and $\sim 41^{\prime\prime} \times 41^{\prime\prime}$, respectively. Therefore, the expected surface brightness is $3.6\times {{10}^{-17}}$ erg s⁻¹ cm⁻² arcsec⁻², which is slightly lower than the detection limit.

Compared with the other bow shock PWNe, the size and intensity both seem to be scattered across a range of two orders of magnitude, possibly reflecting their shock conditions (Chatterjee & Cordes 2002). Therefore, we conclude that this observation provides only a weak upper limit of surface brightness in the Hα band.

The other telescopes, except for the Kiso observatory, carried out photometric observations covering the Ks– B bands from 2011 September 9th to 2011 September 30th. For flux calibration, we chose two reference stars near the target object, U0825_19993817 (R = 17.5) and U0825_19993871 (R = 16.4) in the USNO-2.0 A catalog, so that all of the observatories can employ common references without saturation. The photon fluxes of the references stars were measured and compared to the standard stars in the Landolt catalog (Landolt 1992) with the MSI of the Pirka telescope in Hokkaido prefecture (Japan). Since the Pirka employs the Johnson–Cousins filter system, we estimated the photon flux in the SDSS g' band based on the observed B and V magnitudes using a conversion equation proposed by Smith et al. (2002),

$$\begin{eqnarray}&&g^{\prime} =V+0.54(B-V)-0.07.\end{eqnarray} \tag{ 1 }$$

For J, H, and Ks, we employed the photometric data in the Two Micron All-Sky Survey (2MASS) catalog for flux calibration (Skrutskie et al. 2006). The obtained magnitudes of the reference stars are summarized in Table 2.

Figure 2 shows the light curves of 2FGL J2339.6-0532 obtained by OISTER. We re-confirmed the clear sinusoidal modulation as reported by Kong et al. (2012) and Romani & Shaw (2011). The absolute flux seems consistent with past observations: the modulation amplitude is about 4.5 magnitude in the R band and is larger at shorter wavelengths. In the R band, we successfully observed the maximum phases of the target eight times during the observation campaign. The photon flux at the maximum phase is ${{R}_{{\rm max} }}=17.7$ mag on average and varies among peaks within a range of ±0.1 mag. There was no irregular activity like the flares observed in 2FGL J1311.6-3429 (Kataoka et al. 2012).

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To discuss the energetics quantitatively, we estimated the energy flux based on the photometric data shown in Figure 2. First, we corrected the galactic extinction at the coordinate of the target (Schlafly & Finkbeiner 2011; Cardelli et al. 1989);²⁴ the employed extinction at various wavelength are listed in Table 2. Then, we converted the absorption corrected magnitudes to the energy flux using conversion equations presented in Fukugita et al. (1996) and Tokunaga & Vacca (2005) for optical (B, V, R, I, g') and IR(J, H, Ks) energy bands, respectively.

Figure 3(a) shows the energy fluxes yielded as functions of the binary orbital phase. Phase = 0 was set to be MJD = 55500.0. While the optical light curves show symmetric structures, the IR (H and Ks) light curves possess somewhat asymmetric shapes. This may be due to the geometry of the companion star or the evaporating stellar gas. Panel (b) shows the SED during the brightening phase from the orbital phase = 0–0.5 in panel (a). Clearly the peak frequency increases as the orbital phase increases from orbital phase 0–0.5, implying that the temperature of the companion increases with the orbital phase. At the maximum phase, the SED is fitted with a blackbody model with an effective temperature of ${{T}_{{\rm eff}}}=7540\pm 130$ K, which is consistent with the past study (Romani & Shaw 2011).

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In this paper, we assumed a simple emission model from the surface of the companion star to explain the observed optical emission. As described in Figure 4, we supposed that a companion star with a radius ${{r}_{{\rm comp}}}$ is orbiting around a pulsar at an orbital radius ${{R}_{{\rm orb}}}$, and the hemisphere of the companion that faces the pulsar is heated by the pulsar wind while the opposite side of the companion has ordinal temperature ${{T}_{{\rm cool}}}$. Note that this model does not take into account the effect of energy transfer via convection or advection on the surface of the companion, and therefore the temperature distribution of the companion is simply described by energy injection via the pulsar wind, although the heating efficiency is unclear. In this paper, we assumed that the spin-down energy is perfectly converted into the isotropic pulsar wind and the injected energy via the pulsar wind heats the companion up with a heating efficiency of f for simplicity. We also adopted a spin-down luminosity of $2.3\times {{10}^{34}}$ erg s⁻¹ based on the timing analysis in the radio band recently reported by Ray et al. (2014).

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We then fitted the obtained phase-resolved SED with the model function described above (Figure 5). Since the model seems to correlate weakly with the inclination angle, we fixed the inclination angle i. The resultant model parameters are summarized in Figure 6 as functions of the inclination angle. Although the fit seems rather poor—mainly because of the large residual in the IR band—we found that an inclination angle of $i=59{}^\circ$ minimizes the ${{\chi }^{2}}$. For comparison, we also attempted this analysis without IR data and obtained a best-fit parameter of $i=52{}^\circ$. These results seem consistent with the inclination angle reported by Romani & Shaw (2011). The obtained best-fit parameters are summarized in Table 3. Additionally, the obtained temperature distributions of the companion surface are plotted in Figure 7 as functions of the zenith angle of the pulsar from the measured point on the companion surface.

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Table 3.  Obtained Parameters of the Binary System from the Phase-resolved SED

Data set	Optical+IRa	Opticala
Orbital radius (${{R}_{{\rm orb}}}$)b	$1.08\pm 0.02\;\times {{10}^{11}}$ cm	$1.18\pm 0.02\;\times {{10}^{11}}$ cm
Companion radius (${{r}_{{\rm comp}}}$)	$1.26\pm 0.02\;\times {{10}^{10}}\ {{d}_{1.1}}$ cmc	$1.53\pm 0.02\;\times {{10}^{10}}\ {{d}_{1.1}}$ cmc
Companion Temperature (${{T}_{{\rm cool}}}$)	$3170\pm 70\;$ K	$2740\pm 120\;$ K
Heating Efficiency (f)d	1.42 ± 0.05	1.16 ± 0.04
Inclination angle (i)	$59\buildrel{\circ}\over{.} 0\pm 1\buildrel{\circ}\over{.} 5$	$52\buildrel{\circ}\over{.} 1\pm 1\buildrel{\circ}\over{.} 0$
Bolometric Luminositye	$1.09\pm 0.17\;\times {{10}^{32}}\ d_{1.1}^{2}$ erg s−1	$1.12\pm 0.16\;\times {{10}^{32}}\ d_{1.1}^{2}$ erg s−1
${{\chi }^{2}}$	1392.6	637.6

Note. Errors are with 1σ confidence level.

^a"Optical" and "IR" correspond to the [B, V, R, I, g'] data set and the [J, H, Ks] data set, respectively. ^b ${{R}_{{\rm orb}}}$ are calculated based on the radial velocity of the companion star reported by Romani & Shaw (2011). ^c ${{d}_{1.1}}$ is the distance in units of 1.1 kpc. ^dAssuming an isotropic pulsar wind with a luminosity of $2.3\times {{10}^{34}}$ erg s⁻¹ based on Ray et al. (2014). ^eBolometric luminosity of the companion's heated hemisphere.

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2FGL J2339.6-05312 was observed with the Suzaku satellite on 2011 June 29th. The target was observed at the XIS nominal point with the normal imaging mode. The net exposure time after the standard data reduction process was 96 ks. The accumulated photons are 2555 counts with the front-illuminated CCDs (XIS0 + XIS3) and 1874 counts with the back-illuminated CCD (XIS1) in the 0.4–8 keV energy band. During the observation, the event rates were $\sim 8.25\pm 0.28\times {{10}^{-3}}$ (XIS0, XIS3) photons s⁻¹ and $8.89\pm 0.50\times {{10}^{-3}}$ photons s⁻¹ (XIS1) in the energy band.

Figure 8 shows the X-ray spectrum obtained with Suzaku. At first, we tried to fit the X-ray spectra with a single power-law function, however, the resultant fit was poor (${{\chi }^{2}}/\nu$= 67.71/55) due to residuals below 1 keV implying the presence of a soft excess component. We therefore added a blackbody to the model function for the soft excess, and obtained a better fit (${{\chi }^{2}}/\nu =51.82/55$). The dotted lines in Figure 8 describe the best-fit model functions. The resultant parameters of the model fitting are summarized in Table 4. In both cases, the column density converged to zero. The resultant upper limit is $\lt 1.2\times {{10}^{21}}$ cm⁻² with 90% confidence level, and is consistent with the Galactic absorption of $3.23\times {{10}^{20}}$ cm² for this direction (Dickey & Lockman 1990; Kalberla et al. 2005).

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Table 4.  Results of Model Fitting of the Averaged X-ray Spectra

Model	wabs*(bbody + power law)	wabs*power law
${{N}_{{\rm H}}}$ (${{10}^{21}}$ cm−2)	$\lt 1.2$ (0)	$\lt 0.13$ (0)
Blackbody Temperature (keV)	0.15 ± 0.06	⋯
Blackbody Radius (km)†	$0.28_{-0.16}^{+0.93}\;$	⋯
Power-law Photon Index	$1.14_{-0.15}^{+0.14}$	1.32 ± 0.08
Power-law Flux $_{0.5-10{\rm keV}}$ (${{10}^{-13}}$ erg cm−2 s−1)	2.50 ± 0.16	2.50 ± 0.15
Total flux $_{0.5-10{\rm keV}}$ (${{10}^{-13}}$ erg cm−2 s−1)	$2.67_{-1.25}^{+0.01}$	$2.46_{-0.73}^{+0.04}$
${{\chi }^{2}}$ (dof)	51.82 (51)	67.71(53)

Note. Errors are with 90% confidence level.

^†Blackbody radius assuming a distance of 1.1 kpc.

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In order to clarify the origin of these two components, phase-folded X-ray light curves were generated as shown in Figure 9. In this figure, Phase = 0 was set to be MJD = 55500.0 in the same way as the optical light curves shown in Figure 3(a). Panels (a)–(c) in Figure 9 represent the energy bands 0.4–1.0 keV, 2.0–4.0 keV, and 4.0–8.0 keV, respectively. Clearly, the hard X-ray light curves show clear modulation coinciding with the orbital motion. This timing coincidence may imply that the non-thermal emission originates from the companion surface. However, the shape of the light curves is somewhat different from the sinusoidal shapes observed in the optical, i.e., a double-peaked shape at the 2.0–4.0 keV band and a flat top shape at 4.0–8.0 keV. On the other hand, the soft X-rays seem to be steady. This may imply that the soft component has a different emitting region, namely, the pulsar.

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To evaluate the upper limit of the modulation factor in the soft X-ray energy band, we tried to fit the X-ray light curve with a sinusoidal curve and a constant component, $A{\rm sin} (2\pi x)+B$, where x is the orbital phase. The obtained amplitude of the sinusoidal curve is $A=(0.80\pm 0.34)\times {{10}^{-3}}$ counts s⁻¹ against the constant component of $B=(3.95\pm 0.23)\times {{10}^{-3}}$ counts s⁻¹. Therefore, the upper limit of the modulation factor is $A/B\lt 28.6$% with 1σ confidence level. Note that the maximum point was not fixed to be phase = 0.5 in this estimation; this helped to maximize the modulation factor. The best-fit model curve is shown in Figure 9(a).

If we adopt the two-component model consisting of a blackbody and a power-law function from the X-ray spectroscopy, then we can roughly evaluate the contributions from these two components to the constant emission. The phase-averaged absorbed-photon flux for the blackbody and the power law in the 0.4–1.0 keV energy band are both $2.0\times {{10}^{-5}}$ photons s⁻¹. Assuming that the constant component originates in the blackbody, the modulation factor is expected to be (PL)/(BB + PL)∼50%, which is about twice the measured value. Taking into account the large errors arising from the uncertainties of the blackbody components (see Table 4), the measured modulation factor should be larger because of the tight upper limits to the blackbody component. This may indicate that the constant emission may consist of the blackbody from the neutron star (NS) surface and the non-thermal component originating in the pulsar magnetosphere.

The upper panel of Figure 10 shows the obtained X-ray light curve with a bin size of 600 s for the energy range of 0.4–8.0 keV. Note that the whole length of the light curve is 190 ks, containing occultation periods of Earth and corresponding to twice the net exposure time of 96 ks. Although the photon statistics seem poor, the X-rays show periodic variability coincident with an orbital period of 16,683 s. We expected to observe the flare-like features reported in previous studies (Kataoka et al. 2012; Papitto et al. 2013; Ferrigno et al. 2014; Linares et al. 2014), which may be related to the accretion activity; however, no significant evidence for this was discovered. Nonetheless, the shape of the light curve seems to change over time.

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In order to clarify the temporal variation in the waveform of the X-ray light curve, we traced the temporal changes of the power spectrum with the Lomb-Scargle algorithm, which can be applied to an unevenly sampled data set. In this analysis, we employed a rectangular function as a window function to detect small changes from a short data sequence. The width of the window function was set to 50 ks in order to cover three orbital laps and to detect the light curve variations for the total exposure time of 190 ks. We then scanned the light curve by sweeping the window function and generated a power spectrum for every timespan in the light curve. Note that this method cannot detect rapid variations of the power spectra (faster than a few tens of kiloseconds) because the width of the time window has a finite timespan.

The lower panel of Figure 10 shows the obtained periodogram as a function of time, which represents the central time of the sampled time window. Therefore, the periodogram at t = 25 ks consists of the X-ray light curve in the time span of $0\leqslant t\leqslant 50$ ks. Both ends of the grayscale map are omitted because the time window can sweep in the range of the obtained light curve. The sweeping step size was set to 600 s. Therefore, the time resolution of the running periodogram is about 230, which is much greater than the timescale that can be detected by this method. Nevertheless, a clear peak structure was detected at a frequency of around ${{f}_{1}}=0.6\times {{10}^{-5}}$ Hz, which corresponds to the orbital frequency. On the other hand, ${{f}_{2}}=1.2\times {{10}^{-5}}$ Hz appears to denote the second harmonic of the orbital frequency, which may be related to the dip structure of the double-peaked light curve. Interestingly, these two components in the power spectra decrease sequentially after t = 1.2$\times {{10}^{4}}$ s.

The model fitting of the phase-resolved SED resulted in inclination angles of $i=59{}^\circ$ from the entire data set (covering optical + IR bands) and $i=52{}^\circ$ from the optical-only data. This discrepancy seems to arise from the systematic errors of the reference stars in the IR band (J, H, Ks), resulting in an underestimate of the target luminosity in the IR band. Therefore, the SED of the optical+IR data set tended to return higher companion temperatures than the optical-only data. On the other hand, it is also difficult to constrain the temperature with the optical-only data (B, V, g', R, and I), which may then result in an underestimate of the companion temperature. Therefore, the true inclination angle must be in the range of $52{}^\circ \lt i\lt 59{}^\circ$. Hereafter, we take $i\sim 55{}^\circ \pm 5{}^\circ$.

We should also summarize the pulsar parameters in preparation for the discussion below. Ray et al. (2014) recently reported the detection of radio and gamma-ray pulse emission from the central MSP with a period of 2.88 ms with a spin-down luminosity of ${{L}_{{\rm SD}}}=2.3\times {{10}^{34}}$ erg s⁻¹. Based on these parameters, the pulsar's surface magnetic field can be estimated, assuming that the pulsar's rotation energy is dissipated by dipole radiation (Longair 1994),

$$\begin{eqnarray}&&{{B}_{*}}=3.0\times {{10}^{19}}{{(P\dot{P})}^{1/2}}=1.9\times {{10}^{8}}I_{45}^{-1/2}\quad {\rm G},\end{eqnarray} \tag{ 2 }$$

where ${{I}_{45}}$ is the pulsar's moment of inertia in units of 10⁴⁵ g cm², which is a typical magnetic field for a standard MSP.

In the case of NS binary systems, the mass accretion process is thought to be controlled by the propeller effect (Stella et al. 1986), i.e., the pressure balance between the ram pressure of accreting material ${{p}_{{\rm ram}}}$ and the magnetic pressure of the pulsar ${{p}_{{\rm B}}}$. Here we define ${{r}_{{\rm m}}}$ where ${{p}_{{\rm B}}}$ and ${{p}_{{\rm ram}}}$ are in balance:

$$\begin{eqnarray}\begin{array}{rcl} \frac{B_{*}^{2}}{8\pi }{{\left( \frac{{{r}_{*}}}{{{r}_{{\rm m}}}} \right)}^{6}} & = & \frac{{\dot{m}}}{4\pi r_{{\rm m}}^{2}}{{\left( \frac{2G{{M}_{*}}}{{{r}_{{\rm m}}}} \right)}^{1/2}} \\ {{r}_{{\rm m}}} & = & {{\left( \frac{B_{*}^{4}r_{*}^{12}}{8G{{M}_{*}}{{{\dot{m}}}^{2}}} \right)}^{1/7}} \\ {} & = & 2.5\times {{10}^{6}}{{\left( \frac{{{B}_{*}}}{{{10}^{8}}\;{\rm G}} \right)}^{4/7}}{{\left( \frac{{{r}_{*}}}{10\;{\rm km}} \right)}^{12/7}} \\ {} & {} & \times {{\left( \frac{{{M}_{*}}}{1.4{{M}_{}}} \right)}^{-1/7}}{{\left( \frac{{\dot{m}}}{{{10}^{16}}\;{\rm g}\;{{{\rm s}}^{-1}}} \right)}^{-2/7}}\quad {\rm cm}, \\ \end{array}\end{eqnarray} \tag{ 3 }$$

where G is the gravitational constant, ${{r}_{*}}$ is the NS radius, ${{M}_{*}}$ is the NS mass, and $\dot{m}$ is the mass accretion rate. Near the pulsar, charged particles are trapped by the pulsar magnetosphere and are corotating with the pulsar. If the accreting gas approaches the NS within a radius,

$$\begin{eqnarray}\begin{array}{rcl} {{r}_{{\rm c}}} & = & {{\left( \frac{G{{M}_{*}}}{\omega _{*}^{2}} \right)}^{1/3}}=1.7 \\ {} & {} & \times {{10}^{6}}{{\left( \frac{{{M}_{*}}}{1.4{{M}_{}}} \right)}^{1/3}}{{\left( \frac{P}{2.88\;{\rm ms}} \right)}^{2/3}}\quad {\rm cm} \\ \end{array}\end{eqnarray} \tag{ 4 }$$

at which the centrifugal force and the gravitational attraction are equal, then the gas will accrete onto the NS (where ${{\omega }_{*}}$ is the angular velocity of the NS).

Utilizing ${{B}_{*}}$ from the pulse profile, the lower limit of the accretion rate $\dot{m}$ that fulfills the condition of ${{r}_{{\rm c}}}\gt {{r}_{{\rm m}}}$ can be calculated,²⁵

$$\begin{eqnarray}\begin{array}{rcl} \dot{m}\gt \frac{B_{*}^{2}r_{*}^{6}\omega _{*}^{7/3}}{{{2}^{3/2}}{{G}^{5/3}}M_{*}^{5/3}} & = & 1.3\times {{10}^{16}}{{\left( \frac{{{r}_{*}}}{10\;{\rm km}} \right)}^{8}} \\ {} & {} & \times {{\left( \frac{{{M}_{*}}}{1.4{{M}_{}}} \right)}^{-2/3}}{\rm g}\;{{{\rm s}}^{-1}}. \\ \end{array}\end{eqnarray} \tag{ 5 }$$

Recently, Ray et al. (2014) reported temporal extinctions of the pulse emission in the radio implying that the accretion on the MSP is ongoing. If that is the case, the mass accretion rate must be higher than Equation (5) and the expected luminosity during the mass accretion will amount to $2.4\times {{10}^{36}}$ erg s⁻¹, which is about five orders of magnitude higher than the X-ray luminosity at the 0.5–10.0 keV energy band. Papitto et al. (2013) reported intriguing activities of IGR J18245-2452 in the intermediate stage between the rotation and accretion power. Linares et al. (2014) and Ferrigno et al. (2014) reported weak accretion flows (below $\dot{m}\lt {{10}^{6}}$ g s⁻¹) in IGR J18245-2452; these exhibit a variety of activities possibly reflecting accretion conditions. In case of ${{r}_{{\rm m}}}\approx {{r}_{{\rm c}}}$, namely, the weak-propeller regime, the accretion flow is only partly inhibited and the X-ray luminosity is in the range of ${{10}^{35}}\sim {{10}^{37}}$ erg s⁻¹. For cases of ${{r}_{{\rm m}}}\gt {{r}_{{\rm c}}}$, namely, the strong propeller regime, the X-ray luminosity is in the range of ${{10}^{33}}\sim {{10}^{34}}$ with a very fast and striking variability. Regardless, the X-ray luminosity of 2FGL J2339.6-0532 is still lower than that of IGR J18245-2452 in the strong-propeller regime by an order of magnitude.

In addition, IGR J18245-2452 exhibited another quiescent state in 2002 with an X-ray luminosity of $\sim {{10}^{32}}$ erg s⁻¹, which is comparable to the observed X-ray luminosity of 2FGL J2339.6-0532. Ferrigno et al. (2014) claimed that ${{r}_{{\rm m}}}$ reached the light-cylinder radius in this regime. This condition would allow for the existence of pulsar wind and would also prevent mass accretion. Thus, we conclude that the binary system can be in the same condition seen in IGR J18245-2452 in 2002 or in the late stage of the evolution process without mass accretion. In the latter case, where the mass accretion already ended, the radio-pulse extinction can also be explained by the unstable activity of the pulsar's magnetosphere itself, as with "nulling" pulsars. (Gajjar et al. 2012 and references therein.)

As shown in the spectral analysis, the soft X-rays below 1 keV seem to originate from a blackbody. The obtained radius of 0.28 km for d = 1.1 kpc is unusually small for an accretion disk and thus the radiation can be interpreted as the X-ray radiation from the NS surface. A radius of 0.28 km is still small for a NS, and therefore the emitting region could be a hot spot around the polar cap area. In order to constrain the geometry of the polar cap, a high time resolution X-ray observation is required. In addition, the small variability and the lack of eclipse in the X-ray light curve are consistent with the estimated inclination angle of $i\sim 55{}^\circ$.

In contrast, the hard X-ray light curves vary with the orbital motion. The X-ray luminosity of the non-thermal component from the averaged X-ray spectra amounts to ${{L}_{{\rm pow}}}=3.6\times {{10}^{31}}$ erg s⁻¹ for a distance of 1.1 kpc at 0.5–10.0 keV. Therefore, the ratio of ${{L}_{{\rm pow}}}$ to the spin-down luminosity is about 0.15%, which is the typical value for a standard radio pulsar (Becker & Truemper 1997; Kargaltsev & Pavlov 2008).

To explain the flat-top modulation of the 4–8 keV light curve, two possible emitting regions can be proposed. One is an extended emitting region just around the pulsar like a halo. In this hypothesis, the minimum phase at the inferior conjunction can be explained by an eclipse of the halo. The observed smooth modulation requires the emitting region to be larger than the companion, 10¹⁰cm∼, which is still small for a standard pulsar wind nebula. In many cases, the non-thermal X-rays from a pulsar wind nebula are from downstream of the termination shock and the radius of the termination shock is constrained by the pressure balance. In this case, the upper limit of the emitter size is the orbital radius of ${{R}_{{\rm orb}}}\sim {{10}^{11}}$ cm. At this distance, however, the wind pressure is still too strong to be terminated.

The other hypothesis for the origin of the hard X-rays is that of a shocked pulsar wind interacting with the companion star (Bogdanov et al. 2005, 2014a, 2014b). The companion star orbiting nearby the pulsar can partially terminate the strong pulsar wind. In this case, the flat-top light curve can be explained by the Lorentz boost of the shocked plasma. As shown in Figure 11, we assumed a thin emitting layer covering the hemisphere of the companion star. The surface of the emitting region is the wind termination shock and the injected electron plasma decelerated at the shock to a bulk velocity ${{\beta }_{2}}$ reflecting the magnetization parameter upstream of the shock. At the superior conjunction phase, the shocked plasma is flowing in a direction away from us, and therefore the synchrotron luminosity may be weakened (Pelling et al. 1987). The dashed line in the bottom panel of Figure 9 shows the calculated photon flux for the thin layer of the shocked pulsar wind on the surface of the companion with a photon index of p = 1.14 and an inclination angle of $i=55{}^\circ$. The best-fit bulk velocity of the shocked wind is ${{\beta }_{2}}=0.43\pm 0.15$ in units of the light speed. If that is the case, the X-ray flux is attenuated by a factor of

$$\begin{eqnarray}&&{{\left( \frac{\sqrt{1-\beta _{2}^{2}}}{1-{{\beta }_{2}}{\rm cos} (\pi /2+i)} \right)}^{1+p}}\sim 0.42.\end{eqnarray} \tag{ 6 }$$

Here, we employed a magnetization parameter σ for the pulsar wind upstream of the shock, $\sigma =B_{1}^{2}/(4\pi {{n}_{1}}{{u}_{1}}{{\gamma }_{1}},{{m}_{e}}{{c}^{2}})$ (Kennel & Coroniti 1984), where B₁ is the magnetic field just upstream of the shock, n₁ is the number density of the pulsar wind, u₁ is the flow velocity defined by $1+u_{1}^{2}={\Gamma }_{1}^{2}$ (${{{\Gamma }}_{1}}$ is the bulk Lorentz factor of the wind upstream of the shock), and c is the light velocity. Assuming that half of the wind energy is carried as Poynting flux ($\sigma =1$), B₁ amounts to

$$\begin{eqnarray}&&{{B}_{1}}={{\left( \frac{\sigma }{1+\sigma }\frac{{{L}_{{\rm SD}}}}{R_{{\rm orb}}^{2}c} \right)}^{1/2}}=5.5\quad {\rm G}.\end{eqnarray} \tag{ 7 }$$

Furthermore, the pulsar wind is compressed at the shock, and therefore the downstream magnetic field B₂ is higher than B₁. Adopting ${{B}_{2}}\gt 5.5$ G as a lower limit, we can constrain the gyration radius of the synchrotron electrons emitting 1 keV X-rays,

$$\begin{eqnarray}&&{{r}_{{\rm gyro}}}=\frac{{{\gamma }_{2}}{{m}_{e}}{{c}^{2}}}{eB}\lt 3.5\times {{10}^{6}}{{\left( \frac{{{\epsilon }_{{\rm X}}}}{1\;{\rm keV}} \right)}^{1/2}}{{\left( \frac{{{B}_{2}}}{5.5\;{\rm G}} \right)}^{-1}}\quad {\rm cm},\end{eqnarray} \tag{ 8 }$$

where ${{\epsilon }_{{\rm X}}}$ is the synchrotron photon energy. The obtained gyration radius is far smaller than the companion, ${{r}_{{\rm comp}}}\sim {{10}^{10}}$ cm, and therefore the shock-heated electrons cannot escape from the downstream immediately. In terms of the enegetics, the phase averaged X-ray luminosity of the power-law component was ${{L}_{{\rm pow},0.5-10\,{\rm keV}}}=3.6\times {{10}^{31}}$ erg s⁻¹ from the spectral fitting. Taking into account the Lorentz boost effect of 1/0.42 and the ratio of the maximum flux against the phase averaged flux of ∼3.0, the intrinsic synchrotron luminosity from the companion becomes $L_{{\rm pow},0.5-10\,{\rm keV}}^{\prime }=1.1\times {{10}^{32}}$, which is comparable to the bolometric luminosity of the heated hemisphere of the companion, ${{L}_{{\rm BB}}}\sim 1.1\times {{10}^{32}}$ ergs s⁻¹. This brief estimation also indicates that the heating efficiency should be smaller than 0.5. This result is obviously different from the heating efficiency obtained from the phase-resolved SED (see Figure 5) in which an isotropic pulsar wind is assumed. This discrepancy may indicate that the pulsar wind from the central MSP is not isotropic as expected in the crab nebula (Bogovalov & Khangoulyan 2002). The wind pressure at the companion is then ${{p}_{{\rm wind}}}={{L}_{{\rm SD}}}/4\pi R_{{\rm orb}}^{2}\;c\sim 4.7$ dyn which may be greater than that of the coronal gas ($T={{10}^{6}}$ K, ${{n}_{{\rm p}}}={{10}^{8}}$ cm⁻³ for the Sun) but much smaller than the photosphere. Therefore the thickness of the emitting region should not be higher than the corona of the companion. On the other hand, the radiation length of the relativistic electrons is quite long: $716A/(Z(Z+1){\rm ln} (278/\sqrt{(Z)})\sim 4\times {{10}^{17}}$ cm for the coronal gas of ${{n}_{{\rm p}}}\sim {{10}^{8}}$ cm⁻³. Therefore, these electrons can radiate synchrotron X-rays even in the immediate area of the photosphere.

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If the hard X-rays originated in the shocked pulsar wind on the surface of the companion star as is discussed, then the composition of the pulsar wind can be constrained based on the downstream flow velocity. Considering the Rankin–Hugoniot relation for magnetized electron–positron plasma for small σ, we can find the downstream flow velocity as a function of the magnetization parameter σ (Kennel & Coroniti 1984):

$$\begin{eqnarray}&&u_{2}^{2}=\frac{1+9\sigma }{8},\end{eqnarray} \tag{ 9 }$$

where ${{u}_{2}}={{{\Gamma }}_{2}}{{\beta }_{2}}$. Finally, we find the downstream flow velocity, ${{\beta }_{2}}=\sqrt{(1+9\sigma )/(7-9\sigma )}$, in units of the light speed. Note that the equation predicts the lower limit of the shocked pulsar wind, ${{\beta }_{2}}=1/\sqrt{7}\sim 0.38$, at $\sigma =0$. On the other hand, the flow velocity of ${{\beta }_{2}}=0.43\pm 0.15$ from the X-ray light curve indicates that the pulsar wind is already in the particle-dominant state, i.e., $\sigma \sim 0.028$, at the surface of the companion, only $1.1\times {{10}^{11}}$ cm apart from the pulsar. Note that the post-shock flow velocity has an inverse-correlation with the inclination angle that affects the resultant magnetization parameter. If we adopt an error range of inclination angle, $50{}^\circ \sim 60{}^\circ$, the magnetization parameter can range from 0.008 (for $i=60{}^\circ$) to 0.1 (for $i=50{}^\circ$). The upper limit of $\sigma \lt 0.1$ is still much smaller than that calculated for the similar system of PSR J1023+0038 reported by Bogdanov et al. (2011), in which a thick post-shock emitting region was assumed. Past theoretical studies claimed that the pulsar wind is highly magnetized at the beginning just around the light cylinder. However, the observed σ is far smaller than 1, and this discrepancy has been called the σ paradox. Recently, Aharonian et al. (2012) reported evidence of particle acceleration just around the pulsar based on gamma-ray pulse analysis of the Crab pulsar. The above argument of σ in this work is consistent with their result and may be one of the σ parameters measured at the nearest distance from a pulsar. Furthermore, this may imply that the old MSPs and the young radio pulsars have the same particle acceleration mechanism.

One of the intriguing features of this object is the double-peak structure in the 2–4 keV X-ray light curve. Since the dip is observed only in the softer band (Figure 9), this feature can be interpreted as absorption of soft X-rays. If we accept that the non-thermal X-rays originate in the shocked pulsar wind on the surface of the companion as discussed above, the absorber must be lying around the pulsar because the dip appears at the optical maximum phase (= the superior conjunction). In addition, the orbital inclination angle $i\sim 55{}^\circ$ requires that the absorber must be extended far from the orbital plane ($\sim 8\times {{10}^{10}}$ cm).

As Ray et al. (2014) claimed, mass accretion onto the pulsar seems to continue intermittently, however, the argument of the propeller effect rules out a powerful accretion. This is consistent with the lack of a bright disk component in X-ray spectra. In addition to the propeller effects, the measured companion radius is about 1/2 of the Roche lobe, and therefore the stellar material cannot overcome the Lagrange point L1 to accrete on the NS. To feed mass to the pulsar, explosive ejection faster than ∼1000 km s⁻¹ may be required for the mass to escape from the gravity potential.

In addition, as inferred from the discussion on the heating efficiency, the pulsar wind may be concentrated on the orbital plane, which would prevent the accretion flow. If the stellar material that is blown away by the equatorial pulsar wind is drifting around the pulsar's polar regions, and it may accrete from the poloidal direction. On the other hand, the running periodogram shown in Figure 10 indicates that the dip structure related to the second harmonic component is unstable, and appears to have disappeared ∼120 ks from the start time of the observation. To confirm the scenario in which the stellar gas is drifting around the pulsar and accretes intermittently, simultaneous X-ray and radio observations are required.