TOWARD IDENTIFYING THE UNASSOCIATED GAMMA-RAY SOURCE 1FGL J1311.7-3429 WITH X-RAY AND OPTICAL OBSERVATIONS

The Large Area Telescope (LAT; Atwood et al. 2009) on board the Fermi Gamma-Ray Space Telescope is a successor to EGRET on board the Compton Gamma-Ray Observatory (Hartman et al. 1999), with much improved sensitivity, resolution, and energy range. The second Fermi-LAT catalog, based on the first 24 months of all-sky survey data (2FGL; Nolan et al. 2012), provides source location, flux, and spectral information, as well as light curves on month time bins for 1873 γ-ray sources detected and characterized in the 100 MeV–100 GeV range. Thanks to their small localization error circles (or ellipses) with typical 95% confidence radii, r₉₅  ≃  01–02, for relatively bright sources, 69% of the 2FGL sources are reliably associated or firmly identified with counterparts of known or likely γ-ray producing sources. In particular, more than 1000 sources are proposed to be associated with active galactic nuclei (AGNs; of mainly the blazar class) and 87 sources with pulsars (PSRs), including 21 millisecond pulsars (MSPs), which are a new category of γ-ray sources discovered with Fermi-LAT (Nolan et al. 2012; Abdo et al. 2009a). Other sources, albeit of a relative minority compared to AGNs and PSRs, also constitute important categories of new GeV sources like supernova remnants (SNRs; Abdo et al. 2009b, 2010a, 2010b, 2010c), low-mass/high-mass binaries (Abdo et al. 2009c, 2009d, 2009e), pulsar wind nebula (Abdo et al. 2010d, 2010e), one nova (Abdo et al. 2010f), normal and starburst galaxies (Abdo et al. 2010g, 2010h), and the giant lobes of a radio galaxy (Abdo et al. 2010i).

Despite such great advances in the identification of Fermi-LAT sources, 575 (31%) sources in the 2FGL catalog still remain unassociated. Note that a substantial fraction of the unassociated sources (51%) have at least one analysis flag due to various issues, while only 14% of the associated sources have been flagged (Nolan et al. 2012). This may suggest that some of unassociated sources are spurious due to complexity/difficulty of being situated in a crowded region near the Galactic plane. Nevertheless, many of them are bright enough to be listed in the one year Fermi-LAT catalog (1FGL; Abdo et al. 2010j) and some of them are even listed in the bright source list based on the first 3 months of data (0FGL; Abdo et al. 2009f). By comparing the distribution of associated and unassociated sources in the sky, a number of interesting features in the map were reported (Nolan et al. 2012). For example, (1) the number of unassociated sources decreases with increasing Galactic latitude, (2) the number of unassociated sources increases sharply below Galactic latitudes, |b| < 10°, and (3) the fraction of sources with curved gamma-ray spectra among the unassociated sources is greater (28%) than the fraction of curved spectra sources among the associated sources (16%). Further extensive studies based on a statistical approach in an effort to correlate their gamma-ray properties with the AGN and PSR populations was presented for 1FGL unassociated sources (Ackermann et al. 2012).

In this context, 1FGL J1311.7-3429 (or 2FGL name, 2FGL J1311.7-3429) is a classical unassociated gamma-ray source situated at high Galactic latitude (l = 3076859, b = 281951), and was first discovered by EGRET about 20 years ago as 3EG J1314-3431 (Hartman et al. 1999) or EGR J1314-3417 (Casandjian & Grenier 2008). The source was also reported by Fermi-LAT in the 0FGL list with a gamma-ray flux F_0.1-20 GeV = (11.7 ± 1.1) × 10⁻⁸ photons cm⁻² s⁻¹, which is marginally consistent with the gamma-ray flux determined by EGRET, F_0.1-20 GeV = (18.7 ± 3.1) × 10⁻⁸ photons cm⁻² s⁻¹, within the 2σ level. In the 2FGL catalog, the detected significance of 1FGL J1311.7-3429 is 43.1σ, which is one of the brightest sources with an unid flag. Based on the one-month binned >100 MeV gamma-ray light curve of 1FGL J1311.7-3429 over two years of data as published in the 2FGL catalog,⁸ no statistically significant variability was observed (Variability_index = 19.09; Nolan et al. 2012). The gamma-ray spectrum is significantly curved with curved significance Signif_curve of 6.33 (Nolan et al. 2012).⁹

The first X-ray follow-up observation of 1FGL J1311.7-3429 was conducted as a part of Suzaku X-ray observations of 11 unidentified Fermi-LAT objects at high Galactic latitude, |b| > 10° (Maeda et al. 2011; Takahashi et al. 2012). The X-ray source associated with 1FGL J1311.7-3429 showed a very rapid X-ray flare with the count rate changing by a factor of 10. Subsequent Chandra ACIS-I (2010 March 21 for a 19.87 ks exposure, obsID 11790) and Swift XRT observations (2009 February 27 for a 3.34 ks exposure, obsID 31358; see also Table 1) confirmed that the brightest X-ray source within the Fermi-LAT error ellipse is the most credible counterpart and that the X-ray source is also variable on month-to-year timescales. The unabsorbed X-ray flux observed with Chandra was 1.03 × 10⁻¹³ erg cm⁻² s⁻¹ in the 0.5–8 keV band, with a differential photon spectral index, Γ = 1.26^+0.38_{− 0.37} (Cheung et al. 2012).

Motivated by the initial X-ray results, we conducted further deep observations of 1FGL J1311.7-3429 with Suzaku, together with deep optical observations using a 105 cm Ritchey–Chrétien telescope (g', Rc, and Ic bands) at the Ishigakijima Astronomical Observatory (IAO) in Japan, as well as the 1 m telescope (r' band) at Lulin Observatory in Taiwan. In Section 2, we describe the details of the Suzaku observations and optical observations and data reduction procedures. Very recently, Romani (2012) reported quasi-sinusoidal optical modulation of this source with a 1.56 hr (5626 s) period, suggesting that the source is another black-widow-type MSP like that recently discovered for 1FGL J2339.7-0531 (Romani & Shaw 2011; Kong et al. 2012). Our paper confirms some of those optical findings for 1FGL J1311.7-3429, plus provides results from multiple epoch optical monitoring between 2012 March and May and completely new X-ray data based on a long Suzaku observation conducted in 2011 together with our previously published archival 2009 data. The results of these observations are given in Section 3. Based on our new observational data in optical and X-ray, and various observed gamma-ray parameters compiled in the 2FGL source catalog, we support that 1FGL J1311.7-3429 could be a "radio-quiet" gamma-ray emitting MSP candidate like 1FGL J2339.7-0531. The variable optical/X-ray source is posited as the counterpart to the gamma-ray source and throughout, we refer to it simply as 1FGL J1311.7-3429.

2.1. Optical/UV

As discussed in Cheung et al. (2012), the brightest X-ray source within the Fermi-LAT error ellipse, CXOU J131145.71-343030.5, is the most credible counterpart and exactly the one detected in our previous (AO4; below) Suzaku observation (Maeda et al. 2011). The source was also detected with the Swift XRT (observation ID 31358). Within the Chandra error circle (06 at 90% level), there is a R = 17.9 mag, B = 20.5 mag star in the USNO A-2.0 catalog (Muslimov & Harding 2003), that is 056 apart from CXOU J131145.71-343030.5. The same star is also listed as R = 18.8 mag, B = 21.0 mag in USNO-B1.0 catalog, suggesting a hint of temporal variability (a typical uncertainty of these measurements is ≃0.3 mag; Muslimov & Harding 2003). The same optical source is also seen in the DSS (Digital Sky Survey), but its optical magnitude is unclear. Moreover, Swift UVOT observations taken simultaneously with the XRT detected the source. Our analysis using archival Swift UVOT data indicate: v > 19.51 (upper limit only), b = 20.10 ± 0.30, u = 20.77 ± 0.27, uvw1 = 21.70 ± 0.31, uvm2 = 21.58 ± 0.24, and uvw2 = 22.05 ± 0.22.

We made further deep follow-up observations of the field of CXOU J131145.71-343030.5, centered at (R.A., decl.) = (197940400, −34508306), with the 105 cm Ritchey–Chrétien telescope at the Ishigakijima Astronomical Observatory in Japan. These observations were obtained on 2012 May 25 and started at 12:31:11:13 and ended 15:41:11:63 (UT). The telescope in IAO is equipped with a tricolor camera that performs simultaneous imaging in the SDSS-g' (hereafter, g'), Rc and Ic bands. The total net exposure amounts to 8400 s (300 s × 28 frames; see Table 1 for the observation log). All images were flat field and bias corrected. The absolute magnitudes were calibrated against the four reference stars shown in Figure 1. In the Rc and Ic bands, the reference star magnitudes were based on the NOMAD catalog (Monet et al. 2003). Because the target area was not covered by the SDSS, we employed a system conversion formula of USNO-B Bc and Rc magnitudes (Sesar et al. 2006) for the four reference stars to obtain g' magnitudes. Moreover, the observed magnitudes were corrected for Galactic extinction using $A_{g^{\prime }} = 0.247$ mag, A_Rc = 0.167 mag, and A_Ic = 0.120 mag.

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We also conducted optical SDSS-r' (hereafter r') band monitoring observations with the Lulin One-meter Telescope (LOT; Huang et al. 2005). Observations were conducted on five nights between 2012 March and May (see Table 1). Photometric images with 300 s exposure were obtained using the PI1300B CCD camera. We performed the dark-subtraction and flat-fielding correction using the appropriate calibration data. For these LOT data, the four reference stars used in the IAO photometry were saturated in the detector and therefore could not be used. Instead, the LOT photometric results are presented as differential magnitudes against two other fainter reference stars (boxed in Figure 1).

2.2. Suzaku XIS

3.1. Optical/UV

Figure 1 shows a multicolor image of 1FGL J1311.7-3429 constructed from the IAO g' (blue), Rc (green), and Ic (red) data from 2012 May 24. The optical counterpart of the X-ray source is clearly detected in the image, but apparently the source is rather "blue" compared with reference stars and nearby galaxies. Aperture photometry yielded average magnitudes of the source, g' = 20.97 ± 0.13, Rc = 21.17 ± 0.16, and Ic < 18.38 (3σ upper limit). We also checked the temporal profile of the optical emission for the IAO data (Figure 2). Relative photometry for the IAO images against the four field stars shows large amplitude (Δm ∼ 2 mag) quasi-sinusoidal modulation in the g' and Rc bands with a timescale of 1.5 hr, as suggested by Romani (2012).

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To search for possible long-term variability, Figure 3 (top) compares the r'-band light curve reconstructed only from LOT data between 2012 March and May. The differential magnitudes are derived by comparison with two reference stars in the field (see Figure 1). Note, the r'-band magnitude of the reference stars remain constant within Δm = 0.068 mag over the five nights of observations. Interestingly, the amplitude of modulation and the light-curve profile seems to have changed among the five nights of observations. Specifically, a clear modulation of Δm ∼ 2 mag is visible in the May 24 data, while Δm ∼ 1 mag in the March 24 data, and almost unseen (Δm ≲ 0.2 mag) in the March 26 data. Moreover, the peak magnitude differs by Δm ∼ 0.5 mag among the five nights, much larger than the fluctuations in the magnitudes of reference stars. Figure 3 (bottom) shows the folded light curves of differential r'-band magnitudes with a best-fit period of 1.56278 hr (5626 s) proposed by Romani (2012). Phase zero is defined here as MJD 56010.76808, so that the time of the observed minimum r'-band magnitude in the May 24 data is set at orbital phase ϕ = 1.0. The peak r'-band magnitude is around ≃20.5 for five nights of data from 2012 March to April. Note, this is exactly consistent with what has been observed with IAO on May 25 (Figure 2, right). To further investigate the temporal variability/flaring in the UV data, we also reanalyzed the archival Swift UVOT data. However, the UVOT exposures for each filter (b, u, uvw1, uvm2, uvw2) were too short to search for variability (see Table 1).

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3.2. Suzaku XIS

During the AO-4 observation, significant X-ray variability was detected at the beginning of the observation, where the count rate changed by a factor of 10 (Maeda et al. 2011). Figure 4 compares the Suzaku XIS FI (XIS0+3) images in the 0.5–10 keV range, reconstructed by using the data during the first 20 ks (top) and the last 74 ks (bottom). The images are corrected for exposure and vignetting, and are non-X-ray (detector) background subtracted. The images were also smoothed by a Gaussian function with σ = 017, following the procedure given in Maeda et al. (2011). Note that the source is clearly detected in the first 20 ks, but almost unseen in the last 74 ks. Also Cheung et al. (2012) argues that the 0.3–10 keV Swift XRT count rate of (6.1 ± 1.8) × 10⁻³ counts s⁻¹ is equivalent to a 0.5–8 keV flux of ≃3.1 × 10⁻¹³ erg cm⁻² s⁻¹, indicating a ∼3× brighter source about one year prior to the Chandra observation, and providing further evidence of long-term X-ray variability in this source.

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Figure 5 summarizes the X-ray light curve of 1FGL J1311.7-3429 thus obtained during the AO-6 observation and compares them with those obtained in the AO-4 observation. All the XIS0, 1, 3 count rates are summed in the various energy bands of 0.4–1 keV, 1–2 keV, 2–4 keV, and 4–8 keV (from top to bottom). Note that X-ray variability is clearly seen above 1 keV, but not in the 0.4–1 keV light curve. To see this more quantitatively, we calculated the normalized excess variance σ²_NXS (Vaughan et al. 2003; see also Kataoka et al. 2007) for the AO4 and AO6 light curves and for the combined AO4+AO6 light curves. The σ²_NXS parameter is an estimator of the intrinsic source variance after subtracting the contribution expected from measurement errors. As shown in Figure 6 (top), σ²_NXS is consistent with zero for the 0.4–1 keV band, while almost constant (within error bars) and significantly positive above 1 keV.¹⁰

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Figure 6 (bottom) presents the normalized power spectrum density (NPSD; Hayashida et al. 1998), which is a technique for calculating the PSD of unevenly sampled light curves. Note that data gaps are unavoidable for low Earth orbit X-ray satellites like Suzaku. Since the orbital period of Suzaku is ∼5760 s, Earth occultations create artificial periodic gaps every 5760 s in the data, even when the source is continuously monitored. To calculate the NPSD of our data sets, we made light curves of two different bin sizes of 256 s and 5760 s for each of the AO4 and AO6 light curves (Kataoka et al. 2001). The NPSD calculated for each light curves is well represented by a steep power law with P(f) ∝f^{−2.00  ±  0.32} (AO4) and P(f) ∝ f^{−2.04  ±  0.44} (AO6). Note that the amplitude of the NPSD is larger for the AO4 (red) data than in the AO6 (blue) data. This is due to large flare observed in the first 20 ks of the AO4 observation (Figure 4) and is consistent with the larger value of σ²_NXS compared with variability during AO6 observation (Figure 6, top).

Figure 7 shows the folded X-ray light curves from the Suzaku AO4 (top) and AO6 (bottom) data sets. The XIS0, 1, and 3 data are all summed in 0.4–10 keV band. The phase zero is defined as MJD 56010.76808 as in the optical folded light curves shown in Figure 3 (bottom). The vertical axis represents the source counts divided by the average source intensity in the frame. Although there is a regular exposure gap for phases ϕ = 0.3–0.4 due to Earth occultations, there appears to be a clear excess at phases ϕ = 0.4–0.6 in AO4 data (see also Romani (2012)). Moreover, we found similar structure in the AO6 data, but at different phases of ϕ = 0.6–0.8 with much smaller amount of excess. To check that this excess is not due to artifacts caused by periodic gaps due to Earth occultation, we also made the folded light curves of the nearby X-ray source in the same field of view (src B in Maeda et al. 2011, or CXOU J131147.0-343205 in Cheung et al. 2012; see Figure 4), whose X-ray flux is comparable to the average X-ray flux of 1FGL J1311.7-3429. The results presented as dashed lines in Figure 7 show no clear excess for the nearby source. This suggests that the X-ray excesses in the folded light curves are most likely due to orbital motion of 1FGL J1311.7-3429 itself.

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Finally, Figure 8 compares the unfolded X-ray spectrum for 1FGL J1311.7-3429 averaged over the AO4 (red) and AO6 (blue) observations. The best model fits for both observations consist of power-law continua with photon indices, Γ ≃ 1.3–1.7. Significant curvature (or deficit of photons below 2 keV) was observed only in the 2009 data, which was tentatively modeled by an excess value of Galactic column density N_H; N_H is, however, consistent with zero for the 2011 data. The model fitting results are summarized in Table 2. Although the nearby X-ray source (src B in Maeda et al. 2011, or CXOU J131147.0-343205 in Cheung et al. 2012; see Figure 4) is located only 16 apart to the south, contamination from this source and other nearby faint sources is estimated to be less than 5% for the applied region of interest of 1'.

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Table 2. Fitting Parameters of Suzaku Data for the Power-law Model

Parameter	AO4	AO6
	Value and Errorsa	Value and Errorsa
NH (1020 cm−2)	0.33+0.15− 0.13	<0.07
Γ	1.71+0.18− 0.17	1.26+0.08− 0.07
Flux (0.5–2 keV)b	0.99+0.27− 0.19	0.83+0.08− 0.06
Flux (2–10 keV)b	1.78+0.16− 0.15	2.96 ± 0.15
χ2 (dof)	17.4 (15)	17.6 (15)
P(χ2)	0.29	0.29

Notes. ^aAll errors are 1σ. ^bIn unit of 10⁻¹³ erg cm⁻² s⁻¹.

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During the first (AO4; 2009) and second (AO6; 2011) Suzaku observations, we detected significant variability in 1FGL J1311.7-3429 characterized by repeated flaring activity, with a timescale of ∼10 ks. The variability is only clearly seen above 1 keV. The NPSD is well characterized by P(f) ∝ f⁻², as is the case for the X-ray variability of various classes of AGNs including Seyferts and blazars (e.g., Hayashida et al. 1998; Vaughan et al. 2003). The latter class constitutes the majority of Fermi-LAT sources but the X-ray variability timescales of blazars are in general somewhat longer, typically ≃1 day (e.g., Kataoka et al. 2001). Such "red-noise" PSD behavior is also observed in X-ray (Galactic black hole and neutron star) binary systems, but on much shorter time scales. For example, variability as short as ∼1–10 ms has been observed for the famous Galactic black hole source Cyg X-1 (e.g., Meekins et al. 1984; Hayashida et al. 1998).

Significant variability has also been observed in the optical (g', Rc, r'), where it is rather a quasi-sinusoidal flux modulation with a 1.56 hr period, as recently reported by Romani (2012). Moreover, we also found that the modulation profile, including the amplitude of modulation and peak intensity, has changed largely among the six nights of observations. The apparent modulation of magnitude observed in both the IAO and LOT data is quite similar to those observed in 1FGL J2339.7-0531, which is characterized by a 4.63 hr orbital period in optical and X-ray data (Romani & Shaw 2011; Kong et al. 2012). Note that 1FGL J2339.7-0531 is now suggested to be a "radio-quiet" gamma-ray emitting black-widow MSP with a ≃0.1 M_☉ late-type companion star, viewed at inclination i ≃ 57°. Moreover, this compact object companion in 1FGL J2339.7-0531 is strongly heated, with T_eff varying from ∼6900 K (superior conjunction) to <3000 K at minimum (Romani & Shaw 2011).

In this context, the spectral energy distribution (SED) of 1FGL J1311.7-3419 from radio to gamma-rays (Figure 9, top) may provide some hints on the nature of this mysterious source. 1FGL J1311.7-3419 has been the subject of both radio pulsar counterpart searches and blind searches for gamma-ray pulsations, but to date no pulsed emission has been detected (Ransom et al. 2011), and the situation is quite similar to the case for 1FGL J2339.7-0531. There are no NVSS radio sources catalogued within the 2FGL ellipse of 1FGL J1311.7-3429 down to 1.4 GHz flux completeness limit of ≃2.5 mJy (Condon et al. 1998), which is given as an arrow in Figure 9 (top). From the 0.1–100 GeV gamma-ray flux listed in the 2FGL catalog, F_γ ≡ F_{0.1-100 GeV} ≃ 6.2 × 10⁻¹¹ erg cm⁻² s⁻¹, we obtain F_γ/F_X ≃ 300, F_γ/F_R  ⩾1.7 × 10⁶ for 1FGL J1311.7-3429, where F_X and F_R are the X-ray and radio fluxes measured in 2–10 keV and at 1.4 GHz, respectively. Note, these values are almost comparable to those measured in 1FGL J2339.7-0531, with F_γ ≃ 3.0 × 10⁻¹¹ erg cm² s⁻¹, F_γ/F_X ≃ 150 and F_γ/F_R  ⩾  8.7 × 10⁵. Although its flat spectrum X-ray continua and relatively high γ-ray-to-X-ray energy flux ratio (of ≳100) is typical of the subclass of blazars (FSRQ; Nolan et al. 2012), the non-detection in the radio as well as its curved gamma-ray spectrum seems to strongly disfavor an AGN association for 1FGL J1311.7-3429.

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To further support the MSP association of 1FGL J1311.7-3429, Figure 9 (bottom) shows a close-up of the SED of 1FGL J1311.7-3429 in the optical/UV bands, reconstructed from IAO and Swift UVOT data. Observed magnitudes were converted to flux density based on Fukugita et al. (1995). Red dashed line indicates a tentative fit with a blackbody model of T ≃ 1.2 × 10⁴ K (or kT ≃ 1 eV) assuming an emission volume radius of R_bb ≃ 1.5 × 10⁴ d_kpc km, where d_kpc is the distance to the source in units of 1 kpc. Therefore, the optical/UV spectrum of 1FGL J1311.7-3429 seems compatible with what is expected from a companion star of a radio-quiet MSP like 1FGL J2339.7-0531. A slightly higher temperature than 1FGL J2339.7-0531 (kT ≃ 0.3–0.6 keV; Romani & Shaw 2011) may indicate ×2 smaller orbital radius, ∼5 × 10⁵ km, for the 1FGL J1311.7-3429 binary system, assuming that the mass of the companion star is 0.1 M_☉ and the pulsar spin-down luminosity is L ≃ 10³⁴ erg s⁻¹ (parameters suggested for 1FGL J2339.7-0531 binary system; Romani & Shaw 2011). A change of the modulation profile observed in the r' band may be accounted for by rapid changes in the companion star temperature, but this remains uncertain.

Since both the optical and X-ray light curves in the case of 1FGL J2339.7-0531 clearly exhibits a 4.63 hr orbital modulation (Romani & Shaw 2011; Kong et al. 2012), the detection of periodicity in the X-ray light curve of 1FGL J1311.7-3429 is also likely. In fact, the folded X-ray light curve exhibits an excess feature around ϕ = 0.5. As indicated by Romani (2012), this is presumably a pulsar superior conjunction, although both the normalized intensity as well as the phase peak appear to have changed substantially between the 2009 (AO4) and 2011 (AO6) observations. We therefore expect that X-ray variability consists of at least two different components—one associated with the binary motion as for the optical data, and the other a rather random fluctuation well represented by the NPSD of P(f) ∝ f⁻², whose physical origin is still unknown but possibly related with perturbations associated with shock acceleration.

Such flaring X-ray variability has not yet been observed for 1FGL J2339.7-3429, but solely in 1FGL J1311.7-3429. In a review of X-ray emission from MSPs, Zavlin (2007) describes three primary sources of X-ray emission: (1) intrabinary shock, (2) the neutron star (NS) itself, and (3) pulsar wind nebula outside the binary system (see also Archibald et al. 2010). In fact, thermal emission of kT ∼ 0.1–0.2 keV is often observed from MSPs, which is thought to arise from the surface of the NS and is steady with time (e.g., Marelli et al. 2011; Maeda et al. 2011). More recently, thermal emission of kT ≃ 0.1 keV was also detected from 1FGL J2339.7-0531 (Kong et al. 2012, in prep), which is again steady despite the large flux modulation associated with binary motion being observed above 2 keV. Therefore, the fact that X-ray variability is not clearly seen below 1 keV may suggest that there could be some contribution from the surface of the NS, although from the spectral fitting it is not statistically significant. Then the variable, hard X-ray emission could arise from the intrabinary shock rather than the nebula because variability as short as ≃10 ks is unlikely to originate from the extended pulsar wind nebula.¹¹ Such a shock could readily produce gamma-ray emission (Arons & Tavani 1993). If localized, it could easily account for the orbital modulation as seen in the X-ray emission from 1FGL J2339.7-0531. But if material leaving the companion star, either through Roche lobe overflow or a stellar wind is non-uniform or patchy, we might expect random flaring activity as we see in the X-ray data of 1FGL J1311.7-3429.

We can also speculate on the nature of 1FGL J1311.7-3429 based solely on the gamma-ray properties, an approach already applied to the 1FGL unIDs in Ackermann et al. (2012). Figure 10 (top) presents a comparison of the 2FGL associated (either AGNs (blue) or PSRs (green)) and unassociated sources (red) in the Variability_index and Signif_curve plane. Apparently, 1FGL J1311.7-3429 is situated in the typical PSR regions of this diagnostic plane. Similarly, Figure 10 (bottom) plots the distribution of PSRs and AGNs in the Photon index versus F_{0.1-100 GeV} plane. In this case, 1FGL J1311.7-3429 is at the boundary of AGN and PSR sources, so is still consistent with a PSR association. For comparison, we also plot the gamma-ray parameters for 1FGL J2339.7-0531. In both panels, the gamma-ray properties of 1FGL J1311.7-3429 and 1FGL J2339.7-0531 are quite similar. Again, this supports the idea that 1FGL J1311.7-3429 is a black-widow system and may be a second example of a "radio-quiet" MSP after 1FGL J2339.7-0531.

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Finally, if the rapid X-ray flaring variability observed with Suzaku may be due to inhomogeneity of shock material and/or rapid changes in the beaming factor, this could be expected to occur also in gamma-rays, as suggested by a smooth connection of the spectrum between X-ray and gamma-ray energies. Moreover, we may see correlated variability also in the optical, which may be related to the change of modulation profile in the r'-band magnitudes that we see in Figure 3. Unfortunately, such fast variability is difficult to observe in gamma-rays as we mentioned for the one-month binned light curve in Section 1, despite the excellent sensitivity of Fermi-LAT. The low gamma-ray statistics also make it difficult to run a cross-correlation in order to measure any possible correlated optical, X-ray and gamma-ray variability. Further continuous investigation is necessary to confirm the origin of "variable" X-ray emission observed in the 1FGL J1311.7-3429 system.

This work is partially supported by the Japanese Society for the Promotion of Science (JSPS) KAKENHI 19047002. Work by C.C.C. at NRL is supported in part by NASA DPR S-15633-Y. We thank the anonymous referee for his/her helpful comments that improved the manuscript.