A SEARCH FOR VERY HIGH ENERGY GAMMA RAYS FROM THE MISSING LINK BINARY PULSAR J1023+0038 WITH VERITAS

The data are analyzed with a standard VERITAS software pipeline for reconstructing the primary parameters of the gamma rays (see, e.g., Acciari et al. 2008) and cross-checked using an independent calibration and analysis software package. The images are first flat-fielded by recording the response of the cameras to a pulsed UV LED system (Hanna et al. 2010). The images are cleaned to remove contamination by night-sky background (Daniel 2008) and parameterized by their principal moments (Hillas 1985). Arrival directions and impact distances are estimated by analyzing the orientation of shower images in different telescopes (Hofmann et al. 1999). Background estimation is achieved by comparison of the parameters of the recorded events with those computed in Monte Carlo gamma-ray simulations (Krawczynski et al. 2006).

A search for a VHE gamma-ray excess signal from the direction of PSR J1023+0038 is carried out independently for the two states of the system observed with VERITAS. None of these searches yield a significant excess over the estimated background from the location of PSR J1023+0038. Upper limits (ULs) on the integral flux above 300 GeV from PSR J1023+0038 for each state are set. The approach of Rolke et al. (2005) is used to determine these ULs at the 95% confidence level (CL) assuming a power-law source spectrum with a photon index of ${\rm{\Gamma }}=2.5$. The 95% CL ULs are $8.1\times {10}^{-13}$ and $9.6\times {10}^{-13}$ cm⁻² s⁻¹, respectively. For more information, refer to Table 1.

Given that PSR J1023+0038 shows orbital modulation in the X-ray band, a search for VHE gamma-ray emission at different orbital phases is also performed. The data are divided into 10 phase bins and undergo the same standard analysis as described in Section 3.1. For both the radio MSP state and the accretion/LMXB state, no significant excess is found in any of the orbital bins.

A search for pulsed gamma-ray emission in the VHE band from the position of PSR J1023+0038 is performed in two parts using data recorded by VERITAS during time periods in which the radio MSP was active and after the disappearance of the MSP and re-emergence of an accretion disk (accretion/LMXB state). After applying the background rejection and data quality cuts outlined in Section 3.1, photon arrival times are barycentered and phase-folded to the pulsar period in the Tempo2 software package (Hobbs et al. 2006) using a PSR J1023+0038 Jodrell Bank ephemeris derived from radio data spanning MJD 55,540 to 55,644 (2010 December 10 to 2011 March 24). Details on the creation of the Jodrell Bank radio ephemeris can be found in Section 3 of Archibald et al. (2013). Since the pulsar ephemeris used is no longer valid during the accretion/LMXB phase, only results from the radio MSP state are shown. The phase-folded light curve of PSR J1023+0038 is shown in Figure 1. De Jager's H-test is employed to compute H statistics that reflect the likelihood of the presence of a periodic signal in the light curve (de Jager 1989). Application of the H-test does not yield any evidence of periodicity in the VHE gamma-ray data. Subsequently, integral flux limits above an energy threshold of 166 GeV are computed with the method of de Jager (1994) assuming a pulsar duty cycle of 10%, a Gaussian pulse shape, and a spectral index of 3.8 (the same index measured by VERITAS for the Crab pulsar in Aliu et al. 2011). H statistics and integral VHE flux limits are given in Table 2.

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During the MSP phase, radio emission from PSR J1023+0038 was characterized by highly frequency-dependent eclipses at superior conjunction accompanied by short, irregular eclipses at all orbital phases (Archibald et al. 2009). Assuming a pulsar mass $M=1.4{M}_{\odot }$ and an orbital inclination $i\sim 46^\circ$, it has been shown that the line of sight between the pulsar and Earth does not intersect the Roche lobe of the companion at any point of the orbit (Archibald et al. 2009). Therefore, the eclipses must be caused by material driven off the surface of the companion by the impinging pulsar wind.

The V magnitude of the system is orbitally modulated, reaching a minimum during the inferior conjunction of the companion star (Thorstensen & Armstrong 2005). Such behavior is consistent with a Roche-lobe-filling companion near ${T}_{\mathrm{eff}}=5650$ K being illuminated by a pulsar with an isotropic luminosity of ∼2${L}_{\odot }$.

Orbitally modulated X-ray emission from PSR J1023+0038 was observed by the XMM-Newton and Chandra X-ray observatories in 2004, 2008, and 2010 (Homer et al. 2006; Archibald et al. 2010; Bogdanov et al. 2011). In Archibald et al. (2010), it is shown that in the energy range 0.25–2.5 keV, the X-ray emission is also modulated at the 1.6 ms rotational period of the MSP with a mean-squared pulsed fraction of 0.11(2). X-ray emission observed with Swift-XRT in the 0.3–8 keV energy range suggests a dominant nonthermal synchrotron component originating at the intrabinary shock. In the case of a magnetically dominated wind (with a ratio of magnetic energy to kinetic energy $\sigma \gg 1$), the shock should occur in a relatively strong magnetic field ($B\sim 40$ G) due to the small separation between the pulsar and the companion (Bogdanov et al. 2011). In Bogdanov et al. (2011) it is shown that the depth and duration of the X-ray eclipses imply that the intrabinary shock is localized close to the L1 Lagrangian point and has a size of about R ∼ 5 × 10¹⁰ cm. NuSTAR has detected a power law throughout the 3–79 keV band with an estimated luminosity of $7.4\times {10}^{32}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Tendulkar et al. 2014). If the estimate of the shock size by Bogdanov et al. (2011) is correct, then a very large fraction of the energy in the shocked portion of the wind must be converted to X-ray emission, which supports the high-σ scenario. In Archibald et al. (2010) it is also noted that emission from the pulsar magnetosphere can contribute to the nonthermal X-ray emission, but the orbital modulation indicates that this component is not dominant.

In addition to the aforementioned nonthermal emission, there also is a faint thermal component possibly originating from the hot polar caps of the pulsar and optically thin thermal plasma responsible for the radio eclipses. There is no evidence in X-ray data for a wind nebula associated with the pulsar. The observed X-ray luminosity in the 0.5–10 keV energy range of ${L}_{{\rm{X}}}\sim {10}^{32}$ erg s⁻¹ (assuming a distance of 1.4 kpc; Deller et al. 2012) is much less than the spin-down luminosity: ${L}_{\mathrm{sd}}\simeq 3.2\times {10}^{34}$ erg s⁻¹ (Archibald et al. 2013).

The broadband spectrum of PSR J1023+0038 from X-rays to VHE gamma rays is shown in Figure 2. While the X-ray data can be described by synchrotron emission from relativistic electrons exhibiting a power law with an exponential cutoff spectral shape, ${dN}/{dE}\propto {E}^{-2.52}\exp (-E/{E}_{\mathrm{cut}})$, the GeV data are not readily fitted with the same component. However, since the X-ray and GeV gamma-ray data are not strictly contemporaneous, spectral variability cannot be ruled out. The situation is similar if the observed GeV emission is produced in the pulsar magnetosphere. The typical spectral shape of the GeV MSPs is a power law with an exponential cutoff (e.g., Espinoza et al. 2013); see the red dashed line in Figure 2 for a best fit to the Fermi-LAT data (Tam et al. 2010). This spectral shape is thought to be a result of curvature acceleration in a gap region in the magnetosphere (Harding et al. 2005). More data are needed to distinguish between a synchrotron or curvature radiation origin of the GeV emission, although neither predicts emission above 10 GeV.

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Synchrotron photons can inverse Compton scatter on relativistic electrons and become VHE photons. The ratio of the total power radiated by the synchrotron radiation and by inverse Compton scattering by the same distribution of electrons is equal to $\eta ={({dE}/{dt})}_{\mathrm{sync}.}/{({{dE}}_{e}/{dt})}_{\mathrm{IC}}$. The value for η reaches a maximum in the Thomson limit in which ${\eta }_{{\rm{T}}}=\tfrac{{B}^{2}/8\pi }{{U}_{\mathrm{rad}}}$, where ${U}_{\mathrm{rad}}$ is the energy density of the synchrotron photons. It turns out that for PSR J1023+0038, the total energy of scattered photons is much smaller than the total energy of the synchrotron photons even in the Thomson limit where

$$\begin{eqnarray}&&{\eta }_{{\rm{T}}}\sim 600\displaystyle \frac{{(B/40{\rm{G}})}^{2}{(R/5\times {10}^{10}\mathrm{cm})}^{2}}{L/{10}^{32}\,\mathrm{erg}\,{{\rm{s}}}^{-1}}.\end{eqnarray} \tag{ 1 }$$

An additional potential source of VHE emission is external inverse Compton scattering of soft photons from the optically bright companion with an effective temperature of $T=5650\,{\rm{K}}$ (Thorstensen & Armstrong 2005). This inverse Compton component is shown in Figure 2 as a black dashed line. Given the assumed value of the magnetic field, $B=40\,{\rm{G}}$, the component lies well below the VHE flux upper limit. However, for a lower magnetic field strength, the difference between the peak flux values of the synchrotron and inverse Compton components will become smaller, allowing VERITAS observations to set a lower limit on the magnetic field strength. As shown by the green lines in Figure 2, the case of a 2 G magnetic field gives close to the peak inverse Compton flux allowed by the upper limit derived from the VERITAS data.

Note that for a 2 G magnetic field, ${\eta }_{{\rm{T}}}$ defined by Equation (1) is close to unity. However, X-ray photons will be upscattered in the Klein–Nishina regime, and in this case the total energy of scattered photons is much smaller than in the Thomson regime:

$$\begin{eqnarray}&&{\eta }_{\mathrm{KN}}=\displaystyle \frac{{B}^{2}/8\pi }{\tfrac{9}{32}{U}_{\mathrm{rad}}}\displaystyle \frac{\mathrm{ln}{({\hslash }{\omega }_{0}\gamma /{m}_{e}c)}^{2}}{{\gamma }^{2}{{\hslash }}^{2}{\omega }_{0}^{2}/{({m}_{e}{c}^{2})}^{2}}\sim {\eta }_{{\rm{T}}}/2000\end{eqnarray} \tag{ 2 }$$

for 1 keV photons scattered into the VHE band by electrons with $\gamma ={10}^{4}$ (Longair 2011). Although lower-energy photons are scattered in the transition regime between the Thomson and Klein–Nishina regimes, their energy density is much lower than that of the X-ray photons, and so the self-scattering process is not important in this case either.

The reappearance of the accretion disk in 2013 June was accompanied by the disappearance of radio pulsations and an increase of the X-ray and HE gamma-ray luminosities. Accreting binary systems are not typically bright in the GeV domain. The only two binaries detected by Fermi-LAT in which the presence of an accretion disk is certain are Cyg X-3 and Cyg X-1 (Corbel et al. 2012; Malyshev et al. 2013), and in both cases the HE emission is not believed to come from the disk, but rather to be generated in the relativistic jet. The formation of a jet in PSR J1023+0038 has not been observed in VLBI imaging, although variable point-source emission has been seen (Deller et al. 2015). Further, it appears that the X-ray pulsations, indicating accretion onto the neutron star surface, are intermittent (Archibald et al. 2014). Therefore, it could be the case that, as discussed by Takata et al. (2014), Coti Zelati et al. (2014), Li et al. (2014), and Papitto & Torres (2015), the rotation-powered MSP is still at least partially active in PSR J1023+0038, and the complete disappearance of the pulsations is due to absorption by matter evaporating from the accretion disk. In this case, the principal differences from the radio MSP state discussed in the previous section would be (a) the presence of additional soft photons emitted by the accretion disk and (b) the shift of the shock closer to the pulsar due to the inward pressure of the disk.

The presence of additional photons from the accretion disk leads to an increase of the HE luminosity as a result of scattering of those photons on the unshocked electrons of the pulsar wind (Takata et al. 2014). The result of the scattering of the UV photons with temperature T = 10 eV on the cold relativistic electrons with Lorentz factor $\gamma ={10}^{4}$ is shown in Figure 3 with a red dot-dashed line. The shift of the shock closer to the pulsar up to a distance $r=5\times {10}^{10}$ cm (Takata et al. 2014) will lead to the increase of the magnetic field by a factor of two in comparison to the field strength discussed in the previous section if the magnetic field is dominated by that in the pulsar wind. The resulting synchrotron and inverse Compton emission from the shocked electrons generated in the region with B = 80 G is shown in Figure 3 with black solid and dashed lines, respectively. The VERITAS upper limit clearly shows that the field in the region cannot be much smaller than 10 G (green lines in Figure 3). Thus, the VERITAS observations before and after the source-state change put limits on the minimum value of the magnetic field in a compact, synchrotron-emitting region, regardless of the precise mechanism of the charge acceleration or the source of the magnetic field.

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We note that Papitto & Torres (2015) have proposed pulsar magnetic field threading of the accretion disk down to the corotation radius of PSR J1023+0038 (∼24 km) as a field source for the synchrotron emission. Were this the case, the strength of the magnetic field could be much larger.

The VERITAS limits support the conclusion of the magnetically dominated pulsar wind discussed in Bogdanov et al. (2011). However, in both the MSP and accretion/LMXB states, there are alternative sources of magnetic fields that should be considered, namely, that of the companion in both cases and that of the accretion disk itself in the second case. Assuming that the companion is tidally locked, observations of rapidly rotating, low-mass stars suggest a surface magnetic field strength on the order of 1 kG (Morin 2012). The observed orbital variations may also indicate a strong, subsurface magnetic field in the companion (Archibald et al. 2013).