Deep search for gamma-ray emission from the accreting X-ray pulsar 1A 0535+262

X. Hou Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650216, China W. Zhang Institute of Space Sciences (ICE, CSIC), Campus UAB, 08193 Barcelona, Spain Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain D.F. Torres Institute of Space Sciences (ICE, CSIC), Campus UAB, 08193 Barcelona, Spain Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain Institució Catalana de Recerca i Estudis Avançats (ICREA), E-08010 Barcelona, Spain L. Ji School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai 519082, China J. Li CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei, China

(Accepted for publication in ApJ)

Abstract

Binary systems are a well-established subclass of gamma-ray sources. The high mass X-ray binary pulsar 1A 0535+262 has been considered to be a possible gamma-ray emitter for a long time, although former gamma-ray searches using Fermi-LAT and VERITAS data resulted in upper limits only. We aim at a deep search for gamma-ray emission and pulsations from 1A 0535+262 using more than 13 years of Fermi-LAT data. The analysis was performed for both the whole Fermi-LAT data set, as well as for the X-ray outbursts that 1A 0535+262 has experienced since the launch of Fermi. Various X-ray observations have been used to generate the ephemeris for the pulsation search. We also investigate the long-term gamma-ray flux variability and perform orbital phase-resolved analysis for the outbursts. We did not detect any steady or pulsed gamma-ray emission from 1A 0535+262 during the whole Fermi-LAT mission span or its X-ray outbursts. We thus derived the deepest gamma-ray luminosity upper limits to date at the 95% confidence level to be around (2.3 $-$ 4.7) $\times 10^{32}\,\rm erg\,s^{-1}$ depending on different spectral indices assumed, which results in a ratio of $L_{\rm\gamma}$ to $L_{\rm X}$ (2 $-$ 150 keV) being (1.9 $-$ 3.9) $\times 10^{-6}$ .

stars: neutron — X-rays: binaries — Gamma rays

1 Introduction

Among the various gamma-ray sources detected in the MeV/GeV and/or even the TeV band, binary systems are a well-established subclass, although their number is yet small. Interestingly, despite their small number, several varieties of binaries exist with different gamma-ray emission mechanisms. For a recent review, see Dubus2015. First, Fermi-LAT has detected gamma-ray binaries themselves, usually defined as a subclass of high mass X-ray binaries (HMXBs) with O or B companion star, with two main features: they emit modulated gamma rays peaking above 1 MeV and present orbital variability at all frequencies. The spectral energy distribution is usually thought to be powered by the pulsar/stellar wind interaction, although so far the central compact object has been associated to known pulsars only in three cases: PSR B1259-63/LS 2883 (see HESS2020; Chernyakova2020a, and references therein), PSR J2032+4127/MT91 213 (see Coe2019, and references therein), and the recent identification of LS I +61 303 (Weng2022).

Recycled pulsars in binaries, called redbacks & black widow systems, are tight (orbital periods less than a day), low mass ( $<0.1M_{\odot}$ ) gamma-ray binaries with a main sequence degenerate companion. In these systems the pulsar wind is ablating the companion star, leading to eclipses, radio variability, X-ray/radio anti-correlation, and pulsar nulling (see, e.g., Bogdanov2018). Transitional pulsars are special among these systems, since they exhibit two different states (accretion and rotation powered) which may interchange in a matter of weeks and persist for years (see e.g., Archibald2009; Papitto2013; deMartino2015). These state changes produce significant gamma-ray variability (Stappers2014; Torres2017).

Other Fermi-LAT detected binaries include microquasars, for which the gamma rays seem to be associated with a relativistic jet. Notable examples are Cyg X-1 (see e.g., Albert2007; Zanin2016; Zdziarski2017) and Cyg X-3 (see e.g., Abdo2009c; Tavani2009; Zdziarski2018; Sinitsyna2019). The microquasar SS 433, whose central object is still undetected, was unexpectedly found to produce gamma rays far from the jet (HAWC2018; Rasul2019; Xing2019a; Fang2020) with a GeV source showing variability with the precession period of the system (Li2020).

Finally, one finds the accreting millisecond pulsar SAX J1808.4 $-$ 3658 (Emma2016): a “bona fide” accreting system apparently emitting gamma rays, although yet not significantly. This is the only such system for which a gamma-ray detection was hinted so far. Putting upper limits on accreting sources or detecting them is a must to understand the different variety.

1A 0535+262 is one of the best studied HMXB accreting pulsars. It was discovered in 1975 by the Rotation Modulation Collimator on Ariel V, with a pulsation period of 104 s (Rosenberg1975). The compact object in the system is a highly magnetized neutron star which accretes mass from the O9.7IIIe companion star (Steele1998). The orbital period of the system is $\sim 111$ days (Coe2006) and the eccentricity of the orbit is $e=0.47\pm 0.02$ (Finger1996). 1A 0535+262 is relatively close to Earth with a distance of $1.8\pm 0.1$ kpc, as measured by Gaia (Bailer2018). Since its discovery, 1A 0535+262 has exhibited different X-ray outbursts with peak flux ranging from $\sim 100$ mCrab to $\sim 12.5$ Crab. In particular, three giant X-ray outbursts were detected since the launch of the Fermi satellite: in 2009 December (Acciari2011), 2011 February (Sartore2015) and 2020 November (Kong2022; Mandal2022, and references therein). Figure 1 shows the long-term light curves of 1A 0535+262 in different energy bands obtained from the Swift/BAT and MAXI/GSC Broadband Transient Monitor¹¹1http://sakamotoagu.mydns.jp/bat_gsc_trans_mon/web_lc/1_Day.php?name=1A_0535+262. There was also a double-peaked outburst (Caballero2013) just prior to the 2009 giant one, which is, however, not included in the monitor database. VLA observations during the 2020 outburst revealed non-thermal radio emission from the source position (Eijnden2020).

1A 0535+262 was earlier associated with the EGRET unidentified gamma-ray source 3EG J0542+2610 (Romero2001) and thus has long been considered as a high-energy (HE; $E>100$ MeV) and very-high-energy (VHE; $E>100$ GeV) emitter candidate. The first gamma-ray search for 1A 0535+262 dates back to more than 10 years, during its giant 2009 outburst. On that occasion, the X-ray outburst in December of 2009 triggered VHE VERITAS observations. Only upper limits have been derived (Acciari2011). These authors also did a search for HE gamma-ray emission from 1A 0535+262 with Fermi-LAT in a period spanning the onset of the X-ray outburst to the successive apastron of the pulsar (2009 November 30 to 2010 February 22). No significant GeV excess was seen and a flux upper limit of $F(>0.2{\,\rm GeV})<1.9\times 10^{-8}$ photons cm^-2 s^-1 at 99% confidence level was imposed. Recently, Lundy2021 updated the VERITAS VHE search for 1A 0535+262 during its 2020 giant outburst. Again, only upper limits have been obtained. Also, Harvey2022 used 12.5 years LAT data to search for gamma-ray emission from 1A 0535+262. They claimed a marginal persistent gamma-ray excess (3.5 $\sigma$ ) at the position of the source and found that the gamma-ray activity may be correlated with the X-ray outbursts. In addition, they found that essentially all of the gamma-ray excess is concentrated in the orbital phase bin preceding periastron, thus providing evidence of the gamma-ray excess originating from this binary system. If real, these hints are relevant, and thus can help to get insights to the particle acceleration and emission process during the accretion.

In this work, we analyze the three giant outbursts, in 2009, 2011 and 2020, and the previous double-peaked outburst of 1A 0535+262. The time span of each outburst was defined by investigating the X-ray light curves presented in the literature (Acciari2011; Sartore2015; Mandal2022; Kong2022). We perform a deep search for gamma-ray emission and pulsations from 1A 0535+262 using more than 13 years of Fermi-LAT data and the latest 12-year source catalog. We use the latest Instrument Response Functions (IRFs) and background diffuse models. Our work therefore extends the result presented in Harvey2022. The paper is organized as follows: we describe the data analysis procedure and results in Section 2, and discuss our findings in Section 3. We finally conclude in Section 4.

2 Data analysis and results

2.1 Timing solutions

For the 2009 double-peaked and giant outbursts, we adopted the spin measurements and the orbital ephemeris of 1A 0535+262 from the Fermi/GBM monitoring²²2https://gammaray.nsstc.nasa.gov/gbm/science/pulsars/lightcurves/a0535.html. We used a polynomial function to describe the spin evolution approximately. For the 2011 outburst, we used the timing solution reported in Sartore2015 derived using INTEGRAL observations. For the recent 2020 outburst, thanks to the extensive coverage of Insight-HXMT observations (Wang2022), we used the phase-connection technique (Deeter1981) to determine the spin evolution accurately. In practice, for each 1000 s segment we folded background-subtracted light curves in the energy range of 25 $-$ 80 keV, for which the pulse profile shape is relatively stable. The 1000 s was chosen because this is the typical interval for Insight-HXMT’s good time. The time-of-arrival (TOA) of each segment was estimated by cross-correlating these pulse profiles with an averaged template. Then the spin evolution was determined by using the software Tempo2 (Hobbs2006). We summarize the timing solutions for different outbursts used in the following pulsation search (Section 2.5) in Table 2.

2.2 Fermi-LAT data set and reduction

We used the Pass 8 data set (pass8Atwood; Bruel2018) available at the Fermi Science Support Center (FSSC)³³3http://fermi.gsfc.nasa.gov/ssc/. This spans 166 months, from 2008 August 4 to 2022 June 9, with reconstructed energy in the range 0.1 $-$ 300 GeV. We selected SOURCE class events (Front and Back) with a zenith angle smaller than $90^{\circ}$ to avoid the Earth limb contamination. The events were further filtered based on the criteria ‘‘DATA_QUAL>0 && LAT_CONFIG==1’’ to get the good time intervals in which the satellite was working in standard data taking mode and the data quality was good. We did not apply a Region of Interest (ROI)-based zenith angle cut⁴⁴4https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/data_preparation.html. The data set was centered at 1A 0535+262 with coordinates $(\alpha,\delta)=(84\fdg 7274,26\fdg 3158)$ , with a radius of $10^{\circ}$ . The coordinates of 1A 0535+262 were taken from the SIMBAD⁵⁵5http://simbad.u-strasbg.fr/simbad/ database and in the J2000 frame. The analysis was performed using the P8R3_SOURCE_V3 IRFs and the latest Fermitools⁶⁶6https://fermi.gsfc.nasa.gov/ssc/data/analysis/software/ (v2.2.0) available at the FSSC.

2.3 Fermi-LAT spectral analysis

In the spectral analysis, the latest 4FGL-DR3⁷⁷7https://fermi.gsfc.nasa.gov/ssc/data/access/lat/12yr_catalog/ (gll_psc_v30.fit) (4DFL-DR3) sources within a $20^{\circ}$ circle around 1A 0535+262 were included to build a complete spatial and spectral source model. We also included the latest Galactic interstellar emission model, “gll_iem_v07.fits”, as well as the isotropic emission spectrum “iso_P8R3_SOURCE_V3_v1.txt”, with the latter taking into account the extragalactic emission and the residual instrumental background⁸⁸8https://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html. Both the normalizations and spectral indices of sources within $5^{\circ}$ around 1A 0535+262 were set free to vary except for 4FGL J0534.5+2201i, which is recommended to be fixed to account for the Inverse Compton Scattering component of the Crab Nebula. Extended sources were modeled using the 12-year templates. Since the closest source in the model is $\sim 1.6^{\circ}$ away from 1A 0535+262, we added 1A 0535+262 manually in the model as a point source with a simple Power Law spectral model. This allows us to check whether the addition of such source is significant.

Model fitting was performed in a $14^{\circ}\times 14^{\circ}$ ROI using the maximum likelihood method (mattox96). We followed the binned likelihood procedure outlined in the FSSC using a $0\fdg 1\times 0\fdg 1$ pixel size and thirty logarithmic energy bins over 0.1 $-$ 300 GeV. Two extra energy bins have been added to take into account the energy dispersion except for the isotropic component. The significance of a given source in the model is characterized by the Test Statistic (TS), which is expressed as TS $=2(\log\mathcal{L}-\log\mathcal{L}_{0})$ , where $\log\mathcal{L}$ and $\log\mathcal{L}_{0}$ are the logarithms of the maximum likelihood of the complete source model and of the background model (i.e. the source model without the given source included), respectively.

We first performed a global binned likelihood fit to the whole data set by fixing the spectral index of 1A 0535+262 to 2, 2.3 and 3, respectively. Such spectral indices are chosen to represent possible emission mechanisms. At the same flux level, if the source were to emit a hard spectrum (as the assumed 2) across the Fermi-LAT energy regime, it should be easier to detect it due to the diminishing background at higher energies. Then, using the best-fit source model from the whole data set fit, we performed binned likelihood fits to the different X-ray outbursts that 1A 0535+262 has experienced in the past, following the same fitting setup and procedure as for the whole data set. To increase the detection possibility and statistics, we also stacked all the outbursts together to perform the fit. 1A 0535+262 was not detected in any of these cases and we therefore computed a 95% confidence level energy flux upper limit accordingly. The fitting results are presented in Table 1.

2.4 Gamma-ray variability

We performed two different types of variability analysis for 1A 0535+262. First, to investigate the long-term gamma-ray flux variability, we computed light curves with a 180-day binning as in Harvey2022 in the energy range of 0.1 $-$ 300 GeV for all spectral indices used in the spectral analysis (Figure 1). The full data best-fit source model was used as an input for each time bin and the normalizations of sources within $3^{\circ}$ around 1A 0535+262 were set free to vary. Upper limits at 95% confidence level were calculated when 1A 0535+262 had TS $<4$ in a given time bin. We did not see any significant detection in all the time bins when fixing the spectral index to 2 or 2.3. For the light curve with index fixed to 3, there are two bins with TS being about 10 and 20, corresponding to approximately 3 $\sigma$ and 4 $\sigma$ . However, these two bins correspond to the period where its X-ray emission was faint according to the X-ray monitoring of 1A 0535+262 (Figure 1). Thus, we conclude that no correlation between gamma-ray and X-ray was observed, contrary to what Harvey2022 has claimed. Furthermore, the variability significance was computed following the same method used in 3FGL. Only the light curve with index fixed to 3 has a non-negligible significance ( $1.7\sigma$ for 27 degrees of freedom), but this is far from declaring a significant variability, which requires usually a significance of at least $3\sigma$ . Any gamma-ray emission is thus consistent with being steady on a timescale of a few months based on our analysis.

Since gamma-ray binaries usually exhibit orbital flux variability, we also computed the orbital flux for 1A 0535+262 with 10 bins per orbit and calculated upper limits at 95% confidence level when 1A 0535+262 had TS $<4$ in a given orbital bin, as was done in Harvey2022. Similar to the long-term light curve, the full data best-fit source model was used as an input for each orbital bin and the spectral index was fixed to 2, 2.3 and 3, respectively. No significant orbital variability was observed. The orbital light curves are shown in Figure 2.

2.5 Gamma-ray pulsation search

We performed a pulsation search using reconstructed LAT photons within $1^{\circ}$ of 1A 0535+262 in the energy range of 0.1 $-$ 300 GeV. The signal significance was qualified using the weighted H-test developed by Kerr2011, which is based on the original one proposed by Jager1989:

H_{mw}={\rm max}\left[Z^{2}_{iw}-c\times(i-1)\right],\,\,\,\,\,\,1\leq i\leq m,

(1)

where

Z^{2}_{mw}=\frac{2}{\sum_{i=1}^{N}w_{i}^{2}}\times\sum_{k=1}^{m}(\alpha_{wk}^{2}+\beta_{wk}^{2}),

(2)

and

\alpha_{wk}=\sum_{i=1}^{N}w_{i}\cos{(2\pi k\phi_{i})},\;\;\;\;\;\;\beta_{wk}=\sum_{i=1}^{N}w_{i}\sin{(2\pi k\phi_{i})}.

(3)

Here, $N$ is the total photon number, $\phi_{i}$ is the pulsar rotational phase and $w_{i}$ is the photon weight, $m$ is the maximum search harmonic and $c$ is the offset for each successive harmonic. We used the standard value $c=4$ and varied $m$ in our analysis. We verified that taking the standard value $m=20$ did not change the result.

We employed the Simple Weights method descried in Bruel2019 and Smith2019 to compute the weight for each photon. This is considered as a proxy for the probability that the photon comes from 1A 0535+262. Assuming that the target source is faint compared to the diffuse background and that the background emission is isotropic, for a photon with energy $E$ (in MeV) and angular distance $\Delta\theta$ to the target source, the weight is:

w(E,\Delta\theta)=f(E)\times g(E,\Delta\theta),

(4)

where

f(E)=\rm exp(-2log_{10}^{2}(\it E/E_{\rm ref}))

(5)

is the weight at the pulsar position, which depends on the pulsar and background spectra and on the LAT’s energy-dependent Point Spread Function (PSF). The geometrical factor $g(E,\Delta\theta)$ describes the angular distribution of the gamma-ray photons emitting from a point source and can be written as

g(E,\Delta\theta)=\left(1+\frac{9\Delta\theta^{2}}{4\sigma_{\rm psf}^{2}(E)}\right)^{-2},

(6)

where

\sigma_{\rm psf}(E)=\sqrt{p_{0}^{2}(E/100)^{-2p_{1}}+p_{2}^{2}}

(7)

is the PSF 68% containment angle with $p_{0}=5.445,p_{1}=0.848$ and $p_{2}=0.084$ for LAT P305 Pass 8 data (pass8Atwood).

Defining the reference energy $E_{\rm ref}=10^{\mu_{w}}$ , the H-test versus $\mu_{w}$ follows a Gaussian distribution (Bruel2019). Thus, searching for pulsations means finding the maximum H-test by scanning over $\mu_{w}$ . After searching a thousand radio pulsars for possible gamma-ray emission, Smith2019 indicate that in most cases $\mu_{w}=3.6$ is a good choice to yield a significant signal. We adopted this value in our pulsation search for 1A 0535+262. Considering that this value was found for non-accreting (and many isolated) radio pulsars that have a power law with an exponential cutoff (PLEC) spectrum (Abdo2013), and thus may not be appropriate for an accreting system that could have a different spectral shape, we also verified that scanning over $\mu_{w}$ to find the best value does not affect the result significantly. We used the ephemerides for different observations (Table 2) to phase-fold the gamma-ray photons of 1A 0535+262, restricting the pulsation search range to the validity of the corresponding ephemerides. However, no significant pulsation was detected during the individual outbursts. Although a signal of $\sim 1.5\sigma$ was hinted for the 2009 outburst, the significance is far from the LAT detection threshold of 4 $\sigma$ .

3 Discussion

In general, we obtained very different results compared to Harvey2022. We had no detection of either persistent or transient or pulsed gamma-ray emission from 1A 0535+262. Although we have two time bins with TS $\sim$ 20 and $\sim$ 10, they did not correspond to the X-ray outburst periods. Therefore, our result does not support their conclusion that the gamma-ray emission is correlated with the X-ray outburst of the source and is mostly concentrated in specific orbital bins. Such difference may mainly come from the fitting procedure and whether or not considering the energy dispersion. We normally fitted the sources within $5^{\circ}$ around 1A 0535+262 in the spectral fit and orbital flux variability study, and within $3^{\circ}$ for the long-term light curves, while they fitted only $1^{\circ}$ around 1A 0535+262. In addition, the spectral index was fixed to different values to account for possible emission mechanisms in our study, while they let the index free to vary. Actually, for the long-term variability, no detailed fitting procedure information was found in Harvey2022, making a detailed comparison difficult.

Unlike those cases when a detection is found from an astrophysical source, the possible reasons for a non-detection are essentially unlimited. Gamma-ray binary systems such as LS I +61 303 are radio sources, and their X-ray spectra contain a significant non-thermal component. Recently, radio pulsations were detected from this system (Weng2022). Thus, it is worth noting that LS I +61 303 is probably not a significantly accreting system, and thus it likely has a different acceleration and emission mechanism than that acting in 1A 0535+26, if there is any in the latter. On the other hand, in 1A 0535+262, the absence of a significant quiescent radio emission that could later be associated with non-thermal processes may simply indicate that leptons are not sufficiently accelerated there. This observation had earlier promoted hadronic models. From our results, though, we can also rule out hadronic production acting according to a mechanism originally proposed by Cheng1991, where a proton beam accelerated in a magnetospheric electrostatic gap impacts the transient accretion disk. This model was applied to 1A 0535+262 by Romero2001, Anchordoqui2003 and Orellana2007. Particularly in the latter paper the theoretical flux prediction of $3.8\times 10^{-8}\,\rm ph\ cm^{-2}$ (derived by extrapolating the result of Orellana2007), i.e., a gamma-ray luminosity of about 10³³ erg s^-1 at 0.3 TeV at the end of giant outbursts to the Fermi-LAT energy range (see Acciari2011) is above our limit which is $\sim$ (2.3 $-$ 4.7) $\times 10^{32}\,\rm erg\,s^{-1}$ by one order of magnitude (and should have been detected earlier on in the mission) depending on different spectral indices assumed. Taking the X-ray luminosity (2 $-$ 150 keV) reported for the largest 2020 outburst (Kong2021) to be 1.2 $\times$ 10 ${}^{38}\,\rm erg\,s^{-1}$ , the ratio of $L_{\rm\gamma}$ to $L_{\rm X}$ is then calculated to be (1.9 $-$ 3.9) $\times 10^{-6}$ .

It remains to be seen, of course, whether the flux was overestimated but the mechanism is still viable, or whether a longer integration might lead to low-flux quiescent emission or to an occasional detection. None of these possibilities has happened in the long integration time we have analyzed. At least with the current gamma-ray sensitivity, 1A 0535+262 is not a gamma-ray source. With our current limits, there appears to be no reasonable combination of the hadronic model parameters to still accommodate a persistent gamma-ray flux.

Another interpretation could simply be that none of the possible shocks in the system is energetic enough to produce sufficiently accelerated particles able to emit gamma-rays. Or that if they do, the radiation produced is absorbed due to the matter in the surroundings, see e.g., the discussion in Orellana2007. Regarding the latter, it would be reasonable to expect that any absorption would be quite variable. Thus if the emission is produced in the system at all, it would be unlikely that it is absorbed all the time. In addition, secondary electrons (and positrons) from the pair production process would generate gamma rays at MeV–GeV energies, (see e.g., Bednarek1997; Bednarek2006; Sierpowska-Bartosik2008). These could be attenuated by X-ray photons, but probably not fully attenuated after the X-ray peak has passed.

Giant (or Type II) outbursts, though they are rare and unrelated to the orbital cadence, may have X-ray luminosities close to the Eddington limit. They are likely associated with the formation of a transient accretion disk. Recently, Eijnden2020 detected a radio counterpart during the 2020 outburst. This was the first time that a coupled increase in X-ray and radio flux was seen in 1A 0535+262 and shows that the radio emission may relate to the accretion state. This would be similar to the behaviour seen in the transient Be X-ray binary Swift J0243.6+6124 (Eijnden2018). Bednarek2009; Bednarek2009b proposed that it is possible that HMXBs produce gamma-ray emission during accretion periods. The possibility that particle acceleration can take place even when mass accretion is going on is supported by some observational results: the hinted gamma-ray emission from SAX J1808.4 $-$ 3658 (Emma2016), the gamma-ray emission found from the sub-luminous state of the transitional pulsars (as quoted in the introduction) and interpreted as propeller emission (see e.g., Papitto2014; Papitto2015) or a mini pulsar wind nebula (Papitto2019, see also Veledina2019) and finally, the discovery of optical and ultraviolet pulsed emission from the accreting millisecond pulsar SAX J1808.4 $-$ 3658 (Ambrosino2021). However, the neutron star Eddington luminosity ( $L_{\rm Edd}\sim 1.8\times 10^{38}$ erg s^-1) is many orders of magnitude above our upper limits, pointing to a very inefficient mechanism, if at play at all. Similarly to the case of other transients, for instance, the Be X-Ray Binary 4U 1036 $-$ 56 (RX J1037.5 $-$ 5647), which could be associated to AGILE transients, we cannot discard that a low level of gamma-ray flux is emitted at lower energies, below 100 MeV (see Li2012, and in particular their figure 6 for an associated discussion). This remains to be tested with the advent of MeV missions such as AMEGO (McEnery2019), e-ASTROGAM (Angelis2018), or COSI (Beechert2022).

4 Conclusions

We have searched for gamma-ray emission and pulsations from 1A 0535+262 using more than 13 years of Fermi-LAT data. Neither persistent nor transient nor pulsed gamma-ray emission has been detected significantly in our study for the whole data set or during the X-ray outbursts that 1A 0535+262 has experienced since the launch of the Fermi satellite. Upper limits on the luminosity at the 95% confidence level were derived to be around (2.3 $-$ 4.7) $\times 10^{32}\,\rm erg\,s^{-1}$ depending on different spectral indices assumed, the deepest ones to date. The emission of 1A 0535+262 is considered to be consistent with being steady on a timescale of a few months. Although two time bins in the long-time light curve hint to have gamma-ray emission at roughly 3 and 4 $\sigma$ , they occurred when the source was faint in X-rays. Thus, no correlation between gamma-ray and X-ray activities was observed based on our result. In addition, we did not see any significant orbital gamma-ray variation. We conclude that 1A 0535+262 is not a gamma-ray emitter at the level of the current gamma-ray sensitivity.

The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l’Energie Atomiqueand and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This work was performed in part under DOE Contract DE-AC02-76SF00515. The authors are supported by the National Natural Science Foundation of China through grants U1938103, 12041303, 12173103, U2038101, 11733009. WZ and DFT work have been supported by the grant PID2021-124581OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by the Spanish program Unidad de Excelencia María de Maeztu CEX2020-001058-M. DFT acknowledges as well USTC and the Chinese Academy of Sciences International Presidential Fellowship Initiative 2021VMA0001. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

References

Abdalla et al. (2020) Abdalla, H., Adam, R., Aharonian, F., et al. 2020, A&A, 633, A102, doi: 10.1051/0004-6361/201936621
Abdo et al. (2009) Abdo, A. A., Ackermann, M., Ajello, M., et al. 2009, Science, 326, 1512, doi: 10.1126/science.1182174
Abdo et al. (2013) Abdo, A. A., Ajello, M., Allafort, A., et al. 2013, ApJS, 208, 17, doi: 10.1088/0067-0049/208/2/17
Abeysekara et al. (2018) Abeysekara, A. U., Albert, A., Alfaro, R., et al. 2018, Nature, 562, 82, doi: 10.1038/s41586-018-0565-5
Acciari et al. (2011) Acciari, V. A., Aliu, E., Araya, M., et al. 2011, ApJ, 733, 96, doi: 10.1088/0004-637X/733/2/96
Acero et al. (2015) Acero, F., Ackermann, M., Ajello, M., et al. 2015, ApJS, 218, 23, doi: 10.1088/0067-0049/218/2/23
Albert et al. (2007) Albert, J., Aliu, E., Anderhub, H., et al. 2007, ApJ, 665, L51, doi: 10.1086/521145
Ambrosino et al. (2021) Ambrosino, F., Miraval Zanon, A., Papitto, A., et al. 2021, Nature Astronomy, 5, 552, doi: 10.1038/s41550-021-01308-0
Anchordoqui et al. (2003) Anchordoqui, L. A., Torres, D. F., McCauley, T. P., Romero, G. E., & Aharonian, F. A. 2003, ApJ, 589, 481, doi: 10.1086/374551
Archibald et al. (2009) Archibald, A. M., Stairs, I. H., Ransom, S. M., et al. 2009, Science, 324, 1411, doi: 10.1126/science.1172740
Atwood et al. (2013) Atwood, W., Albert, A., Baldini, L., et al. 2013, ArXiv e-prints. https://arxiv.org/abs/1303.3514
Bailer-Jones et al. (2018) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58, doi: 10.3847/1538-3881/aacb21
Bednarek (1997) Bednarek, W. 1997, A&A, 322, 523
Bednarek (2006) —. 2006, MNRAS, 368, 579, doi: 10.1111/j.1365-2966.2006.10121.x
Bednarek (2009a) —. 2009a, MNRAS, 397, 1420, doi: 10.1111/j.1365-2966.2009.14893.x
Bednarek (2009b) —. 2009b, Phys. Rev. D, 79, 123010, doi: 10.1103/PhysRevD.79.123010
Beechert et al. (2022) Beechert, J., Lazar, H., Boggs, S. E., et al. 2022, Nuclear Instruments and Methods in Physics Research A, 1031, 166510, doi: 10.1016/j.nima.2022.166510
Bogdanov et al. (2018) Bogdanov, S., Deller, A. T., Miller-Jones, J. C. A., et al. 2018, ApJ, 856, 54, doi: 10.3847/1538-4357/aaaeb9
Bruel (2019) Bruel, P. 2019, A&A, 622, A108, doi: 10.1051/0004-6361/201834555
Bruel et al. (2018) Bruel, P., Burnett, T. H., Digel, S. W., et al. 2018, arXiv e-prints, arXiv:1810.11394. https://arxiv.org/abs/1810.11394
Caballero et al. (2013) Caballero, I., Pottschmidt, K., Marcu, D. M., et al. 2013, ApJ, 764, L23, doi: 10.1088/2041-8205/764/2/L23
Cheng & Ruderman (1991) Cheng, K. S., & Ruderman, M. 1991, ApJ, 373, 187, doi: 10.1086/170036
Chernyakova et al. (2020) Chernyakova, M., Malyshev, D., Mc Keague, S., et al. 2020, MNRAS, 497, 648, doi: 10.1093/mnras/staa1876
Coe et al. (2006) Coe, M. J., Reig, P., McBride, V. A., Galache, J. L., & Fabregat, J. 2006, MNRAS, 368, 447, doi: 10.1111/j.1365-2966.2006.10127.x
Coe et al. (2019) Coe, M. J., Okazaki, A. T., Steele, I. A., et al. 2019, MNRAS, 485, 1864, doi: 10.1093/mnras/stz515
de Angelis et al. (2018) de Angelis, A., Tatischeff, V., Grenier, I. A., et al. 2018, Journal of High Energy Astrophysics, 19, 1, doi: 10.1016/j.jheap.2018.07.001
de Jager et al. (1989) de Jager, O. C., Raubenheimer, B. C., & Swanepoel, J. W. H. 1989, A&A, 221, 180
de Martino et al. (2015) de Martino, D., Papitto, A., Belloni, T., et al. 2015, MNRAS, 454, 2190, doi: 10.1093/mnras/stv2109
de Oña Wilhelmi et al. (2016) de Oña Wilhelmi, E., Papitto, A., Li, J., et al. 2016, MNRAS, 456, 2647, doi: 10.1093/mnras/stv2695
Deeter et al. (1981) Deeter, J. E., Boynton, P. E., & Pravdo, S. H. 1981, ApJ, 247, 1003, doi: 10.1086/159110
Dubus (2015) Dubus, G. 2015, Comptes Rendus Physique, 16, 661, doi: 10.1016/j.crhy.2015.08.014
Fang et al. (2020) Fang, K., Charles, E., & Blandford, R. D. 2020, ApJ, 889, L5, doi: 10.3847/2041-8213/ab62b8
Fermi-LAT collaboration (2022) Fermi-LAT collaboration. 2022, arXiv e-prints, arXiv:2201.11184. https://arxiv.org/abs/2201.11184
Finger et al. (1996) Finger, M. H., Wilson, R. B., & Harmon, B. A. 1996, ApJ, 459, 288, doi: 10.1086/176892
Harvey et al. (2022) Harvey, M., Rulten, C. B., & Chadwick, P. M. 2022, MNRAS, 512, 1141, doi: 10.1093/mnras/stac375
Hobbs et al. (2006) Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655, doi: 10.1111/j.1365-2966.2006.10302.x
Kerr (2011) Kerr, M. 2011, ApJ, 732, 38, doi: 10.1088/0004-637X/732/1/38
Kong et al. (2021) Kong, L. D., Zhang, S., Ji, L., et al. 2021, ApJ, 917, L38, doi: 10.3847/2041-8213/ac1ad3
Kong et al. (2022) Kong, L.-D., Zhang, S., Ji, L., et al. 2022, ApJ, 932, 106, doi: 10.3847/1538-4357/ac6e66
Li et al. (2020) Li, J., Torres, D. F., Liu, R.-Y., et al. 2020, Nature Astronomy, 4, 1177, doi: 10.1038/s41550-020-1164-6
Li et al. (2012) Li, J., Torres, D. F., Zhang, S., et al. 2012, ApJ, 761, 49, doi: 10.1088/0004-637X/761/1/49
Lundy (2021) Lundy, M. 2021, arXiv e-prints, arXiv:2108.09350. https://arxiv.org/abs/2108.09350
Mandal & Pal (2022) Mandal, M., & Pal, S. 2022, MNRAS, 511, 1121, doi: 10.1093/mnras/stac111
Mattox et al. (1996) Mattox, J. R., Bertsch, D. L., Chiang, J., et al. 1996, ApJ, 461, 396, doi: 10.1086/177068
McEnery et al. (2019) McEnery, J., van der Horst, A., Dominguez, A., et al. 2019, in Bulletin of the American Astronomical Society, Vol. 51, 245. https://arxiv.org/abs/1907.07558
Orellana et al. (2007) Orellana, M., Romero, G. E., Pellizza, L. J., & Vidrih, S. 2007, A&A, 465, 703, doi: 10.1051/0004-6361:20066238
Papitto & Torres (2015) Papitto, A., & Torres, D. F. 2015, ApJ, 807, 33, doi: 10.1088/0004-637X/807/1/33
Papitto et al. (2014) Papitto, A., Torres, D. F., & Li, J. 2014, MNRAS, 438, 2105, doi: 10.1093/mnras/stt2336
Papitto et al. (2013) Papitto, A., Ferrigno, C., Bozzo, E., et al. 2013, Nature, 501, 517, doi: 10.1038/nature12470
Papitto et al. (2019) Papitto, A., Ambrosino, F., Stella, L., et al. 2019, ApJ, 882, 104, doi: 10.3847/1538-4357/ab2fdf
Rasul et al. (2019) Rasul, K., Chadwick, P. M., Graham, J. A., & Brown, A. M. 2019, MNRAS, 485, 2970, doi: 10.1093/mnras/stz559
Romero et al. (2001) Romero, G. E., Kaufman Bernadó, M. M., Combi, J. A., & Torres, D. F. 2001, A&A, 376, 599, doi: 10.1051/0004-6361:20011044
Rosenberg et al. (1975) Rosenberg, F. D., Eyles, C. J., Skinner, G. K., & Willmore, A. P. 1975, Nature, 256, 628, doi: 10.1038/256628a0
Sartore et al. (2015) Sartore, N., Jourdain, E., & Roques, J. P. 2015, ApJ, 806, 193, doi: 10.1088/0004-637X/806/2/193
Sierpowska-Bartosik & Torres (2008) Sierpowska-Bartosik, A., & Torres, D. F. 2008, Astroparticle Physics, 30, 239, doi: 10.1016/j.astropartphys.2008.09.009
Sinitsyna & Sinitsyna (2019) Sinitsyna, V. G., & Sinitsyna, V. Y. 2019, in European Physical Journal Web of Conferences, Vol. 208, European Physical Journal Web of Conferences, 14008, doi: 10.1051/epjconf/201920814008
Smith et al. (2019) Smith, D. A., Bruel, P., Cognard, I., et al. 2019, ApJ, 871, 78, doi: 10.3847/1538-4357/aaf57d
Stappers et al. (2014) Stappers, B. W., Archibald, A. M., Hessels, J. W. T., et al. 2014, ApJ, 790, 39, doi: 10.1088/0004-637X/790/1/39
Steele et al. (1998) Steele, I. A., Negueruela, I., Coe, M. J., & Roche, P. 1998, MNRAS, 297, L5, doi: 10.1046/j.1365-8711.1998.01593.x
Tavani et al. (2009) Tavani, M., Bulgarelli, A., Piano, G., et al. 2009, Nature, 462, 620, doi: 10.1038/nature08578
Torres et al. (2017) Torres, D. F., Ji, L., Li, J., et al. 2017, ApJ, 836, 68, doi: 10.3847/1538-4357/836/1/68
van den Eijnden et al. (2018) van den Eijnden, J., Degenaar, N., Russell, T. D., et al. 2018, Nature, 562, 233, doi: 10.1038/s41586-018-0524-1
van den Eijnden et al. (2020) van den Eijnden, J., Degenaar, N., Wijnands, R., et al. 2020, The Astronomer’s Telegram, 14193, 1
Veledina et al. (2019) Veledina, A., Nättilä, J., & Beloborodov, A. M. 2019, ApJ, 884, 144, doi: 10.3847/1538-4357/ab44c6
Wang et al. (2022) Wang, P. J., Kong, L. D., Zhang, S., et al. 2022, ApJ, 935, 125, doi: 10.3847/1538-4357/ac8230
Weng et al. (2022) Weng, S.-S., Qian, L., Wang, B.-J., et al. 2022, Nature Astronomy, 6, 698, doi: 10.1038/s41550-022-01630-1
Xing et al. (2019) Xing, Y., Wang, Z., Zhang, X., Chen, Y., & Jithesh, V. 2019, ApJ, 872, 25, doi: 10.3847/1538-4357/aafc60
Zanin et al. (2016) Zanin, R., Fernández-Barral, A., de Oña Wilhelmi, E., et al. 2016, A&A, 596, A55, doi: 10.1051/0004-6361/201628917
Zdziarski et al. (2017) Zdziarski, A. A., Malyshev, D., Chernyakova, M., & Pooley, G. G. 2017, MNRAS, 471, 3657, doi: 10.1093/mnras/stx1846
Zdziarski et al. (2018) Zdziarski, A. A., Malyshev, D., Dubus, G., et al. 2018, MNRAS, 479, 4399, doi: 10.1093/mnras/sty1618

Refer to caption — Figure 1: Upper panel: Long-term X-ray light curves of 1A 0535+262 in different energy bands observed by Swift/BAT and MAXI/GSC as obtained from http://sakamotoagu.mydns.jp/bat_gsc_trans_mon/web_lc/1_Day.php?name=1A_0535+262. Low three panels: Long-term gamma-ray light curves of 1A 0535+262 with a time binning of 180 days. Spectral index was fixed to 2, 2.3 and 3, respectively. Upper limits at 95% confidence level are computed for bins with TS $<$ 4.

Table 1: Fermi-LAT spectral analysis results

Whole dataset
Period^a	Time Range	Spectral Index	TS	Energy Flux Upper Limit^b
	(MJD)			$(10^{-12}\,\rm erg\,cm^{-2}\,s^{-1})$
full	54682-59739	$2.0$	$0.0$	$0.6$
full	54682-59739	$2.3$	$0.0$	$0.7$
full	54682-59739	$3.0$	$0.0$	$1.2$
Stacked outbursts
Rising+Falling	55040-59207	$2.0$	$0.0$	$11.9$
Rising+Falling	55040-59207	$2.3$	$0.0$	$9.3$
Rising+Falling	55040-59207	$3.0$	$0.0$	$20.9$
The 2009 double-peaked outburst
Rising+Falling	55040-55070	$2.0$	$0.4$	$34.9$
Rising+Falling	55040-55070	$2.3$	$0.4$	$27.3$
Rising+Falling	55040-55070	$3.0$	$0.0$	$21.9$
The 2009 giant outburst
ALL	55165.9-55249.6	$2.0$	$0.0$	$9.9$
ALL	55165.9-55249.6	$2.3$	$0.0$	$10.5$
ALL	55165.9-55249.6	$3.0$	$0.0$	$16.5$
Rising+Falling	55165.9-55193.6	$2.0$	$0.0$	$27.9$
Rising+Falling	55165.9-55193.6	$2.3$	$0.0$	$24.7$
Rising+Falling	55165.9-55193.6	$3.0$	$0.0$	$28.4$
Rising	55165.9-55177.6	$2.0$	$0.0$	$49.3$
Rising	55165.9-55177.6	$2.3$	$0.0$	$45.8$
Rising	55165.9-55177.6	$3.0$	$0.0$	$45.4$
Falling	55178.4-55193.6	$2.0$	$0.0$	$39.4$
Falling	55178.4-55193.6	$2.3$	$0.0$	$31.7$
Falling	55178.4-55193.6	$3.0$	$0.0$	$29.5$
Apastron	55199.4-55216.6	$2.0$	$0.0$	$23.6$
Apastron	55199.4-55216.6	$2.3$	$0.0$	$18.1$
Apastron	55199.4-55216.6	$3.0$	$0.0$	$18.6$
Periastron	55230.4-55249.6	$2.0$	$0.0$	$44.9$
Periastron	55230.4-55249.6	$2.3$	$0.0$	$39.3$
Periastron	55230.4-55249.6	$3.0$	$0.0$	$34.5$
The 2011 giant outburst
Rising+Falling	55600-55645	$2.0$	$0.0$	$14.6$
Rising+Falling	55600-55645	$2.3$	$0.0$	$13.4$
Rising+Falling	55600-55645	$3.0$	$0.0$	$19.6$
Rising	55600-55617	$2.0$	$0.0$	$33.0$
Rising	55600-55617	$2.3$	$0.0$	$30.7$
Rising	55600-55617	$3.0$	$0.0$	$40.0$
Falling	55618-55645	$2.0$	$0.0$	$30.9$
Falling	55618-55645	$2.3$	$0.0$	$30.6$
Falling	55618-55645	$3.0$	$0.0$	$20.0$
The 2020 giant outburst
Rising+Falling	59159-59207	$2.0$	$0.0$	$33.4$
Rising+Falling	59159-59207	$2.3$	$0.0$	$27.2$
Rising+Falling	59159-59207	$3.0$	$0.0$	$31.4$
Rising	59159-59172.5	$2.0$	$4.2$	$131.5$
Rising	59159-59172.5	$2.3$	$3.2$	$91.8$
Rising	59159-59172.5	$3.0$	$0.5$	$90.0$
Falling	59173-59207	$2.0$	$0.0$	$24.2$
Falling	59173-59207	$2.3$	$0.0$	$22.0$
Falling	59173-59207	$3.0$	$0.0$	$30.5$

•

^a Full: the whole dataset used in this work; ALL: the dataset including the rising, falling, apastron and periastron portions of the outburst.
•

^b The upper limits are given at the 95% confidence level in the energy range of 0.1 $-$ 300 GeV.

Table 2: Parameters of the spin evolution of 1A 0535+026.

\nu_{i}

is the

i

th order derivative of the frequency.

Parameters	2009 double outburst^a	2009 outburst^a	2011 outburst^b	2020 outburst^c
Epoch (MJD)	55040	55166.99	55616.202	59170
$T_{\rm start}$ (MJD)	55040	55166.99	55608	59159.15
$T_{\rm stop}$ (MJD)	55070	55201	55637	59207.92
$\nu_{0}$ ( $\rm 10^{-3}\,Hz$ )	9.66041(4)	9.6618(1)	9.6793(1)	9.66045(2)
$\nu_{1}$ ( $\rm 10^{-12}\,Hz\,s^{-1}$ )	0.67(3)	-4.6(6)	6.43(5)	19.27(4)
$\nu_{2}$ ( $\rm 10^{-17}\,Hz\,s^{-2}$ )		3.3(0.3)	0.121(7)	1.17(4)
$\nu_{3}$ ( $\rm 10^{-23}\,Hz\,s^{-3}$ )		-4.8(6)	-1.43(9)	-5.8(2)
$\nu_{4}$ ( $\rm 10^{-29}\,Hz\,s^{-4}$ )		3(1)	1.67(5)	-2.8(9)
$\nu_{5}$ ( $\rm 10^{-36}\,Hz\,s^{-5}$ )		-8(6)		737(7)
$\nu_{6}$ ( $\rm 10^{-39}\,Hz\,s^{-6}$ )				-1.6(2)
$\nu_{7}$ ( $\rm 10^{-45}\,Hz\,s^{-6}$ )				-5(2)
$\nu_{8}$ ( $\rm 10^{-50}\,Hz\,s^{-6}$ )				3(1)
$\nu_{9}$ ( $\rm 10^{-56}\,Hz\,s^{-6}$ )				-8(2)
$\nu_{10}$ ( $\rm 10^{-62}\,Hz\,s^{-6}$ )				7(1)

•

^a: Derived form the Fermi/GBM monitoring (see text).
•

^b: Adopted from Sartore2015.
•

^c: Derived from Insight-HXMT observations (Wang2022, see text).