Gamma-ray Orbital Modulation in Spider Pulsars: Three Discoveries and a Universal Modulated Fraction

Abstract

Compact binary millisecond pulsars (also known as spiders) allow us to probe pulsar winds in their innermost regions, between the light cylinder (radius $\sim10^{7}$ cm) and the companion star (at $\sim10^{11}$ cm). Their flux is known to vary along the orbit, from radio to X-rays. During the past decade, gamma-ray orbital modulation (GOM) has been discovered in a handful of spiders, but its origin remains largely unknown. We present the results of a systematic search for GOM among 43 systems, selecting pulsed 0.1-1 GeV photons and using spin and orbital ephemeris from Fermi's Third Pulsar Catalog. We discover GOM from three spiders - PSR J1124-3653, PSR J1946-5403 and PSR J2215+5135 - and confirm four previous detections. In all seven cases so far, the GOM peaks near the pulsar's superior conjunction. The X-ray orbital light curves are usually in anti-phase, peaking when the pulsar is at inferior conjunction, but we find one case where both gamma-rays and X-rays peak around superior conjunction: PSR J1946-5403. We measure the modulated fractions of the GOM and find consistent values for all seven spiders, with an average $22.0\pm2.6\%$. Including eclipsing systems seen edge-on, we find no clear dependence of the modulated fraction on the orbital inclination (within $\simeq$45-90$^\circ$). Our results challenge previous models proposed to explain GOM in spiders, based on inverse Compton and synchrotron emission close to the companion, since these predict a clear dependence with orbital inclination (stronger modulation at high inclinations). We nearly double the number of GOM detections in spiders, showing that it is more common than previously thought.

Figures (16)

• Figure 1: Our gamma-ray timing results for PSR J2215+5135 in the $0.1-300$ GeV energy band. Top panel: the black curve represents the folded light curve, the blue curve shows the template pulse profile, and the dashed red line indicates the background level. Bottom left: photon spin phases are plotted against time, with the color representing the weights of the photons. Bottom right: the cumulative H-test for pulsations significance is shown over time. Dashed blue lines in the bottom panels indicate the start and end of the timing solution used.
• Figure 2: Constraints on the MF ($\alpha$) and phase shift ($\Phi_0$). Left: parameter space for PSR J2215+5135, with the color scale representing the likelihood values. Contours indicate the 1-, 2-, and 3-$\sigma$ confidence intervals. Right: Parameter space for PSR J0610-2100, which does not exhibit GOM. The 3$\sigma$ upper limits on the MF are shown.
• Figure 3: Reweighted, phase-folded gamma-ray light curves in the $0.1–1$ GeV energy range for all systems with detected GOM (except for PSR J1227-4853, where regular weights were used; Secs. \ref{['sec:LAT']} and \ref{['sec:J1227']}). The black points represent the folded data and uncertainties. The blue line and shaded area show the sinusoidal fit with its $1\sigma$ uncertainty, while the red dashed line and shaded area represent the background level and its uncertainty. Two orbital periods are shown for clarity.
• Figure 4: Weighted H-test significance for the seven systems with detected GOM, accumulated over time, using reweighted $0.1-1$ GeV photons (except for PSR J1227-4853, where regular photon weights were used). Grey lines indicate systems where no significant GOM was detected. The dashed horizontal lines represent the thresholds for a 3-, 4- and 5-$\sigma$ confidence level. Systems with newly discovered GOM are shown in bold face.
• Figure 5: Weighted, phase-folded gamma-ray light curves of J1227 in the $0.1-1$ GeV band, in the disk (left) and the pulsar (right) states.