The Synchrotron Emission Pattern of Intrabinary Shocks

Abstract

We model millisecond pulsars winds colliding with radiatively-driven companion winds in black widow and redback systems. For the redbacks, the geometry of this intrabinary shock (IBS) is quite sensitive to the expected equatorial concentration in the pulsar outflow. We thus analytically extend IBS thin-shock models to ∼ sin 2n θ pulsar winds. We compute the synchrotron emission from such shocks, including the build-up and cooling of the particle population as it accelerates along the IBS. For reasonable parameters, this IBS flux dominates the binary emission in the X-ray band. The modeling shows subtle variation in spectrum across the IBS peak, accessible to sensitive X-ray studies. As example applications, we fit archival CXO/XMM data from the black widow pulsar J1959+2048 and the redback PSR J2339-0533, finding that the model reproduces well the orbital light curve profiles and energy spectra. The results show a very hard injected electron spectrum, indicating likely dominance by reconnection. The light curve fitting is sensitive to the geometric parameters, including the very important orbital inclination i. Coupled with optical fits of the companion star, such IBS X-ray light curve modeling can strongly constrain the binary geometry and the energetics of the MSP wind.

A New Likely Redback Millisecond Pulsar Binary with a Massive Neutron Star: 4FGL J2333.1–5527

“…In redbacks, heating patterns like these typically occur when the pulsar spin-down power is reprocessed in an intrabinary shock formed from the interaction between the pulsar and companion winds (Romani & Sanchez 2016;Wadiasingh et al 2017;Kandel et al 2019). Such a shock would also produce a characteristic hard power-law X-ray spectrum (e.g., Roberts et al 2015;Werner et al 2016), consistent with our observations ( § 3.2).…”

NuSTAR and Parkes observations of the transitional millisecond pulsar binary XSS J12270–4859 in the rotation-powered state

“…This suggested a variability in the intrabinary shock over a timescale of a few months. The hard spectral shape in the soft range is similar to other RBs, with a few also observed above 10 keV and detected up to 40-70 keV without displaying a spectral break (Tendulkar et al 2014;Kong et al 2017;Al Noori et al 2018;Kandel et al 2019).…”

“…The lack of a detectable orbital modulation above 25 keV is unexpected result, not reported before for any of the other four RBs observed with NuSTAR, namely PSR J1023+0038 (Tendulkar et al 2014), PSR J2129-0429 (Al Noori et al 2018), PSR J1723-2837 (Kong et al 2017) and PSR J2339-0533 (Kandel et al 2019), although this could well depend on the choice of the energy bands used to study the X-ray modulations. Indeed, a more detailed study of the energy resolved X-ray orbital modulation in PSR J1023+0038 as observed with NuSTAR during its previous rotation-powered state reveals that above ∼25 keV the modulation has a fractional amplitude ∼ 15 ± 3%, lower than that below 25 keV, ∼ 25 ± 2% (1σ uncertainty) (Coti Zelati et al, in prep.).…”

“…Small changes in the spectral shape between the minimum and maximum of the orbital modulation, although here undetected, could produce energy dependent modulation amplitudes. For PSR J2339-0533 Kandel et al (2019) find subtle changes in the phase-resolved X-ray spectra and a double-peaked light curve only below 15 keV, while between 15-40 keV it is single peaked. We here note that also for J1227, if studied over this wider energy range (e.g.…”

Gamma-ray orbital modulation of the transitioning millisecond pulsar binary XSS J12270-4859

“…In the MSP state, like in pulsar binaries, the companion is heated by the pulsar's energy output and so exhibits day-night cycles. The heating can make the companion wind strong, and it interacts with the pulsar wind to form an intra-binary shock (IBS; e.g., Wadiasingh et al 2017;Kandel et al 2019;van der Merwe et al 2020). Pulsar wind particles are accelerated in the shock and emit synchrotron radiation, producing characteristic double peaks in the Xray light curve around a maximum (e.g., Roberts et al 2015).…”