Pulsed fraction of super-critical column accretion flows on to neutron stars: Modeling of ultraluminous X-ray pulsars

Abstract

We calculate the pulsed fraction (PF) of the super-critical column accretion flows onto magnetized neutron stars (NSs), of which the magnetic axis is misaligned with the rotation axis, based on the simulation results by Kawashima et al.(2016, PASJ, 68, 83). Here, we solve the geodesic equation for light in the Schwarzschild spacetime in order to take into account the light bending effect. The gravitational redshift and the relativistic doppler effect from gas motions of the accretion columns are also incorporated. The pulsed emission appears since the observed luminosity, which exceeds the Eddington luminosity for the stellar-mass black holes, periodically changes via precession of the column caused by the rotation of the NS. The PF tends to increase as θ obs approaching to θ B , where θ obs and θ B are the observer's viewing angle and the polar angle of the magnetic axis measured from the rotation axis. The maximum PF is around 50 %. Also, we find that the PF becomes less than 5 % for θ obs < ∼ 5 • or for θ B < ∼ 5 • . Our results are consistent with observations of ultraluminous X-ray pulsars (ULXPs) with few exceptions, since the ULXPs mostly exhibit the PF of < ∼ 50 %. Our present study supports the hypothesis that the ULXPs are powered by the super-critical column accretion onto NSs.

Long-term X-ray spectral evolution of ultraluminous X-ray sources: implications on the accretion flow geometry and the nature of the accretor

“…As argued before, we understand the hardening of the source as a decrease in the viewing angle as the system precesses. Considering the pulsefraction calculations for super-critical accretion columns proposed by Inoue et al (2020), this might imply that the angle between the rotational axis and the magnetic field axis (Θ B ) is greater than the angle between the observer's line of sight and the rotational axis (Θ obs ; e.g., Θ B > 30 • and Θ obs < 30 • , see Fig. 5 from Inoue et al 2020).…”

“…Considering the pulsefraction calculations for super-critical accretion columns proposed by Inoue et al (2020), this might imply that the angle between the rotational axis and the magnetic field axis (Θ B ) is greater than the angle between the observer's line of sight and the rotational axis (Θ obs ; e.g., Θ B > 30 • and Θ obs < 30 • , see Fig. 5 from Inoue et al 2020). Assuming the same applies to M 81-X6, this could imply that pulsations are more likely to be found in softer and dimmer states (HR ∼ 1.5, L ∼ 2.5 × 10 39 erg s −1 ) where we expect the pulse fraction to be higher.…”

Pulsating ULXs: large pulsed fraction excludes strong beaming

“…The distribution of the sources over the amplification factor and the PF depend on the sharpness of the initial beam. The initial beam can be complicated and affected by several factors like geometry of emitting region (Basko & Sunyaev 1976), the gravitational bending of Xray photons (Mushtukov et al 2018;Inoue et al 2020), and photon reprocessing by the accretion flow between the accretion disc inner radius and the NS surface (Siuniaev 1976;Mushtukov et al 2017). The sharpness of the initial beam from a NS surface is described in our simulations by parameter n (see equation 2).…”

Pulsing and non-pulsing ULXs: the iceberg emerges

“…a -forν = 2.8 × 10 −10 ; b -forν = 3.1 × 10 −11 (Vasilopoulos et al 2019). al. (2016); , Inoue, Ohsuga & Kawashima (2020) who show that emission from the neutron star surface at the bottom of the accretion column is negligible. It is well established that the presence or absence of a critical (sonic) point above the accretor surface completely changes the nature of the accretion flow (Abramowicz, et al 2010;Lipunova 1999).…”