Effects of resistivity on standing shocks in low angular momentum flows around black holes

Abstract

We study two-dimensional low angular momentum flow around a black hole using the resistive magnetohydrodynamic module of PLUTO code. Simulations have been performed for the flows with parameters of specific angular momentum, specific energy and magnetic field which may be expected for the flow around Sgr A*. For flows with lower resistivity η = 10−6 and 0.01, the luminosity and shock location on the equator vary quasi-periodically. The power density spectra of luminosity variation show peak frequencies which correspond to the periods of 5 × 105, 1.4 × 105 and 5 × 104 s. These quasi-periodic oscillations (QPOs) occur due to interaction between the outer oscillating standing shock and the inner weak shocks occurring at the innermost hot blob. While for cases with higher resistivity η = 0.1 and 1.0, the high resistivity considerably suppresses the magnetic activity such as MHD turbulence and the flows tend to be steady and symmetric with respect to the equator. The steady standing shock is formed more outward compared with the hydrodynamical flow. The low angular momentum flow model with the above flow parameters and with low resistivity has a possibility to explain long-term flares of Sgr A* with frequencies ∼ one per day and ∼ 5 – 10 days in the latest observations by Chandra, Swift and XMM-Newton monitoring of Sgr A*.

Radiative shock oscillation model for the long-term flares of Sgr A*

“…The principle of our oscillating shock model for Sgr A* is that the hydrodynamical flow with a low angular momentum forms a standing shock in the inner region of the accretion disc if the angular momentum is properly selected and that the shock oscillates in the MHD flow under an appropriate magnetic field. The method to get the primitive variables of the density ρout, the angular momentum λout, the temperature Tout, the radial velocity vout, and the disc height hout at the outer R-boundary responsible for such standing shock are shown in Okuda et al (2019) and Singh, Okuda & Aktar (2021). However, in the present radiation problem, we have to specify another parameter as well, radiation energy density (Er)out.…”

“…Table 1 gives the primitive variables of the specific angular momentum λout, the plasma beta βout, the radial velocity vout, the sound velocity aout, the input density ρout, the temperature Tout, the injection height of accretion flow hout, the radiation energy density (Er)out, the input accretion rate Ṁinput at the outer radial boundary Rout= 200, which are same as those in the previous studies (Okuda et al 2019;Singh, Okuda & Aktar 2021) except for the angular momentum λ. Here, λ = 1.3 in unit of Rgc is taken to be a little smaller than the previous λ = 1.35, to examine the flow how to behave differently from the previous results.…”

“…The low angular momentum of the accretion flow around Sgr A* may be attributed to the stellar wind from nearby hot stars orbiting around Sgr A* (Loeb 2004;Mościbrodzka, Das & Czerny 2006;Czerny & Mościbrodzka 2008). Motivated by these works, we examined the shock oscillating model with low angular momentum for Sgr A* using 2D time-dependent MHD calculations and showed that the magnetized flows yield large modulations of luminosities with a time-scale of ∼ 5 and 10 days with an accompanying, more rapid, small modulation with a period of 25 hours (Okuda et al 2019;Singh, Okuda & Aktar 2021) which are compatible with luminous flares with a frequency of ∼ every half a day, one, five, and ten days in the latest observations by Chandra, Swift, and XMM-Newton monitoring of Sgr A* (Degenaar et al 2013;Neilson et al 2013Neilson et al , 2015Ponti et al 2015). Recent observations of Sgr A* show characteristic spectra in radio, near-infrared (NIR), and X-ray bands (Ponti et al 2017;Capellupo et al 2017;Witzel et al 2021).…”

“…The magnetic field is amplified rapidly by the MRI, and the MHD turbulence prevails near the equatorial plane. Since analyses of the MRI and the turbulent flow are explained in detail in the previous papers(Okuda et al 2019;Singh, Okuda & Aktar 2021), we do not repeat them here.…”

Dynamical Properties of Magnetized Low-angular-momentum Accretion Flows around a Kerr Black Hole

“…With the most advanced general-relativistic magnetohydrodynamic (GRMHD) simulations, large numbers of studies have been performed to understand different kinds of flows (for reviews, see Davis & Tchekhovskoy 2020;Mizuno 2022). In the last few decades, some efforts have been made to understand lowangular-momentum accretion flows in a pseudo-Newtonian, axisymmetric (2D), hydrodynamic approach targeting the formation of standing as well as oscillating shocks (e.g., Molteni et al 1994Molteni et al , 1996aMolteni et al , 1996bRyu et al 1995;Lanzafame et al 1998;Proga & Begelman 2003;Chakrabarti et al 2004;Giri et al 2010;Okuda & Molteni 2012;Okuda 2014;Okuda & Das 2015;Okuda et al 2019Okuda et al , 2022Singh et al 2021). However, so far, not much effort has been devoted to understanding lowangular-momentum flows in a GRMHD framework that is related to multitransonic accretion flows.…”