Three‐dimensional Simulations of Disk Accretion to an Inclined Dipole. II. Hot Spots and Variability

Abstract

The physics of the "hot spots" on stellar surfaces and the associated variability of accreting magnetized rotating stars is investigated for the first time using fully three-dimensional magnetohydrodynamic simulations. The magnetic moment of the star µ is inclined relative to its rotation axis Ω by an angle Θ (we will call this angle the "misalignment angle") while the disk's rotation axis is parallel to Ω. A sequence of misalignment angles was investigated, between Θ = 0 • and 90 • . Typically at small Θ the spots are observed to have the shape of a bow which is curved around the magnetic axis, while at largest Θ the spots have a shape of a bar, crossing the magnetic pole. The physical parameters (density, velocity, temperature, matter and energy fluxes, etc.) increase toward the central regions of the spots, thus the size of the spots is different at different values of these parameters. At relatively low density and temperature, the spots occupy approximately 10 − 20% of the stellar surface, while at the highest values of these parameters this area may be less than 1% of the area of the star. The size of the spots increases with the accretion rate. The light curves were calculated for different Θ and inclination angles of the disk i. They show a range of variability patterns, including one maximum-per-period curves (at most of angles Θ and i), and two maximum-per-period curves (at large Θ and i). At small Θ, the funnel streams may rotate faster/slower than the star, and this may lead to quasi-periodic variability of the star. The results are of interest for understanding the variability and quasi-variability of Classical T Tauri Stars, millisecond pulsars and cataclysmic variables.

Accretion onto stars with octupole magnetic fields: Matter flow, hot spots and phase shifts

“…The correlation of the pulsephase offsets with X-ray flux may be an argument in favor of a "moving spots" model, in which the position of hot spots on the stellar surface depends on the accretion rate (Patruno et al 2009a,b). Spot motions have been observed in 3D MHD simulations (Romanova et al 2003(Romanova et al , 2004) and have been proposed as an explanation of timing noise by Lamb et al (2009a,b). This explanation is a possibility.…”

“…For the calculation of the light curves, we use the same approach as Romanova et al(2004). The total energy of the accreting matter is assumed to be converted into isotropic blackbody radiation on the surface of the star.…”

“…In one model, the phase shifts are connected with the motion of accretion spots on the surface of the star (e.g., Lamb et al 2009a,b;Patruno et al 2010). Such spot motion has been observed in global 3D simulations of disc-magnetosphere interactions (Romanova et al 2003(Romanova et al , 2004Bachetti et al 2010). In another model, it is suggested that the timing noise can be connected with variation of the pulse shapes (e.g., Poutanen et al 2009).…”

The Reflares and Outburst Evolution in the Accreting Millisecond Pulsar Sax J1808.4–3658: A Disk Truncated Near Co-Rotation?

“…This value 12 is significantly larger than the co-rotation radius r 31 co = km and it is even larger than the light cylinder radius r 120 lc  km. The co-rotation radius is defined as that point in the disk where the Keplerian rotational velocity of the gas is equal to the rotational velocity of the magnetosphere and as soon as r r m c o > a centrifugal barrier sets in and matter is assumed to be ejected from the system (Illarionov & Sunyaev 1975;Romanova et al 2004). Therefore when r r m c o > one cannot use Equation (2) since the Ṁ inferred from the luminosity might become a bad indicator of the mass flowing in the accretion flow (for example because of mass ejection).…”

Flow Structure in Magnetic CVs

“…However, since the problem is very complicated, the investigations have been performed either in the frame of simplified models (King 1993;Wynn & King 1995;Wynn et al 1997;King & Wynn 1999;Norton et al 2004;Ikhsanov et al 2004;Norton et al 2008), or in a limited region of the stellar magnetosphere (Koldoba et al 2002;Romanova et al 2003Romanova et al , 2004aRomanova et al , 2004b. Only over the last few years, the authors have managed to develop a comprehensive 3D numerical model to calculate the flow structure in close binaries (Zhilkin & Bisikalo 2009, 2010a, 2010b, 2010c.…”