Three-dimensional simulations of disk accretion to an inclined dipole. II. Hot spots and variability

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, mu, is inclined relative to its rotation axis, Omega, by an angle Theta (we call this angle the misalignment angle''), while the disk's rotation axis is parallel to Omega. A sequence of misalignment angles between Theta=0degrees and 90degrees was investigated. The hot spots arise on the stellar surface because of the impact on the surface of magnetically channeled accretion streams. The distribution of different parameters in the hot spots reflects those in the funnel streams near the surface of the star. Typically, at small Theta the spots as observed are shaped like a bow curved around the magnetic axis, while at the largest values of Theta the spots are shaped like a bar crossing the magnetic pole. The physical parameters (density, velocity, temperature, matter, 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. Rotation of the star leads to the observed variability of brightness. The light curves were calculated for different values of Theta and inclination angles of the disk, i. They show a range of variability patterns, including curves with one maximum per period (at most angles Theta and i) and curves with two maxima per period (at large Theta and i). At small Theta, the funnel streams may rotate faster or 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.