Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Hydrodynamic simulations of irradiated secondaries in dwarf novae

Abstract: Context. Secondary stars in dwarf novae are strongly irradiated during outbursts. It has been argued that this could result in an enhancement of the mass transfer rate even though the L 1 region is shaded from the primary irradiation by the accretion disc. Previous investigations of the possibility of a circulation flow transporting heat from hot regions to L 1 have given opposite answers. Aims. We investigate the surface flow of irradiated secondaries numerically. We consider the full time-dependent problem and take the two-dimensional nature of the flow into account. Methods. We use a simple model for the irradiation and the geometry of the secondary star: the irradiation temperature is treated as a free parameter and the secondary is replaced by a spherical star with a space-dependent Coriolis force that mimics the effect of the Roche geometry. The Euler equations are solved in spherical coordinates with the TVD-MacCormack scheme. Results. We show that the Coriolis force leads to the formation of a circulation flow from the high-latitude region to the close vicinity of the L 1 point. However, no heat can be efficiently transported to the L 1 region due to the rapid radiative cooling of the hot material as it enters the equatorial belt shaded from irradiation. Under the assumption of hydrostatic equilibrium, the Coriolis force could lead to a moderate increase in the mass transfer by pushing the gas in the vertical direction in the vicinity of L 1 , but only during the initial phases of the outburst (about 15-20 orbital periods). It remains possible, however, that this assumption breaks up due to the strong surface velocity of the flow transiting by L 1 , close to the sound speed. In this case, however, a three-dimensional approach would then be needed to determine the mass flux leaving the secondary. Conclusions. We therefore conclude that the Coriolis force does not prevent a flow from the heated regions of the secondary towards the L 1 region, at least during the initial phases of an outburst, but the resulting increase in the mass transfer rate is moderate, so unlikely to be able to account for the duration of long outbursts.

Gravity variations induced by core flows

Abstract: SUMMARY The temporal variation in the density structure associated with convective motions in the outer core causes a change in the Earth’s gravity field. Core flows also lead to a gravity change through the global elastic deformations that accompany changes in the non-hydrostatic pressure at the core–mantle boundary (CMB). In this work, we present predictions of the gravity changes from these two processes during the past century. These predictions are built on the basis of flows at the surface of the core that are reconstructed from the observed geomagnetic secular variation. The pressure-induced gravity variations can be reconstructed directly from surface core flows under the assumption of tangential geostrophy; predicted variations in the Stokes coefficients of degree 2, 3 and 4 are of the order of 10 −11 ,3 × 10 −12 and 10 −12 , respectively, with a typical timescale of a few decades. These correspond to changes in gravity of 70, 30 and 15 nGal, and to equivalent geoid height variations of 0.15, 0.05 and 0.02 mm, respectively. The density-induced gravity variations cannot be determined solely from surface core flows, though a partial recovery is possible if flows with important axial gradients dominate the dynamics at decadal timescales. If this is the case, the density-induced gravity signal is of similar amplitude and generally anti-correlated with the pressure-induced signal, thus reducing the overall amplitude of the gravity changes. However, because we expect decadal flows to be predominantly axially invariant, the amplitude of the density-induced gravity changes should be much smaller. Our prediction also allows to determine upper bounds in pressure change at the CMB and density change within the core that have taken place during the past 20 yr such that observed gravity variations are not exceeded; for harmonic degree 2, we find a maximum pressure change of approximately 350 Pa and a maximum departure from hydrostatic density of approximately 1 part in 10 7 . Although the predicted gravity changes from core flows are small, they are at the threshold of detectability with high-precision gravity measurements from satellite missions such as GRACE. The most important challenge to identifying a core signal will be the removal of interannual gravity variations caused by surface processes which are an order of magnitude larger and mask the core signal.