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Register a new userThe Planetary Accretion Shock. II. Grid of Post-Shock Entropies and Radiative Shock Efficiencies for Non-Equilibrium Radiation Transport
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Gabriel-Dominique Marleau
Publication date
2019
fields
Physics
and research's language is
English
Authors
Gabriel-Dominique Marleau
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In the core-accretion formation scenario of gas giants, most of the gas accreting onto a planet is processed through an accretion shock. In this series of papers we study this shock since it is key in setting the forming planets structure and thus its post-formation luminosity, with dramatic observational consequences. We perform one-dimensional grey radiation-hydrodynamical simulations with non-equilibrium (two-temperature) radiation transport and up-to-date opacities. We survey the parameter space of accretion rate, planet mass, and planet radius and obtain post-shock temperatures, pressures, and entropies, as well as global radiation efficiencies. We find that usually, the shock temperature T_shock is given by the free-streaming limit. At low temperatures the dust opacity can make the shock hotter but not significantly. We corroborate this with an original semi-analytical derivation of T_shock . We also estimate the change in luminosity between the shock and the nebula. Neither T_shock nor the luminosity profile depend directly on the optical depth between the shock and the nebula. Rather, T_shock depends on the immediate pre-shock opacity, and the luminosity change on the equation of state (EOS). We find quite high immediate post-shock entropies (S ~ 13-20 kB/mH), which makes it seem unlikely that the shock can cool the planet. The global radiation efficiencies are high (eta^phys > 97%) but the remainder of the total incoming energy, which is brought into the planet, exceeds the internal luminosity of classical cold starts by orders of magnitude. Overall, these findings suggest that warm or hot starts are more plausible.
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The key aspect determining the post-formation luminosity of gas giants has long been considered to be the energetics of the accretion shock at the planetary surface. We use 1D radiation-hydrodynamical simulations to study the radiative loss efficiency and to obtain post-shock temperatures and pressures and thus entropies. The efficiency is defined as the fraction of the total incoming energy flux which escapes the system (roughly the Hill sphere), taking into account the energy recycling which occurs ahead of the shock in a radiative precursor. We focus here on a constant equation of state to isolate the shock physics but use constant and tabulated opacities. While robust quantitative results will require a self-consistent treatment including hydrogen dissocation and ionization, the results show the correct qualitative behavior and can be understood semi-analytically. The shock is found to be isothermal and supercritical for a range of conditions relevant to core accretion (CA), with Mach numbers greater than ca. 3. Across the shock, the entropy decreases significantly, by a few entropy units (k_B/baryon). While nearly 100 percent of the incoming kinetic energy is converted to radiation locally, the efficiencies are found to be as low as roughly 40 percent, implying that a meaningful fraction of the total accretion energy is brought into the planet. For realistic parameter combinations in the CA scenario, a non-zero fraction of the luminosity always escapes the system. This luminosity could explain, at least in part, recent observations in the LkCa 15 and HD 100546 systems.
Hydrogen-line emission from an accretion shock has recently been observed at planetary-mass objects. Our previous work predicted the shock spectrum and luminosity for a shock on the circumplanetary disc. We extend this to the planet-surface shock. We calculate the global spectral energy distribution (SED) of accreting planets by combining our model emission spectra with photospheric SEDs, and predict the line-integrated flux for several hydrogen lines, especially H alpha, but also H beta, Pa alpha, Pa beta, Pa gamma, Br alpha, and Br gamma. We apply our non-equilibrium emission model to the surface accretion shock for a wide range of accretion rates Mdot and masses M_p . Fits to formation calculations provide radii and effective temperatures. Extinction by the surrounding material is neglected, which is arguably often relevant. We find that the line luminosity increases monotonically with Mdot and M_p , depending mostly on Mdot and weakly on M_p for the relevant range of parameters. The Lyman, Balmer, and Paschen continua can exceed the photosphere. The H beta line is fainter by 0 to 1 dex than H alpha, whereas other lines are weaker (by 1 to 3 dex). Shocks on the planet or the CPD surface are distinguishable at very high spectral resolution, but the planet surface shock likely dominates if both are present. Applied to recent non-detections of H alpha, our models imply looser constraints on the Mdot of putative planets than when extrapolating fits from the stellar regime. These hydrogen-line luminosity predictions are useful for interpreting (non-)detections of accreting planets.
We model the post-shock accretion column (PSAC) for intermediate polars (IPs), with parameterizing specific accretion rate between 0.0001 and 100 g cm-2 s-1 and metal abundance between 0.1 and 2 times of solar abundance, and taking into account the gravitational potential and non-equipartition between ions, electrons and ionization degree. We assume the cylinder and dipole as geometry of the PSAC. The PSAC becomes higher against the white dwarf (WD) radius for lower specific accretion rate and more massive WD, and may be comparable to the WD radius. The consideration of the dipolar geometry significantly reduces the density and temperature over the whole PSAC comparing with the cylindrical case when the specific accretion rate is lower than a threshold which the PSAC height reachs 0.2 RWD with and is decreased by the more massive white dwarf. We calculate the spectra of the cylindrical and dipolar PSACs with the wide range of the specific accretion rate. Although the spectra soften as the specific accretion rate decreases for the both geometrical assumptions under the specific accretion rate threshold, the softening is more speedy for the dipolar PSAC. The fact means that the both geometrical assumptions lead the different WD masses for each other when their spectra are applied to the IPs hosting the low accretion or a massive WD. Although the ionization non-equilibrium are also involved for the spectral calculation, the effects are trivial because the radiation from ionization non-equilibrium plasma is a few percent of the whole at most.
We report on the design and first results from experiments looking at the formation of radiative shocks on the Shenguang-II (SG-II) laser at the Shanghai Institute of Optics and Fine Mechanics in China. Laser-heating of a two-layer CH/CH-Br foil drives a $sim$40 km/s shock inside a gas-cell filled with argon at an initial pressure of 1 bar. The use of gas-cell targets with large (several mm) lateral and axial extent allows the shock to propagate freely without any wall interactions, and permits a large field of view to image single and colliding counter-propagating shocks with time resolved, point-projection X-ray backlighting ($sim20$ $mu$m source size, 4.3 keV photon energy). Single shocks were imaged up to 100 ns after the onset of the laser drive allowing to probe the growth of spatial non-uniformities in the shock apex. These results are compared with experiments looking at counter-propagating shocks, showing a symmetric drive which leads to a collision and stagnation from $sim$40 ns onward. We present a preliminary comparison with numerical simulations with the radiation hydrodynamics code ARWEN, which provides expected plasma parameters for the design of future experiments in this facility.
The densities in the outer regions of clusters of galaxies are very low, and the collisional timescales are very long. As a result, heavy elements will be under-ionized after they have passed through the accretion shock. We have studied systematically the effects of non-equilibrium ionization for relaxed clusters in the LambdaCDM cosmology using one-dimensional hydrodynamic simulations. We found that non-equilibrium ionization effects do not depend on cluster mass but depend strongly on redshift which can be understood by self-similar scaling arguments. The effects are stronger for clusters at lower redshifts. We present X-ray signatures such as surface brightness profiles and emission lines in detail for a massive cluster at low redshift. In general, soft emission (0.3-1.0 keV) is enhanced significantly by under-ionization, and the enhancement can be nearly an order of magnitude near the shock radius. The most prominent non-equilibrium ionization signature we found is the O VII and O VIII line ratio. The ratios for non-equilibrium ionization and collisional ionization equilibrium models are different by more than an order of magnitude at radii beyond half of the shock radius. These non-equilibrium ionization signatures are equally strong for models with different non-adiabatic shock electron heating efficiencies. We have also calculated the detectability of the O VII and O VIII lines with the future International X-ray Observatory (IXO). Depending on the line ratio measured, we conclude that an exposure of ~130-380 ksec on a moderate-redshift, massive regular cluster with the X-ray Microcalorimeter Spectrometer (XMS) on the IXO will be sufficient to provide a strong test for the non-equilibrium ionization model.
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