Helium Sedimentation Research Articles

Effect of composition gradient on magnetothermal instability modified by shear and rotation

We model the intracluster medium as a weakly collisional plasma that is a binary mixture of the hydrogen and the helium ions, along with free electrons. When, owing to the helium sedimentation, the gradient of the mean molecular weight (or equivalently, composition or helium ions' concentration) of the plasma is not negligible, it can have appreciable influence on the stability criteria of the thermal convective instabilities, e.g., the heat-flux-buoyancy instability and the magnetothermal instability (MTI). These instabilities are consequences of the anisotropic heat conduction occurring preferentially along the magnetic field lines. In this paper, without ignoring the magnetic tension, we first present the mathematical criterion for the onset of composition gradient modified MTI. Subsequently, we relax the commonly adopted equilibrium state in which the plasma is at rest, and assume that the plasma is in a sheared state which may be due to differential rotation. We discuss how the concentration gradient affects the coupling between the Kelvin--Helmholtz instability and the MTI in rendering the plasma unstable or stable. We derive exact stability criterion by working with the sharp boundary case in which the physical variables---temperature, mean molecular weight, density, and magnetic field---change discontinuously from one constant value to another on crossing the boundary. Finally, we perform the linear stability analysis for the case of the differentially rotating plasma that is thermally and compositionally stratified as well. By assuming axisymmetric perturbations, we find the corresponding dispersion relation and the explicit mathematical expression determining the onset of the modified MTI.

PLASMA INSTABILITIES IN THE CONTEXT OF CURRENT HELIUM SEDIMENTATION MODELS: DYNAMICAL IMPLICATIONS FOR THE ICM IN GALAXY CLUSTERS

Understanding whether Helium can sediment to the core of galaxy clusters is important for a number of problems in cosmology and astrophysics. All current models addressing this question are one-dimensional and do not account for the fact that magnetic fields can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat, and particle diffusion in the weakly collisional intracluster medium (ICM). This anisotropy can lead to a wide variety of instabilities, which could be relevant for understanding the dynamics of heterogeneous media. In this paper, we consider the radial temperature and composition profiles as obtained from a state-of-the-art Helium sedimentation model and analyze its stability properties. We find that the associated radial profiles are unstable, to different kinds of instabilities depending on the magnetic field orientation, at all radii. The fastest growing modes are usually related to generalizations of the Magnetothermal Instability (MTI) and the Heat-flux-driven Buoyancy Instability (HBI) which operate in heterogeneous media. We find that the effect of sedimentation is to increase (decrease) the predicted growth rates in the inner (outer) cluster region. The unstable modes grow fast compared to the sedimentation timescale. This suggests that the composition gradients as inferred from sedimentation models, which do not fully account for the anisotropic character of the weakly collisional environment, might not be very robust. Our results emphasize the subtleties involved in understanding the gas dynamics of the ICM and argue for the need of a comprehensive approach to address the issue of Helium sedimentation beyond current models.

An exploration of double diffusive convection in Jupiter as a result of hydrogen–helium phase separation

Jupiter's atmosphere has been observed to be depleted in helium (Yatm ∼ 0.24), suggesting active helium sedimentation in the interior. This is accounted for in standard Jupiter structure and evolution models through the assumption of an outer, He-depleted envelope that is separated from the He-enriched deep interior by a sharp boundary. Here we aim to develop a model for Jupiter's inhomogeneous thermal evolution that relies on a more self-consistent description of the internal profiles of He abundance, temperature, and heat flux. We make use of recent numerical simulations on H/He demixing, and on layered double diffusive (LDD) and oscillatory double diffusive (ODD) convection, and assume an idealized planet model composed of an H/He envelope and a massive core. A general framework for the construction of interior models with He rain is described. Despite, or perhaps because of, our simplifications made we find that self-consistent models are rare. For instance, no model for ODD convection is found. We modify the H/He phase diagram of Lorenzen et al. to reproduce Jupiter's atmospheric helium abundance and examine evolution models as a function of the LDD layer height, from those that prolong Jupiter's cooling time to those that actually shorten it. Resulting models that meet the luminosity constraint have layer heights of ≈0.1–1 km, corresponding to ≈10 000–20 000 layers in the rain zone between ∼1 and 3–4.5 Mbar. Present limitations and directions for future work are discussed, such as the formation and sinking of He droplets.

The effect of helium sedimentation on galaxy cluster masses and scaling relations

Recent theoretical studies predict that the inner regions of galaxy clusters may have an enhanced helium abundance due to sedimentation over the cluster lifetime. If sedimentation is not suppressed (e.g., by tangled magnetic fields), this may significantly affect the cluster mass estimates. We use Chandra X-ray observations of eight relaxed galaxy clusters to investigate the upper limits to the effect of helium sedimentation on the measurement of cluster masses and the best-fit slopes of the Y_X - M_500 and Y_X - M_2500 scaling relations. We calculated gas mass and total mass in two limiting cases: a uniform, un-enhanced abundance distribution and a radial distribution from numerical simulations of helium sedimentation on a timescale of 11 Gyrs. The assumed helium sedimentation model, on average, produces a negligible increase in the gas mass inferred within large radii (r < r500) (1.3 +/- 1.2 per cent) and a (10.2 +/- 5.5) per cent mean decrease in the total mass inferred within r < r500. Significantly stronger effects in the gas mass (10.5 +/- 0.8 per cent) and total mass (25.1 +/- 1.1 per cent) are seen at small radii owing to a larger variance in helium abundance in the inner region, r < 0.1 r500. We find that the slope of the Y_X -M_500 scaling relation is not significantly affected by helium sedimentation.

THE ULTRAVIOLET UPTURN IN ELLIPTICAL GALAXIES AND ENVIRONMENTAL EFFECTS

It is suspected that the ultraviolet (UV) upturn phenomenon in elliptical galaxies and extended horizontal-branch stars in globular clusters have a common origin. An extremely high abundance of helium (Y~0.4) allows for a working hypothesis, but its origin is unclear. Peng & Nagai (2009) proposed that primordial helium sedimentation in dark haloes over cosmic timescales may lead to extreme helium abundances in galaxy cluster centers. In this scenario UV upturn should be restricted to brightest cluster galaxies (BCGs) only. This is a clear and testable prediction. We present tests of this hypothesis using galaxy clusters from Yoon et al. (2008) that were detected by both the Sloan Digital Sky Survey and the Galaxy Evolution Explorer Medium Imaging Survey. Using a new UV classification scheme based on far-UV, near-UV, and optical photometry we found only 5% of cluster elliptical galaxies show a UV upturn, while 27% and 68% are classified as "recent star-formation" and "UV-weak" ellipticals, respectively. The data reveal a modest positive dependence of the UV upturn fraction on galaxy velocity dispersion, which is in agreement with the earlier findings of Burstein et al. (1988) and possibly with the helium sedimentation theory. However, we do not see any dependency on rank or luminosity of galaxies. Besides, BCGs do not show any marked difference in UV upturn fraction or strength, which is inconsistent with the prediction. We conclude that the aforementioned helium sedimentation theory and its inferred environmental effects are not supported by the available data.

Gravitational diffusion in the intracluster medium

We revisit the process of gravitational sedimentation of helium and heavy elements in the intracluster medium. We find that helium applies an inward drag force on heavy elements, boosting their sedimentation speed to nearly half its own. This speed is almost independent of the mass and the electric charge of heavy elements. In the absence of small-scale magnetic fields, helium sedimentation can increase the He/H abundance ratio in the cores of hot clusters by three orders of magnitude. It also steepens the baryonic density profile yielding a higher X-ray luminosity, which offers an explanation of the observed luminosity–temperature relation. If the primordial He/H ratio is assumed, then the gas density inferred from the observed X-ray emissivity might be underestimated by 30 per cent in the cores of clusters and overestimated by 7 per cent in the outer regions. The dark matter density, on the other hand, might be overestimated by a factor of 2.3 in the cores and underestimated by 18 per cent in the outer regions.

D‐D Fusion in the Interior of Jupiter?

One of the still uncertain and debated questions about Jupiter is the origin of its excess heat. Understanding the source of such heat will certainly shed some light on the physics of the interior of the planet and on scenarios of its formation. Recent measurements of sound velocities in Jupiter show substantial disagreement with the existing models for the Jovian interior. Analysis of these measurements suggests that helium (He) sedimentation (through H-He phase separation) is plausible in the planet's interior, contrary to what is believed from numerical calculations of H-He mixture at conditions prevailing in Jupiter's deep interior. This signals the need for a revision of the existing models of Jupiter and allows for new models to be explored. While He sedimentation might help shift the calculated sound velocities toward the observed ones, we find that it cannot explain the excess heat. Here, we analyze the consequences of deuterium (D) sedimentation on Jupiter's excess heat and discuss its effects on the sound profiles. Such a sedimentation is assumed to have occurred in the early stages of planet formation (here the core-instability model) through planetesimal vaporization in the deeper parts of the envelope. Our interest in investigating D sedimentation resulted from the recent extrapolations of D-D, D-T, D-3He, and p-D fusion to electron volt temperatures, which indicate that D-D fusion largely dominates the other reactions under conditions thought to prevail in the interior of early Jupiter. We find that with a modest degree of interior stratification of D (5%-15% of the total D of the planet), D-D burning naturally explains the excess heat given off by the planet. For our model to operate, we find that D sedimentation must occur during the early stages of planet formation (core-instability scenario) when interior temperatures of 16-18 eV where available. Our model is applied to the family of the Jovian planets as a whole.

The Universe and Globular Clusters: An Age Conflict?

Chaboyer (1995) has recently shown that the range of possible ages of globular clusters, ? ~ 14-18 Gyr, corresponding to different choices of distance scales, is further enlarged mainly by uncertainties in modeling convection. Within the mixing-length theory (MLT) the result is ? = 11-21 Gyr. Bolte & Hogan (1995) adopted the field subdwarfs as indicators of the distance scale and, assuming that ? is insensitive to the treatment of convection, found that ? = (15.8 ? 2.1) Gyr. Within Chaboyer's findings, it is marginally possible to avoid an age conflict with the expansion age of the universe, even if this latter is t0 = 8-11 Gyr, while this is not the case with the Bolte & Hogan (1995) conclusion. Mazzitelli, D'Antona, & Caloi (1995) have implemented updated macro- and microphysics inputs and determined the distance scale by fitting the horizontal-branch models to the horizontal branch of metal-poor globular clusters. Within the MLT, they find ? 14 Gyr. Switching from MLT to a full spectrum of turbulence (FST) model of convection (Canuto & Mazzitelli 1991) lowers the value of ? by 1-2 Gyr. Since the Mazzitelli et al. (1995) results would alleviate the age conflict to the point of making it disappear, it is important to assess their validity by answering the following questions. Independently of the assumptions on the distance scale: 1. What is the role of convection near turnoff on both its shape and luminosity? Chaboyer (1995) and Mazzitelli et al. (1995) find an appreciable effect, while Bolte & Hogan (1995) a priori assume no such effect. 2. How meaningful is the fit of the red giant branch in the determination of ?? In this paper, we answer question (1) carrying out extensive new stellar model calculations. When we assume the long distance scale, the FST results differ from the MLT values both in the shape and in the luminosity of the turnoff, while there is no appreciable difference if one employs the short distance scale. Helium sedimentation also affects the shape of isochrones and age determination. The long distance scale is also shown to be consistent with the subdwarf location. As for (2), we find that, depending on the correlations between Teff and colors, both FST and MLT results can be made compatible with both distance scales. Models including sedimentation of helium improve the agreement with the red giant-branch location for low ages. At present, red giant branches can even be misleading as age indicators. In conclusion, we choose the long distance scale on the basis of both horizontal-branch luminosities and the present data on subdwarf location, with resulting ages of about 12 Gyr for the most metal-poor globular clusters.