arXiv subjects

Jean-Paul Zahn

Publications and source records attributed to Jean-Paul Zahn.

14 recordsLinked to original sources

arXiv2015

New constraints on Saturn's interior from Cassini astrometric data

Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturn's tidal parameters through their current effects on the orbits of the eight main and four coorbital moons. We have used the latter to make the first determination of Saturn's Love number, $k_2=0.390 \pm 0.024$, a value larger than the commonly used theoretical value of 0.341 (Gavrilov & Zharkov, 1977), but compatible with more recent models (Helled & Guillot, 2013) for which $k_2$ ranges from 0.355 to 0.382. Depending on the assumed spin for Saturn's interior, the new constraint can lead to a reduction of up to 80% in the number of potential models, offering great opportunities to probe the planet's interior. In addition, significant tidal dissipation within Saturn is confirmed (Lainey et al., 2012) corresponding to a high present-day tidal ratio $k_2/Q=(1.59 \pm 0.74) \times 10^{-4}$ and implying fast orbital expansions of the moons. This high dissipation, with no obvious variations for tidal frequencies corresponding to those of Enceladus and Dione, may be explained by viscous friction in a solid core, implying a core viscosity typically ranging between $10^{14}$ and $10^{16}$ Pa.s (Remus et al., 2012). However, a dissipation increase by one order of magnitude at Rhea's frequency could suggest the existence of an additional, frequency-dependent, dissipation process, possibly from turbulent friction acting on tidal waves in the fluid envelope of Saturn (Ogilvie & Li, 2004). Alternatively, a few of Saturn's moons might themselves experience large tidal dissipation.

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arXiv2008

Tidal dissipation in binary systems

To first approximation, a binary system conserves its angular momentum while it evolves to its state of minimum kinetic energy: circular orbit, all spins aligned, and components rotating in synchronism with the orbital motion. The pace at which this final state is achieved depends on the physical processes that are responsible for the dissipation of the tidal kinetic energy. For stars (or planets) with an outer convection zone, the dominant mechanism identified so far is the viscous dissipation acting on the equilibrium tide. For stars with an outer radiation zone, it is the radiative damping operating on the dynamical tide. After a brief presentation of the tides, I shall review these physical processes; I shall discuss the uncertainties of their present treatment, describe the latest developments, and compare the theoretical predictions with the observed properties concerning the orbital circularization of close binaries.

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arXiv2007

Inhibition of thermohaline mixing by a magnetic field in Ap star descendants: Implications for the Galactic evolution of 3He

To reconcile the measurements of 3He/H in Galactic HII regions with high values of 3He in a couple of planetary nebulae, we propose that thermohaline mixing is inhibited by a fossil magnetic field in red giant stars that are descendants of Ap stars. We examine the effect of a magnetic field on the salt-finger instability, using a local analysis. We obtain a threshold for the magnetic field of 10^4 - 10^5 Gauss, above which it inhibits thermohaline mixing in red giant stars located at or above the bump. Fields of that order are expected in the descendants of the Ap stars, taking into account the contraction of their core. We conclude that in a large fraction of the descendants of Ap stars thermohaline mixing does not occur. As a consequence these objects must produce 3He as predicted by the standard theory of stellar evolution and as observed in the planetary nebulae NGC3242 and J320. The relative number of such stars with respect to non-magnetic objects that undergo thermohaline mixing is consistent with the statistical constraint coming from observations of the carbon isotopic ratio in red giant stars. It also satisfies the Galactic requirements for the evolution of the 3He abundance.

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arXiv2007

Star formation in accretion discs : from the Galactic Center to Active Galactic Nuclei

Keplerian accretion discs around massive black holes (MBHs) are gravitationally unstable beyond a few hundredths of parsec and should collapse to form stars. Indeed an accretion/star formation episode took place a few millions years ago in the Galactic Center (GC). This raises the question of how the disc can survive in AGN and quasars and continue to transport matter towards the black hole. We study the accretion/star formation process, with one aim in mind, to show that a spectrum similar to the observed AGN one can be produced by the disc. We compute models of stationary accretion discs, both continuous and clumpy. Continuous discs must be maintained in a state of marginal stability for the rate of star formation to remain modest, so they require additional heating and transport of angular momentum. Non-viscous heating can be provided by stellar illumination, but momentum transport by supernovae is insufficient to sustain a marginal state, except at the very periphery of the disc. In clumpy discs it is possible to account for the required accretion rate through interactions between clouds, but this model is unsatisfactory as its parameters are tightly constrained without any physical justification. Finally one must appeal to non-stationary discs with intermittent accretion episodes like those that occurred in the GC, but such a model is probably not applicable to luminous high redshift quasars neither to radio-loud quasars.

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arXiv2007

Thermohaline mixing: A physical mechanism governing the photospheric composition of low-mass giants

Numerous spectroscopic observations provide compelling evidence for a non-canonical mixing process that modifies the surface abundances of Li, C and N of low-mass red giants when they reach the bump in the luminosity function. Eggleton et al. (2006) have proposed that a molecular weight inversion created by the 3He(3He,2p)4He reaction may be at the origin of this mixing, and relate it to the Rayleigh-Taylor instability. In the present work we argue that one is actually dealing with a double diffusive instability referred to as thermohaline convection and we discuss its influence on the red giant branch. We compute stellar models of various initial metallicities using the prescription by Ulrich (1972) (extended to the case of a non-perfect gas) for the turbulent diffusivity produced by the thermohaline instability in stellar radiation zones. Thermohaline mixing simultaneously accounts for the observed behaviour of the carbon isotopic ratio and of the abundances of Li, C and N on the upper part of the red giant branch. It reduces significantly the 3He production with respect to canonical evolution models as required by measurements of 3He/H in galactic HII regions. Thermohaline mixing is a fundamental physical process that must be included in stellar evolution modeling.

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arXiv2006

Concluding remarks

To be published in the proceedings of IAU Symposium 239 "Convection in Astrophysics" (ed. F. Kupka, I. W. Roxburgh, K. L. Chan). Content: 1. From Nice to Prague, 2. The triumph of 3-D simulations, 3. How to lower the cost - what else can be done? 4. A powerful tool to determine surface abundances, 5. The effects of convection are not confined to convection zones, 6. Towards a realistic model of the solar dynamo, 7. The moment of truth: facing observational tests, 8. On my wish-list.

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arXiv2002

Angular momentum extraction by gravity waves in the Sun

We review the behavior of the oscillating shear layer produced by gravity waves below the surface convection zone of the Sun. We show that, under asymmetric filtering produced by this layer, gravity waves of low spherical order, which are stochastically excited at the base of the convection zone of late type stars, can extract angular momentum from their radiative interior. The time-scale for this momentum extraction in a Sun-like star is of the order of 10^7 years. The process is particularly efficient in the central region, and it could produce there a slowly rotating core.

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arXiv2000

Accretion discs models with the "beta"-viscosity prescription derived from laboratory experiments

We examine under which conditions one may apply, to steady state keplerian accretion discs, the "beta"-viscosity prescription which has been derived from rotating shear flow experiments (Richard & Zahn 1999). Using a vertically averaged model, we show that this law may be suitable for all three families of known systems: in young stellar objects, evolved binary stars and Active Galactic Nuclei discs (except in their outer gas pressure dominated regions where turbulence becomes hypersonic). According to the standard criterion for viscous stability, "beta"-discs are always stable throughout. Using realistic opacities and equation of state, we demonstrate that these discs are thermally unstable in the temperature domain where hydrogen recombines, when they are optically thick, and this could lead to limit cycle behavior. Radiation pressure dominated regions are thermally stable, in contrast with "alpha"-discs. This results in a fully stable solution for the innermost parts of AGN discs.

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arXiv1999

Plumes in stellar convection zones

All numerical simulations of compressible convection reveal the presence of strong downwards directed flows. Thanks to helioseismology, such plumes have now been detected also at the top of the solar convection zone, on super- granular scales. Their properties may be crudely described by adopting Taylor's turbulent entrainment hypothesis, whose validity is well established under various conditions. Using this model, one finds that the strong density stratification does not prevent the plumes from traversing the whole convection zone, and that they carry upwards a net energy flux (Rieutord & Zahn 1995). They penetrate to some extent in the adjacent stable region, where they establish a nearly adiabatic stratification. These plumes have a strong impact on the dynamics of stellar convection zones, and they play probably a key role in the dynamo mechanism.

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arXiv1999

Turbulence in differentially rotating flows What can be learned from the Couette-Taylor experiment

The turbulent transport of angular momentum plays an important role in many astrophysical objects, but its modelization is still far from satisfactory. We discuss here what can be learned from laboratory experiments. We analyze the results obtained by Wendt (1933) and Taylor (1936) on the classical Couette-Taylor flow, in the case where angular momentum increases with distance from the rotation axis, which is the most interesting for astrophysical applications. We show that when the gap between the coaxial cylinders is wide enough, the criterion for the onset of the finite amplitude instability can be expressed in terms of a gradient Reynolds number. Based on Wendt's results, we argue that turbulence may be sustained by differential rotation when the angular velocity decreases outward, as in keplerian flows. From the rotation profiles and the torque measurements we deduce a prescription for the turbulent viscosity which is independent of gap width; with some caution it may be applied to stellar interiors and to accretion disks.

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arXiv1999

Angular momentum redistribution by waves in the Sun

We calculate the angular momentum transport by gravito-inertial-Alfvén waves and show that, so long as prograde and retrograde gravity waves are excited to roughly the same amplitude, the sign of angular momentum deposit in the radiative interior of the Sun is such as to lead to an exponential growth of any existing small radial gradient of rotation velocity just below the convection zone. This leads to formation of a strong thin shear layer (of thickness about 0.3% R_\odot) near the top of the radiative zone of the Sun on a time-scale of order 20 years. When the magnitude of differential rotation across this layer reaches about 0.1 μHz, the layer becomes unstable to shear instability and undergoes mixing, and the excess angular momentum deposited in the layer is returned to the convection zone. The strong shear in this layer generates toroidal magnetic field which is also deposited in the convection zone when the layer becomes unstable. This could possibly start a new magnetic activity cycle seen at the surface.

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arXiv1999

Star formation and evolution in accretion disks around massive black holes

We develop a model for the outer gravitationally unstable regions of accretion disks around massive black holes, for primeval or solar abundances. First we study star formation and evolution in a purely gaseous marginally unstable disk, and we show that unstable fragments should collapse rapidly and give rise to protostars which accrete at a high rate, acquire a mass of a few tens of Mo, and explode as supernovae, producing strong enriched outflows. Second we assume that the whole mass transport is ensured by the supernovae which induce a transfer of angular momentum. For a star formation rate proportional to the growth rate of gravitational instability, we find solutions for the gas and stellar densities where the gas is close to gravitational instability, between 0.1 and 10 pc M(BH) =10**6 Mo, and between 1 and 100 pc for M(BH)=10**8 Mo or larger, whatever the abundances, but for relatively low accretion rates. For larger accretion rates the number of stars becomes so large that they inhibit further star formation, and/or the rate of SN is so high that they distroy the homogeneity and the marginal stability of the disk. We postpone the study of this case. Besides the fact that the mechanism solves the problem of mass transport in a region of where global instabilities do not work, there are several consequences of this model: it can explain the high velocity metal enriched outflows implied by Broad Absorption Lines in quasars, it can account for a pregalactic enrichment, if black holes formed early, finally it can trigger starbursts in the central regions of galaxies. A check of the model would be to detect a supernova exploding within a few parsecs from the center of an AGN, an observation which can be performed in the near future.

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arXiv1996

Angular momentum transport by internal waves in the solar interior

The internal gravity waves of low frequency which are emitted at the base of the solar convection zone are able to extract angular momentum from the radiative interior. We evaluate this transport with some simplifying assumptions: we ignore the Coriolis force, approximate the spectrum of turbulent convection by the Kolmogorov law, and couple this turbulence to the internal waves through their pressure fluctuations, following Press (1981) and Garcia Lopez & Spruit (1991). The local frequency of an internal wave varies with depth in a differentially rotating star, and it can vanish at some location, thus leading to enhanced damping (Goldreich & Nicholson 1989). It is this dissipation mechanism only that we take into account in the exchange of momentum between waves and stellar rotation. The flux of angular momentum is then an implicit function of depth, involving the local rotation rate and an integral representing the cumulative effect of radiative dissipation. We find that the efficiency of this transport process is rather high: it operates on a timescale of 10^7 years, and is probably responsible for the flat rotation profile which has been detected through helioseismology.

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arXiv1996

Rotational mixing in early-type stars: the main-sequence evolution of a 9 Mo star

We describe the main-sequence evolution of a rotating 9 $M_\odot$ star. Its interior rotation profile is determined by the redistribution of angular momentum through the meridian circulation and through the shear turbulence generated by the differential rotation; the possible effect of internal waves is neglected. We examine the mixing of chemicals produced by the same internal motions. Our modelization is based on the set of equations established by Zahn (1992) and completed in Matias, Talon & Zahn (1996). Our calculations show that the amount of mixing associated with a typical rotation velocity of $\sim 100 km/s$ yields stellar models whose global parameters are very similar to those obtained with the moderate overshooting ($d/H_P \simeq 0.2$) which has been invoked until now to fit the observations. Fast rotation ($\sim 300 km/s$) leads to significant changes of the C/N and O/N surface ratios, but the abundance of He is barely increased. The modifications of the internal composition profile due to such rotational mixing will certainly affect the post--main-sequence evolution.

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