An optical view of the filament region of Abell 85

We compare the distribution of optically and Halpha (Ha) selected galaxies in the Southern half of the nearby Abell 85 (A85) cluster with the recently discovered X-ray filament (XRF). We search for galaxies where star formation (SF) may have been triggered by interactions with intracluster gas or tidal pressure due to the cluster potential when entering the cluster. Our analysis is based on images obtained with CFHT MegaPrime/MegaCam (1x1 deg2 field) in four bands (ugri) and ESO 2.2mWFI (38'x36' field) in a narrow band filter corresponding to the redshifted Halpha (Ha) line and in a broad R-band filter. The LFs are estimated by statistically subtracting a reference field. Background contamination is minimized by cutting out galaxies redder than the observed red sequence in the g-i vs. i colour-magnitude diagram. The galaxy distribution shows a significantly flattened cluster, whose principal axis is slightly offset from the XRF. The analysis of the broad band LFs shows that the filament region is well populated. The filament is also independently detected as a gravitationally bound structure by the Serna & Gerbal hierarchical method. 101 galaxies are detected in Ha, among which 23 have spectroscopic redshifts in the cluster, 2 have spectroscopic redshifts higher than the cluster and 58 have photometric redshifts that tend to indicate that they are background objects.The 23 galaxies with spectroscopic redshifts in the cluster are mostly concentrated in the South part of the cluster and along the filament. We find a number of galaxies showing evidence for SF in the XRF, and all our results are consistent with the previous hypothesis that the XRF in A85 is a gravitationally bound structure made of groups falling on to the main cluster.Comment: Accepted in A&A. 39 pages, 107 figures. Full resolution images available at ftp://ftp.iap.fr/pub/from_users/gam/A85

A collisionless scenario for Uranus tilting

The origin of the high inclination of Uranus' spin-axis (Uranus' obliquity) is one of the great unanswered questions about the Solar system. Giant planets are believed to form with nearly zero obliquity, and it has been shown that the present behaviour of Uranus' spin is essentially stable. Several attempts were made in order to solve this problem. Here we report numerical simulations showing that Uranus' axis can be tilted during the planetary migration, without the need of a giant impact, provided that the planet had an additional satellite and a temporary large inclination. This might have happened during the giant planet instability phase described in the Nice model. In our scenario, the satellite is ejected after the tilt by a close encounter at the end of the migration. This model can both explain Uranus' large obliquity and bring new constraints on the planet orbital evolution.Comment: 5 pages, 5 figures, ApJL in pres

Tilting Jupiter (a bit) and Saturn (a lot) During Planetary Migration

We study the effects of planetary late migration on the gas giants obliquities. We consider the planetary instability models from Nesvorny & Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be excited when the spin-orbit resonances occur. The most notable resonances occur when the $s_7$ and $s_8$ frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter's and Saturn's spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the $s_8$ resonance. This would set strict constrains on the character of migration during the early stage. Additional effects on Jupiter's obliquity are expected during the last gasp of migration when the $s_7$ resonance was approached. The magnitude of these effects depends on the precise value of the Jupiter's precession constant. Saturn's large obliquity was likely excited by capture into the $s_8$ resonance. This probably happened during the late stage of planetary migration when the evolution of the $s_8$ frequency was very slow, and the conditions for capture into the spin-orbit resonance with $s_8$ were satisfied. However, whether or not Saturn is in the spin-orbit resonance with $s_8$ at the present time is not clear, because the existing observations of Saturn's spin precession and internal structure models have significant uncertainties.Comment: 29 pages, 8 figures, accepted for publication in The Astrophysical Journa

Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy

Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in the spherical, stationary, non-streaming Jeans equation has been handled by assuming a mass profile and fitting models to the observed kinematical data. Here, the opposite approach is considered: the equation of anisotropic kinematic projection is inverted for known arbitrary anisotropy to yield the space radial velocity dispersion profile in terms of an integral involving the radial profiles of anisotropy and isotropic dynamical pressure. Then, through the Jeans equation, the mass profile is derived in terms of double integrals of observable quantities. Single integral formulas for both deprojection and mass inversion are provided for several simple anisotropy models (isotropic, radial, circular, general constant, Osipkov-Merritt, Mamon-Lokas and Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these anisotropy models yield accurate results in the case of perfect observational data, and typically better than 70% (in 4 cases out of 5) accurate mass profiles for the sampling errors expected from current observational data on clusters of galaxies. For the NFW model with mildly increasing radial anisotropy, the mass is found to be insensitive to the adopted anisotropy profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii. This anisotropic mass inversion method is a useful complementary tool to analyze the mass and anisotropy profiles of spherical systems. It provides the practical means to lift the MAD in quasi-spherical systems such as globular clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and clusters of galaxies, when the anisotropy of the tracer is expected to be linearly related to the slope of its density.Comment: Accepted in MNRAS. 19 pages. Minor changes from previous version: Table 1 of nomenclature, some math simplifications, paragraph in Discussion on alternative deprojection method by deconvolution. 19 pages. 6 figure

AMD-stability in presence of first order Mean Motion Resonances

The AMD-stability criterion allows to discriminate between a-priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the Angular Momentum Deficit (AMD) in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopeadia.Comment: Accepted by A and A 07/10/1

High inclination orbits in the secular quadrupolar three-body problem

The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which correspond to the population of stable particles that Verrier & Evans (2008,2009) find in stable, high inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high inclination equilibria in the non restricted case.Comment: 11 pages, 6 figures. Accepted by MNRAS 2009 September 1