Prasenjit Saha

Symplectic integrators for solar system dynamics

Many problems in solar system dynamics are described by Hamiltonians of the form H = H(Kep) + eH(pert) , E 1, where H(Kep) is the usual Hamiltonian for the Kepler two-body problem and eH(pert) represents (for example) much weaker perturbations from the planets. We review symplectic integrators for Hamiltonians of this kind, focusing on methods that exploit the integrability of H(Kep). It is shown that the long-term errors in these integrators can be reduced by a factor of order e by suitable starting procedures, for example, by starting with a very small stepsize and gradually increasing the stepsize to its final value

The behaviour of dark matter associated with four bright cluster galaxies in the 10 kpc core of Abell 3827

Galaxy cluster Abell 3827 hosts the stellar remnants of four almost equally bright elliptical galaxies within a core of radius 10 kpc. Such corrugation of the stellar distribution is very rare, and suggests recent formation by several simultaneous mergers. We map the distribution of associated dark matter, using new Hubble Space Telescope imaging and Very Large Telescope/Multi-Unit Spectroscopic Explorer integral field spectroscopy of a gravitationally lensed system threaded through the cluster core. We find that each of the central galaxies retains a dark matter halo, but that (at least) one of these is spatially offset from its stars. The best-constrained offset is 1.62(-0.49)(+0.47) kpc, where the 68 per cent confidence limit includes both statistical error and systematic biases in mass modelling. Such offsets are not seen in field galaxies, but are predicted during the long infall to a cluster, if dark matter self-interactions generate an extra drag force. With such a small physical separation, it is difficult to definitively rule out astrophysical effects operating exclusively in dense cluster core environments - but if interpreted solely as evidence for self-interacting dark matter, this offset implies a cross-section sigma(DM)/(m) similar to (1.7 +/- 0.7) x 10(-4) cm(2) g(-1) x (t(infall)/10(9) yr)(-2), where t(infall) is the infall duration.

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement. Our results show that for a primary black hole mass of ∼ 1.0 6 -10 7 M ○. , the black hole mass-ratio q > 10 -2 , cusp size ∼1 pc, the tidal disruption rate can be as large as ∼10 -2 -1 M ○. yr -1 . This is at least 10 2 -10 4 times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10 5 yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses - IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223

We present accurate time delays for the quadruply imaged quasar HE 0435-1223. The delays were measured from 575 independent photometric points obtained in the R-band between January 2004 and March 2010. With seven years of data, we clearly show that quasar image A is affected by strong microlensing variations and that the time delays are best expressed relative to quasar image B. We measured ΔtBC = 7.8 ± 0.8 days, ΔtBD = -6.5 ± 0.7 days and ΔtCD = -14.3 ± 0.8 days. We spacially deconvolved HST NICMOS2 F160W images to derive accurate astrometry of the quasar images and to infer the light profile of the lensing galaxy. We combined these images with a stellar population fitting of a deep VLT spectrum of the lensing galaxy to estimate the baryonic fraction, fb, in the Einstein radius. We measured fb = 0.65-0.10+0.13 if the lensing galaxy has a Salpeter IMF and fb = 0.45-0.07+0.04 if it has a Kroupa IMF. The spectrum also allowed us to estimate the velocity dispersion of the lensing galaxy, σap = 222 ± 34 km s-1. We used fb and σap to constrain an analytical model of the lensing galaxy composed of an Hernquist plus generalized NFW profile. We solved the Jeans equations numerically for the model and explored the parameter space under the additional requirement that the model must predict the correct astrometry for the quasar images. Given the current error bars on fb and σap, we did not constrain H0 yet with high accuracy, i.e., we found a broad range of models with χ2 < 1. However, narrowing this range is possible, provided a better velocity dispersion measurement becomes available. In addition, increasing the depth of the current HST imaging data of HE 0435-1223 will allow us to combine ourconstraints with lens reconstruction techniques that make use of the full Einstein ring that is visible in this object. Based on observations made with the 1.2 m Euler Swiss Telescope, the 1.5 m telescope of Maidanak Observatory in Uzbekistan, and with the 1.2 m Mercator Telescope, operated on the island of La Palma by the Flemish Community, at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. The NASA/ESA Hubble Space Telescope data was obtained from the data archive at the Space Telescope Science Institute, which is operated by AURA, the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS-5-26555.Light curves are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/536/A53

Long-term planetary integration with individual time steps

We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are

Non-parametric reconstruction of the galaxy lens in PG 1115 + 080

O(\epsilon\Omega^2\tau^2)

Pixelated Lenses and H0 from Time-Delay Quasars

where

Stellar and total mass in early-type lensing galaxies

\tau

A Portable Modeler of Lensed Quasars

is the timestep,

The Hubble Time Inferred from 10 Time Delay Lenses

\Omega