Hypocoercivity of linear kinetic equations via Harris's Theorem

We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole space $(x,v) \in \mathbb{R}^d \times \mathbb{R}^d$ with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively $L^1$ or weighted $L^1$ norms). The convergence rates are exponential when the equations are posed on the torus, or with a confining potential growing at least quadratically at infinity. Moreover, we give algebraic convergence rates when subquadratic potentials considered. We use a method from the theory of Markov processes known as Harris's Theorem

A deep search for the host galaxies of GRBs with no detected optical afterglow

Gamma-Ray Bursts can provide information about star formation at high redshifts. Even in the absence of a optical/near-infrared/radio afterglow, the high detection rate of X-ray afterglows by swift/XRT and its localization precision of 2-3 arcsec facilitates the identification and study of GRB host galaxies. We focus on the search for the host galaxies of a sample of 17 bursts with XRT error circles but no detected long-wavelength afterglow. Three of these events can also be classified as truly dark bursts: the observed upper limit on the optical flux of the afterglow was less than expected based on the X-ray flux. Our study is based on deep R and K-band observations performed with ESO/VLT instruments, supported by GROND and NEWFIRM. To be conservative, we searched for host galaxies in an area with a radius twice the 90% swift/XRT error circle. For 15 of the 17 bursts we find at least one galaxy inside the doubled XRT error circle. In seven cases we discover extremely red objects in the error circles. The most remarkable case is the host of GRB 080207 which as a colour of R-K~4.7 mag (AB), one of the reddest galaxies ever associated with a GRB. As a by-product of our study we identify the optical afterglow of GRB 070517A. Optically dim afterglows result from cosmological Lyman drop out and dust extinction, but the former process is only equired for a minority of cases (<1/3). Extinction by dust in the host galaxies might explain all other events. Thereby, a seemingly non-negligible fraction of these hosts are globally dust-enshrouded, extremely red galaxies. This suggests that bursts with optically dim afterglows trace a subpopulation of massive starburst galaxies, which are markedly different from the main body of the GRB host galaxy population, namely the blue, subluminous, compact galaxies.Comment: 29 pages, 31 figures, accepted for publication in A&

GRB 071028B, a burst behind large amounts of dust in an unabsorbed galaxy

We report on the discovery and properties of the fading afterglow and underlying host galaxy of GRB 071028B, thereby facilitating a detailed comparison between these two. Observations were performed with the Gamma-ray Burst Optical and Near-infrared Detector at the 2.2 m telescope on the La Silla Paranal Observatory in Chile. We conducted five observations from 1.9 d to 227.2 d after the trigger and obtained deep images in the g'r'i'z' and JHKs bands. Based on accurate seven-channel photometry covering the optical to near-infrared wavelength range, we derive a photometric redshift of z = 0.94 +0.05 -0.10 for the unabsorbed host galaxy of GRB 071028B. In contrast, we show that the afterglow with an intrinsic extinction of AV(SB) = (0.70 +/- 0.11) mag is moderately absorbed and requires a relatively flat extinction curve. According to the reported Swift/BAT observations, the energetics yield an isotropic energy release of E(gamma,iso.,rest) = (1.4 +2.4 -0.7) x 10^51 erg.Comment: 8 pages, 5 figures, accepted for publication in A&

On the nature of the extremely fast optical rebrightening of the afterglow of GRB 081029

Context. After the launch of the Swift satellite, the Gamma-Ray Burst (GRB) optical light-curve smoothness paradigm has been questioned thanks to the faster and better sampled optical follow-up, which has unveiled a very complex behaviour. This complexity is triggering the interest of the whole GRB community. The GROND multi-channel imager is used to study optical and near-infrared (NIR) afterglows of GRBs with unprecedented optical and near-infrared temporal and spectral resolution. The GRB 081029 has a very prominent optical rebrightening event and is an outstanding example of the application of the multi-channel imager to GRB afterglows. Aims. Here we exploit the rich GROND multi-colour follow-up of GRB 081029 combined with XRT observations to study the nature of late-time rebrightenings that appear in the optical-NIR light-curves of some GRB afterglows. Methods. We analyse the optical and NIR observations obtained with the seven-channel Gamma-Ray burst Optical and Near-infrared Detector (GROND) at the 2.2 m MPI/ESO telescope and the X-ray data obtained with the XRT telescope on board the Swift observatory. The multi-wavelength temporal and spectral evolution is discussed in the framework of different physical models. Results. The extremely steep optical and NIR rebrightening observed in GRB 081029 cannot be explained in the framework of the standard forward shock afterglow model. The absence of a contemporaneous X-ray rebrightening and the evidence of a strong spectral evolution in the optical-NIR bands during the rise suggest two separate components that dominate in the early and late-time lightcurves, respectively. The steepness of the optical rise cannot be explained even in the framework of the alternative scenarios proposed in the literature unless a late-time activity of the central engine is assumed.Comment: 9 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

A photometric redshift of z=1.8−0.3+0.4z=1.8^{+0.4}_{-0.3} for the \agile GRB 080514B

Aims: The AGILE gamma-ray burst GRB 080514B is the first burst with detected emission above 30 MeV and an optical afterglow. However, no spectroscopic redshift for this burst is known. Methods: We compiled ground-based photometric optical/NIR and millimeter data from several observatories, including the multi-channel imager GROND, as well as ultraviolet \swift UVOT and X-ray XRT observations. The spectral energy distribution of the optical/NIR afterglow shows a sharp drop in the \swift UVOT UV filters that can be utilized for the estimation of a redshift. Results: Fitting the SED from the \swift UVOT $uvw2$ band to the $H$ band, we estimate a photometric redshift of $z=1.8^{+0.4}_{-0.3}$, consistent with the pseudo redshift reported by Pelangeon & Atteia (2008) based on the gamma-ray data. Conclusions: The afterglow properties of GRB 080514B do not differ from those exhibited by the global sample of long bursts, supporting the view that afterglow properties are basically independent of prompt emission properties.Comment: submitted to A&A letter

CHANDRA Detection of 16 New X-Ray Sources

We have detected 18 sources over 6 sigma threshold within two regions 8.3X16.9 arcmin^2 and 8.3X33.6 arcmin^2 in the vicinity of the point with alpha=03h31m02.45s (J2000) and delta=+43degree47arcmin58.5arcsec (J2000) using a CHANDRA ACIS (S+I) observation. Two of the sources were detected before with $ROSAT$ HRI and one source could be closely identified with a star in the optical catalog, USNO A-2. We have also studied source spectra applying four spectral models to the data. Most of the sources can be classified as Cataclysmic Variable, Low Mass X-ray Binary or single star candidates due to their spectral characteristics and luminosities. We also searched for the extragalactic origin for these 18 sources. The source count rates vary between 5.8X10^{-4}- 4.7X10^{-3} counts/s. Due to low count rates temporal characteristics of the sources can not be studied effectively.Comment: 7 pages, 1 figures, accepted to Astronomy and Astrophysic

Hypocoercivity of linear kinetic equations via Harris's Theorem

We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus (x,v)∈Td×Rd or on the whole space (x,v)∈Rd×Rd with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively L1 or weightedL1 norms). The convergence rates are exponential when the equations are posed on the torus, or with a confining potential growing at least quadratically at infinity. Moreover, we give algebraic convergence rates when subquadratic potentials considered. We use a method from the theory of Markov processes known as Harris's Theorem

A quiescent galaxy at the position of the long GRB 050219A

Long-duration gamma-ray bursts (LGRBs) are produced by the collapse of very massive stars. Due to the short lifetime of their progenitors, LGRBs pinpoint star-forming galaxies. We present here a multi-band search for the host galaxy of the long dark GRB 050219A within the enhanced Swift/XRT error circle. We used spectroscopic observations acquired with VLT/X-shooter to determine the redshift and star-formation rate of the putative host galaxy. We compared the results with the optical/IR spectral energy distribution obtained with different facilities. Surprisingly, the host galaxy is a old and quiescent early-type galaxy at z = 0.211 characterised by an unprecedentedly low specific star-formation rate. It is the first LGRB host to be also an early-type post-starburst galaxy. This is further evidence that GRBs can explode in all kind of galaxies, with the only requirement being an episode of star-formation.Comment: 11 pages, 10 figures, 3 tables; accepted for publication in Astronomy & Astrophysic

A strong optical flare before the rising afterglow of GRB 080129

We report on GROND observations of a 40 sec duration (rest-frame) optical flare from GRB 080129 at redshift 4.349. The rise- and decay time follow a power law with indices +12 and -8, respectively, inconsistent with a reverse shock and a factor 10$^5$ faster than variability caused by ISM interaction. While optical flares have been seen in the past (e.g. GRB 990123, 041219B, 060111B and 080319B), for the first time, our observations not only resolve the optical flare into sub-components, but also provide a spectral energy distribution from the optical to the near-infrared once every minute. The delay of the flare relative to the GRB, its spectral energy distribution as well as the ratio of pulse widths suggest it to arise from residual collisions in GRB outflows \cite{liw08}.If this interpretation is correct and can be supported by more detailed modelling or observation in further GRBs, the delay measurement provides an independent, determination of the Lorentz factor of the outflow.Comment: accepted for publ. in ApJ, 5 Fig