Non-colliding Brownian Motions and the extended tacnode process

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded and many typos correcte

Multi-wavelength observations of 3FGL J2039.6-5618: a candidate redback millisecond pulsar

We present multi-wavelength observations of the unassociated gamma-ray source 3FGL J2039.6-5618 detected by the Fermi Large Area Telescope. The source gamma-ray properties suggest that it is a pulsar, most likely a millisecond pulsar, for which neither radio nor $\gamma$-ray pulsations have been detected yet. We observed 3FGL J2039.6-5618 with XMM-Newton and discovered several candidate X-ray counterparts within/close to the gamma-ray error box. The brightest of these X-ray sources is variable with a period of 0.2245$\pm$0.0081 d. Its X-ray spectrum can be described by a power law with photon index $\Gamma_X =1.36\pm0.09$, and hydrogen column density $N_{\rm H} < 4 \times 10^{20}$ cm$^{-2}$, which gives an unabsorbed 0.3--10 keV X-ray flux of $1.02 \times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. Observations with the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND) discovered an optical counterpart to this X-ray source, with a time-average magnitude $g'\sim 19.5$. The counterpart features a flux modulation with a period of 0.22748$\pm$0.00043 d that coincides, within the errors, with that of the X-ray source, confirming the association based on the positional coincidence. We interpret the observed X-ray/optical periodicity as the orbital period of a close binary system where one of the two members is a neutron star. The light curve profile of the companion star, with two asymmetric peaks, suggests that the optical emission comes from two regions at different temperatures on its tidally-distorted surface. Based upon its X-ray and optical properties, we consider this source as the most likely X-ray counterpart to 3FGL J2039.6-5618, which we propose to be a new redback system.Comment: 35 pages, 8 figures, accepted for publication on Astrophysical Journa

Correlation between the optical veiling and accretion properties: A case study of the classical T Tauri star DK Tau

Classical T Tauri stars (cTTs) accrete from their circumstellar disk. The material falls onto the stellar surface, producing an accretion shock, which generates veiling in a star's spectra. In addition, the shock causes a localized accretion spot at the level of the chromosphere. Our goal is to investigate the accretion, particularly the mass accretion rates (Macc), for the cTTs DK Tau, over two periods of 17 and 29 days, using two different procedures for comparison purposes. The first method relies on the derivation of the accretion luminosity via accretion-powered emission lines. The second compares the variability of the optical veiling with accretion shock models to determine mass accretion rates. We used observations taken in 2010 and 2012 with the ESPaDOnS spectropolarimeter at the CFHT. We find peak values of the veiling (at 550 nm) ranging from 0.2 to 1.3, with a steeper trend across the wavelength range for higher peak values. When using the accretion-powered emission lines, we find mass accretion rate values ranging from log(Macc[Msol/yr]) = -8.20 to log(Macc[Msol/yr]) = -7.40. This agrees with the values found in the literature, as well as the values calculated using the accretion shock models and the veiling. In addition, we identify a power-law correlation between the values of the accretion luminosity and the optical veiling. For the 2010 observations, using the values of the filling factors (which represent the area of the star covered by an accretion spot) derived from the shock models, we infer that the accretion spot was located between +45 degrees and +75 degrees in latitude. We show that both methods of determining the mass accretion rate yield similar results. We also present a helpful means of confirming the accretion luminosity values by measuring the veiling at a single wavelength in the optical

Non-intersecting squared Bessel paths at a hard-edge tacnode

The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of $n$ non-intersecting squared Bessel paths, with all paths starting at the same point $a>0$ at time $t=0$ and ending at the same point $b>0$ at time $t=1$. Our interest lies in the critical regime $ab=1/4$, for which the paths are tangent to the hard edge at the origin at a critical time $t^*\in (0,1)$. The critical behavior of the paths for $n\to\infty$ is studied in a scaling limit with time $t=t^*+O(n^{-1/3})$ and temperature $T=1+O(n^{-2/3})$. This leads to a critical correlation kernel that is defined via a new Riemann-Hilbert problem of size $4\times 4$. The Riemann-Hilbert problem gives rise to a new Lax pair representation for the Hastings-McLeod solution to the inhomogeneous Painlev\'e II equation $q"(x) = xq(x)+2q^3(x)-\nu,$ where $\nu=\alpha+1/2$ with $\alpha>-1$ the parameter of the squared Bessel process. These results extend our recent work with Kuijlaars and Zhang \cite{DKZ} for the homogeneous case $\nu = 0$.Comment: 54 pages, 13 figures. Corrected error in Theorem 2.

Super-solar metallicity at the position of the ultra-long GRB130925A

Over the last decade there has been immense progress in the follow-up of short and long GRBs, resulting in a significant rise in the detection rate of X-ray and optical afterglows, in the determination of GRB redshifts, and of the identification of the underlying host galaxies. Nevertheless, our theoretical understanding on the progenitors and central engines powering these vast explosions is lagging behind, and a newly identified class of `ultra-long' GRBs has fuelled speculation on the existence of a new channel of GRB formation. In this paper we present high signal-to-noise X-shooter observations of the host galaxy of GRB130925A, which is the fourth unambiguously identified ultra-long GRB, with prompt gamma-ray emission detected for ~20ks. The GRB line of sight was close to the host galaxy nucleus, and our spectroscopic observations cover both this region along the bulge/disk of the galaxy, in addition to a bright star-forming region within the outskirts of the galaxy. From our broad wavelength coverage we obtain accurate metallicity and dust-extinction measurements at both the galaxy nucleus, and an outer star-forming region, and measure a super-solar metallicity at both locations, placing this galaxy within the 10-20% most metal-rich GRB host galaxies. Such a high metal enrichment has implications on the progenitor models of both long and ultra-long GRBs, although the edge-on orientation of the host galaxy does not allow us to rule out a large metallicity variation along our line of sight. The spatially resolved spectroscopic data presented in this paper offer important insight into variations in the metal and dust abundance within GRB host galaxies. They also illustrate the need for IFU observations on a larger sample of GRB host galaxies at varies metallicities to provide a more quantitative view on the relation between the GRB circumburst and the galaxy-whole properties.Comment: 9 pages, 3 figures, A&A in press, matches published versio

High birthweights among infants of north African immigrants in Belgium.

OBJECTIVES: This study examined birthweights of North African immigrants in Belgium. METHODS: Analyses focused on Belgian single live birth certificates from 1981 to 1988. RESULTS: Low-birthweight (< 2500 g) rates were 3.1% among 34,686 newborns of North African origin and 4.8% among 804,286 newborns of Belgian origin. The entire North African birthweight distribution was shifted toward higher birthweights than the Belgian distribution. Low frequencies of low birthweights among North Africans were still observed after marital status, occupation of the father, and parity had been taken into account. CONCLUSIONS: Despite their low socioeconomic status, North African immigrants have high birthweights

Non-intersecting squared Bessel paths: critical time and double scaling limit

We consider the double scaling limit for a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t=0$ at the same positive value $x=a$, remain positive, and are conditioned to end at time $t=1$ at $x=0$. After appropriate rescaling, the paths fill a region in the $tx$--plane as $n\to \infty$ that intersects the hard edge at $x=0$ at a critical time $t=t^{*}$. In a previous paper (arXiv:0712.1333), the scaling limits for the positions of the paths at time $t\neq t^{*}$ were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as $n\to \infty$ of the correlation kernel at critical time $t^{*}$ and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections with the Pearcey kernel. The analysis is based on the study of a $3\times 3$ matrix valued Riemann-Hilbert problem by the Deift-Zhou steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions of a particular third-order linear differential equation, and its matching with a global parametrix.Comment: 53 pages, 15 figure

Intramontane lacustrine basins in the Siberian Altai: recorders of Cenozoic intracontinental tectonic and climatic events

The Altai Mountains are part of the vast intracontinental Central Asian orogenic system that formed during the Cenozoic as a distal effect of continued indentation of the Indian plate into the Eurasian continent. In the Siberian part of the Altai Mountains there is ample evidence to suggest that the pre-Cenozoic structural fabric of its basement is a controlling factor in the Cenozoic deformation and development of this intracontinental orogen. We give evidence that important Paleozoic fault zones were reactivated during the Cenozoic, particularly the Late Cenozoic and play a key role in the formation, evolution and current morphology of the Siberian Altai Mountains. Some of these faults are still active and recent and historic movements along them have triggered large seismic events. Late Cenozoic reactivation was expressed as pure thrust, oblique thrust to pure strike-slip faulting, resulting in an overall transpressive tectonic regime. In some cases, as for the graben basin of Lake Teletskoye, local, pure extensional stresses are responsible for its formation as we show in this contribution. Various other intramontane, tectonic basins developed. Some of these are very recent structures (the Teletskoye Basin) and are Pleistocene in age or younger, others have a prolonged history and contain a relatively complete Cenozoic sedimentary section, with evidence of Late Mesozoic precursor basins (Chuya Basin, Dzhulukul Basin). Some of these exhibit indications of marine incursions, but the basins are predominantly continental. The development of these basins is clearly associated with the location and Cenozoic reactivation of aforementioned long-lived fault zones in the Altai tectonic assemblage. Many of these basins accommodated fresh water lakes during their evolution and some are still the site of contemporary mountain lakes. Their stratigraphy, as well as the sedimentary architecture and basin morphology is manifestly influenced by and progresses with the stages of (Late) Cenozoic intracontinental mountain building and erosive denudation of the growing mountain ranges. Together with the clastic sedimentary input and the provenance characteristics, the intramontane Altai basin deposits are affected by evolving climatic conditions. These conditions dictate the main mode of erosion and transport, influence the sedimentary facies and supply rate and create the framework for a specific biocoenosis signature found in the fossil record. Our contribution reviews the data obtained over the last years from a selection of intramontane lacustrine basins in the Siberian Altai Mountains. We direct our attention in particular to the Teletskoye basin, the Chuya-Kurai Basin and the Dzhulukul Basin. We combine sedimentologic-stratigraphic data with basin architecture and morphology, and with basement geochronologic-thermochronologic constraints (apatite fission-track, U/Pb and Ar-dating) in order to show the potential of these basins as recorders of Cenozoic tectonic and climatic events in relation with basement features. While for example the data obtained from the Chuya Basin yields a continuous Cenozoic picture of deformation and climatic evolution of the Altai area, data from the Teletskoye Basin zooms in with higher resolution on the Pleistocene to Recent history. In general, all data point towards intensifying tectonic reactivation and mountain building of the Siberian Altai Mountains since the Middle Cenozoic, with clear peak activity in the Pliocene to Recent. This is demonstrated by the molassetype deposits in these basins, and by thermochronologic constraints. This activity is ongoing and structural, (paleo)seismic, geomorphologic and sedimentologic data corroborates this. The lacustrine Altai basins provide a record for a more or less continuous progressive cooling and aridification of the Altai area during the Cenozoic as manifested in the pollen fossil assemblages found in the Altai sediments