Search

We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$ of finite Lebesgue measure $0<|\Omega|<\infty$ with a real-valued, non-negative, measurable potential $V.$ We investigate the efficiency and the phenomenon of localisation for the torsion function, and their interplay with the geometry of the first Dirichlet eigenfunction., Comment: 33 pages. The published version in Potential Analysis (2022) 57, 571--600 has some typos: Theorem 3(i): the first exponent should read $(m-2)/m$; Example 2 Line 2: .... $B(p_{n+1};cn^{-\beta})$.....; Formula (109): $\kappa^{-1}$ missing after the second inequality

The dynamical production of low-mass X-ray binaries and brighter cataclysmic variables (CVs) in dense globular clusters is well-established. We investigate how the X-ray emissivity of fainter X-ray binaries (principally CVs and coronally active binaries) varies between different environments. We compile calculations (largely from the literature) of the X-ray emissivity of old stellar populations, including open and globular clusters and several galaxies. We investigate three literature claims of unusual X-ray sources in low-density stellar populations. We show that a suggested quiescent neutron star in the open cluster NGC 6819 is a foreground M dwarf. We show that the suggested diffuse X-ray emission from an old nova shell in the globular cluster NGC 6366 is actually a background galaxy cluster. And we show that a suggested population of quiescent X-ray binaries in the Sculptor Dwarf Galaxy is mostly (perhaps entirely) background galaxies. We find that above densities of $10^4$ M$_{\odot}$/pc$^3$, the X-ray emissivity of globular clusters increases, due to dynamical production of X-ray emitting systems. Below this density, globular clusters have lower X-ray emissivity than the other populations, and we do not see a strong dependence of X-ray emissivity due to density effects. We find significant correlations between X-ray emissivity and binary fraction, metallicity, and density. Sampling these fits via bootstrap techniques gives less significant correlations, but confirms the effect of metallicity on low-density populations, and that of density on the full globular cluster sample., Comment: 28 pages, 23 figures. MNRAS, in press

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp., Comment: 12 pages, 4 figures

To confirm the nature of the donor star in the ultra-compact X-ray binary candidate 47 Tuc X9, we obtained optical spectra (3,000$-$10,000 {\AA}) with the Hubble Space Telescope / Space Telescope Imaging Spectrograph. We find no strong emission or absorption features in the spectrum of X9. In particular, we place $3\sigma$ upper limits on the H$\alpha$ and HeII $\lambda 4686$ emission line equivalent widths $-$EW$_{\mathrm{H\alpha}} \lesssim 14$ {\AA} and $-$EW$_{\mathrm{HeII}} \lesssim 9$ {\AA}, respectively. This is much lower than seen for typical X-ray binaries at a similar X-ray luminosity (which, for $L_{\mathrm{2-10 keV}} \approx 10^{33}-10^{34}$ erg s$^{-1}$ is typically $-$EW$_{\mathrm{H\alpha}} \sim 50$ {\AA}). This supports our previous suggestion (by Bahramian et al.) of an H-poor donor in X9. We perform timing analysis on archival far-ultraviolet, $V$ and $I$-band data to search for periodicities. In the optical bands we recover the seven-day superorbital period initially discovered in X-rays, but we do not recover the orbital period. In the far-ultraviolet we find evidence for a 27.2 min period (shorter than the 28.2 min period seen in X-rays). We find that either a neutron star or black hole could explain the observed properties of X9. We also perform binary evolution calculations, showing that the formation of an initial black hole / He-star binary early in the life of a globular cluster could evolve into a present-day system such as X9 (should the compact object in this system indeed be a black hole) via mass-transfer driven by gravitational wave radiation., Comment: 20 pages, 12 figures. Accepted for publication in MNRAS

We obtain bounds for the expected loss of torsional rigidity of a cylinder $\Omega_L=(-L/2,L/2) \times \Omega\subset \R^3$ of length $L$ due to a Brownian fracture that starts at a random point in $\Omega_L,$ and runs until the first time it exits $\Omega_L$. These bounds are expressed in terms of the geometry of the cross-section $\Omega \subset \R^2$. It is shown that if $\Omega$ is a disc with radius $R$, then in the limit as $L \rightarrow \infty$ the expected loss of torsional rigidity equals $cR^5$ for some $c\in (0,\infty)$. We derive bounds for $c$ in terms of the expected Newtonian capacity of the trace of a Brownian path that starts at the centre of a ball in $\R^3$ with radius $1,$ and runs until the first time it exits this ball., Comment: 18 pages

Multi-decade observing campaigns of the globular clusters 47 Tucanae and M15 have led to an outstanding number of discoveries. Here, we report on the latest results of the long-term observations of the pulsars in these two clusters. For most of the pulsars in 47 Tucanae we have measured, among other things, their higher-order spin period derivatives, which have in turn provided stringent constraints on the physical parameters of the cluster, such as its distance and gravitational potential. For M15, we have studied the relativistic spin precession effect in PSR B2127+11C. We have used full-Stokes observations to model the precession effect, and to constrain the system geometry. We find that the visible beam of the pulsar is swiftly moving away from our line of sight and may very soon become undetectable. On the other hand, we expect to see the opposite emission beam sometime between 2041 and 2053., Comment: 4 pages, 1 figure, accepted for publication in the proceedings of IAU Symposium 337 - Pulsar Astrophysics: The Next Fifty Years

We report mid-UV (MUV) observations taken with HST/WFC3, Swift/UVOT and GALEX/NUV of the transitional millisecond pulsars XSS J12270-4859 and PSR J1023+0038 during their radio pulsar states. Both systems were detected in our images and showed MUV variability. At similar orbital phases, the MUV luminosities of both pulsars are comparable. This suggests that the emission processes involved in both objects are similar. We estimated limits on the mass ratio, companion's temperature, inclination, and distance to XSS J12270-4859 by using a Markov Chain Monte Carlo algorithm to fit published folded optical light curves. Using the resulting parameters, we modeled MUV light curves in our HST filters. The resulting models failed to fit our MUV observations. Fixing the mass ratio of XSS J12270-4859 to the value reported in other studies, we obtained a distance of ~3.2 kpc. This is larger than the one derived from radio measurements (~1.4 kpc). Assuming a uniform prior for the mass ratio, the distance is similar to that from radio measurements. However, it requires an undermassive companion (~0.01 M_sun). We conclude that a direct heating model alone can not fully explain the observations in optical and MUV. Therefore, an additional radiation source is needed. The source could be an intrabinary shock which contributes to the MUV flux and likely to the optical one as well. During the radio pulsar state, the MUV orbital variations of PSR J1023+0038 detected with GALEX, suggests the presence of an asymmetric intrabinary shock., Comment: Accepted for publication in MNRAS. 16 pages, 10 figures, 2 tables. Minor changes with respect to previous arXiv version

We present 22 new (+3 confirmed) cataclysmic variables (CVs) in the non core-collapsed globular cluster 47 Tucanae (47 Tuc). The total number of CVs in the cluster is now 43, the largest sample in any globular cluster so far. For the identifications we used near-ultraviolet (NUV) and optical images from the Hubble Space Telescope, in combination with X-ray results from the Chandra X-ray Observatory. This allowed us to build the deepest NUV CV luminosity function of the cluster to date. We found that the CVs in 47 Tuc are more concentrated towards the cluster center than the main sequence turnoff stars. We compared our results to the CV populations of the core-collapsed globular clusters NGC 6397 and NGC 6752. We found that 47 Tuc has fewer bright CVs per unit mass than those two other clusters. That suggests that dynamical interactions in core-collapsed clusters play a major role creating new CVs. In 47 Tuc, the CV population is probably dominated by primordial and old dynamically formed systems. We estimated that the CVs in 47 Tuc have total masses of approx. 1.4 M_sun. We also found that the X-ray luminosity function of the CVs in the three clusters is bimodal. Additionally, we discuss a possible double degenerate system and an intriguing/unclassified object. Finally, we present four systems that could be millisecond pulsar companions given their X-ray and NUV/optical colors. For one of them we present very strong evidence for being an ablated companion. The other three could be CO- or He-WDs., Comment: Published on MNRAS. 31 Pages, 23 Figures, 5 Tables. Minor changes with respect to previous arXiv version

For the past couple of decades, the Parkes radio telescope has been regularly observing the millisecond pulsars in 47 Tucanae (47 Tuc). This long-term timing program was designed to address a wide range of scientific issues related to these pulsars and the globular cluster where they are located. In this paper, the first of a series, we address one of these objectives: the characterization of four previously known binary pulsars for which no precise orbital parameters were known, namely 47 Tuc P, V, W and X (pulsars 47 Tuc R and Y are discussed elsewhere). We determined the previously unknown orbital parameters of 47 Tuc V and X and greatly improved those of 47 Tuc P and W. For pulsars W and X we obtained, for the first time, full coherent timing solutions across the whole data span, which allowed a much more detailed characterization of these systems. 47 Tuc W, a well-known tight eclipsing binary pulsar, exhibits a large orbital period variability, as expected for a system of its class. 47 Tuc X turns out to be in a wide, extremely circular, 10.9-day long binary orbit and its position is ~3.8 arcmin away from the cluster center, more than three times the distance of any other pulsar in 47 Tuc. These characteristics make 47 Tuc X a very different object with respect to the other pulsars of the cluster., Comment: Accepted for publication by MNRAS, 18 pages, 11 figures

Let $\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\Omega|$. We obtain some properties of the set function $F:\Omega\mapsto \R^+$ defined by $$ F(\Omega)=\frac{T(\Omega)\lambda_1(\Omega)}{|\Omega|} ,$$ where $T(\Omega)$ and $\lambda_1(\Omega)$ are the torsional rigidity and the first eigenvalue of the Dirichlet Laplacian respectively. We improve the classical P\'olya bound $F(\Omega)\le 1,$ and show that $$F(\Omega)\le 1- \nu_m T(\Omega)|\Omega|^{-1-\frac2m},$$ where $\nu_m$ depends only on $m$. For any $m=2,3,\dots$ and $\epsilon\in (0,1)$ we construct an open set $\Omega_{\epsilon}\subset \R^m$ such that $F(\Omega_{\epsilon})\ge 1-\epsilon$., Comment: 18 pages, 1 figure

We report the detection of steady radio emission from the known X-ray source X9 in the globular cluster 47 Tuc. With a double-peaked C IV emission line in its ultraviolet spectrum providing a clear signature of accretion, this source had been previously classified as a cataclysmic variable. In deep ATCA imaging from 2010 and 2013, we identified a steady radio source at both 5.5 and 9.0 GHz, with a radio spectral index (defined as $S_{\nu}\propto\nu^{\alpha}$) of $\alpha=-0.4\pm0.4$. Our measured flux density of $42\pm4$ microJy/beam at 5.5 GHz implies a radio luminosity ($\nu L_{\nu}$) of 5.8e27 erg/s, significantly higher than any previous radio detection of an accreting white dwarf. Transitional millisecond pulsars, which have the highest radio-to-X-ray flux ratios among accreting neutron stars (still a factor of a few below accreting black holes at the same X-ray luminosity), show distinctly different patterns of X-ray and radio variability than X9. When combined with archival X-ray measurements, our radio detection places 47 Tuc X9 very close to the radio/X-ray correlation for accreting black holes, and we explore the possibility that this source is instead a quiescent stellar-mass black hole X-ray binary. The nature of the donor star is uncertain; although the luminosity of the optical counterpart is consistent with a low-mass main sequence donor star, the mass transfer rate required to produce the high quiescent X-ray luminosity of 1e33 erg/s suggests the system may instead be ultracompact, with an orbital period of order 25 minutes. This is the fourth quiescent black hole candidate discovered to date in a Galactic globular cluster, and the only one with a confirmed accretion signature from its optical/ultraviolet spectrum., Comment: 15 pages, 6 figures, accepted for publication in MNRAS

We report the discovery of the likely white dwarf companions to radio millisecond pulsars 47 Tuc Q and 47 Tuc S in the globular cluster 47 Tucanae. These blue stars were found in near-ultraviolet images from the Hubble Space Telescope for which we derived accurate absolute astrometry, and are located at positions consistent with the radio coordinates to within 0.016 arcsec (0.2sigma). We present near-ultraviolet and optical colours for the previously identified companion to millisecond pulsar 47 Tuc U, and we unambiguously confirm the tentative prior identifications of the optical counterparts to 47 Tuc T and 47 Tuc Y. For the latter, we present its radio-timing solution for the first time. We find that all five near-ultraviolet counterparts have U300-B390 colours that are consistent with He white dwarf cooling models for masses ~0.16-0.3 Msun and cooling ages within ~0.1-6 Gyr. The Ha-R625 colours of 47 Tuc U and 47 Tuc T indicate the presence of a strong Ha absorption line, as expected for white dwarfs with an H envelope., Comment: Accepted for publication on MNRAS. 12 pages, 5 figures, 3 tables

We present the results of a photometric search for variable stars in the core of the Galactic globular cluster M4. The input data are a large and unprecedented set of deep Hubble Space Telescope WFC3 images (large program GO-12911; 120 orbits allocated), primarily aimed at probing binaries with massive companions by detecting their astrometric wobbles. Though these data were not optimised to carry out a time-resolved photometric survey, their exquisite precision, spatial resolution and dynamic range enabled us to firmly detect 38 variable stars, of which 20 were previously unpublished. They include 19 cluster-member eclipsing binaries (confirming the large binary fraction of M4), RR Lyrae, and objects with known X-ray counterparts. We improved and revised the parameters of some among published variables., Comment: 11 pages, 5 figures, 2 tables. Accepted for publication in MNRAS

Results are obtained for two minimization problems: $$I_k(c)=\inf \{\lambda_k(\Omega): \Omega\ \textup{open, convex in}\ \mathbb{R}^m,\ \mathcal{T}(\Omega)= c \},$$ and $$J_k(c)=\inf\{\lambda_k(\Omega): \Omega\ \textup{quasi-open in}\ \mathbb{R}^m, |\Omega|\le 1, \mathcal {P}(\Omega)\le c \},$$ where $c>0$, $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, $|\Omega|$ denotes the Lebesgue measure of $\Omega$, $\mathcal{P}(\Omega)$ denotes the perimeter of $\Omega$, and where $\mathcal{T}$ is in a suitable class set functions. The latter include for example the perimeter of $\Omega$, and the moment of inertia of $\Omega$ with respect to its center of mass., Comment: 15 pages

Let (M,g) be a compact Riemannian manifold without boundary. Let D be a compact subdomain of M with smooth boundary. We examine the heat content asymptotics for the heat flow from D into M where both the initial temperature and the specific heat are permitted to have controlled singularities on the boundary of D. The operator driving the heat process is assumed to be an operator of Laplace type

The M4 Core Project with HST is designed to exploit the Hubble Space Telescope to investigate the central regions of M4, the Globular Cluster closest to the Sun. In this paper we combine optical and near-infrared photometry to study multiple stellar populations in M4. We detected two sequences of M-dwarfs containing ~38% (MS_I) and ~62% (MS_II) of MS stars below the main-sequence (MS) knee. We compare our observations with those of NGC2808, which is the only other GCs where multiple MSs of very low-mass stars have been studied to date. We calculate synthetic spectra for M-dwarfs, assuming the chemical composition mixture inferred from spectroscopic studies of stellar populations along the red giant branch, and different Helium abundances, and we compare predicted and observed colors. Observations are consistent with two populations, one with primordial abundance and another with enhanced nitrogen and depleted oxygen., Comment: 8 pages, 6 figure, accepted for publication in MNRAS

We present an overview of the ongoing Hubble Space Telescope large program GO-12911. The program is focused on the core of M4, the nearest Galactic globular cluster, and the observations are designed to constrain the number of binaries with massive companions (black holes, neutron stars, or white dwarfs) by measuring the ``wobble'' of the luminous (main-sequence) companion around the center of mass of the pair, with an astrometric precision of ~50 micro-arcseconds. The high spatial resolution and stable medium-band PSFs of WFC3/UVIS will make these measurements possible. In this work we describe: (i) the motivation behind this study, (ii) our observing strategy, (iii) the many other investigations enabled by this unique data set, and which of those our team is conducting, and (iv) a preliminary reduction of the first-epoch data-set collected on October 10, 2012., Comment: 25 pages, 14 figures (9 at low resolution), 3 tables. Published in: Astronomische Nachrichten, Volume 334, Issue 10, pages 1062-1085, December 2013. http://onlinelibrary.wiley.com/doi/10.1002/asna.201311911/abstract

We discuss the heat content asymptotics associated with the heat flow out of a smooth compact manifold in a larger compact Riemannian manifold. Although there are no boundary conditions, the corresponding heat content asymptotics involve terms localized on the boundary. The classical pseudo-differential calculus is used to establish the existence of the complete asymptotic series and methods of invariance theory are used to determine the first few terms in the asymptotic series in terms of geometric data. The operator driving the heat process is assumed to be an operator of Laplace type.

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2} \frac{\partial u}{\partial n} + b|u|^{p-2} u =0$ on $\partial \Om$. We obtain bounds of the $L^\infty$ norm of $u$ {\it only} in terms of the bottom of the spectrum (of the Robin $p$-Laplacian), $b$ and the dimension of the space in the following two extremal cases: the linear framework (corresponding to $p=2$) and arbitrary $b>0$, and the non-linear framework (corresponding to arbitrary $p>1$) and Dirichlet boundary conditions ($b=+\infty$). In the general case, $p\not=2, p \in (1, +\infty)$ and $b>0$ our bounds involve also the Lebesgue measure of $\Om$., Comment: 19 pages

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content., Comment: 18 pages

In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$ of $\mathbb R^m\setminus \beta[0; s]$ for fixed $s$ and $m = 2,3$ in the limit $t \downarrow 0$, when $\beta[0; s]$ is kept at temperature 1 for all $t > 0$ and $\mathbb R^m\setminus \beta[0; s]$ has initial temperature 0, and (ii) the inradius of $\mathbb R^m\setminus \beta[0; s]$ for $m = 2,3,\cdots$ in the limit $s \rightarrow \infty$., Comment: 13 pages

We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings.

Using deep Chandra observations of the globular cluster M28, we study the quiescent X-ray emission of a neutron star in a low-mass X-ray binary in order to constrain the chemical composition of the neutron star atmosphere and the equation of state of dense matter. We fit the spectrum with different neutron star atmosphere models composed of hydrogen, helium or carbon. The parameter values obtained with the carbon model are unphysical and such a model can be ruled out. Hydrogen and helium models give realistic parameter values for a neutron star, and the derived mass and radius are clearly distinct depending on the composition of the atmosphere. The hydrogen model gives masses/radii consistent with the canonical values of 1.4 Msun and 10 km, and would allow for the presence of exotic matter inside neutron stars. On the other hand, the helium model provides solutions with higher masses/radii, consistent with the stiffest equations of state. Measurements of neutron star masses/radii by spectral fitting should consider the possibility of heavier element atmospheres, which produce larger masses/radii for the same data, unless the composition of the accretor is known independently., Comment: accepted for publication in MNRAS, 6 pages, 3 figures, 1 table

We study the asymptotic behaviour of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail.

We present a multi-object optical spectroscopy follow-up study of X-ray sources in a field along the Galactic Plane (l=327.42 deg, b=2.26 deg) which is part of the Chandra Multi-wavelength Plane survey (ChaMPlane). We obtained spectra for 46 stars, including 15 likely counterparts to X-ray sources, and sources showing an H-alpha color excess. This has led to the identification of a new cataclysmic variable (CV), CXOPS J154305.5-522709, also named ChaMPlane Bright Source 7 (CBS~7), and we identified 8 X-ray sources in the field as active late-type stars. CBS~7 was previously studied in X-rays and showed a hard spectrum and two periods: 1.22+/-0.08 h and 2.43+/-0.26 h. We present here clear evidence that the source is a CV through the detection of H, HeI and HeII emission lines in its optical spectrum. The hard X-ray spectrum and the presence of the HeII 4686 in emission with a large equivalent width suggest a magnetic CV. The near-infrared counterpart is significantly variable, and we found a period consistent with the longest X-ray period at 2.39+/-0.05 h but not the shortest X-ray period. If this period is the orbital period, this would place the system in the CV period gap. The possible orbital period suggests a dM4+/-1 companion star. The distance is then estimated to be ~1 kpc. The system could be a relatively hard and X-ray luminous polar or an intermediate polar, possibly nearly-synchronous., Comment: accepted for publication in ApJ; 6 figures, 5 tables, 8 pages with emulateapj style

We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth.

Dwarf novae in globular clusters seem to be rare with only 13 detections in the 157 known Galactic globular clusters. We report the identification of a new dwarf nova in M13, the 14th dwarf nova identified in a globular cluster to date. Using the 2m Faulkes Telescope North, we conducted a search for stars in M13 that show variability over a year (2005-2006) on timescales of days and months. This led to the detection of one dwarf nova showing several outbursts. A Chandra X-ray source is coincident with this dwarf nova and shows both a spectrum and variability consistent with that expected from a dwarf nova, thus supporting the identification. We searched for a counterpart in Hubble Space Telescope ACS/WFC archived images and found at least 11 candidates, of which we could characterize only the 7 brightest, including one with a 3 sigma H-alpha excess and a faint blue star. The detection of one dwarf nova when more could have been expected likely indicates that our knowledge of the global Galactic population of cataclysmic variables is too limited. The proportion of dwarf novae may be lower than found in catalogs, or they may have a much smaller duty cycle in general as proposed by some population synthesis models and recent observations in the field., Comment: Accepted for publication in ApJ, 12 pages, 12 figures, 5 tables (v2 contains corrections of the proofs)

Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initial condition. We show that these upper bounds are close to being sharp if (i) the Dirichlet-Laplace-Beltrami operator acting in $L^2(D)$ satisfies a strong Hardy inequality with weight $r^2$, (ii) the initial temperature distribution, and the specific heat of D are given by $r^{-a}$ and $r^{-b}$ respectively, where $r$ is the distance to the boundary, and 1

We studied the stellar population in the central 6.6x6.6arcmin,region of the ultra-deep (1Msec) Chandra Galactic field - the "Chandra bulge field" (CBF) approximately 1.5 degrees away from the Galactic Center - using the Hubble Space Telescope ACS/WFC blue (F435W) and red (F625W) images. We mainly focus on the behavior of red clump giants - a distinct stellar population, which is known to have an essentially constant intrinsic luminosity and color. By studying the variation in the position of the red clump giants on a spatially resolved color-magnitude diagram, we confirm the anomalous total-to-selective extinction ratio, as reported in previous work for other Galactic bulge fields. We show that the interstellar extinction in this area is = 4 on average, but varies significantly between ~3-5 on angular scales as small as 1 arcminute. Using the distribution of red clump giants in an extinction-corrected color-magnitude diagram, we constrain the shape of a stellar-mass distribution model in the direction of this ultra-deep Chandra field, which will be used in a future analysis of the population of X-ray sources. We also show that the adopted model for the stellar density distribution predicts an infrared surface brightness in the direction of the "Chandra bulge field" in good agreement (i.e. within ~15%) with the actual measurements derived from the Spitzer/IRAC observations., Comment: 9 pages, 9 figures. Accepted for publication in A&A

We study the variational problem $$\inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \},$$ where $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, $\h(\partial \Omega)$ is the $(m-1)$- dimensional Hausdorff measure of the boundary of $\Omega$, and $|\Omega|$ is the Lebesgue measure of $\Omega$. If $m=2$, and $k=2,3, \cdots$, then there exists a convex minimiser $\Omega_{2,k}$. If $m \ge 2$, and if $\Omega_{m,k}$ is a minimiser, then $\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}})$ is also a minimiser, and $\R^m\setminus \Omega_{m,k}^*$ is connected. Upper bounds are obtained for the number of components of $\Omega_{m,k}$. It is shown that if $m\ge 3$, and $k\le m+1$ then $\Omega_{m,k}$ has at most $4$ components. Furthermore $\Omega_{m,k}$ is connected in the following cases : (i) $m\ge 2, k=2,$ (ii) $m=3,4,5,$ and $k=3,4,$ (iii) $m=4,5,$ and $k=5,$ (iv) $m=5$ and $k=6$. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity., Comment: 16 pages

We study the weighted heat trace asymptotics of an operator of Laplace type with Dirichlet boundary conditions where the weight function exhibits radial blowup. We give formulas for the first few terms in the expansion in terms of geometrical data.

We study the heat content asymptotics with either Dirichlet or Robin boundary conditions where the initial temperature exhibits radial blowup near the boundary. We show that there is a complete small-time asymptotic expansion and give explicit geometrical formulas for the first few terms in the expansion.

We present a statistical analysis of simultaneous optical and X-ray light curves, spanning 600 ks, for 814 pre-main-sequence (PMS) stars in the Orion Nebula Cluster. The aim of this study is to establish the relationship, if any, between the sites of optical and X-ray variability, and thereby to elucidate the origins of X-ray production in PMS stars. In a previous paper we showed that optical and X-ray variability in PMS stars are very rarely time-correlated. Here, using time-averaged variability indicators to examine the joint occurrences of optical and X-ray variability, we confirm that the two forms of variability are not directly causally related. However, a strong and highly statistically significant correlation is found between optical variability and X-ray luminosity. As this correlation is found to be independent of accretion activity, we argue that X-ray production in PMS stars must instead be intimately connected with the presence and strength of optically variable, magnetically active surface regions (i.e. spots) on these stars. Moreover, because X-ray variability and optical variability are rarely time-correlated, we conclude that the sites of X-ray production are not exclusively co-spatial with these regions. We argue that solar-analog coronae, heated by topologically complex fields, can explain these findings., Comment: To appear in the Astrophysical Journal. 33 pages, 3 figures

Estimates are obtained for the expected volume of intersection of independent Wiener sausages in Euclidean space in the small time limit. The asymptotic behaviour of the weighted diagonal heat kernel norm on compact Riemannian manifolds with smooth boundary is obtained in the small time limit

We have searched the OGLE-II archive for candidate counterparts of X-ray sources detected in two low-extinction windows included in our Galactic bulge Chandra/HST survey. We find that a significant number - i.e. in excess of the expected level of random associations - can be matched with probable M-giants. Their X-ray properties can be understood if these sources are symbiotic binaries where the X-rays are typically, either directly or indirectly, the result of a white dwarf accreting from the wind of a cool giant. Optical and near-infrared properties of selected sources are consistent with a symbiotic nature, although none of the spectra collected for 8 out of 13 candidate counterparts show the high-ionization nebular emission lines observed for many symbiotics. The hard X-ray emission for several sources (power-law photon indices -1.5 ~< Gamma ~< 1.5) suggests our sample includes systems similar to the symbiotics recently detected with INTEGRAL and Swift., Comment: 4 pages, 3 figures (1 color figure), accepted for publication in ApJ Letters

We present a database of $BVRI$ time-series photometry of the Orion Nebula Cluster obtained with two ground-based telescopes at different longitudes to provide simultaneous coverage with the 13-d Chandra observation of the cluster. The resulting database of simultaneous optical and X-ray light curves for some 800 pre--main-sequence (PMS) stars represents, by a factor of hundreds, the largest synoptic, multi--wavelength-regime, time-series study of young stars to date. This database will permit detailed analyses of the relationship between optical and X-ray variability among a statistically significant ensemble of PMS stars, with the goal of elucidating the origins of PMS X-ray production. In this first paper, we present the optical observations, describe the combined X-ray/optical database, and perform an analysis of time-correlated variability in the optical and X-ray light curves. We identify 40 stars (representing 5% of our study sample) with possible time-correlated optical and X-ray variability. Examples of both positive and negative time-correlations are found, possibly representing X-ray flares and persistent coronal features associated with both cool and hot surface spots (i.e. magnetically active regions and accretion shocks). We also find two possible examples of "white-light" flares coincident with X-ray flares; these may correspond to the impulsive heating phase in solar-analog flares. However, though interesting, these represent unusual cases. More generally, we find very little evidence to suggest a direct causal link between the sources of optical and X-ray variability in PMS stars. The conclusion that accretion is a primary driver of X-ray production in PMS stars is not supported by our findings., Comment: 69 pages, 46 figures, accepted by ApJ

We introduce the Chandra Multiwavelength Plane (ChaMPlane) Survey, designed to measure or constrain the populations of low-luminosity (Lx > ~10^31 erg/s) accreting white dwarfs, neutron stars and stellar mass black holes in the Galactic Plane and Bulge. ChaMPlane incorporates two surveys, X-ray (Chandra) and optical (NOAO 4m-Mosaic imaging), and a followup spectroscopy and IR identification program. The survey has now extended through the first 6 years of Chandra data using serendipitous sources detected in 105 distinct ACIS-I and -S fields observed in 154 pointings and covered by 65 deep Mosaic images in V, R, I, and H-alpha. ChaMPlane incorporates fields with galactic latitude |b| <~ 12 deg and selected to be devoid of bright point or diffuse sources, with exposure time > ~20 ksec, and (where possible) minimum NH. We describe the scientific goals and introduce the X-ray and optical/IR processing and databases. We derive preliminary constraints on the space density or luminosity function of cataclysmic variables from the X-ray/optical data for 14 fields in the Galactic Anticenter. The lack of ChaMPlane CVs in these Anticenter fields suggests their space density is ~ 3x below the value (3 x 10^-5 pc^-3) found for the solar neighborhood by previous X-ray surveys. Companion papers describe the X-ray and optical processing in detail, optical spectroscopy of ChaMPlane sources in selected Anticenter fields and IR imaging results for the Galactic Center field. An Appendix introduces the ChaMPlane Virtual Observatory (VO) for online access to the X-ray and optical images and source catalogs for ready display and further analysis., Comment: 10 pages, 7 figures, 2 tables, accepted in ApJ for publication

We searched for infrared counterparts to the cluster of X-ray point sources discovered by Chandra in the Galactic Center Region (GCR). While the sources could be white dwarfs, neutron stars, or black holes accreting from stellar companions, their X-ray properties are consistent with magnetic Cataclysmic Variables, or High Mass X-ray Binaries (HMXB) at low accretion-rates. A direct way to decide between these possibilities and hence between alternative formation scenarios is to measure or constrain the luminosity distribution of the companions. Using infrared (J, H, K, Br-gamma) imaging, we searched for counterparts corresponding to typical HMXB secondaries: spectral type B0V with K<15 at the GCR. We found no significant excess of bright stars in Chandra error circles, indicating that HMXBs are not the dominant X-ray source population, and account for fewer than 10% of the hardest X-ray sources., Comment: 4 pages, 3 figures, 1 table, accepted in ApJ Letters for publication

The existence of a full asymptotic expansion for the heat content asymptotics of an operator of Laplace type with classical Zaremba boundary conditions on a smooth manifold is established. The first three coefficients in this asymptotic expansion are determined in terms of geometric invariants; partial information is obtained about the fourth coefficient., Comment: 24 pages

We report the discovery of two spectroscopic binaries in the field of the old open cluster M67 -- S1063 and S1113 -- whose positions in the color-magnitude diagram place them approximately 1 mag below the subgiant branch. A ROSAT study of M67 independently discovered these stars to be X-ray sources. Both have proper-motion membership probabilities greater than 97%; precise center-of-mass velocities are consistent with the cluster mean radial velocity. S1063 is also projected within one core radius of the cluster center. S1063 is a single-lined binary with a period of 18.396 days and an orbital eccentricity of 0.206. S1113 is a double-lined system with a circular orbit having a period of 2.823094 days. The primary stars of both binaries are subgiants. The secondary of S1113 is likely a 0.9 Mo main-sequence star, which implies a 1.3 Mo primary star. We have been unable to explain securely the low apparent luminosities of the primary stars; neither binary contain stars presently limited in radius by their Roche lobes. We speculate that S1063 and S1113 may be the products of close stellar encounters involving binaries in the cluster environment, and may define alternative stellar evolutionary tracks associated with mass-transfer episodes, mergers, and/or dynamical stellar exchanges.

We use differential CCD photometry to search for variability in BVI among 990 stars projected in and around the old open cluster M 67. In a previous paper we reported results for 22 cluster members that are optical counterparts to X-ray sources; this study focuses on the other stars in our observations. A variety of sampling rates were employed, allowing variability on time scales ranging from \sim 0.3 hours to \sim 20 days to be studied. Among the brightest sources studied, detection of variability as small as sigma approx 10 mmag is achieved (with > 3 sigma confidence); for the typical star observed, sensitivity to variability at levels sigma approx 20 mmag is achieved. The study is unbiased for stars with 12.5 < B < 18.5, 12.5 < V < 18.5, and 12 < I < 18 within a radius of about 10 arcmin from the cluster centre. In addition, stars with 10 < BVI < 12.5 were monitored in a few small regions in the cluster. We present photometry for all 990 sources studied, and report the variability characteristics of those stars found to be variable at a statistically significant level. Among the variables, we highlight several sources that merit future study, including stars located on the cluster binary sequence, stars on the giant branch, blue stragglers, and a newly discovered W UMa system., Comment: 12 pages, including 6 figures and 5 tables. Tables 1 and 3 only available in electronic version of paper. Accepted by A&A