arXiv subjects

D. Sullivan

Publications and source records attributed to D. Sullivan.

15 recordsLinked to original sources

arXiv2020

Quantitative towers in finite difference calculus approximating the continuum

Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, $d$ and $*$ which are used to describe many nonlinear problems. The point of this paper is to construct consistent direct and inverse systems of finite dimensional approximations to these structures and to calculate combinatorially how these finite dimensional models differ from their continuum idealizations. In a Euclidean background there is an explicit answer which is natural statistically.

math.NA↗

arXiv2015

StarBench: The D-type expansion of an HII region

StarBench is a project focused on benchmarking and validating different star-formation and stellar feedback codes. In this first StarBench paper we perform a comparison study of the D-type expansion of an HII region. The aim of this work is to understand the differences observed between the twelve participating numerical codes against the various analytical expressions examining the D-type phase of HII region expansion. To do this, we propose two well-defined tests which are tackled by 1D and 3D grid- and SPH- based codes. The first test examines the `early phase' D-type scenario during which the mechanical pressure driving the expansion is significantly larger than the thermal pressure of the neutral medium. The second test examines the `late phase' D-type scenario during which the system relaxes to pressure equilibrium with the external medium. Although they are mutually in excellent agreement, all twelve participating codes follow a modified expansion law that deviates significantly from the classical Spitzer solution in both scenarios. We present a semi-empirical formula combining the two different solutions appropriate to both early and late phases that agrees with high-resolution simulations to $\lesssim2\%$. This formula provides a much better benchmark solution for code validation than the Spitzer solution. The present comparison has validated the participating codes and through this project we provide a dataset for calibrating the treatment of ionizing radiation hydrodynamics codes.

astro-ph.SR↗

arXiv2012

Empirical Determination of Convection Parameters in White Dwarfs I : Whole Earth Telescope Observations of EC14012-1446

We report on analysis of 308.3 hrs of high speed photometry targeting the pulsating DA white dwarf EC14012-1446. The data were acquired with the Whole Earth Telescope (WET) during the 2008 international observing run XCOV26. The Fourier transform of the light curve contains 19 independent frequencies and numerous combination frequencies. The dominant peaks are 1633.907, 1887.404, and 2504.897 microHz. Our analysis of the combination amplitudes reveals that the parent frequencies are consistent with modes of spherical degree l=1. The combination amplitudes also provide m identifications for the largest amplitude parent frequencies. Our seismology analysis, which includes 2004--2007 archival data, confirms these identifications, provides constraints on additional frequencies, and finds an average period spacing of 41 s. Building on this foundation, we present nonlinear fits to high signal-to-noise light curves from the SOAR 4.1m, McDonald 2.1m, and KPNO 2m telescopes. The fits indicate a time-averaged convective response timescale of 99.4 +/- 17 s, a temperature exponent 85 +/- 6.2 and an inclination angle of 32.9 +/- 3.2 degrees. We present our current empirical map of the convective response timescale across the DA instability strip.

astro-ph.SR↗

arXiv2010

OGLE 2008--BLG--290: An accurate measurement of the limb darkening of a Galactic Bulge K Giant spatially resolved by microlensing

Gravitational microlensing is not only a successful tool for discovering distant exoplanets, but it also enables characterization of the lens and source stars involved in the lensing event. In high magnification events, the lens caustic may cross over the source disk, which allows a determination of the angular size of the source and additionally a measurement of its limb darkening. When such extended-source effects appear close to maximum magnification, the resulting light curve differs from the characteristic Paczynski point-source curve. The exact shape of the light curve close to the peak depends on the limb darkening of the source. Dense photometric coverage permits measurement of the respective limb-darkening coefficients. In the case of microlensing event OGLE 2008-BLG-290, the K giant source star reached a peak magnification of about 100. Thirteen different telescopes have covered this event in eight different photometric bands. Subsequent light-curve analysis yielded measurements of linear limb-darkening coefficients of the source in six photometric bands. The best-measured coefficients lead to an estimate of the source effective temperature of about 4700 +100-200 K. However, the photometric estimate from colour-magnitude diagrams favours a cooler temperature of 4200 +-100 K. As the limb-darkening measurements, at least in the CTIO/SMARTS2 V and I bands, are among the most accurate obtained, the above disagreement needs to be understood. A solution is proposed, which may apply to previous events where such a discrepancy also appeared.

astro-ph.SR↗

arXiv2010

Pulsational Mapping of Calcium Across the Surface of a White Dwarf

We constrain the distribution of calcium across the surface of the white dwarf star G29-38 by combining time series spectroscopy from Gemini-North with global time series photometry from the Whole Earth Telescope. G29-38 is actively accreting metals from a known debris disk. Since the metals sink significantly faster than they mix across the surface, any inhomogeneity in the accretion process will appear as an inhomogeneity of the metals on the surface of the star. We measure the flux amplitudes and the calcium equivalent width amplitudes for two large pulsations excited on G29-38 in 2008. The ratio of these amplitudes best fits a model for polar accretion of calcium and rules out equatorial accretion.

astro-ph.SR↗

arXiv2009

Mass measurement of a single unseen star and planetary detection efficiency for OGLE 2007-BLG-050

We analyze OGLE-2007-BLG-050, a high magnification microlensing event (A ~ 432) whose peak occurred on 2 May, 2007, with pronounced finite-source and parallax effects. We compute planet detection efficiencies for this event in order to determine its sensitivity to the presence of planets around the lens star. Both finite-source and parallax effects permit a measurement of the angular Einstein radius \theta_E = 0.48 +/- 0.01 mas and the parallax \pi_E = 0.12 +/- 0.03, leading to an estimate of the lens mass M = 0.50 +/- 0.14 M_Sun and its distance to the observer D_L = 5.5 +/- 0.4 kpc. This is only the second determination of a reasonably precise (<30%) mass estimate for an isolated unseen object, using any method. This allows us to calculate the planetary detection efficiency in physical units (r_\perp, m_p), where r_\perp is the projected planet-star separation and m_p is the planet mass. When computing planet detection efficiency, we did not find any planetary signature and our detection efficiency results reveal significant sensitivity to Neptune-mass planets, and to a lesser extent Earth-mass planets in some configurations. Indeed, Jupiter and Neptune-mass planets are excluded with a high confidence for a large projected separation range between the planet and the lens star, respectively [0.6 - 10] and [1.4 - 4] AU, and Earth-mass planets are excluded with a 10% confidence in the lensing zone, i.e. [1.8 - 3.1] AU.

astro-ph.EP↗

arXiv2008

OGLE-2005-BLG-071Lb, the Most Massive M-Dwarf Planetary Companion?

We combine all available information to constrain the nature of OGLE-2005-BLG-071Lb, the second planet discovered by microlensing and the first in a high-magnification event. These include photometric and astrometric measurements from Hubble Space Telescope, as well as constraints from higher order effects extracted from the ground-based light curve, such as microlens parallax, planetary orbital motion and finite-source effects. Our primary analysis leads to the conclusion that the host of Jovian planet OGLE-2005-BLG-071Lb is an M dwarf in the foreground disk with mass M= 0.46 +/- 0.04 Msun, distance D_l = 3.3 +/- 0.4 kpc, and thick-disk kinematics v_LSR ~ 103 km/s. From the best-fit model, the planet has mass M_p = 3.8 +/- 0.4 M_Jup, lies at a projected separation r_perp = 3.6 +/- 0.2 AU from its host and so has an equilibrium temperature of T ~ 55 K, i.e., similar to Neptune. A degenerate model less favored by \Delta\chi^2 = 2.1 (or 2.2, depending on the sign of the impact parameter) gives similar planetary mass M_p = 3.4 +/- 0.4 M_Jup with a smaller projected separation, r_\perp = 2.1 +/- 0.1 AU, and higher equilibrium temperature T ~ 71 K. These results from the primary analysis suggest that OGLE-2005-BLG-071Lb is likely to be the most massive planet yet discovered that is hosted by an M dwarf. However, the formation of such high-mass planetary companions in the outer regions of M-dwarf planetary systems is predicted to be unlikely within the core-accretion scenario. There are a number of caveats to this primary analysis, which assumes (based on real but limited evidence) that the unlensed light coincident with the source is actually due to the lens, that is, the planetary host. However, these caveats could mostly be resolved by a single astrometric measurement a few years after the event.

astro-ph↗

arXiv2007

The pulsation modes of the pre-white dwarf PG 1159-035

PG 1159-035, a pre-white dwarf with T_eff=140,000 K, is the prototype of both two classes: the PG1159 spectroscopic class and the DOV pulsating class. Previous studies of PG 1159-035 photometric data obtained with the Whole Earth Telescope (WET) showed a rich frequency spectrum allowing the identification of 122 pulsation modes. In this work, we used all available WET photometric data from 1983, 1985, 1989, 1993 and 2002 to identify the pulsation periods and identified 76 additional pulsation modes, increasing to 198 the number of known pulsation modes in PG 1159-035, the largest number of modes detected in any star besides the Sun. From the period spacing we estimated a mass M = 0.59 +/- 0.02 solar masses for PG 1159-035, with the uncertainty dominated by the models, not the observation. Deviations in the regular period spacing suggest that some of the pulsation modes are trapped, even though the star is a pre-white dwarf and the gravitational settling is ongoing. The position of the transition zone that causes the mode trapping was calculated at r_c = 0.83 +/- 0.05 stellar radius. From the multiplet splitting, we calculated the rotational period P_rot = 1.3920 +/- 0.0008 days and an upper limit for the magnetic field, B < 2000 G. The total power of the pulsation modes at the stellar surface changed less than 30% for l=1 modes and less than 50% for l=2 modes. We find no evidence of linear combinations between the 198 pulsation mode frequencies. PG 1159-035 models have not significative convection zones, supporting the hypothesis that nonlinearity arises in the convection zones in cooler pulsating white dwarf stars.

astro-ph↗

arXiv2005

Mixing of Quantum Walk on Circulant Bunkbeds

We give new observations on the mixing dynamics of a continuous-time quantum walk on circulants and their bunkbed extensions. These bunkbeds are defined through two standard graph operators: the join G + H and the Cartesian product of graphs G and H.Our results include the following: 1. The quantum walk is average uniform mixing on circulants with bounded eigenvalue multiplicity. This extends a known fact about the cycles. 2. Explicit analysis of the probability distribution of the quantum walk on the join of circulants. This explains why complete partite graphs are not average uniform mixing, using the fact the complete n-vertex graph is the join of a 1-vertex graph and the (n-1)-vertex complete graph, and that the complete m-partite graph, where each partition has size n, is the m-fold join of the empty n-vertex graph. 3. The quantum walk on the Cartesian product of a m-vertex path P and a circulant G, is average uniform mixing if G is. This highlights a difference between circulants and the hypercubes. Our proofs employ purely elementary arguments based on the spectra of the graphs.

quant-ph↗

arXiv2005

Dynamical Systems Applied to Asymptotic Geometry

In the paper we discuss two questions about smooth expanding dynamical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with Hölder continuous derivative. The sequences of asymptotic length ratios are precisely those given by a positive Hölder continuous function $s$ (solenoid function) on the Cantor set $C$ of 2-adic integers satisfying a functional equation called the matching condition. The functional equation for the 2-adic integer Cantor set is $s(2x+1)=\frac{s(x)}{s(2x)}(1+\frac{1}{s(2x-1)})-1.$ We also present a one-to-one correspondence between solenoid functions and affine classes of 2-adic quasiperiodic tilings of the real line that are fixed points of the 2-amalgamation operator. (ii) We calculate the precise maximum possible level of smoothness for a representative of the system, up to diffeomorphic conjugacy, in terms of the functions $s$ and $cr(x)=(1+s(x))/(1+(s(x+1))^{-1})$. For example, in the Lipschitz structure on $C$ determined by $s$, the maximum smoothness is $C^{1+α}$ for $0<α\le 1$ if, and only if, $s$ is $α$-Hölder continuous. The maximum smoothness is $C^{2+α}$ for $0<α\le 1$ if, and only if, $cr$ is $(1+α)$-Hölder. A curious connection with Mostow type rigidity is provided by the fact that $s$ must be constant if it is $α$-Hölder for $α> 1$.

math.DS↗

arXiv2004

The Nonradially-Pulsating Primary of the Cataclysmic Variable GW Librae

The dwarf nova GW Librae is the first cataclysmic variable discovered to have a primary in a white dwarf instability strip, making it the first multi-mode, nonradially-pulsating star known to be accreting. The primaries of CVs, embedded in hot, bright accretion discs, are difficult to study directly. Applying the techniques of asteroseismology to GW Librae could therefore give us an unprecedented look at a white dwarf that has undergone ~10^9 years of accretion. However, an accreting white dwarf may have characteristics sufficiently different from those of single pulsating white dwarfs to render the standard models of white dwarf pulsations invalid for its study. This paper presents amplitude spectra of GW Lib from a series of observing campaigns conducted during 1997, 1998 and 2001. We find that the dominant pulsation modes cluster at periods near 650, 370 and 230 s, which also appear in linear combinations with each other. GW Lib's pulsation spectrum is highly unstable on time-scales of months, and exhibits clusters of signals very closely spaced in frequency, with separations on the order of a few microHz.

astro-ph↗

arXiv2003

ROTSE-III Observations of the Early Afterglow From GRB 030329

Using two identical telescopes at widely separated longitudes, the ROTSE-III network observed decaying emission from the remarkably bright afterglow of GRB 030329. In this report we present observations covering 56% of the period from 1.5-47 hours after the burst. We find that the light curve is piecewise consistent with a powerlaw decay. When the ROTSE-III data are combined with data reported by other groups, there is evidence for five breaks within the first 20 hours after the burst. Between two of those breaks, observations from 15.9-17.1 h after the burst at 1-s time resolution with McDonald Observatory's 2.1-m telescope reveal no evidence for fluctuations or deviations from a simple power law. Multiple breaks may indicate complex structure in the jet. There are also two unambiguous episodes at 23 and 45 hours after the burst where the intensity becomes consistent with a constant for several hours, perhaps indicating multiple injections of energy into the GRB/afterglow system.

astro-ph↗

arXiv2003

The Everchanging Pulsating White Dwarf GD358

We report 323 hours of nearly uninterrupted time series photometric observations of the DBV star GD 358 acquired with the Whole Earth Telescope (WET) during May 23rd to June 8th, 2000. We acquired more than 232 000 independent measurements. We also report on 48 hours of time-series photometric observations in Aug 1996. We detected the non-radial g-modes consistent with degree l=1 and radial order 8 to 20 and their linear combinations up to 6th order.We also detect, for the first time, a high amplitude l=2 mode, with a period of 796s. In the 2000 WET data, the largest amplitude modes are similar to those detected with the WET observations of 1990 and 1994, but the highest combination order previously detected was 4th order. At one point during the 1996 observations, most of the pulsation energy was transferred into the radial order k=8 mode, which displayed a sinusoidal pulse shape in spite of the large amplitude. The multiplet structure of the individual modes changes from year to year, and during the 2000 observations only the k=9 mode displays clear normal triplet structure. Even though the pulsation amplitudes change on timescales of days and years, the eigenfrequencies remain essentially the same, showing the stellar structure is not changing on any dynamical timescale.

astro-ph↗

arXiv2000

Recent results by the MOA group on gravitational microlensing

Recent work by the MOA gravitational microlensing group is briefly described, including (i) the current observing strategy, (ii) use of a high-speed parallel computer for analysis of results by inverse ray shooting, (iii) analysis of the light curve of event OGLE-2000-BUL12 in terms of extra-solar planets, and (iv) the MOA alert system using difference imaging.

astro-ph↗

arXiv1999

Test by JANZOS of the Standard Model of Cosmic Ray Acceleration in the COMPTEL/ROSAT Supernova Renmant

A search for ultra-high energy gamma-rays emitted by the young, nearby supernova remnant that was discovered recently by the COMPTEL and ROSAT satellites was made using the JANZOS database for the period 1987-1993. A 95% confidence upper limit on the flux above 100 TeV of 3x10^(-13)cm^(-2)sec^(-1) was obtained. This is an order of magnitude below the expected flux based on the standard model of cosmic ray acceleration in supernova shocks. An optical survey of the region that has been commenced is also reported. This uses UK and ESO Schmidt plates, and CCD images by a NZ/Japan microlensing group.

astro-ph↗