arXiv subjects

Andrew Cumming

Publications and source records attributed to Andrew Cumming.

At least 73 records · Page 4Linked to original sources

arXiv2010

Crystallization of classical multi-component plasmas

We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multi-component plasma. Our method is a semi-analytic calculation that relies on extending the accurate fitting formulae available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of Horowitz, Berry, & Brown (Phys. Rev. E, 75, 066101, 2007), who use a molecular dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an accreting neutron star, at the point where half the mixture has solidified. Given the same initial composition as Horowitz et al., we are able to reproduce to good accuracy both the liquid and solid compositions at the half-freezing point; we find abundances for most species within 10% of the simulation values. Our method allows the phase diagram of complex mixtures to be explored more thoroughly than possible with numerical simulations. We briefly discuss the implications for the nature of the liquid-solid boundary in accreting neutron stars.

astro-ph.SR↗

arXiv2010

Radiative Hydrodynamic Simulations of HD209458b: Temporal Variability

We present a new approach for simulating the atmospheric dynamics of the close-in giant planet HD209458b that allows for the decoupling of radiative and thermal energies, direct stellar heating of the interior, and the solution of the full 3D Navier Stokes equations. Simulations reveal two distinct temperature inversions (increasing temperature with decreasing pressure) at the sub-stellar point due to the combined effects of opacity and dynamical flow structure and exhibit instabilities leading to changing velocities and temperatures on the nightside for a range of viscosities. Imposed on the quasi-static background, temperature variations of up to 15% are seen near the terminators and the location of the coldest spot is seen to vary by more than 20 degrees, occasionally appearing west of the anti-solar point. Our new approach introduces four major improvements to our previous methods including simultaneously solving both the thermal energy and radiative equations in both the optical and infrared, incorporating updated opacities, including a more accurate treatment of stellar energy deposition that incorporates the opacity relevant for higher energy stellar photons, and the addition of explicit turbulent viscosity.

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arXiv2009

An Integrated Analysis of Radial Velocities in Planet Searches

We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate chi-squared for multiple values of orbital parameters, and to carry out the marginalization integrals for a single planet including the possibility of a long term trend. The result is a robust algorithm that is rapid enough for use in real time analysis that outputs constraints on orbital parameters and false alarm probabilities for the planet and long term trend. The constraints on parameters and odds ratio that we derive compare well with previous calculations based on Markov Chain Monte Carlo methods, and we compare our results with other techniques for estimating false alarm probabilities and errors in derived orbital parameters. False alarm probabilities from the Bayesian analysis are systematically higher than frequentist false alarm probabilities, due to the different accounting of the number of trials. We show that upper limits on the velocity amplitude derived for circular orbits are a good estimate of the upper limit on the amplitude of eccentric orbits for eccentricities less than about 0.5.

astro-ph.IM↗

arXiv2009

Mapping crustal heating with the cooling lightcurves of quasi-persistent transients

The monitoring of quiescent emission from neutron star transients with accretion outbursts long enough to significantly heat the neutron star crust has opened a new vista onto the physics of dense matter. In this paper we construct models of the thermal relaxation of the neutron star crust following the end of a protracted accretion outburst. We confirm the finding of Shternin et al., that the thermal conductivity of the neutron star crust is high, consistent with a low impurity parameter. We describe the basic physics that sets the broken power-law form of the cooling lightcurve. The initial power law decay gives a direct measure of the temperature profile, and hence the thermal flux during outburst, in the outer crust. The time of the break, at hundreds of days post-outburst, corresponds to the thermal time where the solid transitions from a classical to quantum crystal, close to neutron drip. We calculate in detail the constraints on the crust parameters of both KS 1731-260 and MXB 1659-29 from fitting their cooling lightcurves. Our fits to the lightcurves require that the neutrons do not contribute significantly to the heat capacity in the inner crust, and provide evidence in favor of the existence of a neutron superfluid throughout the inner crust. Our fits to both sources indicate an impurity parameter of order unity in the inner crust.

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arXiv2008

An Accurate Determination of the Optical Periodic Modulation in the X-Ray Binary SAX J1808.4-3658

We report on optical imaging of the X-ray binary SAX J1808.4-3658 with the 8-m Gemini South Telescope. The binary, containing an accretion-powered millisecond pulsar, appears to have a large periodic modulation in its quiescent optical emission. In order to clarify the origin of this modulation, we obtained three time-resolved $r'$-band light curves (LCs) of the source in five days. The LCs can be described by a sinusoid, and the long time-span between them allows us to determine optical period P=7251.9 s and phase 0.671 at MJD 54599.0 (TDB; phase 0.0 corresponds to the ascending node of the pulsar orbit), with uncertainties of 2.8 s and 0.008 (90 % confidence), respectively. This periodicity is highly consistent with the X-ray orbital ephemeris. By considering this consistency and the sinusoidal shape of the LCs, we rule out the possibility of the modulation arising from the accretion disk. Our study supports the previous suggestion that the X-ray pulsar becomes rotationally powered in quiescence, with its energy output irradiating the companion star, causing the optical modulation. While it has also been suggested that the accretion disk would be evaporated by the pulsar, we argue that the disk exists and gives rise to the persistent optical emission. The existence of the disk can be verified by long-term, multi-wavelength optical monitoring of the source in quiescence, as an increasing flux and spectral changes from the source would be expected based on the standard disk instability model.

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arXiv2008

The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets

We analyze 8 years of precise radial velocity measurements from the Keck Planet Search, characterizing the detection threshold, selection effects, and completeness of the survey. We carry out a systematic search for planets by assessing the false alarm probability associated with Keplerian orbit fits to the data. This allows us to understand the detection threshold for each star in terms of the number and time baseline of the observations, and size of measurement errors and stellar jitter. We show that all planets with orbital periods <2000 days, velocity amplitudes >20 m/s, and eccentricities <0.6 have been announced, and summarize the candidates at lower amplitudes and longer orbital periods. For the remaining stars, we calculate upper limits on the velocity amplitude of a companion, typically 10 m/s, and use the non-detections to derive completeness corrections at low amplitudes and long orbital periods. We give the fraction of stars with a planet as a function of planet mass and orbital period, and extrapolate to long period orbits and low planet masses. A power law fit for planet masses >0.3 Jupiter masses and periods <2000 days gives a mass-period distribution dN=C M^αP^βdlnM dlnP with α=-0.31 \pm 0.2, β=0.26\pm 0.1, and the normalization constant C such that 10.5% of solar type stars have a planet with mass in the range 0.3-10 Jupiter masses and orbital period 2-2000 days. The orbital period distribution shows an increase in the planet fraction by a factor of 5 for orbital periods beyond 300 days. Extrapolation gives 17-20% of stars having gas giant planets within 20 AU. Finally, taking into account differences in detectability, we find that M dwarfs are 3 to 10 times less likely to harbor a Jupiter mass planet than solar type stars.

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arXiv2007

Models of Type I X-ray Bursts from GS 1826-24: A Probe of rp-Process Hydrogen Burning

The X-ray burster GS 1826-24 shows extremely regular Type I X-ray bursts whose energetics and recurrence times agree well with thermonuclear ignition models. We present calculations of sequences of burst lightcurves using multizone models which follow the rp-process nucleosynthesis with an extensive nuclear reaction network. The theoretical and observed burst lightcurves show remarkable agreement. The models naturally explain the slow ~5s rise and long ~100s tails of these bursts, as well as their dependence on mass accretion rate. This comparison provides further evidence for solar metallicity in the accreted material in this source, and constrains the distance to the source. The main difference is that the observed lightcurves do not show the distinct two-stage rise of the models. This may reflect the time for burning to spread over the stellar surface, or may indicate that our treatment of heat transport or nuclear physics needs to be revised. The trends in burst properties with accretion rate are well-reproduced by our spherically symmetric models which include chemical and thermal inertia from the ashes of previous bursts. Changes in the covering fraction of the accreted fuel are not required.

astro-ph↗

arXiv2006

Helium-rich thermonuclear bursts and the distance to the accretion-powered millisecond pulsar SAX J1808.4-3658

We analysed Rossi X-ray Timing Explorer observations of the accretion-powered 401 Hz pulsar SAX J1808.4-3658, in order to precisely determine the source distance. While the fluences for the five transient outbursts observed from 1996 were constant to within the uncertainties, the outburst interval varied signficantly, so that the time-averaged flux (and accretion rate) decreased by around 40%. By equating the time-averaged X-ray flux with the expected mass transfer rate from gravitational radiation, we derived a lower limit on the distance of 3.4 kpc. Combined with an upper limit from assuming that the four radius-expansion thermonuclear bursts observed during the 2002 October outburst reached at most the Eddington limit for a pure He atmosphere, we found that the probable distance range for the source is 3.4-3.6 kpc. The implied inclination, based on the optical/IR properties of the counterpart, is i<~30 degrees. We compared the properties of the bursts with an ignition model. The time between bursts was long enough for hot CNO burning to significantly deplete the accreted hydrogen, so that ignition occurred in a pure helium layer underlying a stable hydrogen burning shell. This is the first time that this burning regime has been securely observationally identified. The observed energetics of the bursts give a mean hydrogen fraction at ignition of approx. 0.1, and require that the accreted hydrogen fraction X_0 and the CNO metallicity Z_CNO are related by Z_CNO approx. 0.03(X_0/0.7)^2. We show that in this burning regime, a measurement of the burst recurrence time and energetics allows the local accretion rate onto the star to be determined independently of the accreted composition, giving a new method for estimating the source distance which is in good agreement with our other estimates.

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arXiv2006

What can we learn from long term monitoring of X-ray bursters?

The last few years have seen the discovery of a number of new aspects of Type I X-ray bursts: the extremely energetic and long duration superbursts, intermediate duration bursts at low luminosities, mHz QPOs, and burst oscillations. These discoveries promise a new understanding of nuclear burning on accreting neutron stars, and offer a chance to use observations to probe neutron star properties. I discuss what we can learn from future long term monitoring with MIRAX.

astro-ph↗

arXiv2005

Millihertz Quasi-Periodic Oscillations from Marginally Stable Nuclear Burning on an Accreting Neutron Star

We investigate marginally stable nuclear burning on the surface of accreting neutron stars as an explanation for the mHz quasi-periodic oscillations (QPOs) observed from three low mass X-ray binaries. At the boundary between unstable and stable burning, the temperature dependence of the nuclear heating rate and cooling rate almost cancel. The result is an oscillatory mode of burning, with an oscillation period close to the geometric mean of the thermal and accretion timescales for the burning layer. We describe a simple one-zone model which illustrates this basic physics, and then present detailed multizone hydrodynamical calculations of nuclear burning close to the stability boundary using the KEPLER code. Our models naturally explain the characteristic 2 minute period of the mHz QPOs, and why they are seen only in a very narrow range of X-ray luminosities. The oscillation period is sensitive to the accreted hydrogen fraction and the surface gravity, suggesting a new way to probe these parameters. A major puzzle is that the accretion rate at which the oscillations appear in the theoretical models is an order of magnitude larger than the rate implied by the X-ray luminosity when the mHz QPOs are seen. We discuss the implications for our general understanding of nuclear burning on accreting neutron stars. One possibility is that the accreted material covers only part of the neutron star surface at luminosities Lx > ~1E37 erg/s.

astro-ph↗

arXiv2005

Long Type I X-ray Bursts and Neutron Star Interior Physics

Superbursts are very energetic Type I X-ray bursts discovered in recent years by long term monitoring of X-ray bursters, believed to be due to unstable ignition of carbon in the deep ocean of the neutron star. A number of "intermediate duration" bursts have also been observed, probably associated with ignition of a thick helium layer. We investigate the sensitivity of these long X-ray bursts to the thermal profile of the neutron star crust and core. We first compare cooling models of superburst lightcurves with observations, and derive constraints on the ignition mass and energy release, and then calculate ignition models for superbursts and pure helium bursts, and compare to observations. The superburst lightcurves and ignition models imply that the carbon mass fraction is approximately 20% or greater in the fuel layer, constraining models of carbon production. However, the most important result is that when Cooper pairing neutrino emission is included in the crust, the temperature is too low to support unstable carbon ignition at the observed column depths. Some additional heating mechanism is required in the accumulating fuel layer to explain the observed properties of superbursts. If Cooper pair emission is less efficient than currently thought, the observed ignition depths for superbursts imply that the crust is a poor conductor, and the core neutrino emission is not more efficient than modified URCA. The observed properties of helium bursts support these conclusions, requiring inefficient crust conductivity and core neutrino emission.

astro-ph↗

arXiv2005

Superbursts from Strange Stars

Recent models of carbon ignition on accreting neutron stars predict superburst ignition depths that are an order of magnitude larger than observed. We explore a possible solution to this problem, that the compact stars in low mass X-ray binaries that have shown superbursts are in fact strange stars with a crust of normal matter. We calculate the properties of superbursts on strange stars, and the resulting constraints on the properties of strange quark matter. We show that the observed ignition conditions exclude fast neutrino emission in the quark core, for example by the direct Urca process, which implies that strange quark matter at stellar densities should be in a color superconducting state. For slow neutrino emission in the quark matter core, we find that reproducing superburst properties requires a definite relation between three poorly constrained properties of strange quark matter: its thermal conductivity, its slow neutrino emissivity and the energy released by converting a nucleon into strange quark matter.

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arXiv2005

Latitudinal Shear Instabilities during Type I X-ray Bursts

Coherent oscillations have been observed during Type I X-ray bursts from 14 accreting neutron stars in low mass X-ray binaries, providing important information about their spin frequencies. However, the origin of the brightness asymmetry on the neutron star surface producing these oscillations is still not understood. We study the stability of a zonal shearing flow on the neutron star surface using a shallow water model. We show that differential rotation of >2% between pole and equator, with the equator spinning faster than the poles, is unstable to hydrodynamic shear instabilities. The unstable eigenmodes have properties well-matched to burst oscillations: low azimuthal wavenumber m, wave speeds 1 or 2% below the equatorial spin rate, and e-folding times close to a second. Instability is related to low frequency buoyantly driven r-modes that have a mode frequency within the range of rotation frequencies in the differentially rotating shell. We discuss the implications for burst oscillations. Growth of shear instabilities may explain the brightness asymmetry in the tail of X-ray bursts, although some fine tuning of the level of differential rotation and a spin frequency near 300 Hz are required in order for the fastest growing mode to have m=1. If shear instabilities are to operate during a burst, temperature contrasts of 30% across the star must be created during ignition and spreading of the flash.

astro-ph↗

arXiv2004

Radial Velocity Detectability of Low Mass Extrasolar Planets in Close Orbits

Detection of Jupiter mass companions to nearby solar type stars with precise radial velocity measurements is now routine, and Doppler surveys are moving towards lower velocity amplitudes. The detection of several Neptune-mass planets with orbital periods less than a week has been reported. The drive toward the search for close-in Earth-mass planets is on the agenda. Successful detection or meaningful upper limits will place important constraints on the process of planet formation. In this paper, we quantify the statistics of detection of low-mass planets in-close orbits, showing how the detection threshold depends on the number and timing of the observations. In particular, we consider the case of a low-mass planet close to but not on the 2:1 mean motion resonance with a hot jupiter. This scenario is a likely product of the core-accretion hypothesis for planet formation coupled with migration of jupiters in the protoplanetary disk. It is also advantageous for detection because the orbital period is well-constrained. Detection of few Earth mass rocky cores will require ~ 1 m/s velocity precision, and most importantly, a much better understanding of stellar radial velocity jitter.

astro-ph↗

arXiv2004

Detectability of Extrasolar Planets in Radial Velocity Surveys

Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long periods and low amplitudes. In this paper, I derive analytic expressions for the detectability of planets at both short and long periods, for circular and eccentric orbits. I suggest an extension of the Lomb-Scargle periodogram for Keplerian orbits, and describe how to estimate the false alarm probability associated with a Keplerian fit. Using this to investigate the detectability of eccentric orbits shows that there are significant selection effects against eccentric orbits for e>0.6, and the small number of highly eccentric planets discovered so far may reflect this. Finally, I present a Bayesian approach to the periodogram, which emphasises the equivalence of least squares and periodogram techniques.

astro-ph↗

arXiv2004

Magnetic Field Evolution During Neutron Star Recycling

I describe work on two aspects of magnetic field evolution relevant for the "recycling" scenario for making millisecond radio pulsars. First, many of the theoretical ideas for bringing about accretion-induced field decay rely on dissipation of currents in the neutron star crust. I discuss field evolution in the crust due to the Hall effect, and outline when it dominates Ohmic decay. This emphasises the importance of understanding the impurity level in the crust. Second, I briefly discuss the progress that has been made in understanding the magnetic fields of neutron stars currently accreting matter in low mass X-ray binaries. In particular, thermonuclear X-ray bursts offer a promising probe of the magnetic field of these neutron stars.

astro-ph↗

arXiv2004

Magnetic Field Evolution in Neutron Star Crusts due to the Hall Effect and Ohmic Decay

We present calculations of magnetic field evolution by the Hall effect and Ohmic decay in neutron star crusts. We first discuss when and for which neutron stars the Hall effect is important relative to Ohmic decay. We compute the evolution of an initial field distribution by Ohmic decay, and give approximate analytic formulas for both the surface and interior fields as a function of time. We then discuss the subsequent evolution by the Hall effect, giving several examples which illustrate how the field configuration evolves. Hall wave eigenfunctions are computed, including the effect of the large density change across the crust. We estimate the response of the crust to the magnetic stresses induced by Hall waves, and give a detailed discussion of the boundary conditions at the solid-liquid interface. Finally, we discuss the implications for the Hall cascade proposed by Goldreich & Reisenegger.

astro-ph↗

arXiv2004

The Thermal Evolution following a Superburst on an Accreting Neutron Star

Superbursts are very energetic Type I X-ray bursts discovered in recent years by long term monitoring of X-ray bursters, and believed to be due to unstable ignition of carbon in the deep ocean of the neutron star. In this Letter, we follow the thermal evolution of the surface layers as they cool following the burst. The resulting lightcurves agree very well with observations for layer masses and energy releases in the range expected from ignition calculations. At late times, the cooling flux from the layer decays as a power law in time, giving timescales for quenching of normal Type I bursting of weeks, in good agreement with observational limits. We show that simultaneous modelling of superburst lightcurves and quenching times promises to constrain both the thickness of the fuel layer and the energy deposited.

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