Yuri Levin

The International Pulsar Timing Array project: using pulsars as a gravitational wave detector

The International Pulsar Timing Array project combines observations of pulsars from both northern and southern hemisphere observatories with the main aim of detecting ultra-low frequency (similar to 10(-9)-10(-8) Hz) gravitational waves. Here we introduce the project, review the methods used to search for gravitational waves emitted from coalescing supermassive binary black-hole systems in the centres of merging galaxies and discuss the status of the project.

Internal thermal noise in the LIGO test masses: A direct approach

The internal thermal noise in LIGO’s test masses is analyzed by a new technique, a direct application of the fluctuation-dissipation theorem to LIGO’s readout observable, x(t)=(longitudinal position of test-mass face, weighted by laser beam’s Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper’s direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for Sx(f), the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass’s front face (e.g., due to mirror coating) scales as 1/r02, by contrast with homogeneous dissipation, which scales as 1/r0 (r0 is the beam radius); so surface dissipation could become significant for small beam sizes.

Stellar Disk in the Galactic Center: A Remnant of a Dense Accretion Disk?

Observations of the Galactic center revealed a population of young massive stars within 0.4 pc from Sgr A*—the presumed location of a supermassive black hole. The origin of these stars is a puzzle as their formation in situ should be suppressed by the black holes tidal field. We find that out of 13 stars whose three-dimensional velocities have been measured by Genzel et al., 10 lie in a thin disk. The half-opening angle of the disk is consistent with zero within the measurement errors and does not exceed 10°. We propose that a recent burst of star formation has occurred in a dense gaseous disk around Sgr A*. Such a disk is no longer present because, most likely, it has been accreted by the central black hole. The three-dimensional orbit of S2, the young star closest to Sgr A*, has been recently mapped out with high precision. It is inclined to the stellar disk by 75°. We find that the orbit should undergo Lense-Thirring precession with the period of ~(6/a) × 106 yr, where a 0.2(tS2/6 × 106 yr)-1, where tS2 is the age of S2.

PROTOSTELLAR DISKS: FORMATION, FRAGMENTATION, AND THE BROWN DWARF DESERT

We argue that gravitational instability of typical protostellar disks is not a viable mechanism for the fragmentation into multiple systems (binary stars, brown dwarf companions, or gas giant planets) except at periods above roughly 20,000 yr. Our conclusion is based on a comparison between prior numerical work on disk self-gravity by Gammie and our own analytical models for the dynamical and thermal state of protostellar disks. For this purpose we first develop a simple theory for the initial conditions of low-mass star formation, accounting for the effect of turbulence on the characteristic mass, accretion rate, and angular momentum of collapsing cores. We also present formulae for the probability distribution of these quantities for the case of homogeneous Gaussian turbulence. However, our conclusions are not sensitive to this parameterization. Second, we examine the criterion for fragmentation to occur during star formation, concentrating on the self-gravitational instabilities of protostellar accretion disks in their main accretion phase. Self-gravitational instabilities are strongly dependent on the thermal state of the disk, and we find that the combination of viscous heating and stellar irradiation quenches fragmentation due to Toomres local instability. Simulations by Matsumoto & Hanawa, which do not include detailed thermal evolution, predict fragmentation in an early phase of collapse. But, fragments born in this phase are on tight orbits and are likely to merge later due to disk accretion. Global instability of the disk may be required to process mass supply, but this is also unlikely to produce fragments. We conclude that numerical simulations that predict brown dwarf formation by disk fragmentation but do not account for irradiation are unrealistic. Our findings help to explain the dearth of substellar companions to stellar-type stars: the brown dwarf desert.

On the theory of magnetar QPOs

We consider torsional oscillations of magnetars. This problem features rich dynamics due to the strong interaction between the normal modes of a magnetar’s crust and a continuum of magnetohydrodynamic (MHD) modes in its fluid core. We study the dynamics using a simple model of a magnetar possessing a uniform magnetic field and a thin spherical crust. First, we show that global torsional modes only exist when one introduces unphysically large dissipative terms into the equations of motion; thus global modes are not helpful for understanding the magnetar quasi-periodic oscillations (QPOs). Secondly, we solve the initial-value problem by simulating the sudden release of an initially strained crust and monitoring the subsequent crustal motion. We find that the crustal torsional modes quickly exchange their energy with the MHD continuum in the core, and decay by several orders of magnitude over the course of ∼10 oscillation periods. After the initial rapid decay, the crustal motion is stabilized and several time-varying QPOs are observed. The dynamical spectrum of the simulated crustal motion is in qualitative agreement with that of the X-ray light curve in the tail of a giant magnetar flare. The asymptotic frequencies of some of the QPOs are associated with the special spectral points ‐ the turning points or edges ‐ of the MHD continuum, and are not related to those of the crust. The observed steady low-frequency QPO at 18 Hz is almost certainly associated with the lowest frequency of the MHD continuum, or its first overtone. We also find that drifting QPOs get amplified when they come near the frequencies of the crustal modes. This explains why some of the observed QPOs have frequencies close to the expected crustal frequencies, and why these QPOs are highly variable with time.

CHANDRA/HETGS OBSERVATIONS OF THE BRIGHTEST FLARE SEEN FROM Sgr A*

Starting in 2012, we began an unprecedented observational program focused on the supermassive black hole in the center of our Galaxy, Sgr A*, utilizing the High Energy Transmission Grating Spectrometer (HETGS) instrument on the Chandra X-Ray Observatory. These observations will allow us to measure the quiescent X-ray spectra of Sgr A* for the first time at both high spatial and spectral resolution. The X-ray emission of Sgr A*, however, is known to flare roughly daily by factors of a few to ten times over quiescent emission levels, with rarer flares extending to factors of greater than 100 times quiescence. Here we report an observation performed on 2012 February 9 wherein we detected what are the highest peak flux and fluence flare ever observed from Sgr A*. The flare, which lasted for 5.6 ks and had a decidedly asymmetric profile with a faster decline than rise, achieved a mean absorbed 2-8 keV flux of (8.5 +/- 0.9) x 10(-12) erg cm(-2) s(-1). The peak flux was 2.5 times higher, and the total 2-10 keV emission of the event was approximately 10(39) erg. Only one other flare of comparable magnitude, but shorter duration, has been observed in Sgr A* by XMM-Newton in 2002 October. We perform spectral fits of this Chandra-observed flare and compare our results to the two brightest flares ever observed with XMM-Newton. We find good agreement among the fitted spectral slopes (Gamma similar to 2) and X-ray absorbing columns (N-H similar to 15 x 10(22) cm(-2)) for all three of these events, resolving prior differences (which are most likely due to the combined effects of pileup and spectral modeling) among Chandra and XMM-Newton observations of Sgr A* flares. We also discuss fits to the quiescent spectra of Sgr A*.

Runaway Heating by r-Modes of Neutron Stars in Low-Mass X-Ray Binaries

Recently Andersson et al. and Bildsten have independently suggested that an r-mode instability might be responsible for stalling the neutron star spin-up in strongly accreting low-mass X-ray binaries (LMXBs). We show that if this does occur, there are two possibilities for the resulting neutron star evolution. If the r-mode damping is a decreasing function of temperature, then the star undergoes a cyclic evolution: (1) accretional spin-up triggers the instability near the observed maximum spin rate; (2) the r-modes become highly excited through gravitational radiation reaction, and in a fraction of a year (0.13 yr in a particular model that we have considered) they viscously heat the star up to T~2.5 × 109 K; (3) r-mode gravitational radiation reaction then spins the star down in tspindown0.08(ffinal/130 Hz)−6 yr to a limiting rotational frequency ffinal, whose exact value depends on the not fully understood mechanisms of r-mode damping; (4) the r-mode instability shuts off; and (5) the neutron star slowly cools and is spun up by accretion for ~5 × 106 yr, until it once again reaches the instability point, closing the cycle. The shortness of the epoch of r-mode activity makes it unlikely that r-modes are currently excited in the neutron star of any galactic LMXBs, and unlikely that advanced LIGO interferometers will see gravitational waves from extragalactic LMXBs. Nevertheless, this cyclic evolution could be responsible for keeping the rotational frequencies within the observed LMXB frequency range. If, on the other hand, the r-mode damping is temperature independent, then a steady state with constant angular velocity and Tcore 4 × 108 K is reached, in which r-mode viscous heating is balanced by neutrino cooling and accretional spin-up torque is balanced by gravitational radiation reaction spin-down torque. In this case (as Bildsten and Andersson et. al. have shown) the neutron stars in LMXBs could be potential sources of periodic gravitational waves, detectable by enhanced LIGO interferometers.

On measuring the gravitational-wave background using Pulsar Timing Arrays

Long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months-to-years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays (PTA), are being pursued around the world. Here we develop a Bayesian inference method for measuring the stochastic gravitational-wave background (GWB) from the PTA data. Our method has several strengths: (1) It analyses the data without any loss of information, (2) It trivially removes systematic errors of known functional form, including quadratic pulsar spindown, annual modulations and jumps due to a change of equipment, (3) It measures simultaneously both the amplitude and the slope of the GWB spectrum, (4) It can deal with unevenly sampled data and coloured pulsar noise spectra. We sample the likelihood function using Markov Chain Monte Carlo (MCMC) simulations. We extensively test our approach on mock PTA datasets, and find that the Bayesian inference method has significant benefits over currently proposed counterparts. We show the importance of characterising all red noise components in pulsar timing noise by demonstrating that the presence of a red component would significantly hinder a detection of the GWB. Lastly, we explore the dependence of the signal-to-noise ratio on the duration of the experiment, number of monitored pulsars, and the magnitude of the pulsar timing noise. These parameter studies will help formulate observing strategies for the PTA experiments.

Magnetar oscillations – I. Strongly coupled dynamics of the crust and the core

Quasi-periodic oscillations (QPOs) observed at the tail end of soft gamma repeaters giant flares are commonly interpreted as the torsional oscillations of magnetars. From a theoretical perspective, the oscillatory motion is influenced by the strong interaction between the shear modes of the crust and magnetohydrodynamic Alfven-like modes in the core. We study the dynamics which arises through this interaction, and present several new results. (1) We show that discrete edge modes frequently reside near the edges of the core Alfven continuum, and explain using simple models why these are generic and long-lived. (2) We compute the magnetar’s oscillatory motion for realistic axisymmetric magnetic field configurations and core density profiles, but with a simplified model of the elastic crust. We show that one may generically get multiple gaps in the Alfven continuum. One obtains strong discrete gap modes if the crustal frequencies belong to the gaps; the resulting frequencies do not coincide with, but are in some cases close to the crustal frequencies. (3) We deal with the issue of tangled magnetic fields in the core by developing a phenomenological model to quantify the tangling. We show that field tangling enhances the role of the core discrete Alfven modes and reduces the role of the core Alfven continuum in the overall oscillatory dynamics of the magnetar. (4) We demonstrate that the system displays transient QPOs when parts of the spectrum of the core Alfven modes contain discrete modes which are densely and regularly spaced in frequency. The transient QPOs are the strongest when they are located near the frequencies of the crustal modes. (5) We show that if the neutrons are coupled into the core Alfven motion, then the post-flare crustal motion is strongly damped and has a very weak amplitude. We thus argue that magnetar QPOs give evidence that the proton and neutron components in the core are dynamically decoupled and that at least one of them is a quantum fluid. (6) We show that it is difficult to identify the high-frequency 625-Hz QPO as being due to the physical oscillatory mode of the magnetar, if the latter’s fluid core consists of the standard proton–neutron–electron mixture and is magnetized to the same extent as the crust.

The European Pulsar Timing Array:current efforts and a LEAP toward the future

The European Pulsar Timing Array (EPTA) is a multi-institutional, multi-telescope collaboration, with the goal of using high-precision pulsar timing to directly detect gravitational waves. In this paper we discuss the EPTA member telescopes, current achieved timing precision and near-future goals. We report a preliminary upper limit to the amplitude of a gravitational wave background. We also discuss the Large European Array for Pulsars, in which the five major European telescopes involved in pulsar timing will be combined to provide a coherent array that will give similar sensitivity to the Arecibo radio telescope, and larger sky coverage.