Constraining star formation rates in cool-core brightest cluster galaxies

We used broad-band imaging data for 10 cool-core brightest cluster galaxies (BCGs) and conducted a Bayesian analysis using stellar population synthesis to determine the likely properties of the constituent stellar populations. Determination of ongoing star formation rates (SFRs), in particular, has a direct impact on our understanding of the cooling of the intracluster medium (ICM), star formation and AGN-regulated feedback. Our model consists of an old stellar population and a series of young stellar components. We calculated marginalized posterior probability distributions for various model parameters and obtained 68% plausible intervals from them. The 68% plausible interval on the SFRs is broad, owing to a wide range of models that are capable of fitting the data, which also explains the wide dispersion in the star formation rates available in the literature. The ranges of possible SFRs are robust and highlight the strength in such a Bayesian analysis. The SFRs are correlated with the X-ray mass deposition rates (the former are factors of 4 to 50 lower than the latter), implying a picture where the cooling of the ICM is a contributing factor to star formation in cool-core BCGs. We find that 9 out of 10 BCGs have been experiencing starbursts since 6 Gyr ago. While four out of 9 BCGs seem to require continuous SFRs, 5 out of 9 seem to require periodic star formation on intervals ranging from 20 Myr to 200 Myr. This time scale is similar to the cooling-time of the ICM in the central (< 5 kpc) regions.Comment: 33 pages, 14 Figures, 14 Tables. Accepted for publication in MNRA

Stochastic Gravitational Wave Measurements with Bar Detectors: Dependence of Response on Detector Orientation

The response of a cross-correlation measurement to an isotropic stochastic gravitational-wave background depends on the observing geometry via the overlap reduction function. If one of the detectors being correlated is a resonant bar whose orientation can be changed, the response to stochastic gravitational waves can be modulated. I derive the general form of this modulation as a function of azimuth, both in the zero-frequency limit and at arbitrary frequencies. Comparisons are made between pairs of nearby detectors, such as LIGO Livingston-ALLEGRO, Virgo-AURIGA, Virgo-NAUTILUS, and EXPLORER-AURIGA, with which stochastic cross-correlation measurements are currently being performed, planned, or considered.Comment: 17 pages, REVTeX (uses rcs, amsmath, hyperref, and graphicx style files), 4 figures (8 eps image files

Model-Based Cross-Correlation Search for Gravitational Waves from Scorpius X-1

We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. By adjusting the maximum time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a coherence time of 1hr, compared with a directed stochastic background search with 0.25Hz wide bins is about a factor of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30-300Hz; if the coherence time could be increased to 10hr, the range would be 20-500Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search in general and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: the search is sensitive to a combination of the intrinsic signal amplitude and the inclination of the neutron star rotation axis, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of SNR due to unmodelled effects such as signal phase acceleration within the Fourier transform timescale and gradual evolution of the spin frequency.Comment: 27 pages, 12 figures, 4 tables, pdflatex; synchronized to final version published in Phys Rev

The challenging task of determining star formation rates: the case of a massive stellar burst in the brightest cluster galaxy of Phoenix galaxy cluster

Star formation in galaxies at the center of cooling-flow galaxy clusters is an important phenomenon in the context of formation and evolution of massive galaxies in the Universe. Yet, star formation rates (SFRs) in such systems continue to be elusive. We use our Bayesian-motivated spectral energy distribution (SED)-fitting code, BAYESCOOL, to estimate the plausible SFR values in the brightest cluster galaxy of a massive, X-ray luminous galaxy cluster, Phoenix. Previous studies of Phoenix have resulted in the highest measurement of SFR for any galaxy, with the estimates reaching up to 1000 solar masses/yr. However, a very small number of models have been considered in those studies. BAYESCOOL allows us to probe a large parameter space. We consider two models for star formation history, instantaneous bursts and continuous star formation, a wide range of ages for the old and the young stellar population, along with other discrete parameters, such as the initial mass function, metallicities, internal extinction and extinction law. We find that in the absence of any prior except that the maximum cooling rate < 3000 solar masses/yr, the SFR lies in the range (2230-2890) solar masses/yr. If we impose an observational prior on the internal extinction, E(B-V) < 0.6, the best-fit SFR lies in (454-494) solar masses/yr, and we consider this as the most probable range of SFR values for Phoenix. The SFR dependence on the extinction is a reflection of the standard age-extinction degeneracy, which can be overcome by using a prior on one of the two quantities in question.Comment: 12 pages, 4 figures, 1 Table, accepted for publication in MNRA

New Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves

The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters. The division is useful in part because the Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude parameter space allow the GW signal to be written as a linear combination of four template waveforms with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which is more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as CPF (circular polarization factored) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. We illustrate some simplifying applications for these various coordinate systems, such as: a calculation of Jacobians between various coordinate systems; an illustration of the signal coordinate singularities associated with left- and right-circular polarization, which correspond to the origins of the two two-dimensional subspaces; and an elucidation of the form of the log-likelihood ratio between hypotheses of Gaussian noise with and without a continuous GW signal. These are used to illustrate some of the prospects for approximate evaluation of a Bayesian detection statistic defined by marginalization over the physical parameter space. Additionally, in the presence of simplifying assumptions about the observing geometry, we are able to explicitly evaluate the integral for the Bayesian detection statistic, and compare it to the approximate results.Comment: REVTeX, 18 pages, 8 image files included in 7 figure