We extend our previous work on applying CMB techniques to the mapping of gravitational-wave backgrounds to backgrounds which have non-GR polarisations. Our analysis and results are presented in the context of pulsar-timing array observations, but the
overarching methods are general, and can be easily applied to LIGO or eLISA observations using appropriately modified response functions. Analytic expressions for the pulsar-timing response to gravitational waves with non-GR polarisation are given for each mode of a spin-weighted spherical-harmonic decomposition of the background, which permit the signal to be mapped across the sky to any desired resolution. We also derive the pulsar-timing overlap reduction functions for the various non-GR polarisations, finding analytic forms for anisotropic backgrounds with scalar-transverse (breathing) and vector-longitudinal polarisations, and a semi-analytic form for scalar-longitudinal backgrounds. Our results indicate that pulsar-timing observations will be completely insensitive to scalar-transverse mode anisotropies in the polarisation amplitude beyond dipole, and anisotropies in the power beyond quadrupole. Analogously to our previous findings that pulsar-timing observations lack sensitivity to tensor-curl modes for a transverse-traceless tensor background, we also find insensitivity to vector-curl modes for a vector-longitudinal background.
We discuss the detection of gravitational-wave backgrounds in the context of Bayesian inference and suggest a practical definition of what it means for a signal to be considered stochastic---namely, that the Bayesian evidence favors a stochastic sign
al model over a deterministic signal model. A signal can further be classified as Gaussian-stochastic if a Gaussian signal model is favored. In our analysis we use Bayesian model selection to choose between several signal and noise models for simulated data consisting of uncorrelated Gaussian detector noise plus a superposition of sinusoidal signals from an astrophysical population of gravitational-wave sources. For simplicity, we consider co-located and co-aligned detectors with white detector noise, but the method can be extended to more realistic detector configurations and power spectra. The general trend we observe is that a deterministic model is favored for small source numbers, a non-Gaussian stochastic model is preferred for intermediate source numbers, and a Gaussian stochastic model is preferred for large source numbers. However, there is very large variation between individual signal realizations, leading to fuzzy boundaries between the three regimes. We find that a hybrid, trans-dimensional model comprised of a deterministic signal model for individual bright sources and a Gaussian-stochastic signal model for the remaining confusion background outperforms all other models in most instances.
We extend the formalisms developed in Gair et al. and Cornish and van Haasteren to create maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We show that in contrast to pulsar timing arrays, which are insens
itive to half of the gravitational-wave sky (the curl modes), a network of ground-based interferometers is sensitive to both the gradient and curl components of the background. The spatial separation of a network of interferometers, or of a single interferometer at different times during its rotational and orbital motion around the Sun, allows for recovery of both components. We derive expressions for the response functions of a laser interferometer in the small-antenna limit, and use these expressions to calculate the overlap reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of the + and x-polarization modes of the gravitational-wave sky in terms of the response matrix for a network of ground-based interferometers, evaluated at discrete times during Earths rotational and orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple simulated backgrounds (a single point source and spatially-extended distributions having only grad or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on the (pseudo)inverse of the response matrix. The distinction between this approach and standard methods for mapping gravitational-wave power is also discussed.
We have analysed a sample of 18 RR Lyrae stars (17 fundamental-mode - RRab - and one first overtone - RRc) and three Population II Cepheids (two BL Her stars and one W Vir star), for which high-resolution (R $ge$30000), high signal-to-noise (S/N$ge$3
0) spectra were obtained with either SARG at the Telescopio Nazionale Galileo (La Palma, Spain) or UVES at the ESO Very Large Telescope (Paranal, Chile). Archival data were also analyzed for a few stars, sampling $gtrsim$3 phases for each star. We obtained atmospheric parameters (T$_{rm{eff}}$, log$g$, v$_{rm{t}}$, and [M/H]) and abundances of several iron-peak and $alpha$-elements (Fe, Cr, Ni, Mg, Ca, Si, and Ti) for different pulsational phases, obtaining $<$[$alpha$/Fe]$>$=+0.31$pm$0.19 dex over the entire sample covering -2.2$<$[Fe/H]$<$-1.1 dex. We find that silicon is indeed extremely sensitive to the phase, as reported by previous authors, and cannot be reliably determined. Apart from this, metallicities and abundance ratios are consistently determined, regardless of the phase, within 0.10-0.15 dex, although caution should be used in the range $0lesssimphilesssim0.15$. Our results agree with literature determinations for both variable and non-variable field stars, obtained with very different methods, including low and high-resolution spectroscopy. W Vir and BL Her stars, at least in the sampled phases, appear indistinguishable from RRab from the spectroscopic analysis point of view. Our large sample, covering all pulsation phases, confirms that chemical abundances can be obtained for RR Lyrae with the classical EW-based technique and static model atmospheres, even rather close to the shock phases.
Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array. The correlation signature of an isotropic, unpolarized gravitat
ional-wave background predicted by general relativity follows the so-called Hellings and Downs curve, which is a relatively simple function of the angle between a pair of Earth-pulsar baselines. In this paper, we give a pedagogical discussion of the Hellings and Downs curve for pulsar timing arrays, considering simpler analogous scenarios involving sound and electromagnetic waves. We calculate Hellings-and-Downs-type functions for these two scenarios and develop a framework suitable for doing more general correlation calculations.
We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterise the polarisation of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptio
ns about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarised and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics.
We have explored the Eu production in the Milky Way by means of a very detailed chemical evolution model. In particular, we have assumed that Eu is formed in merging neutron star (or neutron star black hole) binaries as well as in type II supernovae.
We have tested the effects of several important parameters influencing the production of Eu during the merging of two neutron stars, such as: i) the time scale of coalescence, ii) the Eu yields and iii) the range of initial masses for the progenitors of the neutron stars. The yields of Eu from type II supernovae are very uncertain, more than those from coalescing neutron stars, so we have explored several possibilities. We have compared our model results with the observed rate of coalescence of neutron stars, the solar Eu abundance, the [Eu/Fe] versus [Fe/H] relation in the solar vicinity and the [Eu/H] gradient along the Galactic disc. Our main results can be summarized as follows: i) neutron star mergers can be entirely responsible for the production of Eu in the Galaxy if the coalescence time scale is no longer than 1 Myr for the bulk of binary systems, the Eu yield is around $3 times 10^{-7}$ M$_odot$, and the mass range of progenitors of neutron stars is 9-50 M$_odot$; ii) both type II supernovae and merging neutron stars can produce the right amount of Eu if the neutron star mergers produce $2 times 10^{-7}$ M$_odot$ per system and type II supernovae, with progenitors in the range 20-50 M$_odot$, produce yields of Eu of the order of $10^{-8}-10^{-9}$ M$_odot$; iii) either models with only neutron stars producing Eu or mixed ones can reproduce the observed Eu abundance gradient along the Galactic disc.
We study the chemical evolution and formation of the Galactic halo through the analysis of its stellar metallicity distribution function and some key elemental abundance patterns. Starting from the two-infall model for the Galaxy, which predicts too
few low-metallicity stars, we add a gas outflow during the halo phase with a rate proportional to the star formation rate through a free parameter, lambda. In addition, we consider a first generation of massive zero-metal stars in this two-infall + outflow model adopting two different top-heavy initial mass functions and specific population III yields. The metallicity distribution function of halo stars, as predicted by the two-infall + outflow model shows a good agreement with observations, when the parameter lambda=14 and the time scale for the first infall, out of which the halo formed, is not longer than 0.2 Gyr, a lower value than suggested previously. Moreover, the abundance patterns [X/Fe] vs. [Fe/H] for C, N and alpha-elements O, Mg, Si, S, Ca show a good agreement with the observational data. If population III stars are included, under the assumption of different initial mass functions, the overall agreement of the predicted stellar metallicity distribution function with observational data is poorer than in the case without population III. We conclude that it is fundamental to include both a gas infall and outflow during the halo formation to explain the observed halo metallicity distribution function, in the framework of a model assuming that the stars in the inner halo formed mostly in situ. Moreover, we find that it does not exist a satisfactory initial mass function for population III stars which reproduces the observed halo metallicity distribution function. As a consequence, there is no need for a first generation of only massive stars to explain the evolution of the Galactic halo.
Uncertainty in the calibration of gravitational-wave (GW) detector data leads to systematic errors which must be accounted for in setting limits on the strength of GW signals. When cross-correlation measurements are made using data from a pair of ins
truments, as in searches for a stochastic GW background, the calibration uncertainties of the individual instruments can be combined into an uncertainty associated with the pair. With the advent of multi-baseline GW observation (e.g., networks consisting of multiple detectors such as the LIGO observatories and Virgo), a more sophisticated treatment is called for. We describe how the correlations between calibration factors associated with different pairs can be taken into account by marginalizing over the uncertainty associated with each instrument.
Galaxies are complex systems the evolution of which apparently results from the interplay of dynamics, star formation, chemical enrichment, and feedback from supernova explosions and supermassive black holes. The hierarchical theory of galaxy formati
on holds that galaxies are assembled from smaller pieces, through numerous mergers of cold dark matter. The properties of an individual galaxy should be controlled by six independent parameters including mass, angular-momentum, baryon-fraction, age and size, as well as by the accidents of its recent haphazard merger history. Here we report that a sample of galaxies that were first detected through their neutral hydrogen radio-frequency emission, and are thus free of optical selection effects, shows five independent correlations among six independent observables, despite having a wide range of properties. This implies that the structure of these galaxies must be controlled by a single parameter, although we cannot identify this parameter from our dataset. Such a degree of organisation appears to be at odds with hierarchical galaxy formation, a central tenet of the cold dark matter paradigm in cosmology.
