Gravitational waves from compact binaries

In this review, I give a summary of the history of our understanding of gravitational waves and how compact binaries were used to transform their status from mathematical artefact to physical reality. I also describe the types of compact (stellar) binaries that LISA will observe as soon as it is switched on. Finally, the status and near future of LIGO, Virgo and GEO are discussed, as well as the expected detection rates for the Advanced detectors, and the accuracies with which binary parameters can be determined when BH/NS inspirals are detected.Comment: 15 pages, 3 figures, 2 tables. To be published in "Evolution of compact binaries", editors: Linda Schmidtobreick, Matthias Schreiber and Claus Tapper

Masses and envelope binding energies of primary stars at the onset of a common envelope

We present basic properties of primary stars that initiate a common envelope (CE) in a binary, while on the giant branch. We use the population-synthesis code described in Politano et al. (2010) and follow the evolution of a population of binary stars up to the point where the primary fills its Roche lobe and initiates a CE. We then collect the properties of each system, in particular the donor mass and the binding energy of the donor's envelope, which are important for the treatment of a CE. We find that for most CEs, the donor mass is sufficiently low to define the core-envelope boundary reasonably well. We compute the envelope-structure parameter {\lambda_\mathrm{env}} from the binding energy and compare its distribution to typical assumptions that are made in population-synthesis codes. We conclude that {\lambda_\mathrm{env}} varies appreciably and that the assumption of a constant value for this parameter results in typical errors of 20--50%. In addition, such an assumption may well result in the implicit assumption of unintended and/or unphysical values for the CE parameter {\alpha_\mathrm{CE}}. Finally, we discuss accurate existing analytic fits for the envelope binding energy, which make these oversimplified assumptions for {\lambda_\mathrm{env}}, and the use of {\lambda_\mathrm{env}} in general, unnecessary.Comment: 6 pages, 3 figures, 1 table; to be published in the proceedings of the conference "Binary Star Evolution", in Mykonos, Greece, held in June 22-25, 201

Analytical expressions for the envelope binding energy of giants as a function of basic stellar parameters

The common-envelope (CE) phase is an important stage in the evolution of binary stellar populations. The most common way to compute the change in orbital period during a CE is to relate the binding energy of the envelope of the Roche-lobe filling giant to the change in orbital energy. Especially in population-synthesis codes, where the evolution of millions of stars must be computed and detailed evolutionary models are too expensive computationally, simple approximations are made for the envelope binding energy. In this study, we present accurate analytic prescriptions based on detailed stellar-evolution models that provide the envelope binding energy for giants with metallicities between Z = 10-4 and Z = 0.03 and masses between 0.8 Msun and 100 Msun, as a function of the metallicity, mass, radius and evolutionary phase of the star. Our results are also presented in the form of electronic data tables and Fortran routines that use them. We find that the accuracy of our fits is better than 15% for 90% of our model data points in all cases, and better than 10% for 90% of our data points in all cases except the asymptotic giant branches for three of the six metallicities we consider. For very massive stars (M > 50 Msun), when stars lose more than ~20% of their initial mass due to stellar winds, our fits do not describe the models as accurately. Our results are more widely applicable - covering wider ranges of metallicity and mass - and are of higher accuracy than those of previous studies

Why Halley did not discover proper motion and why Cassini did

In 1717 Halley compared contemporaneous measurements of the latitudes of four stars with earlier measurements by ancient Greek astronomers and by Brahe, and from the differences concluded that these four stars showed proper motion. An analysis with modern methods shows that the data used by Halley do not contain significant evidence for proper motion. What Halley found are the measurement errors of Ptolemaios and Brahe. Halley further argued that the occultation of Aldebaran by the Moon on 11 March 509 in Athens confirmed the change in latitude of Aldebaran. In fact, however, the relevant observation was almost certainly made in Alexandria where Aldebaran was not occulted. By carefully considering measurement errors Jacques Cassini showed that Halley's results from comparison with earlier astronomers were spurious, a conclusion partially confirmed by various later authors. Cassini's careful study of the measurements of the latitude of Arcturus provides the first significant evidence for proper motion.Comment: 15 pages, 3 figures, accepted for publication in the Journal for the History of Astronom

Why Halley did not discover proper motion and why Cassini did

In 1717 Halley compared contemporaneous measurements of the latitudes of four stars with earlier measurements by ancient Greek astronomers and by Brahe, and from the differences concluded that these four stars showed proper motion. An analysis with modern methods shows that the data used by Halley do not contain significant evidence for proper motion. What Halley found are the measurement errors of Ptolemaios and Brahe. Halley further argued that the occultation of Aldebaran by the Moon on 11 March 509 in Athens confirmed the change in latitude of Aldebaran. In fact, however, the relevant observation was almost certainly made in Alexandria where Aldebaran was not occulted. By carefully considering measurement errors Jacques Cassini showed that Halley's results from comparison with earlier astronomers were spurious, a conclusion partially confirmed by various later authors. Cassini's careful study of the measurements of the latitude of Arcturus provides the first significant evidence for proper motion

SolTrack: a free, fast and accurate routine to compute the position of the Sun

We present a simple, free, fast and accurate C/C++ and Python routine called SolTrack, which can compute the position of the Sun at any instant and any location on Earth. The code allows tracking of the Sun using a low-specs embedded processor, such as a PLC or a microcontroller, and can be used for applications in the field of (highly) concentrated (photovoltaic) solar power ((H)CPV and CSP), such as tracking control and yield modelling. SolTrack is accurate, fast and open in its use, and compares favourably with similar algorithms that are currently available for solar tracking and modelling. SolTrack computes $1.5 \times 10^6$ positions per second on a single 2.67GHz CPU core. For the period between the years 2017 and 2116 the uncertainty in position is $0.0036 \pm 0.0042^\circ$, that in solar distance 0.0017 $\pm$ 0.0029%. In addition, SolTrack computes rise, transit and set times to an accuracy better than 1 second. The code is freely available online (http://soltrack.sf.net, https://pypi.org/project/soltrack/)

Type Ia Supernovae and Accretion Induced Collapse

Using the population synthesis binary evolution code StarTrack, we present theoretical rates and delay times of Type Ia supernovae arising from various formation channels. These channels include binaries in which the exploding white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a white dwarf accretes from a helium-rich companion and explodes as a SN Ia before reaching the Chandrasekhar mass limit. We find that using a common envelope parameterization employing energy balance with alpha=1 and lambda=1, the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a burst of star formation at t=0. Additionally, the delay time distribution of the sub-Chandrasekhar model can be divided in to two distinct evolutionary channels: the `prompt' helium-star channel with delay times < 500 Myr, and the `delayed' double white dwarf channel with delay times > 800 Myr spanning up to a Hubble time. These findings are in agreement with recent observationally-derived delay time distributions which predict that a large number of SNe Ia have delay times < 1 Gyr, with a significant fraction having delay times < 500 Myr. We find that the DDS channel is also able to account for the observed rates of SNe Ia. However, detailed simulations of white dwarf mergers have shown that most of these mergers will not lead to SNe Ia but rather to the formation of a neutron star via accretion-induced collapse. If this is true, our standard population synthesis model predicts that the only progenitor channel which can account for the rates of SNe Ia is the sub-Chandrasekhar mass scenario, and none of the other progenitors considered can fully account for the observed rates.Comment: 6 pages, 1 figure, 1 table, to appear in proceedings for "Binary Star Evolution: Mass Loss, Accretion and Mergers

Parameter estimation of spinning binary inspirals using Markov-chain Monte Carlo

We present a Markov-chain Monte-Carlo (MCMC) technique to study the source parameters of gravitational-wave signals from the inspirals of stellar-mass compact binaries detected with ground-based gravitational-wave detectors such as LIGO and Virgo, for the case where spin is present in the more massive compact object in the binary. We discuss aspects of the MCMC algorithm that allow us to sample the parameter space in an efficient way. We show sample runs that illustrate the possibilities of our MCMC code and the difficulties that we encounter.Comment: 10 pages, 2 figures, submitted to Classical and Quantum Gravit

Black Hole Spin Evolution: Implications for Short-hard Gamma Ray Bursts and Gravitational Wave Detection

The evolution of the spin and tilt of black holes in compact black hole - neutron star and black hole - black hole binary systems is investigated within the framework of the coalescing compact star binary model for short gamma ray bursts via the population synthesis method. Based on recent results on accretion at super critical rates in slim disk models, estimates of natal kicks, and the results regarding fallback in supernova models, we obtain the black hole spin and misalignment. It is found that the spin parameter, a_spin}, is less than 0.5 for initially non rotating black holes and the tilt angle, i_tilt, is less than 45 deg for 50% of the systems in black hole - neutron star binaries. Upon comparison with the results of black hole - neutron star merger calculations we estimate that only a small fraction (~ 0.01) of these systems can lead to the formation of a torus surrounding the coalesced binary potentially producing a short-hard gamma ray burst. On the other hand, for high initial black hole spin parameters (a_spin>0.6) this fraction can be significant (~ 0.4). It is found that the predicted gravitational radiation signal for our simulated population does not significantly differ from that for non rotating black holes. Due to the (i) insensitivity of signal detection techniques to the black hole spin and the (ii) predicted overall low contribution of black hole binaries to the signal we find that the detection of gravitational waves are not greatly inhibited by current searches with non spinning templates. It is pointed out that the detection of a black hole - black hole binary inspiral system with LIGO or VIRGO may provide a direct measurement of the initial spin of a black hole.Comment: ApJ accepted: major revision

Population Synthesis of Common Envelope Mergers: I. Giant Stars with Stellar or Substellar Companions

Using a population synthesis technique, we have calculated detailed models of the present-day field population of objects that have resulted from the merger of a giant primary and a main-sequence or brown dwarf secondary during common-envelope evolution. We used a grid of 116 stellar and 32 low-mass/brown dwarf models, a crude model of the merger process, and followed the angular momentum evolution of the binary orbit and the primary's rotation prior to merger, as well as the merged object's rotation after the merger. We find that present-day merged objects that are observable as giant stars or core-helium burning stars in our model population constitute between 0.24% and 0.33% of the initial population of ZAMS binaries, depending upon the input parameters chosen. The median projected rotational velocity of these merged objects is ~16 km/sec, an order of magnitude higher than the median projected rotational velocity in a model population of normal single stars calculated using the same stellar models and initial mass function. The masses of the merged objects are typically less than ~2 solar masses, with a median mass of 1.28 solar masses, which is slightly more than, but not significantly different from, their normal single star counterparts. The luminosities in our merged object population range from ~10-100 solar luminosities, with a strong peak in the luminosity distribution at ~60 solar luminosities, since the majority of the merged objects (57%) lie on the horizontal branch at the present epoch. The results of our population synthesis study are discussed in terms of possible observational counterparts either directly involving the high rotational velocity of the merger product or indirectly, via the effect of rotation on envelope abundances and on the amount and distribution of circumstellar matter.Comment: 16 pages, 12 figures, accepted for publication in the Astrophysical Journa