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Register a new userEnergy Dissipation through Quasi-Static Tides in White Dwarf Binaries
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We study tidal interactions in white dwarf binaries in the limiting case of quasi-static tides. The formalism is valid for arbitrary orbital eccentricities and therefore applicable to white dwarf binaries in the Galactic disk as well as globular clusters. In the quasi-static limit, the total perturbation of the gravitational potential shows a phase shift with respect to the position of the companion, the magnitude of which is determined primarily by the efficiency of energy dissipation through convective damping. We determine rates of secular evolution of the orbital elements and white dwarf rotational angular velocity for a 0.3 solar mass helium white dwarf in binaries with orbital frequencies in the LISA gravitational wave frequency band and companion masses ranging from 0.3 to 10^5 solar masses. The resulting tidal evolution time scales for the orbital semi-major axis are longer than a Hubble time, so that convective damping of quasi-static tides need not be considered in the construction of gravitational wave templates of white dwarf binaries in the LISA band. Spin-up of the white dwarf, on the other hand, can occur on time scales of less than 10Myr, provided that the white dwarf is initially rotating with a frequency much smaller than the orbital frequency. For semi-detached white dwarf binaries spin-up can occur on time scales of less than 1Myr. Nevertheless, the time scales remain longer than the orbital inspiral time scales due to gravitational radiation, so that the degree of asynchronism in these binaries increases. As a consequence, tidal forcing eventually occurs at forcing frequencies beyond the quasi-static tide approximation. For the shortest period binaries, energy dissipation is therefore expected to take place through dynamic tides and resonantly excited g-modes.
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Tidal interactions can play an important role as compact white dwarf (WD) binaries are driven together by gravitational waves (GWs). This will modify the strain evolution measured by future space-based GW detectors and impact the potential outcome of the mergers. Surveys now and in the near future will generate an unprecedented population of detached WD binaries to constrain tidal interactions. Motivated by this, I summarize the deviations between a binary evolving under the influence of only GW emission and a binary that is also experiencing some degree of tidal locking. I present analytic relations for the first and second derivative of the orbital period and braking index. Measurements of these quantities will allow the inference of tidal interactions, even when the masses of the component WDs are not well constrained. Finally, I discuss tidal heating and how it can provide complimentary information.
We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band ($0.1-100,{rm mHz}$). We show that for stars not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.
Although not nearly as numerous as binaries with two white dwarfs, eccentric neutron star-white dwarf (NS-WD) binaries are important gravitational-wave (GW) sources for the next generation of space-based detectors sensitive to low frequency waves. Here we investigate periastron precession in these sources as a result of general relativistic, tidal, and rotational effects; such precession is expected to be detectable for at least some of the detected binaries of this type. Currently, two eccentric NS-WD binaries are known in the galactic field, PSR J1141-6545 and PSR B2303+46, both of which have orbits too wide to be relevant in their current state to GW observations. However, population synthesis studies predict the existence of a significant Galactic population of such systems. Though small in most of these systems, we find that tidally induced periastron precession becomes important when tides contribute to more than 3% of the total precession rate. For these systems, accounting for tides when analyzing periastron precession rate measurements can improve estimates of the WD component mass inferred and, in some cases, will prevent us from misclassifying the object. However, such systems are rare due to rapid orbital decay. To aid the inclusion of tidal effects when using periastron precession as a mass measurement tool, we derive a function that relates the WD radius and periastron precession constant to the WD mass.
We explore the prospects of detecting of Galactic double white dwarf (DWD) binaries with the space-based gravitational wave (GW) observatory TianQin. In this work, we analyze both a sample of currently known DWDs and a realistic synthetic population of DWDs to assess the number of guaranteed detections and the full capacity of the mission. We find that TianQin can detect 12 out of $sim100$ known DWDs; GW signals of these binaries can be modeled in detail ahead of the mission launch, and therefore they can be used as verification sources. Besides we estimate that TianQin has potential to detect as many as $10^4$ DWDs in the Milky Way. TianQin is expected to measure their orbital periods and amplitudes with accuracies of $sim10^{-7}$ and $sim0.2$, respectively, and to localize on the sky a large fraction (39%) of the detected population to better than 1 deg$^2$. We conclude that TianQin has the potential to significantly advance our knowledge on Galactic DWDs by increasing the sample up to 2 orders of magnitude, and will allow their multi-messenger studies in combination with electromagnetic telescopes. We also test the possibilities of different configurations of TianQin: (1) the same mission with a different orientation, (2) two perpendicular constellations combined into a network, and (3) the combination of the network with the ESA-led Laser Interferometer Space Antenna. We find that the network of detectors boosts the accuracy on the measurement of source parameters by 1-2 orders of magnitude, with the improvement on sky localization being the most significant.
The spectroscopic catalogue of white dwarf-main sequence (WDMS) binaries from the Sloan Digital Sky Survey (SDSS) is the largest and most homogeneous sample of compact binary stars currently known. However, because of selection effects, the current sample is strongly biased against systems containing cool white dwarfs and/or early type companions, which are predicted to dominate the intrinsic population. In this study we present colour selection criteria that combines optical (ugriz DR8 SDSS) plus infrared (yjhk DR9 UKIRT Infrared Sky Survey (UKIDSS), JHK Two Micron All Sky Survey (2MASS) and/or w1w2 Wide-Field Infrared Survey Explorer (WISE)) magnitudes to select 3419 photometric candidates of harbouring cool white dwarfs and/or dominant (M dwarf) companions. We demonstrate that 84 per cent of our selected candidates are very likely genuine WDMS binaries, and that the white dwarf effective temperatures and secondary star spectral types of 71 per cent of our selected sources are expected to be below <~10000-15000K, and concentrated at ~M2-3, respectively. We also present an updated version of the spectroscopic SDSS WDMS binary catalogue, which incorporates 47 new systems from SDSS DR8. The bulk of the DR8 spectroscopy is made up of main-sequence stars and red giants that were targeted as part of the Sloan Extension for Galactic Understanding and Exploration (SEGUE) Survey, therefore the number of new spectroscopic WDMS binaries in DR8 is very small compared to previous SDSS data releases. Despite their low number, DR8 WDMS binaries are found to be dominated by systems containing cool white dwarfs and therefore represent an important addition to the spectroscopic sample. The updated SDSS DR8 spectroscopic catalogue of WDMS binaries consists of 2316 systems.
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