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  1. ABSTRACT

    We revisit the classical KZ problem – determination of the vertical force and implied total mass density distribution of the Milky Way disc – for a wide range of Galactocentric radius and vertical height using chemically selected thin and thick disc samples based on Apache Point Observatory Galactic Evolution Experiment spectroscopy combined with the Gaia astrometry. We derived the velocity dispersion profiles in Galactic cylindrical coordinates, and solved the Jeans equation for the two samples separately. The result is surprising that the total surface mass density as a function of vertical height as derived for these two chemically distinguished populations is different. The discrepancies are larger in the inner compared to the outer Galaxy, with the density calculated from thick disc being larger, independent of the Galactic radius. Furthermore, while there is an overall good agreement between the total mass density derived for the thick disc population and the standard halo model for vertical heights larger than 1 kpc, close to the mid-plane the mass density observed using the thick disc population is larger than that predicted from the standard halo model. We explore various implications of these discrepancies, and speculate their sources, including problems associated with the assumed density laws, velocity dispersion profiles, and the Galactic rotation curve, potential non-equilibrium of the Galactic disc, or a failure of the Navarro-Frenk-White (NFW) dark matter halo profile for the Milky Way. We conclude that the growing detail in hand on the chemodynamical distributions of Milky Way stars challenges traditional analytical treatments of the KZ problem.

     
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  2. Abstract

    We study tidal dissipation in hot Jupiter host stars due to the nonlinear damping of tidally driveng-modes, extending the calculations of Essick & Weinberg to a wide variety of stellar host types. This process causes the planet’s orbit to decay and has potentially important consequences for the evolution and fate of hot Jupiters. Previous studies either only accounted for linear dissipation processes or assumed that the resonantly excited primary mode becomes strongly nonlinear and breaks as it approaches the stellar center. However, the great majority of hot Jupiter systems are in the weakly nonlinear regime in which the primary mode does not break but instead excites a sea of secondary modes via three-mode interactions. We simulate these nonlinear interactions and calculate the net mode dissipation for stars that range in mass from 0.5MM≤ 2.0Mand in age from the early main sequence to the subgiant phase. We find that the nonlinearly excited secondary modes can enhance the tidal dissipation by orders of magnitude compared to linear dissipation processes. For the stars withM≲ 1.0Mof nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periodsPorb≲ 1 day. ForM≳ 1.2M, the orbital decay time only becomes short on the subgiant branch, where it can be ≲10 Myr forPorb≲ 2 days and result in significant transit time shifts. We discuss these results in the context of known hot Jupiter systems and examine the prospects for detecting their orbital decay with transit timing measurements.

     
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  3. ABSTRACT

    Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral and hence imprint a signature on their gravitational wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve the accuracy and explanatory power of waveform models. We set up and numerically solve the coupled differential equations for the orbit and the modes and analytically derive solutions of the system’s equilibrium configuration. Our analytical solutions agree well with the numerical ones up to the merger and involve only algebraic relations, allowing for fast phase shift and waveform evaluations for different equations of state over a large parameter space. We find that, at Newtonian order, non-linear fluid effects can enhance the tidal phase shift by $\gtrsim 1\, {\rm radian}$ at a GW frequency of 1000 Hz, corresponding to a $10{{\%}}-20{{\%}}$ correction to the linear theory. The scale of the additional phase shift near the merger is consistent with the difference between numerical relativity and theoretical predictions that account only for the linear tide. Non-linear fluid effects are thus important when interpreting the results of numerical relativity and in the construction of waveform models for current and future GW detectors.

     
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  4. Abstract

    High-eccentricity tidal migration is a potential formation channel for hot Jupiters. During this process, the planetary f-mode may experience a phase of diffusive growth, allowing its energy to quickly build up to large values. In Yu et al., we demonstrated that nonlinear mode interactions between a parent f-mode and daughter f- and p-modes expand the parameter space over which the diffusive growth of the parent is triggered. We extend that study by incorporating (1) the angular momentum transfer between the orbit and the mode, and consequently the evolution of the pericenter distance; (2) a prescription to regulate the nonlinear frequency shift at high parent mode energies; and (3) dissipation of the parent’s energy due to both turbulent convective damping of the daughter modes and strongly nonlinear wave-breaking events. The new ingredients allow us to follow the coupled evolution of the mode and orbit over ≳104yr, covering the diffusive evolution from its onset to its termination. We find that the semimajor axis shrinks by a factor of nearly 10 over 104yr, corresponding to a tidal quality factor10. The f-mode’s diffusive growth terminates while the eccentricity is still high, at arounde= 0.8–0.95. Using these results, we revisit the eccentricity distribution of proto-hot Jupiters. We estimate that less than 1 proto-HJ with eccentricity >0.9 should be expected in Kepler's data once the diffusive regime is accounted for, explaining the observed paucity of this population.

     
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  6. ABSTRACT

    The space-borne gravitational wave interferometer, Laser Interferometer Space Antenna, is expected to detect signals from numerous binary white dwarfs. At small orbital separation, rapid rotation and large tidal bulges may allow for the stellar internal structure to be probed through such observations. Finite-size effects are encoded in quantities like the moment of inertia (I), tidal Love number (Love), and quadrupole moment (Q). The universal relations among them (I–Love–Q relations) can be used to reduce the number of parameters in the gravitational-wave templates. We here study I–Love–Q relations for more realistic white dwarf models than used in previous studies. In particular, we extend previous works by including (i) differential rotation and (ii) internal temperature profiles taken from detailed stellar evolution calculations. We use the publicly available stellar evolution code mesa to generate cooling models of both low- and high-mass white dwarfs. We show that differential rotation causes the I–Q relation (and similarly the Love–Q relation) to deviate from that of constant rotation. We also find that the introduction of finite temperatures causes the white dwarf to move along the zero-temperature mass sequence of I–Q values, moving towards values that suggest a lower mass. We further find that after only a few Myr, high-mass white dwarfs are well described by the zero-temperature model, suggesting that the relations with zero temperature may be good enough in most practical cases. Low-mass, He-core white dwarfs with thick hydrogen envelopes may undergo long periods of H burning which sustain the stellar temperature and allow deviations from the I–Love–Q relations for longer times.

     
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