Tidal evolution of eccentric binary systems containing at least one massive main-sequence (MS) star plays an important role in the formation scenarios of merging compact-object binaries. The dominant dissipation mechanism in such systems involves tidal excitation of outgoing internal gravity waves at the convective-radiative boundary and dissipation of the waves at the stellar envelope/surface. We have derived analytical expressions for the tidal torque and tidal energy transfer rate in such binaries for arbitrary orbital eccentricities and stellar rotation rates. These expressions can be used to study the spin and orbital evolution of eccentric binaries containing massive MS stars, such as the progenitors of merging neutron star binaries. Applying our results to the PSR J0045-7319 system, which has a massive B-star companion and an observed, rapidly decaying orbit, we find that for the standard radius of convective core based on non-rotating stellar models, the B-star must have a significant retrograde and differential rotation in order to explain the observed orbital decay rate. Alternatively, we suggest that the convective core may be larger as a result of rapid stellar rotation and/or mass transfer to the B-star in the recent past during the post-MS evolution of the pulsar progenitor.
We examine the reasons for discrepancies between two alternative approaches to modeling small-amplitude tides in binary systems. The direct solution (DS) approach solves the governing differential equations and boundary conditions directly, while the modal decomposition (MD) approach relies on a normal-mode expansion. Applied to a model for the primary star in the heartbeat system KOI-54, the two approaches predict quite different behavior of the secular tidal torque. The MD approach exhibits the pseudosynchronization phenomenon, where the torque due to the equilibrium tide changes sign at a single, well-defined, and theoretically predicted stellar rotation rate. The DS approach instead shows “blurred” pseudosynchronization, where positive and negative torques intermingle over a range of rotation rates. We trace a major source of these differences to an incorrect damping coefficient in the profile functions describing the frequency dependence of the MD expansion coefficients. With this error corrected, some differences between the approaches remain; however, both are in agreement that pseudosynchronization is blurred in the KOI-54 system. Our findings generalize to any type of star for which the tidal damping depends explicitly or implicitly on the forcing frequency.
more » « less- NSF-PAR ID:
- 10437566
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 953
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 48
- Size(s):
- Article No. 48
- Sponsoring Org:
- National Science Foundation
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