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Equilibrium Configurations of Synchronous Binaries: Numerical Solutions and Application to Kuiper Belt Binary 2001 QG298

Gnat, Orly and Sari, Re'em (2010) Equilibrium Configurations of Synchronous Binaries: Numerical Solutions and Application to Kuiper Belt Binary 2001 QG298. Astrophysical Journal, 719 (2). pp. 1602-1618. ISSN 0004-637X. http://resolver.caltech.edu/CaltechAUTHORS:20100902-133503627

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Abstract

We present numerical computations of the equilibrium configurations of tidally locked homogeneous binaries rotating in circular orbits. Unlike the classical Roche approximations, we self-consistently account for the tidal and rotational deformations of both components, and relax the assumptions of ellipsoidal configurations and Keplerian rotation. We find numerical solutions for mass ratios q between 10^(–3) and 1, starting at a small angular velocity for which tidal and rotational deformations are small, and following a sequence of increasing angular velocities. Each series terminates at an appropriate "Roche limit," above which no equilibrium solution can be found. Even though the Roche limit is crossed before the "Roche lobe" is filled, any further increase in the angular velocity will result in mass-loss. For close, comparable-mass binaries, we find that local deviations from ellipsoidal forms may be as large as 10%-20%, and departures from Keplerian rotation are significant. We compute the light curves that arise from our equilibrium configurations, assuming their distance is ≫1 AU (e.g., in the Kuiper Belt). We consider both backscatter (proportional to the projected area) and diffuse (Lambert) reflections. Backscatter reflection always yields two minima of equal depths. Diffuse reflection, which is sensitive to the surface curvature, generally gives rise to unequal minima. We find detectable intensity differences of up to 10% between our light curves and those arising from the Roche approximations. Finally, we apply our models to Kuiper Belt binary 2001 QG298, and find a nearly edge-on binary with a mass ratio q = 0.93^(+0.07)_(–0.03), angular velocity ω^2/Gρ = 0.333 ± 0.001 (statistical errors only), and pure diffuse reflection. For the observed period of 2001 QG_(298), these parameters imply a bulk density ρ = 0.72 ± 0.04 g cm^(–3).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1088/0004-637X/719/2/1602DOIUNSPECIFIED
http://iopscience.iop.org/0004-637X/719/2/1602PublisherUNSPECIFIED
Additional Information:© 2010 American Astronomical Society. Received 2010 March 29; accepted 2010 June 28; published 2010 August 2. We thank Oded Aharonson, Peter Goldreich, Ehud Nakar, Eran Ofek, David Polishook, and Hilke Schlichting for helpful discussions. Some of the numerical calculations presented in this work were performed on Caltech’s Division of Geological and Planetary Sciences Dell cluster. We thank Oded Aharonson for his assistance with our use of the cluster. O.G. acknowledges support provided by NASA through Chandra Postdoctoral Fellowship grant number PF8-90053 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. The research of R.S. is supported by IRG and ERC grants, and a Packard Fellowship.
Funders:
Funding AgencyGrant Number
NASAPF8-90053
IRG grantUNSPECIFIED
ERC grantUNSPECIFIED
Packard FellowshipUNSPECIFIED
Subject Keywords:Kuiper Belt: general; Kuiper Belt objects: individual (2001 QG298); minor planets, asteroids: general
Classification Code:PACS: 95.75.-z; 96.25.Nc; 96.30.Xa; 96.25.De
Record Number:CaltechAUTHORS:20100902-133503627
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100902-133503627
Official Citation:Orly Gnat and Re'em Sari 2010 ApJ 719 1602 doi: 10.1088/0004-637X/719/2/1602
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19771
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:03 Sep 2010 17:31
Last Modified:26 Dec 2012 12:23

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