Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tidal Evolution of Asteroidal Binaries. Ruled by Viscosity. Ignorant of
  Rigidity   The rate of tidal evolution of asteroidal binaries is defined by the
dynamical Love numbers divided by quality factors. Common is the (often
illegitimate) approximation of the dynamical Love numbers with their static
counterparts. As the static Love numbers are, approximately, proportional to
the inverse rigidity, this renders a popular fallacy that the tidal evolution
rate is determined by the product of the rigidity by the quality factor:
$\,k_l/Q\propto 1/(\mu Q)\,$. In reality, the dynamical Love numbers depend on
the tidal frequency and all rheological parameters of the tidally perturbed
body (not just rigidity). We demonstrate that in asteroidal binaries the
rigidity of their components plays virtually no role in tidal friction and
tidal lagging, and thereby has almost no influence on the intensity of tidal
interactions (tidal torques, tidal dissipation, tidally induced changes of the
orbit). A key quantity that determines the tidal evolution is a product of the
effective viscosity $\,\eta\,$ by the tidal frequency $\,\chi\,$. The
functional form of the torque's dependence on this product depends on who wins
in the competition between viscosity and self-gravitation. Hence a quantitative
criterion, to distinguish between two regimes. For higher values of
$\,\eta\chi\,$ we get $\,k_l/Q\propto 1/(\eta\chi)\;$; $\,$while for lower
values we obtain $\,k_l/Q\propto \eta\chi\,$. Our study rests on an assumption
that asteroids can be treated as Maxwell bodies. Applicable to rigid rocks at
low frequencies, this approximation is used here also for rubble piles, due to
the lack of a better model. In the future, as we learn more about mechanics of
granular mixtures in a weak gravity field, we may have to amend the tidal
theory with other rheological parameters, ones that do not show up in the
description of viscoelastic bodies.

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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph