Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tidal heating of Earth-like exoplanets around M stars: Thermal,
  magnetic, and orbital evolutions   The internal thermal and magnetic evolution of rocky exoplanets is critical
to their habitability. We focus on the thermal-orbital evolution of Earth-mass
planets around low mass M stars whose radiative habitable zone overlaps with
the "tidal zone". We develop a thermal-orbital evolution model calibrated to
Earth that couples tidal dissipation, with a temperature-dependent Maxwell
rheology, to orbital circularization and migration. We illustrate
thermal-orbital steady states where surface heat flow is balanced by tidal
dissipation and cooling can be stalled for billions of years until
circularization occurs. Orbital energy dissipated as tidal heat in the interior
drives both inward migration and circularization, with a circularization time
that is inversely proportional to the dissipation rate. We identify a peak in
the internal dissipation rate as the mantle passes through a visco-elastic
state at mantle temperatures near 1800 K. Planets orbiting a 0.1 solar-mass
star within $0.07$ AU circularize before 10 Gyr, independent of initial
eccentricity. Once circular, these planets cool monotonically and maintain
dynamos similar to Earth. Planets forced into eccentric orbits can experience a
super-cooling of the core and rapid core solidification, inhibiting dynamo
action for planets in the habitable zone. We find that tidal heating is
insignificant in the habitable zone around $0.45$ (or larger) solar mass stars
because tidal dissipation is a stronger function of orbital distance than
stellar mass, and the habitable zone is further from larger stars. Suppression
of the planetary magnetic field exposes the atmosphere to stellar wind erosion
and the surface to harmful radiation. In addition to weak magnetic fields,
massive melt eruption rates and prolonged magma oceans may render eccentric
planets in the habitable zone of low mass stars inhospitable for life.

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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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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: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: econ