TIDALLY_RR HEATED_JJ TERRESTRIAL_JJ EXOPLANETS_NN2 :_: VISCOELASTIC_JJ RESPONSE_NN1 MODELS_NN2 1_MC1 ._. 
INTRODUCTION_NN1 The_AT discovery_NN1 and_CC study_NN1 of_IO planetary_JJ systems_NN2 around_II different_JJ stars_NN2 has_VHZ revealed_VVN a_AT1 rich_JJ diversity_NN1 of_IO orbital_JJ architectures_NN2 ,_, many_DA2 of_IO them_PPHO2 not_XX anticipated_VVN ._. 
Among_II the_AT surprises_NN2 is_VBZ wide_JJ evidence_NN1 for_IF planet_NN1 migration_NN1 ,_, orbital_JJ resonances_NN2 ,_, and_CC the_AT ubiquity_NN1 of_IO high_JJ orbital_JJ eccentricities_NN2 ._. 
These_DD2 interactions_NN2 may_VM often_RR lead_VVI to_II orbits_NN2 that_CST allow_VV0 for_IF durable_JJ nonzero_NN1 eccentricities_NN2 close_RR to_II the_AT star_NN1 ,_, especially_RR for_IF terrestrial_JJ mass_JJ planets_NN2 ._. 
Our_APPGE goal_NN1 is_VBZ to_TO investigate_VVI the_AT range_NN1 of_IO tidal_JJ magnitudes_NN2 that_CST result_VV0 from_II such_DA orbital_JJ conditions_NN2 ._. 
This_DD1 paper_NN1 examines_VVZ the_AT global_JJ temperature_NN1 behavior_NN1 of_IO a_AT1 simplified_JJ terrestrial_JJ planet_NN1 during_II long-term_JJ extreme_JJ tidal_JJ heating_NN1 ,_, perhaps_RR driven_VVN by_II mean_JJ motion_NN1 or_CC secular_JJ orbital_JJ resonances_NN2 ,_, using_VVG several_DA2 different_JJ models_NN2 of_IO viscoelastic_JJ material_NN1 response_NN1 ._. 
We_PPIS2 first_MD present_JJ results_NN2 across_II a_AT1 range_NN1 of_IO orbit_NN1 periods_NN2 using_VVG a_AT1 blackbody_NN1 model_NN1 with_IW fixed_JJ material_NN1 parameters_NN2 ._. 
Each_DD1 of_IO these_DD2 alternative_JJ rock_NN1 models_NN2 has_VHZ the_AT potential_JJ to_TO exhibit_VVI complex_JJ behaviors_NN2 because_CS their_APPGE frictional_JJ work_NN1 function_NN1 is_VBZ non-monotonic_JJ in_II temperature._NNU 2_MC ._. 
RESONANCE_NN1 AND_CC STABILITY_NN1 The_AT first_MD condition_NN1 for_IF extreme_JJ tidal_JJ heating_NN1 is_VBZ proximity_NN1 to_II a_AT1 massive_JJ host_NN1 ,_, providing_VVG a_AT1 large_JJ change_NN1 in_II gravity_NN1 gradient_NN1 between_II pericenter_JJR and_CC apocenter_VV0 ._. 
While_CS moons_NN2 often_RR meet_VV0 this_DD1 criterion_NN1 ,_, only_RR now_RT have_VH0 a_AT1 large_JJ number_NN1 of_IO planets_NN2 been_VBN detected_VVN in_II regions_NN2 near_II stars_NN2 where_RRQ tidal_JJ heating_NN1 becomes_VVZ of_IO geological_JJ concern_NN1 ._. 
For_IF extreme_JJ tides_NN2 around_II a_AT1 typical_JJ main_JJ sequence_NN1 star_NN1 ,_, planets_NN2 must_VM be_VBI well_JJ inside_II the_AT 88_MC day_NNT1 orbit_NN1 of_IO Mercury_NP1 ,_, but_CCB precisely_RR within_II the_AT 1-20_MCMC day_NNT1 range_NN1 of_IO Hot_JJ and_CC Warm_JJ Jupiters_NP2 ._. 
The_AT order_NN1 of_IO capture_NN1 for_IF a_AT1 migrating_JJ perturber_NN1 favors_VVZ the_AT presence_NN1 of_IO bodies_NN2 in_II the_AT 2:1_MC and_CC 3:2_MC resonances_NN2 ._. 
Capture_VV0 here_RL is_VBZ likely_JJ ,_, and_CC bodies_NN2 must_VM have_VHI either_RR missed_VVN capture_NN1 or_CC have_VH0 been_VBN otherwise_RR scattered_VVN to_TO reach_VVI and_CC populate_VVI the_AT resonances_NN2 closer_RRR to_II the_AT perturber._NNU 2.2_MC ._. 
Secular_JJ Perturbations_NN2 Secular_JJ perturbations_NN2 occur_VV0 in_II two-planet_JJ systems_NN2 and_CC lead_VV0 to_II an_AT1 equilibrium_NN1 forced_JJ eccentricity_NN1 ._. 
Relativistic_JJ corrections_NN2 can_VM reduce_VVI these_DD2 values_NN2 somewhat_RR further_RRR ._. 
Secular_JJ timescales_NN2 are_VBR often_RR of_IO order_NN1 10,000_MC years_NNT2 ,_, while_CS moderate_JJ tidal_JJ timescales_NN2 are_VBR often_RR on_II the_AT order_NN1 of_IO a_AT1 few_DA2 million_NNO years_NNT2 ,_, suggesting_VVG that_CST conditions_NN2 can_VM exist_VVI where_RRQ modest_JJ geologically_RR significant_JJ tidal_JJ heating_NN1 is_VBZ supported_VVN by_II secular_JJ perturbations_NN2 alone_RR ._. 
While_CS extreme_JJ tides_NN2 may_VM damp_VVI forced_JJ eccentricities_NN2 ,_, temporarily_RR cessations_NN2 perhaps_RR due_II21 to_II22 mantle_NN1 melting_NN1 will_VM allow_VVI windows_NN2 for_IF secular_JJ forced_JJ eccentricities_NN2 to_TO be_VBI restored._NNU 2.3_MC ._. 
Capture_VV0 It_PPH1 is_VBZ favorable_JJ if_CS the_AT MMR_NP1 reaches_VVZ a_AT1 rocky_JJ planet_NN1 prior_II21 to_II22 a_AT1 secular_JJ resonance_NN1 that_CST could_VM pump_VVI up_RP high_JJ eccentricities_NN2 ._. 
Secular_JJ resonance_NN1 positions_NN2 depend_VV0 on_II the_AT overall_JJ solar_JJ system_NN1 configuration_NN1 and_CC shift_VV0 when_RRQ precession_NN1 rates_NN2 or_CC masses_NN2 change_VV0 (_( Nagasawa_NP1 et_RA21 al_RA22 ._. 
2005_MC )_) ._. 
While_CS many_DA2 scenario_NN1 geometries_NN2 can_VM prevent_VVI a_AT1 secular_JJ singularity_NN1 from_II disturbing_VVG a_AT1 candidate_NN1 2:1_MC Hot_JJ Earth_NN1 ,_, one_MC1 such_DA case_NN1 is_VBZ a_AT1 system_NN1 with_IW only_RR one_MC1 gas_NN1 giant_NN1 and_CC thus_RR a_AT1 lack_NN1 of_IO unstable_JJ secular_JJ resonances_NN2 ._. 
Since_CS only_RR 5%_NNU of_IO sunlike_JJ stars_NN2 appear_VV0 to_TO have_VHI gas_NN1 giants_NN2 (_( Udry_NP1 &;_NULL Santos_NP1 2007_MC )_) ,_, such_DA cases_NN2 may_VM be_VBI common_JJ ._. 
If_CS the_AT trapped_JJ Hot_JJ Earth_NN1 is_VBZ able_JK to_TO survive_VVI in_II resonance_NN1 all_DB the_AT way_NN1 down_RP to_II short_JJ periods_NN2 ,_, it_PPH1 may_VM do_VDI so_RR with_IW a_AT1 large_JJ initial_JJ reservoir_NN1 of_IO eccentricity_NN1 to_TO feed_VVI further_JJR tides_NN2 ._. 
Undamped_JJ resonant_JJ migration_NN1 by_II a_AT1 factor_NN1 of_IO 9_MC leads_VVZ inner_JJ bodies_NN2 to_II resonance_NN1 release_NN1 on_II nearly_RR circular_JJ retrograde_NN1 orbits_NN2 ._. 
For_IF these_DD2 reasons_NN2 2:1_MC trapped_VVD Hot_JJ Earths_NN2 may_VM be_VBI more_RGR favorable_JJ at_II dimmer_JJR stars_NN2 ,_, where_CS snow_NN1 lines_NN2 are_VBR closer_JJR and_CC requisite_JJ migration_NN1 distances_NN2 shorter_JJR ._. 
Alternately_RR ,_, orbital_JJ resonances_NN2 can_VM be_VBI traps_NN2 where_RRQ scattered_JJ planetesimals_NN2 congregate_VV0 without_IW invoking_VVG the_AT sweeping_JJ capture_NN1 mechanism_NN1 above_RL ._. 
Mandell_NP1 et_RA21 al._RA22 (_( 2007_MC )_) demonstrate_VV0 in_II numerical_JJ simulations_NN2 of_IO gas-disk_JJ induced_JJ migrations_NN2 the_AT formation_NN1 of_IO a_AT1 variety_NN1 of_IO Hot_JJ Earths_NN2 via_II scattering_VVG ,_, often_RR near_II the_AT 2:1_MC resonance_NN1 points_NN2 of_IO migrating_VVG Hot_JJ Jupiters_NP2 ,_, and_CC with_IW inner_JJ solar_JJ systems_NN2 often_RR cleared_VVN of_IO further_JJR material_NN1 ._. 
Denser_JJR inner_JJ gas_NN1 disks_NN2 appear_VV0 correlated_VVN with_IW having_VHG Hot_JJ Earths_NN2 at_II the_AT end_NN1 of_IO their_APPGE 200_MC Myr_NN1 simulations_NN2 ._. 
These_DD2 simulations_NN2 did_VDD not_XX include_VVI tidal_JJ damping_NN1 or_CC attempt_VV0 to_TO address_VVI long_JJ term_NN1 stability._NNU 2.4_MC ._. 
Circularization_NN1 While_CS ongoing_JJ perturbations_NN2 are_VBR favorable_JJ to_II supertidal_JJ conditions_NN2 ,_, they_PPHS2 are_VBR not_XX necessary_JJ ._. 
Circularization_NN1 timescales_NN2 may_VM still_RR be_VBI of_IO the_AT order_NN1 0.1-10_MCMC Gyr_NN1 for_IF short_JJ period_NN1 Earth-mass_NN1 planets_NN2 ._. 
Jackson_NP1 et_RA21 al_RA22 ._. 
(_( 2008_MC )_) also_RR examine_VV0 the_AT tidal_JJ heating_NN1 of_IO non-resonant_JJ terrestrial_JJ exoplanets_NN2 ,_, and_CC discuss_VV0 how_RGQ tidal_JJ orbital_JJ migration_NN1 further_RRR lengthens_VVZ circularization_NN1 times_NNT2 ._. 
Observations_NN2 will_VM ultimately_RR decide_VVI the_AT matter_NN1 ._. 
Overall_RR we_PPIS2 consider_VV0 it_PPH1 likely_RR enough_RR that_CST some_DD terrestrial_JJ planets_NN2 can_VM be_VBI swept_VVN or_CC scattered_VVN into_II resonances_NN2 by_II migrating_VVG Hot_JJ Jupiters_NP2 ,_, or_CC may_VM otherwise_RR have_VHI their_APPGE eccentricities_NN2 sustained_VVN at_II nonzero_NN1 values_NN2 for_IF geologically_RR significant_JJ times_NNT2 ,_, to_TO move_VVI forward_RL and_CC consider_VVI the_AT tidal_JJ heat_NN1 magnitudes_NN2 that_CST then_RT result._NNU 3_MC ._. 
FIXED_JJ Q_ZZ1 TIDAL_JJ MODEL_NN1 Tidal_JJ heating_NN1 is_VBZ modeled_VVN in_II many_DA2 ways_NN2 ,_, but_CCB the_AT starting_NN1 point_NN1 is_VBZ the_AT global_JJ heat_NN1 generation_NN1 rate_NN1 Etidal_NP1 (_( Peale_NP1 &;_NULL Cassen_NP1 1978_MC ;_; Peale_NP1 et_RA21 al_RA22 ._. 
1979_MC ;_; Showman_NN1 &;_NULL Malhotra_NP1 1996_MC )_) ._. 
For_IF a_AT1 homogeneous_JJ spinsynchronous_JJ body_NN1 whose_DDQGE stiffness_NN1 and_CC viscous_JJ dissipation_NN1 are_VBR both_RR assumed_VVN to_TO be_VBI constant_JJ and_CC uniform_NN1 ,_, the_AT global_JJ tidal_JJ heat_NN1 rate_NN1 can_VM be_VBI expressed_VVN following_II the_AT detailed_JJ derivation_NN1 in_II Murray_NP1 &;_NULL Dermott_NP1 (_( 2005_MC )_) ._. 
3.1_MC ._. 
Energy_NN1 Balance_NN1 This_DD1 in_II effect_NN1 assumes_VVZ a_AT1 turbulent_JJ interstellar_JJ medium_NN1 well_RR mixed_VVN by_II random_JJ supernovae_NN2 ,_, and_CC is_VBZ generally_RR supported_VVN by_II observations_NN2 (_( Elmegreen_NP1 &;_NULL Scalo_NP1 2004_MC )_) ._. 
However_RR ,_, the_AT time_NNT1 since_CS the_AT nearest_JJT supernovae_NN2 can_VM vary_VVI the_AT concentration_NN1 of_IO 26Al_FO and_CC hence_RR the_AT initial_JJ pulse_NN1 of_IO heat_NN1 to_II a_AT1 planet_NN1 ._. 
The_AT occurrence_NN1 or_CC absence_NN1 of_IO an_AT1 early_JJ giant_JJ impact_NN1 might_VM have_VHI a_AT1 similar_JJ effect._NNU 3.2_MC ._. 
Fixed_JJ Q_ZZ1 Results_VVZ Figure_NN1 1_MC1 compares_VVZ the_AT ratios_NN2 of_IO tidal_JJ heat_NN1 to_II insolation_NN1 and_CC radiogenic_JJ heat_NN1 for_IF hypothetical_JJ Hot_JJ Earths_NN2 (_( designated_VVN by_II the_AT suffix_NN1 x_ZZ1 )_) trapped_VVD in_II 2:1_MC resonances_NN2 with_IW known_JJ short_JJ period_NN1 exoplanets_NN2 as_CSA taken_VVN from_II the_AT exoplanet._NNU eu_NNU database_NN1 of_IO Jean_NP1 Schneider_NP1 ._. 
Scatter_VV0 of_IO the_AT points_NN2 is_VBZ due_II21 to_II22 the_AT varied_JJ luminosity_NN1 of_IO certain_JJ stars_NN2 ,_, with_IW higher_JJR outliers_NN2 being_VBG M_NN1 dwarf_NN1 hosts_NN2 ._. 
A_AT1 sufficient_JJ atmosphere_NN1 is_VBZ assumed_VVN to_TO transport_VVI heat_NN1 evenly_RR to_II the_AT nightside._NNU 4_MC ._. 
VISCOELASTICITY_NP1 Using_VVG equation_NN1 1_MC1 to_TO calculate_VVI global_JJ tidal_JJ heat_NN1 is_VBZ useful_JJ for_IF estimates_NN2 ,_, however_RRQV it_PPH1 ignores_VVZ the_AT frequency_NN1 dependence_NN1 of_IO a_AT1 material_NN1 's_GE response_NN1 to_II loading_NN1 ._. 
This_DD1 formula_NN1 still_RR assumes_VVZ a_AT1 homogeneous_JJ body_NN1 ._. 
A_AT1 complete_JJ calculation_NN1 of_IO tides_NN2 would_VM consider_VVI variations_NN2 by_II layers_NN2 using_VVG a_AT1 propagator_NN1 matrix_NN1 method_NN1 (_( Takeuchi_NP1 et_RA21 al_RA22 ._. 
1962_MC )_) as_II31 well_II32 as_II33 the_AT full_JJ three_MC dimensional_JJ stress_NN1 and_CC strain_VV0 tensors_NN2 to_TO compute_VVI tides_NN2 as_II a_AT1 function_NN1 of_IO latitude_NN1 and_CC longitude_NN1 (_( Peale_NP1 &;_NULL Cassen_NP1 1978_MC ;_; Segatz_NP1 et_RA21 al_RA22 ._. 
1988_MC )_) ._. 
However_RRQV equation_NN1 6_MC is_VBZ effective_JJ in_II seeking_VVG estimates_NN2 and_CC extrema_NN1 of_IO a_AT1 globally_RR averaged_JJ behavior_NN1 ._. 
A_AT1 parallel_JJ spring-dashpot_JJ pair_NN is_VBZ known_VVN as_II the_AT Voigt-Kelvin_JJ model_NN1 ._. 
Here_RL viscous_JJ relaxation_NN1 is_VBZ ultimately_RR limited_VVN by_II the_AT spring_NN1 ._. 
All_DB deformation_NN1 is_VBZ recovered_VVN when_CS a_AT1 load_NN1 is_VBZ removed_VVN ._. 
Either_DD1 of_IO the_AT two_MC ways_NN2 to_TO arrange_VVI two_MC springs_NN2 and_CC one_MC1 damper_NN1 in_II a_AT1 series-parallel_JJ combination_NN1 are_VBR mathematically_RR equivalent_JJ a_AT1 four_MC parameter_NN1 model_NN1 ,_, or_CC Burgers_NN2 body_NN1 ,_, allows_VVZ the_AT modeling_NN1 of_IO transient_JJ molecular_JJ creep_NN1 behavior_NN1 in_II minerals_NN2 ._. 
It_PPH1 can_VM exhibit_VVI transient_JJ creep_NN1 ,_, recovery_NN1 ,_, and_CC take_VV0 on_RP a_AT1 permanent_JJ set_NN1 ,_, modeling_VVG a_AT1 broad_JJ range_NN1 of_IO materials_NN2 ._. 
The_AT Burgers_NN2 or_CC SAS_NP1 models_NN2 may_VM both_RR be_VBI reduced_VVN to_II the_AT Maxwell_NP1 or_CC Voigt-Kelvin_JJ models_NN2 through_II appropriate_JJ selection_NN1 of_IO parameters._NNU 4.3_MC ._. 
Melting_VVG Model_NN1 A_ZZ1 description_NN1 of_IO silicate_NN1 melting_NN1 allows_VVZ us_PPIO2 to_TO resolve_VVI both_DB2 the_AT rapid_JJ increase_NN1 in_II convective_JJ vigor_NN1 and_CC the_AT decoupling_NN1 of_IO tides_NN2 that_CST simultaneously_RR occur_VV0 when_RRQ viscosity_NN1 and_CC shear_VV0 modulus_NN1 decrease_NN1 ._. 
Parametric_JJ models_NN2 of_IO melting_VVG for_IF Io_NP1 are_VBR presented_VVN by_II Moore_NP1 (_( 2003b_FO )_) and_CC Fischer_NP1 &;_NULL Spohn_NP1 (_( 1990_MC )_) based_VVN on_II laboratory_NN1 experiments_NN2 by_II Berckhemer_NP1 et_RA21 al_RA22 ._. 
(_( 1982_MC )_) ._. 
These_DD2 models_NN2 variously_RR represent_VV0 the_AT essential_JJ feature_NN1 of_IO a_AT1 breakdown_NN1 temperature_NN1 :_: at_II some_DD point_NN1 in_II the_AT partial_JJ melting_NN1 (_( or_CC crystallization_NN1 )_) process_VV0 ,_, a_AT1 material_NN1 switches_VVZ from_II being_VBG best_RRT described_VVN as_II a_AT1 solid_JJ matrix_NN1 with_IW fluid_NN1 pores_NN2 ,_, to_II a_AT1 fluid_NN1 bath_NN1 with_IW isolated_JJ floating_JJ crystals_NN2 grains_NN2 ._. 
When_RRQ grains_NN2 loose_JJ contact_NN1 with_IW one_PPX121 another_PPX122 ,_, the_AT material_NN1 looses_NN2 shear_VV0 strength_NN1 and_CC switches_VVZ to_II the_AT viscous_JJ properties_NN2 of_IO the_AT fluid_NN1 ._. 
The_AT time_NNT1 it_PPH1 takes_VVZ a_AT1 planet_NN1 to_TO reach_VVI equilibrium_NN1 depends_VVZ mainly_RR on_II initial_JJ conditions_NN2 ._. 
Our_APPGE simulations_NN2 show_VV0 typical_JJ tidal_JJ response_NN1 peaks_NN2 are_VBR crossed_VVN rapidly_RR ,_, on_II the_AT order_NN1 of_IO 10-50_MCMC million_NNO years_NNT2 ._. 
This_DD1 will_VM be_VBI manifested_VVN in_II the_AT planetary_JJ history_NN1 as_II a_AT1 sudden_JJ episode_NN1 of_IO extreme_JJ heating_NN1 ,_, possibly_RR recorded_VVN on_II the_AT planet_NN1 's_GE surface_NN1 ,_, followed_VVD typically_RR by_II more_RGR moderate_JJ equilibrium_NN1 heat_NN1 rates_NN2 ._. 
We_PPIS2 looked_VVD for_IF cases_NN2 where_RRQ the_AT peak_NN1 in_II W_ZZ1 (_( T_ZZ1 )_) could_VM lead_VVI to_II cyclic_JJ overshoot_NN1 events_NN2 but_CCB found_VVD the_AT system_NN1 dynamically_RR overdamped_VVD ,_, with_IW cyclic_JJ ,_, quasiperiodic_JJ ,_, and_CC chaotic_JJ solutions_NN2 prevented_VVN by_II a_AT1 planet_NN1 's_GE high_JJ thermal_JJ inertia_NN1 and_CC long_JJ heat_NN1 transport_NN1 timescale_NN1 ._. 
Single_JJ overshoots_NN2 do_VD0 occur_VVI ,_, in_RR21 particular_RR22 after_II heating_NN1 across_II a_AT1 strong_JJ resonance_NN1 peak_NN1 when_CS the_AT hot_JJ stable_JJ equilibrium_NN1 is_VBZ well_JJ below_II the_AT solidus_NN1 ._. 
This_DD1 supports_VVZ our_APPGE discussion_NN1 in_II section_NN1 2.4_MC that_DD1 maximum_JJ dissipation_NN1 states_NN2 tend_VV0 be_VBI brief_JJ ,_, unless_CS equilibrium_NN1 occurs_VVZ at_II a_AT1 W_ZZ1 (_( T_ZZ1 )_) peak_NN1 ._. 
Figure_NN1 8c_FO ,_, f_ZZ1 shows_VVZ the_AT same_DA information_NN1 for_IF a_AT1 Burgers_NN2 body_NN1 with_IW two_MC response_NN1 peaks_NN2 ,_, thus_RR two_MC bifurcation_NN1 points_NN2 ,_, two_MC stable_JJ branches_NN2 ,_, and_CC two_MC unstable_JJ branches_NN2 ._. 
More_RGR complex_JJ planetary_JJ histories_NN2 may_VM occur_VVI ._. 
In_RR21 particular_RR22 ,_, planets_NN2 may_VM become_VVI trapped_VVN at_II a_AT1 colder_JJR tidal_JJ equilibrium_NN1 associated_VVN with_IW the_AT grain_NN1 boundary_NN1 slip_NN1 mechanism_NN1 ._. 
However_RR ,_, as_CSA inhomogeneous_JJ mantles_NN2 may_VM blur_VVI distinct_JJ peaks_NN2 ,_, our_APPGE Burgers_NN2 results_NN2 are_VBR best_RRT viewed_VVN as_II a_AT1 demonstration_NN1 of_IO the_AT increase_NN1 in_II behavioral_JJ complexity_NN1 that_CST occurs_VVZ when_RRQ additional_JJ response_NN1 frequencies_NN2 are_VBR taken_VVN into_II account._NNU 6_MC ._. 
DISCUSSION_NN1 This_DD1 work_NN1 highlights_VVZ the_AT question_NN1 of_IO what_DDQ will_VM be_VBI the_AT ultimate_JJ shutdown_NN1 mechanism_NN1 for_IF an_AT1 extreme_JJ tidal_JJ terrestrial_JJ planet_NN1 ._. 
Both_DB2 the_AT fixed_JJ Q_NN1 method_NN1 and_CC the_AT generally_RR more_RGR conservative_JJ viscoelastic_JJ methods_NN2 predict_VV0 that_CST in_II some_DD circumstances_NN2 tidal_JJ heating_NN1 can_VM reach_VVI millions_NNO2 of_IO terawatts_NN2 within_II a_AT1 planet_NN1 modeled_VVD as_RG homogeneous_JJ ._. 
Our_APPGE models_NN2 of_IO tidal-convective_JJ equilibria_NN2 are_VBR very_RG effective_JJ in_II exploring_VVG planetary_JJ behaviors_NN2 prior_II21 to_II22 equilibration_NN1 ,_, but_CCB only_RR coarsely_RR resolve_VV0 actual_JJ equilibrium_NN1 heat_NN1 rates_NN2 due_II21 to_II22 the_AT assumption_NN1 of_IO homogeneity._NNU 6.1_MC ._. 
Inhomogeneous_JJ Melting_NN1 Onset_NN1 partial_JJ melting_NN1 can_VM begin_VVI in_II an_AT1 inhomogeneous_JJ planet_NN1 at_II much_RR lower_JJR heat_NN1 rates_NN2 ._. 
To_TO roughly_RR determine_VVI the_AT location_NN1 of_IO melt_VV0 initiation_NN1 ,_, we_PPIS2 follow_VV0 Valencia_NP1 et_RA21 al_RA22 ._. 
(_( 2006_MC )_) to_TO calculate_VVI the_AT temperature_NN1 profile_NN1 with_IW depth_NN1 ,_, or_CC geotherm_VV0 T_ZZ1 (_( z_ZZ1 )_) ,_, of_IO a_AT1 tidally_RR heated_JJ exoplanet_NN1 ._. 
Where_CS sufficient_JJ local_JJ partial_JJ melting_NN1 occurs_VVZ ,_, tidal_JJ friction_NN1 will_VM decrease_VVI while_CS continuing_VVG in_RP better_RRR tuned_VVN viscous_JJ regions_NN2 ._. 
This_DD1 suggests_VVZ how_RRQ a_AT1 planet_NN1 may_VM have_VHI difficulty_NN1 generating_VVG the_AT millions_NNO2 of_IO TW_NP1 solutions_NN2 found_VVD earlier_RRR in_II this_DD1 paper_NN1 ._. 
We_PPIS2 also_RR find_VV0 core_NN1 temperature_NN1 is_VBZ a_AT1 nearly_RR linear_JJ function_NN1 of_IO tidal_JJ input_NN1 ,_, primarily_RR because_II21 of_II22 the_AT strong_JJ linear_JJ dependence_NN1 of_IO the_AT conductive_JJ geotherm_NN1 through_II the_AT lithosphere_NN1 on_II total_JJ heat_NN1 flow_NN1 ._. 
We_PPIS2 assume_VV0 no_AT tidal_JJ heat_NN1 is_VBZ deposited_VVN in_II the_AT core_NN1 itself_PPX1 ,_, however_RGQV small_JJ amounts_NN2 of_IO tidal_JJ heat_NN1 (_( 10TW_FO )_) can_VM shift_VVI the_AT geotherm_NN1 such_CS21 that_CS22 the_AT entire_JJ core_NN1 becomes_VVZ liquid_NN1 (_( based_VVN on_II the_AT shallow_JJ slope_NN1 of_IO the_AT Simon_NP1 Law_NN1 solidus_NN1 for_IF pure_JJ Iron_NN1 )_) ._. 
Thus_RR even_RR weak_JJ tidal_JJ exoplanets_NN2 may_VM have_VHI no_AT inner_JJ cores_NN2 ,_, disrupting_VVG magnetic_JJ dynamo_NN1 activity_NN1 ,_, just_RR as_CSA with_IW younger_JJR exoplanets_NN2 prior_II21 to_II22 core_NN1 crystallization_NN1 ._. 
Models_NN2 were_VBDR tested_VVN with_IW an_AT1 upper-lower_JJR mantle_NN1 thermal_JJ separation_NN1 at_II 660km_NNU depth_NN1 ,_, as_II31 well_II32 as_II33 asthenospheric_JJ only_JJ tidal_JJ input_NN1 ._. 
Onset_NN1 melting_NN1 results_NN2 were_VBDR largely_RR the_AT same_DA ,_, except_II21 for_II22 a_AT1 weaker_JJR dependence_NN1 of_IO the_AT core_NN1 temperature_NN1 on_II tides_NN2 ,_, since_CS vigorous_JJ upper_JJ mantle_NN1 activity_NN1 led_VVN to_II thinner_JJR conductive_JJ lithospheres_NN2 ._. 
Varying_VVG the_AT planet_NN1 's_GE mass_NN1 ,_, we_PPIS2 find_VV0 above_II 2.6ME_FO the_AT mantle_NN1 adiabat_NN1 may_VM curve_VVI sufficiently_RR for_IF onset_NN1 melting_VVG to_TO also_RR occur_VVI at_II the_AT core-mantle_JJ boundary_NN1 (_( using_VVG a_AT1 Birch-Murgnahan_NP1 equation_NN1 of_IO state_NN1 )_) ._. 
6.2_MC ._. 
Magma_NN1 Oceans_NN2 Hot_JJ Earth_NN1 planets_NN2 may_VM have_VHI insolation_NN1 supported_VVN magma_NN1 oceans_NN2 where_RRQ basal_JJ friction_NN1 due_II21 to_II22 tidal_JJ slosh_NN1 plays_VVZ an_AT1 important_JJ role_NN1 ._. 
Full_JJ magma_NN1 ocean_NN1 build-up_NN1 via_II outpourings_NN2 is_VBZ likely_JJ to_TO require_VVI half_DB a_AT1 million_NNO TW_NP1 or_CC more_RRR ._. 
So_RR while_CS planet-wide_JJ resurfacing_NN1 may_VM occur_VVI ,_, it_PPH1 is_VBZ difficult_JJ for_IF tidal_JJ heating_NN1 to_TO build_VVI up_RP a_AT1 surface_NN1 magma_NN1 ocean_NN1 with_IW no_AT assistance_NN1 from_II insolation_NN1 ._. 
Alternatively_RR ,_, sub-lithospheric_JJ melting_NN1 and_CC subsequent_JJ thinning_NN1 may_VM produce_VVI insulated_JJ near-surface_JJ magma_NN1 oceans_NN2 or_CC crystalline_JJ slush_NN1 layers_NN2 at_II lower_JJR tidal_JJ rates_NN2 ._. 
Individual_JJ volcanic_JJ vents_NN2 may_VM produce_VVI lava_NN1 flows_VVZ greater_JJR than_CSN 8m/yr_NNU and_CC produce_VV0 significant_JJ localized_JJ magma_NN1 lakes._NNU 7_MC ._. 
CONCLUSIONS_NN2 In_II this_DD1 paper_NN1 we_PPIS2 have_VH0 shown_VVN how_RRQ a_AT1 range_NN1 models_NN2 produce_VV0 extreme_JJ tidal_JJ heating_NN1 in_RR21 short_RR22 period_NN1 terrestrial_JJ exoplanets_NN2 ._. 
The_AT existence_NN1 of_IO broad_JJ regions_NN2 of_IO extreme_JJ tidal_JJ solutions_NN2 lying_VVG alongside_II negligible_JJ solutions_NN2 is_VBZ robust_JJ to_II parameter_NN1 uncertainty_NN1 ._. 
However_RRQV this_DD1 dual_JJ nature_NN1 makes_VVZ it_PPH1 difficult_JJ to_TO specify_VVI a_AT1 given_JJ planetary_JJ heat_NN1 output_NN1 based_VVN on_II tidal_JJ forcing_NN1 strength_NN1 alone_RR ,_, without_IW knowledge_NN1 of_IO the_AT interior_NN1 ._. 
Broadly_RR we_PPIS2 find_VV0 tidal_JJ heating_NN1 in_II31 excess_II32 of_II33 radionuclide_NN1 heating_NN1 occurs_VVZ below_RG approximately_RR 10-30_MCMC day_NNT1 orbital_JJ periods_NN2 ._. 
