{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/24849"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/24849","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"Tidal Dissipation in Extrasolar Planets","abstract":"Many known extra-solar giant planets lie close to their host stars. Around 60 have their semi-major axes smaller than 0.05 AU. In contrast to planets further out, the vast majority of these close-in planets have low eccentricity orbits. This suggests that their orbits have been circularized likely due to tidal dissipation inside the planets. These exoplanets share with our own Jupiter at least one trait in common: when they are subject to periodic tidal forcing, they behave like a lossy spring, with a tidal ``quality factor'', Q, of order 10^5. This parameter is the ratio between the energy in the tide and the energy dissipated per period. To explain this, a possible solution is resonantly forced internal oscillation. If the frequency of the tidal forcing happens to land on that of an internal eigenmode, this mode can be resonantly excited to a very large amplitude. The damping of such a mode inside the planet may explain the observed Q value. The only normal modes that fall in the frequency range of the tidal forcing (~ few days) are inertial modes, modes restored by the Coriolis force. We present a new numerical technique to solve for inertial modes in a convective, rotating sphere. This technique combines the use of an ellipsoidal coordinate system with a pseudo-spectral method to solve the partial differential equation that governs the inertial oscillations. We show that, this technique produces highly accurate solutions when the density profile is smooth. In particular, the lines of nodes are roughly parallel to the ellipsoidal coordinate axes. In particular, using these accurate solutions, we estimate the resultant tidal dissipation for giant planets, and find that turbulent dissipation of inertial modes in planets with smooth density profiles do not give rise to dissipation as strong as the one observed. We also study inertial modes in density profiles that exhibit discontinuities, as some recent models of Jupiter show. We found that, in this case, our method could not produce convergent solutions for the inertial modes. Additionally, we propose a way to observe inertial modes inside Saturn indirectly, by observing waves in its rings that may be excited by inertial modes inside Saturn.","abstract_html":"Many known extra-solar giant planets lie close to their host stars. Around 60 have their semi-major axes smaller than 0.05 AU. In contrast to planets further out, the vast majority of these close-in planets have low eccentricity orbits. This suggests that their orbits have been circularized likely due to tidal dissipation inside the planets. These exoplanets share with our own Jupiter at least one trait in common: when they are subject to periodic tidal forcing, they behave like a lossy spring, with a tidal ``quality factor'', Q, of order 10^5. This parameter is the ratio between the energy in the tide and the energy dissipated per period. To explain this, a possible solution is resonantly forced internal oscillation. If the frequency of the tidal forcing happens to land on that of an internal eigenmode, this mode can be resonantly excited to a very large amplitude. The damping of such a mode inside the planet may explain the observed Q value. The only normal modes that fall in the frequency range of the tidal forcing (~ few days) are inertial modes, modes restored by the Coriolis force. We present a new numerical technique to solve for inertial modes in a convective, rotating sphere. This technique combines the use of an ellipsoidal coordinate system with a pseudo-spectral method to solve the partial differential equation that governs the inertial oscillations. We show that, this technique produces highly accurate solutions when the density profile is smooth. In particular, the lines of nodes are roughly parallel to the ellipsoidal coordinate axes. In particular, using these accurate solutions, we estimate the resultant tidal dissipation for giant planets, and find that turbulent dissipation of inertial modes in planets with smooth density profiles do not give rise to dissipation as strong as the one observed. We also study inertial modes in density profiles that exhibit discontinuities, as some recent models of Jupiter show. We found that, in this case, our method could not produce convergent solutions for the inertial modes. Additionally, we propose a way to observe inertial modes inside Saturn indirectly, by observing waves in its rings that may be excited by inertial modes inside Saturn.","abstract_has_math":false,"creators":["Pena, Fernando Gabriel"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Astronomy and Astrophysics","school":null,"contributors":[],"advisors":["Wu, Yanqin"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-09-01T15:33:11Z","date_published":"2010-09-01T15:33:11Z","updated_at":"2026-07-27T21:28:05Z","subjects":["tidal dissipation","inertial modes","close binaries","hot Jupiters","Rings of Saturn","pseudospectral method","Chebyshev expansion","astrophysics","dynamical tide","asteroseismology"],"languages":["en_ca"],"rights":["Attribution-NonCommercial-NoDerivs 2.5 Canada"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/24849","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Wu, Yanqin"]},{"key":"dc:contributor.department","label":"Department","values":["Astronomy and Astrophysics"]},{"key":"dc:creator","label":"Author","values":["Pena, Fernando Gabriel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-06"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2010-09-01T15:33:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["NO_RESTRICTION","2010-09-01T15:33:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2010-09-01T15:33:11Z"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["tidal dissipation","inertial modes","close binaries","hot Jupiters","Rings of Saturn","pseudospectral method","Chebyshev expansion","astrophysics","dynamical tide","asteroseismology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_ca"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution-NonCommercial-NoDerivs 2.5 Canada"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/24849"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Many known extra-solar giant planets lie close to their host stars. Around 60 have their semi-major axes smaller than 0.05 AU. In contrast to planets further out, the vast majority of these close-in planets have low eccentricity orbits. This suggests that their orbits have been circularized likely due to tidal dissipation inside the planets. These exoplanets share with our own Jupiter at least one trait in common: when they are subject to periodic tidal forcing, they behave like a lossy spring, with a tidal ``quality factor'', Q, of order 10^5. This parameter is the ratio between the energy in the tide and the energy dissipated per period. To explain this, a possible solution is resonantly forced internal oscillation. If the frequency of the tidal forcing happens to land on that of an internal eigenmode, this mode can be resonantly excited to a very large amplitude. The damping of such a mode inside the planet may explain the observed Q value. The only normal modes that fall in the frequency range of the tidal forcing (~ few days) are inertial modes, modes restored by the Coriolis force. We present a new numerical technique to solve for inertial modes in a convective, rotating sphere. This technique combines the use of an ellipsoidal coordinate system with a pseudo-spectral method to solve the partial differential equation that governs the inertial oscillations. We show that, this technique produces highly accurate solutions when the density profile is smooth. In particular, the lines of nodes are roughly parallel to the ellipsoidal coordinate axes. In particular, using these accurate solutions, we estimate the resultant tidal dissipation for giant planets, and find that turbulent dissipation of inertial modes in planets with smooth density profiles do not give rise to dissipation as strong as the one observed. We also study inertial modes in density profiles that exhibit discontinuities, as some recent models of Jupiter show. We found that, in this case, our method could not produce convergent solutions for the inertial modes. Additionally, we propose a way to observe inertial modes inside Saturn indirectly, by observing waves in its rings that may be excited by inertial modes inside Saturn."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["PhD"]},{"key":"dc:title","label":"Title","values":["Tidal Dissipation in Extrasolar Planets"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wu, Yanqin"],"dc:contributor.department":["Astronomy and Astrophysics"],"dc:creator":["Pena, Fernando Gabriel"],"dc:date":["2010-06"],"dc:date.accessioned":["2010-09-01T15:33:11Z"],"dc:date.available":["NO_RESTRICTION","2010-09-01T15:33:11Z"],"dc:date.issued":["2010-09-01T15:33:11Z"],"dc:description.abstract":["Many known extra-solar giant planets lie close to their host stars. Around 60 have their semi-major axes smaller than 0.05 AU. In contrast to planets further out, the vast majority of these close-in planets have low eccentricity orbits. This suggests that their orbits have been circularized likely due to tidal dissipation inside the planets. These exoplanets share with our own Jupiter at least one trait in common: when they are subject to periodic tidal forcing, they behave like a lossy spring, with a tidal ``quality factor'', Q, of order 10^5. This parameter is the ratio between the energy in the tide and the energy dissipated per period. To explain this, a possible solution is resonantly forced internal oscillation. If the frequency of the tidal forcing happens to land on that of an internal eigenmode, this mode can be resonantly excited to a very large amplitude. The damping of such a mode inside the planet may explain the observed Q value. The only normal modes that fall in the frequency range of the tidal forcing (~ few days) are inertial modes, modes restored by the Coriolis force. We present a new numerical technique to solve for inertial modes in a convective, rotating sphere. This technique combines the use of an ellipsoidal coordinate system with a pseudo-spectral method to solve the partial differential equation that governs the inertial oscillations. We show that, this technique produces highly accurate solutions when the density profile is smooth. In particular, the lines of nodes are roughly parallel to the ellipsoidal coordinate axes. In particular, using these accurate solutions, we estimate the resultant tidal dissipation for giant planets, and find that turbulent dissipation of inertial modes in planets with smooth density profiles do not give rise to dissipation as strong as the one observed. We also study inertial modes in density profiles that exhibit discontinuities, as some recent models of Jupiter show. We found that, in this case, our method could not produce convergent solutions for the inertial modes. Additionally, we propose a way to observe inertial modes inside Saturn indirectly, by observing waves in its rings that may be excited by inertial modes inside Saturn."],"dc:description.degree":["PhD"],"dc:identifier.uri":["http://hdl.handle.net/1807/24849"],"dc:language.iso":["en_ca"],"dc:rights":["Attribution-NonCommercial-NoDerivs 2.5 Canada"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"],"dc:subject":["tidal dissipation","inertial modes","close binaries","hot Jupiters","Rings of Saturn","pseudospectral method","Chebyshev expansion","astrophysics","dynamical tide","asteroseismology"],"dc:title":["Tidal Dissipation in Extrasolar Planets"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:28:05Z"}