Figure 1. Two examples (left-hand and right-hand panels) of the orbital evolution of a planet tidally interacting with ... Figure 1. Two examples (left-hand.

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Figure 1. Two examples (left-hand and right-hand panels) of the orbital evolution of a planet tidally interacting with ... Figure 1. Two examples (left-hand and right-hand panels) of the orbital evolution of a planet tidally interacting with a white dwarf, where definitions of σ<sub>a</sub>, σ<sub>e</sub>, and σ<sub>i</sub> are given in equations (14)–(16). In both examples, a(0) = 5r<sub>Roche</sub>, e(0) = 0.20, M = 10M<sub>⊕</sub>, ρ = ρ<sub>⊕</sub>, and (dθ/dt)(0) = 360°/(20 h). In the left-hand panels, η = 10<sup>20</sup> Pa·s, whereas in the right-hand panels, η = 10<sup>19</sup> Pa·s; i.e. the only difference in the simulations is a one order of magnitude variation in the planetary viscosity. In the left-hand panels, over 100 Myr, the semimajor axis evolution is increased overall, but in a non-uniform manner and only after shifting direction. In contrast, in the right-hand panels, the planet changes direction twice, and is eventually destroyed by entering the Roche radius after 54 Myr. In both panels, the initial inclination of the orbit i(0) = 140° with respect to the planet’s equator is quickly reduced to within 1°. The damping of i′ (inclination with respect to the stellar equator) is even quicker (note the different scales of the time axes). Unless provided in the caption above, the following copyright applies to the content of this slide: © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Mon Not R Astron Soc, Volume 486, Issue 3, 01 May 2019, Pages 3831–3848, https://doi.org/10.1093/mnras/stz965 The content of this slide may be subject to copyright: please see the slide notes for details.

Figure 2. Outcomes of planetary movement due to tidal interactions with a white dwarf. For our adopted rheological ... Figure 2. Outcomes of planetary movement due to tidal interactions with a white dwarf. For our adopted rheological model, a single value for planetary dynamic viscosity (y-axis) does not easily map to a specific known rocky and differentiated body, although a relatively homogenous dirty snowball like Enceladus corresponds well with η ≈ 0.24 × 10<sup>14</sup> Pa·s (Efroimsky 2018). Each box represents the state of a single simulation after 100 Myr of evolution. Red crosses indicate that the planet’s semimajor axis has come within the white dwarf’s Roche radius r<sub>Roche</sub>, destroying the planet. Otherwise, the net migration of the planet after 100 Myr is either outwards (green carets) or inwards (red ‘V’s). The number within those symbols gives the magnitude of the migration, and is of the order of log|σ<sub>a</sub>|. Other variables that were assumed for these simulations are e(0) = 0.2, M = M<sub>⊕</sub>, R = R<sub>⊕</sub>, and (dθ/dt)(0) = 360°/(20 h). This figure illustrates that the outcome is strongly dependent on planetary viscosity and suggests the existence of a fractal boundary and chaos due to the largest outward migrations neighbouring destructive spiral-ins. Unless provided in the caption above, the following copyright applies to the content of this slide: © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Mon Not R Astron Soc, Volume 486, Issue 3, 01 May 2019, Pages 3831–3848, https://doi.org/10.1093/mnras/stz965 The content of this slide may be subject to copyright: please see the slide notes for details.

Figure 3. Same as Fig. 2 but for planet mass dependence, and assuming ρ = ρ⊕ in all cases, with η = ... Figure 3. Same as Fig. 2 but for planet mass dependence, and assuming ρ = ρ<sub>⊕</sub> in all cases, with η = 10<sup>20</sup> Pa·s for the top panel and η = 10<sup>16</sup> Pa·s for the bottom panel. The final outcome is strongly dependent on planetary mass. Unless provided in the caption above, the following copyright applies to the content of this slide: © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Mon Not R Astron Soc, Volume 486, Issue 3, 01 May 2019, Pages 3831–3848, https://doi.org/10.1093/mnras/stz965 The content of this slide may be subject to copyright: please see the slide notes for details.

Figure 4. Same as Fig. 2 but for planetary spin period dependence, and assuming η = 1020 Pa·s. The upper ... Figure 4. Same as Fig. 2 but for planetary spin period dependence, and assuming η = 10<sup>20</sup> Pa·s. The upper grid gives results for prograde planetary spins (relative to orbit orientation), and the bottom grid for retrograde planetary spins. The grids are 79 per cent coincident; grey squares in the bottom grid locate the discrepancies. The final outcome has a complex dependence on planetary spin period. Unless provided in the caption above, the following copyright applies to the content of this slide: © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Mon Not R Astron Soc, Volume 486, Issue 3, 01 May 2019, Pages 3831–3848, https://doi.org/10.1093/mnras/stz965 The content of this slide may be subject to copyright: please see the slide notes for details.

Figure 5. Same as Fig. 2 but for planetary eccentricity dependence, and assuming η = 1020 Pa·s. The critical ... Figure 5. Same as Fig. 2 but for planetary eccentricity dependence, and assuming η = 10<sup>20</sup> Pa·s. The critical engulfment distance appears to be weakly dependent on initial eccentricity, and near-circular orbits produce non-obvious outcomes as a function of a(0). Unless provided in the caption above, the following copyright applies to the content of this slide: © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Mon Not R Astron Soc, Volume 486, Issue 3, 01 May 2019, Pages 3831–3848, https://doi.org/10.1093/mnras/stz965 The content of this slide may be subject to copyright: please see the slide notes for details.