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Thread: [Worldbuilding] Tidal Locking Timescale in Fictional System

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    Question [Worldbuilding] Tidal Locking Timescale in Fictional System

    I'm building a fictional system of 5 planets orbiting a blue giant (mass = ~17.8 Sol). The system is based loosely on sci-fi source material but I'm exercising a lot of liberty with it.

    To start with, the 17.8 Solar mass star is of spectral type B0 V; its estimated main sequence lifetime cannot exceed ~8-11 million years. Here are the planets' orbital distances (assuming circular orbits):

    Planet A - terrestrial: 76.4 AU
    Planet B - gas giant: 99.45 AU
    Planet C - terrestrial: 199 AU
    Planet D - ice giant: 363.73 AU
    Planet E - gas giant: 710 AU

    My question is whether the star's main sequence lifetime is long enough for at least the inner couple of planets to be tidally locked. The source material suggests that at least planets A and C are tidally locked (i.e. the terrestrial ones), however I find this highly unlikely and would like some clarification.

    My gut says none of the planets would be tidally locked in such a short span of time, despite the massive star and everything. I can't think of any scenario that would cause them to be tidally locked so quickly, but I would still like to see comments since I could be missing something.
    Last edited by Fiery Phoenix; 2020-Feb-13 at 04:44 PM.
    “Of all the sciences cultivated by mankind, Astronomy is acknowledged to be, and undoubtedly is, the most sublime, the most interesting, and the most useful. For, by knowledge derived from this science, not only the bulk of the Earth is discovered, but our very faculties are enlarged with the grandeur of the ideas it conveys, our minds exalted above their low contracted prejudices.” - James Ferguson

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    Quote Originally Posted by Fiery Phoenix View Post
    ... My gut says none of the planets would be tidally locked in such a short span of time, despite the massive star and everything. I can't think of any scenario that would cause them to be tidally locked so quickly, but I would still like to see comments since I could be missing something.
    My gut agrees with yours, but in addition, I believe that it is not just that it isn't enough time, but more importantly the planet would be too far for differential gravity to have much of a slowing effect. Goldilocks planets around red dwarfs are likely tidally locked, and will get that way quickly.
    Forming opinions as we speak

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    Nah. Plugging the Earth into the location of your inner terrestrial, the spindown to synchrony (from an original rotation rate of 5 hours) is of the order of 10^19 years.

    Grant Hutchison

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    Quote Originally Posted by Fiery Phoenix View Post
    I'm building a fictional system of 5 planets orbiting a blue giant (mass = ~17.8 Sol). Here are the planets' orbital distances (assuming circular orbits):

    Planet A - terrestrial: 76.4 AU
    Planet B - gas giant: 99.45 AU
    Planet C - terrestrial: 199 AU
    Planet D - ice giant: 363.73 AU
    Planet E - gas giant: 710 AU

    My gut says none of the planets would be tidally locked in such a short span of time, despite the massive star and everything.
    Don´t even bother "plugging in". Tidal forces depend on the mass of the star, but in exact same manner as the orbital period of planet does. So just check how the orbital period of the planet comes out and consider whether a planet of such orbital planet is liable to get tidally locked, irrespective of specific mass and distance of star.

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    Indeed. The time to spin down to synchrony varies inversely with the star's mass squared, but directly with the orbital distance to the sixth power. So such distant world are always going to be little affected by tidal slowing.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Indeed. The time to spin down to synchrony varies inversely with the star's mass squared, but directly with the orbital distance to the sixth power. So such distant world are always going to be little affected by tidal slowing.

    Grant Hutchison
    The formula I found on Wiki seemed to suggest as such; even a small change in the orbital distance makes a huge difference. For this system, orbital periods range between around 158 years to ~4478 years (!!) for the farthest planet.

    I figured there was no way these worlds could be tidally locked within the parent star's lifetime, but it never hurts to ask.
    “Of all the sciences cultivated by mankind, Astronomy is acknowledged to be, and undoubtedly is, the most sublime, the most interesting, and the most useful. For, by knowledge derived from this science, not only the bulk of the Earth is discovered, but our very faculties are enlarged with the grandeur of the ideas it conveys, our minds exalted above their low contracted prejudices.” - James Ferguson

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    Sorry to get off the tidal-locking theme, but...

    The major problem I have here is the extremely short lifetime of the star, and the extreme youth of the planets around it.

    Look at Earth's geological past in this Wikipedia article on the Hadean period. https://en.wikipedia.org/wiki/Hadean

    I'm not sure any of the terrestrial planets or large moons would be in a habitable condition at such a young age. I'm thinking magma oceans and poisonous atmospheres.

    LATER: It might work better for a rogue planet to be captured by the star, to become the colony base, or have the rogue planet become a satellite of a gas giant. More in a moment.
    Last edited by Roger E. Moore; 2020-Feb-14 at 03:25 PM. Reason: correction
    Do good work. —Virgil Ivan "Gus" Grissom

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    Papers in arXiv.org indicate that high-mass stars are very likely to have giant planets or brown dwarfs in orbit about them. This does not rule out Earthlike or super-Earth planets (which are overall far more common than Earth-size planets), but the planets in giant-star systems seem likely to be about the physical size of Jupiter but many times Jupiter's mass. See references below, applicable to A-type stars and other giants. While brown dwarfs appear to have formed in a manner different from planets, they function very much as planetary bodies and probably have their own extensive satellite systems. You can think of them as hypermassive Jovians.

    ===

    https://ui.adsabs.harvard.edu/abs/20.....18Q/abstract

    Precise radial velocities of giant stars. XI. Two brown dwarfs in 6:1 mean motion resonance around the K giant star ν Ophiuchi
    Quirrenbach, Andreas; Trifonov, Trifon; Lee, Man Hoi; Reffert, Sabine
    April 2019

    We present radial-velocity (RV) measurements for the K giant ν Oph (= HIP 88048, HD 163917, HR 6698), which reveal two brown dwarf companions with a period ratio close to 6:1. For our orbital analysis we use 150 precise RV measurements taken at the Lick Observatory between 2000 and 2011, and we combine them with RV data for this star available in the literature. Using a stellar mass of M = 2.7M☉ for ν Oph and applying a self-consistent N-body model we estimate the minimum dynamical companion masses to be m1 sin i ≈ 22.2 MJup and m2 sin i ≈ 24.7 MJup, with orbital periods P1 ≈ 530 d and P2 ≈ 3185 d. We study a large set of potential orbital configurations for this system, employing a bootstrap analysis and a systematic χν2 grid-search coupled with our dynamical fitting model, and we examine their long-term stability. We find that the system is indeed locked in a 6:1 mean motion resonance (MMR), with ∆ω and all six resonance angles θ1-θ6 librating around 0°. We also test a large set of coplanar inclined configurations, and we find that the system will remain in a stable resonance for most of these configurations. The ν Oph system is important for probing planetary formation and evolution scenarios. It seems very likely that the two brown dwarf companions of ν Oph formed like planets in a circumstellar disk around the star and have been trapped in an MMR by smooth migration capture.

    ===

    https://ui.adsabs.harvard.edu/abs/20...0201Q/abstract

    Planets around Giant Stars: Results from the Lick Survey
    Quirrenbach, Andreas; Reffert, Sabine; Trifonov, Trifon; Bergmann, Christoph; Schwab, Christian
    December 2015

    We present results from a radial-velocity survey of 373 giant stars at Lick Observatory, which started in 1999. We have detected planets around 15 of these stars; an additional 20 stars host planet candidates. Companions with up to 25 Jupiter masses are rather commonly found around stars with about 2 Solar masses. The frequency of detected planetary companions appears to increase with metallicity. No planets or planet candidates are found around stars with more than 2.7 Solar masses, although our sample contains 113 such stars. We conclude that the occurrence rate of giant planets as a function of Stellar mass peaks around 2 Solar masses. This has important consequences for our understanding of giant planet formation.The stars 91 Aqr and tau Gem have companions with orbits that are among those with the lowest eccentricities of all known exoplanets, perhaps due to tidal circularization during the RGB phase. If confirmed, this would be the first evidence of planetary orbits modified through stellar evolution.We have discovered several multiple systems in our sample. An extensive dynamical analysis of the eta Cet system indicates that it contains two massive planets in a 2:1 orbital resonance. The star nu Oph is orbited by two brown dwarf companions in a 6:1 resonance. It is likely that they arrived in this resonance through migration in a circumstellar disk, arguing strongly that objects with more than 20 Jupiter masses can be formed in disks around Herbig Ae stars.

    ===

    https://ui.adsabs.harvard.edu/abs/20....135S/abstract

    Substellar Companions to Seven Evolved Intermediate-Mass Stars
    Sato, Bun'ei; Omiya, Masashi; Harakawa, Hiroki; Izumiura, Hideyuki; Kambe, Eiji; Takeda, Yoichi; Yoshida, Michitoshi; Itoh, Yoichi; Ando, Hiroyasu; Kokubo, Eiichiro; Ida, Shigeru
    December 2012

    We report on the detections of substellar companions orbiting around seven evolved intermediate-mass stars from precise Doppler measurements at Okayama Astrophysical Observatory. o UMa (G4 II-III) is a giant with a mass of 3.1M', and hosts a planet with a minimum mass of m2 sini = 4.1MJ in an orbit with a period P = 1630 d and an eccentricity e = 0.13. The star also exhibits a linear velocity trend, suggesting the existence of an outer, more massive companion. 75 Cet (G3 III) is a 2.5M☉ giant hosting a planet of m2 sini = 3.0MJ in a 692 d orbit with e = 0.12. The star also shows a possible additional periodicity of about 200 d and 1880 d with a velocity amplitude of ̃7-10 m s-1, although these are not significant at this stage. ν Oph (K0 III) is a 3.0M☉ giant, and has two brown-dwarf companions of m2 sini = 24MJ and 27MJ, in orbits with P = 530.3 d and 3190 d, and e = 0.126 and 0.17, respectively, which were independently announced by Quirrenbach, Reffert, and Bergmann (2011, AIP Conf. Proc. 1331, 102). The ratio of the periods is close to 1:6, suggesting that the companions are in mean motion resonance. We also independently confirmed planets around κ CrB (K0 III-IV) and HD 210702 (K1 IV), which were announced by Johnson et al. (2008, ApJ, 675, 784) and Johnson et al. (2007a, ApJ, 665, 785), respectively. All of the orbital parameters we obtained are consistent with the previous results.
    Last edited by Roger E. Moore; 2020-Feb-14 at 03:32 PM.
    Do good work. —Virgil Ivan "Gus" Grissom

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    Within the last month, a substellar object (giant Jovian planet) was discovered in a group of stars estimated to be 3-5 million years old. Given the likely young age of the planets in your hypothetical system, you might find this information to be of help. The giant planet here was several hundred AU from its sun-star.

    NEWS: http://www.sci-news.com/astronomy/ne...ant-08118.html

    PAPER: https://iopscience.iop.org/article/1...15-5172/ab7344
    Do good work. —Virgil Ivan "Gus" Grissom

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    Last thoughts: the larger planets or brown dwarfs in the system might still be accreting material, as they are so young, but perhaps the blue giant's solar wind has blown a lot of the interplanetary material away and stopped the growth process. Just a suggestion/thought, YMMV.

    ===

    https://arxiv.org/abs/2001.08890

    Sporadic and intense accretion in a 1 Myr-old brown dwarf candidate
    D. Nguyen-Thanh, N. Phan-Bao, S. J. Murphy, M. S. Bessell
    (Submitted on 24 Jan 2020)

    Studying the accretion process in very low-mass objects has important implications for understanding their formation mechanism. Many nearby late-M dwarfs that have previously been identified in the field are in fact young brown dwarf members of nearby young associations. Some of them are still accreting. They are therefore excellent targets for further studies of the accretion process in the very low-mass regime at different stages. We aim to search for accreting young brown dwarf candidates in a sample of 85 nearby late-M dwarfs. Using photometric data from DENIS, 2MASS, and WISE, we constructed the spectral energy distribution of the late-M dwarfs based on BT-Settl models to detect infrared excesses. We then searched for lithium and Hα emission in candidates that exhibit infrared excesses to confirm their youth and the presence of accretion.

    ==

    Two hypergiant blue stars with dust rings around them. Several A-type giants have been found with planets, like Fomalhaut, but no B-types yet.

    https://en.wikipedia.org/wiki/HD_37974

    https://en.wikipedia.org/wiki/HD_268835

    https://www.nasa.gov/vision/universe...-20060208.html

    ===

    From the mass of the star in your example, would that not be a blue supergiant?

    https://en.wikipedia.org/wiki/Blue_supergiant_star
    Last edited by Roger E. Moore; 2020-Feb-14 at 07:24 PM. Reason: more
    Do good work. —Virgil Ivan "Gus" Grissom

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    Intensely interested in hearing how your concept develops, Fiery Phoenix. Unique idea.

    What SF sources did you use for the idea?
    Do good work. —Virgil Ivan "Gus" Grissom

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    Quote Originally Posted by Roger E. Moore View Post
    Intensely interested in hearing how your concept develops, Fiery Phoenix. Unique idea.

    What SF sources did you use for the idea?
    Thanks for your input, Roger. I've considered some of the things mentioned in the papers you linked.

    My sci-fi sources are all over the place. I would say Hal Clement has been the biggest inspiration. Some non-book inspirations from Star Trek and Mass Effect are also worth mentioning.

    To visualize the system, I've actually created it in full using SpaceEngine. It's great to be able to actually see what it looks like. Helps tons with writing.
    “Of all the sciences cultivated by mankind, Astronomy is acknowledged to be, and undoubtedly is, the most sublime, the most interesting, and the most useful. For, by knowledge derived from this science, not only the bulk of the Earth is discovered, but our very faculties are enlarged with the grandeur of the ideas it conveys, our minds exalted above their low contracted prejudices.” - James Ferguson

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    Hal Clement, MOST excellent.
    Do good work. —Virgil Ivan "Gus" Grissom

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