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What Life would see around other Stars

  1. Dec 8, 2008 #1
    Bigger stars are significantly brighter. That pushes back their Habitable Zones (HZs), where D2 ~ L, which makes them look smaller in the skies of (hypothetical) habitable planets, whose years are also alot longer:
    Code (Text):

    Type Mass Temperature Radius  Luminosity HZ-Distance Apparent-Size HZ-Year
    O    64.0    50,000     16.0   1,400,000       1180       0.00016   5250      
    B    18.0    28,000      7.0      20,000        141       0.0025     396      
    A     3.1    10,000      2.1          40          8.9     0.078       15.0    
    F     1.7     7,400      1.4           6          2.4     0.28         2.94  
    G     1.1     6,000      1.1           1.2        1.1     1            1.09    
    K     0.8     4,900      0.9           0.4        0.63    2            0.53  
    M     0.4     3,000      0.5           0.04       0.20    4            0.16  
    Conversely, cooler stars keep their (hypothetical) HZ planets much closer, where orbital speeds are significantly higher. And, since Impactors typically travel at approximately orbital speeds, Impact Events on those worlds would be correspondingly more severe (since KE ~ v2):
    Code (Text):

    Star-Type   HZ-Orbital-Speed   Impactor-Damage-Ratio  Distance-to-Snow-Line ?
    O                  0.23                 0.051                      4700
    B                  0.36                 0.13                        640
    A                  0.60                 0.36                         36
    F                  0.83                 0.69                         10
    G                  1.00                 1.00                          4.4
    K                  1.13                 1.26                          2.4
    M                  1.23                 1.5                           0.80
    The Distance-to-Snow-Line parameter represents the radial distance from the star's HZ to its Snow-Line, where water turns to ice. This is seemingly crucial in the formation of Gas Giants, like Jupiter, which formed on the Sun's Snow-Line*. Thus, for our Solar System, that distance parameter is (5.2 - 1.0 =) 4.2 AU. If Jupiter-sized Gas Giants formed too close to the HZ, they would surely disrupt any proto-planets coalescing therein.
    * Carroll & Ostlie. Introduction to Modern Astrophysics, pg. 893.
  2. jcsd
  3. Dec 10, 2008 #2
    According to the History Channel documentary The Universe -- Alien Faces (TV), Tidal Forces could cause close-in planets (ie., around M-Class stars) to become Tidally Locked (cf. Mercury's 3:2 Resonance). Thus:
    [tex]D_{HZ}^{2} \approx L[/tex]
    [tex]\partial_{D} F_{G} \approx \frac{M}{D^{3}} \approx \frac{M}{L^{3/2}}[/tex]​
    Code (Text):

    Type Mass Temperature Radius  Luminosity HZ-Distance    Tidal-Force-ratio
    O    64.0    50,000     16.0   1,400,000       1180         3.9e-8
    B    18.0    28,000      7.0      20,000        141         6.4e-6
    A     3.1    10,000      2.1          40          8.9       0.012
    F     1.7     7,400      1.4           6          2.4       0.12
    G     1.1     6,000      1.1           1.2        1.1       0.84
    K     0.8     4,900      0.9           0.4        0.63      1.4
    M     0.4     3,000      0.5           0.04       0.20     50
    By way of comparison (to Earth), Mercury's Tidal-Force-ratio is ~16, and it is only partially Tide-Locked in a 3:2 Resonance. Conversely, the Moon's Tidal-Force-ratio is ~180, and it has long been fully Tide-Locked.

    CONCLUSION: Only planets orbiting M-Class stars can plausibly become Tide-Locked over "reasonable" time scales, as indicated in the documentary.

    ADDENDUM: Given these powerful Tidal Interactions, it seems unlikely that M-Class stars' habitable planets could keep their own Moons.

    Moreover, if such planets became Tidally Locked, that might halve their effective surface area for thermal re-radiation, of incoming starlight. That would tend to increase their Black Body temperatures by a factor of ~21/4 = 1.2. In turn, that would tend to increase the orbital distance of the Habitable Zone by a factor of ~21/2 = 1.4.

    That would halve the M-Class parent star's Apparent Size, and would cut down the Tidal Force interaction by a factor of ~23/2 = 2.8, from 50 ---> 18, about the same as Mercury.

    Thus, it may not be possible to have (fully) Tide-Locked habitable planets orbiting M-Class stars, b/c they would over-heat. And, by the time you ventured far enough away, to cool the planet back down, you would only experience moderate Tidal Forces.

    Even so, such planets would probably be partially Tide-Locked, like Mercury.
  4. Dec 10, 2008 #3
    According to Carroll & Ostlie (pg. 891), O/B/A-Class stars do not form planetary systems.

    ALLEGATION: This is b/c, during formation, those bright & hot stars keep all their nebular gases roiling, so that no proto-planetary cores can condense. Thus, O/B/A-Class stars swallow down all their swirling gases.

    But, around cooler stars, iron & rock can condense out & solidify, seeding planetary systems.
  5. Dec 18, 2008 #4
    Potential Impactors, at distance D from the Sun, typically travel w/ velocities:
    vorb2 ~ G Msun / D
    If these velocities exceed the Escape Velocity (vesc2 = 2 G Mplanet / Rplanet) of a particular planet, the potential Impactor is unbound, and an impact is unlikely. We therefore calculate the planets' Impact Ratios (Earth units):
    [tex]\frac{v_{esc}^{2}}{v_{orb}^{2}} = \frac{M_{p} \times D_{p}}{R_{p}}[/tex]​
    Code (Text):

    Planet         Impact Ratio
    Mercury        0.056
    Venus          0.621
    Earth          1.000
    Moon           0.045
    Mars           0.307
    Jupiter      148
    Saturn        98
    Uranus        70
    Neptune      134
    Pluto          0.44
  6. Jan 12, 2009 #5

    Vanadium 50

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    And they are wrong. Fomalhaut has a planet.
  7. May 2, 2009 #6
    Fomalhaut-b is a Jupiter-type planet, orbiting (D ~ 100 AU, P = 872 years) inside the inner edge of a large Debris Ring (cf. Solar Kuiper Belt) surrounding the system.

    Fomalhaut is an A3-Class star, right at the cusp between Planet-forming Star Systems (A5 and below) and non-Planet-forming Star Systems (A0 and above), as indicated in Carroll & Ostlie, pg. 891, figure 21.16.

    To conclusively prove that Carroll & Ostlie are "wrong", would require observing planets orbiting stars larger than about A0 (see figure, it's rough and inexact) -- to wit, O/B-Class stars.

    Does anybody know of any planets orbiting O/B-Class stars, or even A0-Class ?
  8. May 2, 2009 #7
    According to Wikipedia (link),
    Most known exoplanets orbit stars roughly similar to our own Sun, that is, main-sequence stars of spectral categories F, G, or K. One reason is simply that planet search programs have tended to concentrate on such stars. But even after taking this into account, statistical analysis suggests that lower-mass stars (red dwarfs, of spectral category M) are either less likely to have planets or have planets that are themselves of lower mass and hence harder to detect. Recent observations by the Spitzer Space Telescope indicate that stars of spectral category O, which are much hotter than our Sun, produce a Photo-Evaporation effect that inhibits Planetary Formation.​
    For the record, Carroll & Ostlie's figure 21.16 does not extend to stars below G-Class. To quote them exactly,
    As can be seen in Fig. 21.16, a very discernible break occurs in the amount of angular mometum per unit mass, as a function of mass, near spectral class A5. If the total angular momentum of the solar system were included, rather than just the anguluar momentum of the Sun, the trend along the upper end of the main sequence would extend to include our solar system as well (recall that the Sun is a G2 star). Does this observation indicate that the formation of most (or all) low-mass stars leads to the formation of planetary systems that contain the "missing" angular momentum hinted at in Fig. 21.16? As w/ most problems associated w/ understanding the solar system, it is dangerous to extrapolate from one known example (our own) in order to draw general conclusions. However, the growing number of observations of nebular disks orbiting young stars tends to support this conjecture.
    It seems that Planetary Formation is "quenched" (as it were), by Photo-Evaporation effects, somewhere above Spectral Classes A5 and A0 (and, evidently, between A3 and A0, as V50 indicated).
    Last edited: May 2, 2009
  9. May 3, 2009 #8

    Vanadium 50

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    Look, you made the claim that A class stars don't have planets. I gave you a counter-example. That means you are wrong. Simple as that.

    If someone says there is no planet around any A, B or O star, you only have to show a planet around any one of them to disprove this statement. You can't turn around and then say "A doesn't count - it has to be B or O". That's nonsense.

    Your claim that there are no planets with stars hotter than A3 is pure speculation on your part. It's also mighty convenient that the threshold where your speculation begins happens to be the point where the data ends.
  10. May 8, 2009 #9
    Stellar Habitable Zones are defined by L* / DHZ2 = constant. Thus, the strength of Gravity, in those Habitable Zones, is highest for low-mass stars:
    constant = L* / DHZ2 = (L* / M*) x (M* / DHZ2)​
    Gravity at HZ ~ M* / L*
    which is largest for the smallest stars.

    Surely, the strength of Gravity correlates to the local Spacetime Curvature. If so, the Habitable Zones of low-mass stars experience the greatest Spacetime Curvature.
  11. May 8, 2009 #10

    Vanadium 50

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    First, this discussion of spacetime curvature is a complete non-sequitur.

    Second, it's not true that "the strength of Gravity correlates to the local Spacetime Curvature". It's the potential that is related to the curvature, not the field strength.
  12. May 9, 2009 #11

    Attached Files:

  13. May 9, 2009 #12


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    Planets have been detected orbiting neutron stars, so how improbable is it they may be found orbiting M stars?
  14. May 9, 2009 #13

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    I notice that the "max planets" that you keep using this cite to support was written in by hand.
  15. May 9, 2009 #14
    SciLab plot, of Exoplanet Eccentricity vs. Star Spectral Type (data from Wikipedia; Pulsar Planets & Multi-Star Systems omitted).

    Attached Files:

  16. May 9, 2009 #15
    Stellar Habitable Zones are defined by L* / DHZ2 = constant. Thus, the Gravitational Potential, in those Habitable Zones, is deepest for low-mass stars. For, Stellar Luminosity scales as L* ~ M*4 (Bowers & Deeming. Astrophysics I: Stars, pg. ~28.). So,
    constant = L* / DHZ2 ~ (M*4 / DHZ2)​
    And so,
    DHZ ~ M*2
    And so,
    UHZ = -G M* / DHZ ~ - M*-1
    So, since the Gravitational Potential apparently correlates to the local Spacetime Curvature, the Habitable Zones of low-mass stars experience the greatest Spacetime Curvature.

    QUESTION: The product of Newton's Gravitational Constant, times a Density, divided by the Speed of Light squared, has the units of Curvature K (m-2), according to Wikipedia. Thus,
    ||K|| ~ - (G M*) / (c2 x DHZ3)​
    Is there a closed-form solution, for the Spacetime Curvature, produced by a Point Mass ? If so, would somebody please share it, or cite it ?
    Last edited: May 9, 2009
  17. May 10, 2009 #16


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    Tidally locked planets orbitting M stars would struggle to retain their atmospheres, which would be adverse to life. It is possible, however, life could arise before tidal locking advanced enough to make them uninhabitable. Given the rapidity of life arising on earth, anything may be possible. A remote M class system may well not be subject to the repeated annihilation events suffered by life on earth. Intelligent life could arise much more quickly, and perhaps advance sufficiently to flee or engineer solutions to conditions on their dying planet.
  18. May 11, 2009 #17
  19. May 12, 2009 #18


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    Agreed, widdekind, stars with 1/2 - 2/3 solar mass are very likely to support a habitable zone much longer than our own sun - without the problems posed by M class stars. As Guinan pointed out, orange stars are also much more abundant than G class stars. Good catch.
  20. May 12, 2009 #19
    main sequence maximum mass habitable zone...

    Minimum time required for main sequence third generation planet to form:
    [tex]t_p = t_{\odot} - t_E = (4.57 - 4.54) \cdot 10^9 \; \text{y} = 0.03 \cdot 10^9 \; \text{y}[/tex]
    [tex]t_{\odot}[/tex] - solar age
    [tex]t_E[/tex] - Terra age

    [tex]\boxed{t_p = 0.03 \cdot 10^9 \; \text{y}}[/tex]

    Main sequence solar lifetime:
    [tex]t_{L} = 11 \cdot 10^{9} \; \text{y}[/tex]

    Main sequence stellar lifetime:
    [tex]\tau_{ms} = t_{L} \left( \frac{m_{\odot}}{m_s} \right)^{2.5}[/tex]
    [tex]m_{\odot}[/tex] - solar mass
    [tex]m_s[/tex] - stellar mass

    Main sequence stellar lifetime greater than or equivalent to third generation planetary formation time:
    [tex]\boxed{\tau_{ms} \geq t_p}[/tex]

    Integration by substitution:
    [tex]t_{L} \left( \frac{m_{\odot}}{m_s} \right)^{2.5} \geq (t_{\odot} - t_E)[/tex]

    Main sequence third generation maximum stellar mass for habitable zone:
    [tex]\boxed{m_s \leq m_{\odot} \left( \frac{t_{\odot} - t_E}{t_{L}} \right)^{-0.4}}[/tex]

    [tex]\boxed{m_s \leq 10.609 \cdot m_{\odot}}[/tex]

    A third generation main sequence star with this mass is a class B blue giant.

    http://en.wikipedia.org/wiki/Giant_star" [Broken]
    Last edited by a moderator: May 4, 2017
  21. May 13, 2009 #20
    Here is a professional plot, of the Hertzsprung-Russell Diagram in Luminosity - Mass space, also indicating known Exoplanet-bearing systems (W.T. Sullivan III & J.A. Baross. Planets & Life, pg. 445).

    Attached Files:

  22. May 14, 2009 #21
    The probability of planetary formation...

    Planetary existential probability formation appears to increase exponentially from 0 to 1.5 solar mass and decrease exponentially as stellar mass increases above 1.5 solar mass, with a planetary resonance peak around 1 to 1.5 solar mass.

    The majority of the planets discovered have a mass less than 2.5 Jupiter mass, with existential probability decreasing exponentially with increasing planetary mass.

    Planetary existential probability increases with decreasing planetary mass. A dwarf planet is the smallest planet that can exist with the least amount of mass and has the highest existential probability, therefore the majority of planets that exist are dwarf planets.

    A dwarf planet must have sufficient mass to overcome its compressive strength and achieve hydrostatic equilibrium.

    It is suspected that at least another 40 known objects in the Solar System are dwarf planets, and estimates are that up to 200 dwarf planets may be found when the entire region known as the Kuiper belt is explored, and that the number might be as high as 2,000 when objects scattered outside the Kuiper belt are considered.

    http://en.wikipedia.org/wiki/Dwarf_planet" [Broken]

    Attached Files:

    Last edited by a moderator: May 4, 2017
  23. May 15, 2009 #22
    SciLab histograms, of Number of Exoplanets vs. Star Age (data from Wikipedia, as above).

    The first histogram includes only Confirmed Exoplanets (n=27), whose stars' ages were directly cited on Wikipedia. It shows that most Exo-Planetary Systems are young (< 3 Gyr).

    The second histogram includes all Exoplanets (Confirmed & Suspected) (n=188), and this author estimated the ages for roughly 2 dozen of said systems. For example, 18 Delphini is a G6-Class Yellow Giant. Since it is exiting the Main Sequence, this author estimated its age as 8 Gyr. This plot shows that Exo-Planetary Systems are uniformly frequent, out to ages of ~7 Gyr, before becoming increasingly infrequent.

    OBSERVATION: It is well-known, that Exoplanet-bearing stars tend to be Metal-Rich. It is also well-known, that Metal-Rich stars tend to be younger (since Metal Enrichment has gradually accumulated over the ~12 billion year lifetime of the Universe). So, it stands to reason, that Exoplanet-bearing stars could tend to be younger.

    COMPARISON: A "few billion years ago", the Milky Way was very different from today -- it was surely smaller, and had no Spiral Structure in the Galactic Disk. Its Star Formation Rate was also, surely, higher*.
    * History Channel The Universe -- Milky Way Galaxy (TV). Younger Galaxies, having Star Formation Rates ~10 times higher than the Milky Way today, are called Star Burst Galaxies. Thus, the Milky Way may have been a Star Burst Galaxy up until about 3 billion years ago.

    Attached Files:

    Last edited: May 15, 2009
  24. May 15, 2009 #23
    Thanks Chronos & Orion1.
  25. May 16, 2009 #24
    According to the brief book Star Factories, by University of Toronto Prof. Ray Jayawardhana, roughly half of all observed young stars, forming from GMCs, are surrounded by disks of gas & dust. Now, according to Wikipedia cited above, the disks of big bright O/B-Class stars are destroyed by "Photo-Evaporation effects".

    But, what typically stops the disks of M-Class stars from forming into Planetary Systems ? Is it, that those stars' lower masses, mean that the disks spin, & evolve, more slowly, so that the central star's Stellar Wind strips out the gas and dust before the Planetary Embryos have had enough time to "gestate" and grow into full-fledged planets ? The same Wikipedia link said that M-Class stars' planets might exist, but are probably very small... could the "aborted" Planetary Systems of M-Class stars resemble the dim & cold Kuiper Belt about the Sun, out where Planetary Formation was slow & stagnated, and so is only populated by ~Pluto-sized Icy Bodies ??
  26. May 17, 2009 #25
    Very roughly speaking, M* ~ R*3/2. However, the exponent is closer to 1.3 for M thru A-Class stars. Then, the exponent is much higher for big, bright, O/B-Class stars. I understand, that this, too, is where the Main Sequence on the Hertzsprung-Russell Diagram begins to curve upwards. Apparently, O/B-Class stars are a "class unto themselves", being "overbright", for the same Temperature, b/c they puff up so much, from their prodigeous rates of fusion.

    Does this not correspond, to the aforesaid onset of "Photo-Dissociation Effects", disrupting their Proto-Planetary Disks ?
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