| Subject: Re: How smart are SETI@homers? |
| From: Joseph Lazio |
| Date: 23/05/2004, 11:38 |
| Newsgroups: sci.astro.seti,alt.sci.seti,sci.space.policy |
[I thought this exchange on the number of terrestrial mass planets
to be getting to the point where a followup was not necessary.
However, I've since realized that there is an important point.]
R> In infinite wisdom Joseph Lazio answered:
"R" == Rich <someone@somewhere.com> writes:
R> Almost exclusively gas giants, only a few oddball terrestrial
R> planets. I don't see how you can derive that there are "more
R> lower-mass planets than Jupiter-mass planets" from the data at
R> hand.
From Marcy et al. (2003, "Properties of Extrasolar Planets," ...)
The distribution of masses rises rapidly toward the lower masses,
dN/dM ~ M^{-0.7} ....
R> Where M is 1 jupiter mass.
This is both incorrect and highlights an important point. The mass
distribution I write above is a function. It is valid over a range of
masses, not just at 1 Jupiter mass as Rich seems to believe. It might
have helped had I have written this as dN/dM = A*M^{-0.7}, where A is
a constant that is determined from the data.
To make this point more explicit, we can use this mass distribution to
compare the number of planets of different masses. Suppose we want to
know how many more 0.5 Jupiter mass planets there are compared to the
number of 2 Jupiter mass planets. Then dN/dM(2M_J) ~ (2M_J)^{-0.7}
and dN/dM(0.5M_J) ~ (0.5M_J)^{-0.7}, and their ratio is
(0.5M_J/2M_J)^{-0.7} = 2.6. That is, there are about 3 times as many
0.5 Jupiter mass planets as there are 2 Jupiter mass planets.
This brings me to the important point. How low in mass does this
function apply. Planets with masses of 0.1M_J have been discovered,
and the function seems to apply at least this low. Earth is about
0.003M_J. One might worry that there could be some difference in the
way that gas giants and terrestrial planets form. If that is the
case, extrapolating this mass distribution to terrestrial planet
masses may not be valid.
So what is the evidence for terrestrial mass planets? I'd now have to
say, not much.
If I were a gambling man, though, I'd be willing to bet that
terrestrial planets are numerous, for the following reasons. First,
if Jupiter mass planets can form, it seems like forming something only
0.3% of their mass should be much easier. Indeed, at a party last
night, somebody pointed out that we actually know of three extrasolar
*cometary* systems. Second, we know of three terrestrial mass planets
orbiting PSR B1257+12, and there were not supposed to be any planets
orbiting pulsars.