| Subject: Re: How smart are SETI@homers? |
| From: Joseph Lazio |
| Date: 03/06/2004, 01:02 |
| Newsgroups: sci.astro.seti,alt.sci.seti,sci.space.policy |
"R" == Rich <someone@somewhere.com> writes:
R> In infinite wisdom Joseph Lazio answered:
[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.]
This may once again be reaching the point where no reply is
necessary. For the benefit of any other readers though....
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.
R> It's not a function as such, it's more of a relationship. A
R> function takes one input and produces one output. Even if M is
R> defined, and it does not appear to be, you relate any N to any M,
R> or vice verse.
From the data, the mass distribution function above is valid over the
range of roughly 0.1 M_J to 10 M_J. As to your distinction between
"relationships" and "functions," you don't define it and it doesn't
seem to be important. (Call it a relationship if you'd like, that
doesn't change the mathematical expression.)
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.
R> Are there? I don't see any planets with 2 jupiter masses
R> hereabouts.
Hmm. Chinese speakers are claimed to be approximately 20% of the
planet's population. There were no Chinese speakers in my high
school. Ergo, the statistic is wrong.
R> If you claim the relationship has universal validity, perhaps you
R> can show me the observational basis.
I pointed you to the paper.
So what is the evidence for terrestrial mass planets? I'd now have
to say, not much.
R> Odd, when I made that claim it was considered an attack on SETI.
Agreed. You still haven't answered my other question, though. Given
the lack of observational evidence for terrestrial planets, is it
worth searching for them?
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.
R> Should be? Seems to me that they require different materials. As to
R> the dynamics of planetary formation, some of the planets exist
R> where our current models say they cannot exist. I don't think we
R> have any solid basis for making predictions.
Actually, current models involving planetary migration seem to do
reasonably well in explaining the locations of "hot Jupiters."
Indeed, models of planetary migration are helping to explain some
long-standing puzzles about Uranus and Neptune.
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,
R> Lower bounds again, they may well be of the 0.1 jupiter mass class.
I don't think so. I'd have to check Wolszczan's papers, but I think
the detection of the mutual gravitational interactions between the
planets pretty well nails their masses to be terrestrial.