From: Dani Eder (firstname.lastname@example.org)
Date: Tue Oct 05 2004 - 10:14:38 MDT
There is a relevant table and graph about 40% of the
way down this page:
The definition of a planet (<13xJupiter Mass) vs
brown dwarf (13-70x Jupiter mass) is that a planet
never gets hot enough in formation to cause
deuterium fusion (~2M Kelvin), while a brown
dwarf fuses deuterium but not hydrogen.
The masses quoted on the page are M sin(i) where
i is the unknown inclination. The radial velocity
doppler shift of the primary star is how most of
these objects are being found. If the secondary
object orbits edge on (i=90 deg), the doppler shift
is maximized. If the object orbits face-on (i=0
deg), the shift would be zero. Since we don't
know the inclination (for now), we only know
M sin(i). Therefore the actual mass is larger by
some unknown amount. So some of the objects
listed will turn out to be brown dwarfs rather than
planets. The significance of that is brown
dwarfs got hot from gravitational collapse and
deuterium fusion, and have not had time to cool
off to a temperature that supports life as we
know it, i.e. T(surface)>1000K at present.
As a side note, our Jupiter is still cooling off
from it's formation too. It releases twice as
much heat from the interior as it receives from
the sun. But it is small enough that it is no
longer glowing hot at the surface.
You can see the number of objects gets larger
as the M sin(i) gets smaller, which is the encouraging
trend I noted previously.
The table lists:
M sin (i) which I have discussed above,
P(d) - orbital period in days. We are biased towards
short orbital periods because orbits like Jupiter's
have a half period (6 years) which is longer than
the time we have had instruments this good to observe
with. You need to observe a half orbit or more to
measure the maximum doppler shift
a - semimajor axis of orbit. In a circular orbit
that is just the radius. In an elliptical orbit that
is the half the long axis. We are biased towards
small orbits because they increase the doppler shift
e - eccentricity, defined as ratio of ellipse focus
distance from center/semimajor axis. Values are
0 for circle to 1.0 for parabola. A sizeable fraction
are in the range of our solar system's planets
(0 to 0.2 neglecting Pluto).
K(m/s) is the doppler shift in meters/sec. Since
the width of a star's spectral line is at least
due to the random motion of the atoms that create
the line, which is several km/s, what is actually
being measured is a doppler shift of a few percent
of the width of the line, which is why these
measurements are hard to do.
The web page talks a lot about how narrow the
range of conditions is for 'life as we know it' to
develop, since most stars get hotter over time.
Therefore the orbit range over which liquid water
can exist shifts. Thus the range over which
liquid water exists for the 3.5 billion years of
evolution time is narrow.
I suggest he failed to account for large moons of
large planets or brown dwarfs (see Europa), where
the combination of tidal heating and direct
radiation from the larger object (cooling over time)
counteracts the star's brightening.
As I had said in an earlier message, the data are
not quite good enough to say much about Earthlike
planets yet, but give it another 5-10 years and it
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