From: Amara Graps (amara@amara.com)
Date: Sun Dec 05 1999 - 14:23:45 MST
From: "Robert J. Bradbury" <bradbury@www.aeiveos.com>,
Sat, 4 Dec 1999 05:17:38:
>Now, in the vicinity of our Solar System, even when you are
>out of the sun, you don't quite get down to the cosmic
>microwave background temperature.
It depends how you define "vicinity". If you consider ~1 parsec
away from the Sun as "vicinity", then that's OK. (see below)
>This is due to the infrared
>radiation being reflected back from the dust that remains from
>the original nebula from which the planets formed and the
>comet detritus.
Most of the dust in our Solar System now is probably "second
generation dust". The only original material left from the formation
of our Solar System is that locked up in meterorites (Anders and
Zinner, 1993), or else in the more primitive comet material in
comets from the Oort Cloud.
It's probably second-generation because the dynamical processes
occuring in our solar system remove the dust on time scales shorter
than the age of the Solar System. Radiation pressure forces ejects,
from the Solar System, tiny grains (say ~micron in radius) in about
one grain solar orbit period. Grains large enough not to be expelled
are instead driven to spiral in towards the sun by
Poynting-Robertson drag. The P-R time scale to "de-orbit" a
~10-micron grain starting at 1 AU is about 10^5 yr.
>My impression is that this makes infrared
>observations in the planetary plane problematic.
Yes. When I attended a workshop about the zodiacal cloud a couple of
years ago, the participants' opinion in the beginning of the
conference about the structure of the cloud was that it was a kind
of "patchwork". But by the end of the workshop, after hearing
everyone's observational reports, even that patchwork was too
"structured." The structure of the cloud is really messy and really
dynamic (that's why I like it :-) ).
It has (Reach, W., 1997):
* at least 8 dust trails -- source is thought to be short-period
comets,
* at least 5 dust bands -- source is thought to be the asteroid belt,
in particular the three asteroid families: Koronis, Eos, Themis,
* at least 2 resonant dust rings (the Earth resonant dust ring, for
example, but every planet in our Solar System is thought to have a
resonant ring with a "wake", Dermott, S.F. et al., 1994, 1997)
On the other hand, the zodiacal dust cloud is the most prominent
sign of the presence of planetesimal-sized objects in our solar
system. So any other intelligences could look at our zody clould and
its specific features, such as the "resonant dust rings" as signatures
of planets, and _find us_ .
>The lowest temperature you can radiate into would probably be
>the temperature of the dark side of the moon or Mercury. If
>Amara reads this she might be able to tell us the effective
>temperature when you are facing the planetary plane (say on
>most planets equators) vs. facing away from from the plane
>(say on the poles of most planets).
I don't think that there would be much of a difference in the
temperature between those two places in our Solar System.
And our Solar System is warm compared to interstellar or
intergalactic space (~100K versus 3K).
Here's how you estimate the temperature. One would make an energy
balance with the central star and the dust grains, along with the
Stefan-Boltzman equation (to get the temperature).
The luminosity of the dust = some geometrical fraction of the
luminosity of the star, times the total power output of the star.
(to answer your question more precisely, you'd use this geometrical
factor, but I'm too tired to do that)
so:
f x L_sun = L_dust
f = the cross section of the dust particles / the surface area of the
shell that the dust particles occupy.
Say for now, that f ~ 1.
Then:
L_sun =~ L_dust
and the luminosity of the dust is:
L_dust =~ Solar System "disk area" * sigma * T_dust^4
( ^^^^^^ Stephan-Boltzman's const)
If we assume that the radius of our Solar System is ~ 30 AU (the
inner edge of the Kuiper Belt), then the disk surface area of our
Solar System ~ pi * (30 AU)^2
So our equation that gives us the approximate Solar System dust
temperature (assuming equilibrium!) is:
==> T_dust =~ (L_sun / (pi * (30 AU)^2 * sigma) ) ^{1/4}
What is L_sun? It's the Sun's bolometric luminosity. Here we suppose
that the Sun radiates like a blackbody with an effective
temperature T_sun, and it emits its radiation isotropically.
T_sun = 5770 K
R_sun = 6.97x10^10 cm
L_sun = 4 * pi * R_sun^2 * (sigma * T_sun^4) (from S-B's Law again)
L_sun = 3.8x10^33 ergs/sec
and (30AU)^2 = 2.02x10^29 cm^2,
constant sigma = 5.67x10^{-5} erg-cm^2-sec^{-1}-K^{-4}
Then T_dust = (3.8x10^33 / (pi * 2.02x10^29 * 5.67x10^{-5}) )^{1/4}
=~ 101 K
The assumptions here are that the grains "back" sides (facing away
from the star) and their "front" sides have the same temperature
(so they are either rapidly rotating or thermally conductive),
and the grains are black, with albedo 0.
To do a little better calculation, you can assume some properties of
the grains, say that the grain emissivity = 1-albedo, and silicate
grains are very reflective and have an albedo of about .3, and then
you balance the energy again.
Then for silicate grains, the T_dust =~ 150K
(And there are even more ways to make the calculation more
realistic, but you get the idea.)
So what about the temperature in interstellar space?
Around a star, like our Sun, we assumed that the energy input into
the grain is from a single star, so the source of heating radiation
to the grain sitting in a "cavity" is a blackbody of temperature
~10 000 K (say, for an average effective temperature of a star).
But in interstellar space, the energy of the blackbody cavity is
"diluted" by some factor (there is no "central star"), and one of
my texts (Evans, pg. 137), gives this factor psi as ~10^{-14}. So
the radiation field in interstellar space resembles that in a blackbody
cavity at 10^4K, but diluted by 10^{-14}. And with that, you get a
grain temperature of about 3.2 K. One can even calculate the effect
of the microwave radiation on the grain, and it raises it to 3.6K.
Near a star, there are far more grains per volume, than in
interstellar space, and so one can ask how far away from the star
one should be before the number density of grains has declined to
the general interstellar value. Astronomers often use a density
power law n(r), that varies with distance r from the star. And once
one has that number density relationship, you plug it into an
equation that sums up the total mass of the circumstellar grains,
and solve for r, and you would find that the properties of the
circumstellar dust merges with those of the interstellar dust at
about 1 pc from the central star (Evans, pg. 155).
Hope that this answers your question ...
Amara
----------
References
----------
Anders, Edward, and Ernst Zinner, (1993), "Interstellar grains in
primitive meteorites- diamond, silicon carbide, and graphite," in
_Meteoritics_, 28, 490-514.
Dermott, S.F. Jayaraman, S., Xu, Y.L., Gustafson, A.A.S., Liou, J.C.,
(1994), "A circumsolar ring of asteroid dust in resonant lock with the
Earth," Nature 369, June 30, 1994, pg. 79.
Dermott, S.F., in talk titled "Signatures of Planets in Zodiacal Light,"
Exozody Workshop, NASA-Ames, October 23, 1997.
Evans, Aneurin, _The Dusty Universe_ , Ellis Horwood, 1994. (my
favorite dusty reference)
Reach, W., in talk titled "General Structure of the Zodiacal Dust
Cloud," Exozody Workshop, NASA-Ames, October 23, 1997.
***************************************************************
Amara Graps | Max-Planck-Institut fuer Kernphysik
Interplanetary Dust Group | Saupfercheckweg 1
+49-6221-516-543 | 69117 Heidelberg, GERMANY
Amara.Graps@mpi-hd.mpg.de * http://galileo.mpi-hd.mpg.de/~graps
***************************************************************
"Never fight an inanimate object." - P. J. O'Rourke
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