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.
>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):
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
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, GERMANYAmara.Graps@mpi-hd.mpg.de * http://galileo.mpi-hd.mpg.de/~graps
"Never fight an inanimate object." - P. J. O'Rourke