Bending light with gravity
henry l. barwood
other source that can answer a question. I know that the bending of light
near a massive body (the sun) has been measured. Does the amount of
deflection increase evenly as the light path nears the sun, or is it
anisotropic? Do all wavelengths deflect the same or are they dispersed?
Any help will be welcome. TIA.
Henry Barwood
john baez
>I know that the bending of light
>near a massive body (the sun) has been measured. Does the amount of
>deflection increase evenly as the light path nears the sun, or is it
>anisotropic?
I don't know what you mean by that.
>Do all wavelengths deflect the same or are they dispersed?
General relativity predicts a wee bit of dispersion, but nobody has ever
seen "gravity's rainbow", because the amount of dispersion caused by
something like the sun is very small. See Misner Thorne and Wheeler's
"Gravitation" for a nice discussion of this.
Patrick van Esch
Can you explain where this comes from ? I would have thought light
folows ds = 0 geodesics and how can this depend on frequency ?
cheers,
Patrick.
--
Patrick Van Esch
http://www.iihe.ac.be/hep/pp/vanesch
mail: van...@dice2.desy.de
for PGP public key: finger van...@dice2.desy.de
LBsys
>>I know that the bending of light
>>near a massive body (the sun) has been measured. Does the amount of
>>deflection increase evenly as the light path nears the sun, or is it
>>anisotropic?
>
>I don't know what you mean by that.
As gravitation is stronger near the sun, dispersion/deflection should
increase when the light path is close to the sun. Is that what the
question was? Is the answer correct?
>>Do all wavelengths deflect the same or are they dispersed?
>
>General relativity predicts a wee bit of dispersion, but nobody has ever
>seen "gravity's rainbow", because the amount of dispersion caused by
>something like the sun is very small.
If GR predicts this, then gravity should have something one could call a
refraction index. Correct?
Feynman says, refraction is due to light travelling slower eg in glass
(looking for the shorter way). And dispersion is b/c the refraction index
differs for different wavelengths, i.e.: different colours have different
velocities in glass. Correct?
Someone else mentioned (in a post I unfortunately dumped), that, yes, "the
envelope of a package of white light is getting larger, when the package
is passing through eg glass.
(Off topic: is that true for sound waves also? Is their velocity through
air dependent of their respective frequency? Is this, why we hear the high
pitch crackling noises of a distant thunder first and then the rolling
deep frequencies?)
If GR thus predicts a 'rainbow', the 'enevelope' of a package of light
coming from a distant star, should be enlarged, travelling through gravity
for so far. Is this correct?
We thus should find the blue light first and then the red part in this
package? Correct?
This is more to astronomers: Would a distant pulsar allow us to measure
this? And if so: Could we thus calculate its distance?
(Sorry, this sounds more stupid than the thoughts behind: I often read
here, that spacetime is curved and thus 'creates' gravity. Is it then
right to say that the shortest way between two points is in effect the
shortest way regarding time, whereas the way looked upon from a cubic
space would be a curve, just like the shortest way on earth always has to
be a curve also, when adding the third dimension? This naturally would
lead to measure distances in time, [which is done anyway by the expression
of lightyears: who says that light proceeds in a 'straight line'?]. As
gravity is everywhere light should make a nice snakeline through space,
right :-) ? What would a difference in blue/red light velocity tell us
then? Actually, it should tell us the 'amount' of gravity light had to
pass through on it's way. Which in reverse would tell us something about
the 'length of the way through' the curved spacetime it had to pass,
right? Sorry, if all of this doesn't make any sense, I'm still a layman
:-)
And another experiment: If we look at a distant star, whichs light is bent
by a massive gravity center (like a black hole), and we do this in summer
and in winter (i.e. from two different angles), the maximum intensity in
the spectrum should have shifted from red to blue (or vice versa). Has
this been done? Any objections?
Cheerio
Lorenz Borsche (FRG)
Dubium sapientiae initium. [Descartes]
henry l. barwood
by gravity. What I was refering to was polarization analogous to
different directions in a uniaxial or biaxial crystal. Has such
polarization been observed in gravitation lensing? I'm also interested in
an apparent increase in the deflection as light grazes the gravitational
source - does this happen and what is the magnitude of the effect.
Conventional optics equates the dispersion of light with a variable speed
of transit through a transparent medium. If dispersion or polarization
occur with gravitational bending would this imply that gravitational
optical effects are analogous to classical optical effects and that
differing wavelengths propagate through a gravitational field at
differing velocities? I repeat, I'm not a physicist, but a mineralogist
who works with optical mineralogy and I'm curious about what has been
observed. In examples of gravitational lensing observed by astronomers,
do the images display dispersion of spectral color, or does the light
focus as white light? Thanks to those who have replied and to any
additional help I may receive.
Henry Barwood
Geoffrey A. Landis
hbar...@indiana.edu writes:
>...
> In examples of gravitational lensing observed by astronomers,
>do the images display dispersion of spectral color, or does the light
>focus as white light?
Astronomical gravitational lenses have no spectral dispersion of the
lensing effect. In fact, in some of the tests being conducted using
gravitational lenses, the absence of a spectral effect is used as the
test of whether it's really gravitational lensing-- if there is any
difference between red and blue light, then it's not gravitational
lensing.
Baez says that
>General relativity predicts a wee bit of dispersion
[wavelength dependence]
but this must be a very tiny, very high order effect, because the
experimentalists all take gravitational lensing to be completely
wavelength independent.
[he goes on:
>but nobody has ever
>seen "gravity's rainbow", because the amount of dispersion caused by
>something like the sun is very small. ]
--I would be interested in hearing the answer to the question posed by
Patrick van Esch:
>Can you explain where this comes from ? I would have thought light
>folows ds = 0 geodesics and how can this depend on frequency ?
____________________________________________
Geoffrey A. Landis,
Ohio Aerospace Institute at NASA Lewis Research Center
physicist and part-time science fiction writer
Steve Carlip
: Let me clarify my post asking about anisotropy in light deflected (bent)
: different directions in a uniaxial or biaxial crystal. Has such
: polarization been observed in gravitation lensing?
Classical general relativity predicts that there should be no
such gravitational birefringence. It has quite recently been
realized that many alternatives to general relativity *do*
predict different deflections for different polarizations,
and data from polarization measurements from extragalactic
sources has been used to put sharp limits on such theories.
The presence of this phenomenon in non-GR theories was first
pointed out by Gabriel et al., Phys. Rev. D43 (1991) 308; for
a preprint describing (I believe) the sharpest observational
limits, see Haugan and Kauffmann, gr-qc/9504032.
(Quantum corrections to electromagnetism in a gravitational
background can produce birefringence, as well as frequency
dependence of gravitational deflection, by inducing nonminimal
coupling terms in the interaction between electromagnetism
and gravity. But these effects are *very* small.)
Steve Carlip
car...@dirac.ucdavis.edu
Lawrence R. Mead
: other source that can answer a question. I know that the bending of light
: deflection increase evenly as the light path nears the sun, or is it
: Any help will be welcome. TIA.
:
: Henry Barwood
:
The bending depends on the mass of the star and procedes "evenly" (the
path is differentiable, for example) all along. The amount of bending
does not depend on wavelenth.
--
Lawrence R. Mead (lrm...@whale.st.usm.edu)
ESCHEW OBFUSCATION ! ESPOUSE ELUCIDATION !
http://www.usm.edu/usmhburg/sci_tech/phy/mead.html
john baez
>john baez (ba...@guitar.ucr.edu) wrote:
>:In article <4kr6n2$h...@usenet.ucs.indiana.edu> "henry l. barwood"
<hbar...@indiana.edu> writes:
>: >Do all wavelengths deflect the same or are they dispersed?
>: General relativity predicts a wee bit of dispersion, but nobody has ever
>: seen "gravity's rainbow", because the amount of dispersion caused by
>: something like the sun is very small. See Misner Thorne and Wheeler's
>: "Gravitation" for a nice discussion of this.
>Can you explain where this comes from ? I would have thought light
>folows ds = 0 geodesics and how can this depend on frequency ?
If light followed ds = 0 geodesics it would not diffract through a slit.
The point is: in the geometrical optics limit, the limit in which we can
think of light as made of little massless pellets that follow geodesics,
we may say that light follows geodesics. In general relativity, this is
the limit in which spacetime curves significantly only over distances
much longer than the wavelength of the light. Far from the geometrical
optics limit, to figure out what's going on we need to sit down and
solve Maxwell's equation. (Actually we are willing to ignore polarization
of light we can save some work and use the wave equation.) This will
give rise to some dispersion effects.
When I answered Barwood's question I *thought* Misner Thorne and Wheeler
had a nice discussion of this, but upon checking, I'm afraid they don't.
They have a nice discussion of how to derive the geometrical optics
limit from Maxwell's equation, and a nice discussion of what light does
near a massive object in the geometrical optics limit --- here you get
not rainbows, but glories. But I can't seem to find any discussion of
what the dispersion of light around a massive object is like. I
know for the above reasons that it must in principle exist, but I don't
know what it's like in detail, and I also know that this effect is
completely negligible in practice, unless one happens to be shining
low-frequency radar at a very small black hole or something.
john baez
>In article <4l08im$p...@usenet.ucs.indiana.edu> henry l. barwood,
>hbar...@indiana.edu writes:
>Baez says that
>>General relativity predicts a wee bit of dispersion
>[wavelength dependence]
>but this must be a very tiny, very high order effect, because the
>experimentalists all take gravitational lensing to be completely
>wavelength independent.
Oh, of course. The effect must be ridiculously small in the case you
mention. I guess it's proportional to the wavelength of light divided by the
radius of the galaxy that's doing the lensing, or some power of that, or
something like that. To make the effect big we want long wavelengths of
light and a very small massive gravitating body... but I don't expect
we'll ever actually see it.
I'm sorry if I caused any confusion here. Remember, I have a certain
fascination for issues of principle, so I like to point out effects that
must exist even if they are much too small for any sane person to worry
about.
Once on sci.physics I noted that a spinning brick in the depths of
intergalactic space would eventually slow to a halt due to the emission
of gravitational radiation. To me this is fascinating simply because
it's not true in classical mechanics. But I got some flack for it,
because it would take a ridiculously long time to happen.
In fact, someone had fun trying to work out what would actually make it
spin down first: the emission of gravitational radiation, tidal coupling
to galaxies, or friction with the occaisional atom wandering about in
intergalactic space. I forget which effect won.
Here's a silly question I just thought of. Say you have a brick in a
perfect vacuum, at some very low temperature, but not absolute zero.
Wouldn't the random motion of its molecules occaisionally concentrate
enough kinetic energy in one near the surface to make that molecule
break free and fly off? So, wouldn't the brick very very gradually
dissipate?
The question is not whether this happens anytime soon (it obviously
doesn't), but whether it *ever* happens. If it did happen, maybe the
spinning brick in intergalactic space would dissipate before it spun
down. (The answer here might depend on the pressure of intergalactic
gas.)
john baez
>Let me clarify my post asking about anisotropy in light deflected (bent)
>by gravity. What I was refering to was polarization analogous to
>different directions in a uniaxial or biaxial crystal. Has such
>polarization been observed in gravitation lensing?
I immensely doubt it.
>I'm also interested in
>an apparent increase in the deflection as light grazes the gravitational
>source - does this happen and what is the magnitude of the effect.
Say you have a stationary gravitational source of mass M and a light
beam passing by it. If you let b stand for the distance of closest
approach, the angle of deflection of the light is about 4M/b when b/M is
large, in units where c = G = hbar = 1. So in short, the angle of
deflection is inversely proportional to the distance of closest approach
in the limit where b/M is large. This approximation is probably not bad
for many situations. When b/M gets really small --- and our source is
really small --- things get complicated. One gets "glories" as
described in Misner Thorne and Wheeler page 677-678.
Doug Merritt
>Can you explain where this comes from ? I would have thought light
>folows ds = 0 geodesics and how can this depend on frequency ?
The different frequencies have different energies and therefore
make their own tiny contributions to the stress-energy tensor, changing
the curvature and therefore changing their own geodesic.
Doug
--
Doug Merritt do...@netcom.com
Professional Wild-eyed Visionary Member, Crusaders for a Better Tomorrow
Unicode Novis Cypherpunks Gutenberg Wavelets Conlang Logli Alife Anthro
Computational linguistics Fundamental physics Cogsci Egyptology GA TLAs
Norbert Pfannerer
>>Do all wavelengths deflect the same or are they dispersed?
>seen "gravity's rainbow", because the amount of dispersion caused by
>something like the sun is very small. See Misner Thorne and Wheeler's
>"Gravitation" for a nice discussion of this.
Could you please explain where that dispersion comes from. In my naive
view of GR a lightlike path through spacetime is the same for all photons.
-------------------------------------------------------------------
All opinions are my own, not my employer's
Norbert Pfannerer norbert_...@vnet.ibm.com
Vienna, Austria, Europe
Jonathan Scott
on 16 Apr 1996 14:11:30 GMT,
Geoffrey A. Landis <Geoffrey> writes:
>Baez says that
>>General relativity predicts a wee bit of dispersion
I find that very surprising. I've never noticed any such result.
>--I would be interested in hearing the answer to the question posed by
>Patrick van Esch:
>>Can you explain where this comes from ? I would have thought light
>>folows ds = 0 geodesics and how can this depend on frequency ?
I would have thought exactly the same. Are we really talking about
"dispersion" in the sense of variation with wavelength?
Jonathan Scott
jonatha...@vnet.ibm.com or jsc...@winvmc.vnet.ibm.com
Patrick van Esch
: In article <4l00f7$a...@dscomsa.desy.de> van...@jamaica.desy.de (Patrick van Esch) writes:
: >Can you explain where this comes from ? I would have thought light
: The different frequencies have different energies and therefore
: make their own tiny contributions to the stress-energy tensor, changing
: the curvature and therefore changing their own geodesic.
I don't think so. After all, then it should depend on INTENSITY, not on
frequency. (stress-energy being a classical measure of energy)
Aparently John was talking about diffraction around the hills and valleys
in spacetime... (which is purely theoretical, because most of the changes
in spacetime occur on scales which are _many_ orders of magnitude
larger than the wavelength considered).
Klaus Kassner
>
>Here's a silly question I just thought of. Say you have a brick in a
>perfect vacuum, at some very low temperature, but not absolute zero.
>Wouldn't the random motion of its molecules occaisionally concentrate
>enough kinetic energy in one near the surface to make that molecule
>break free and fly off? So, wouldn't the brick very very gradually
>dissipate?
at a certain small but nonzero pressure (as long as temperature is nonzero).
So if it is in perfect vacuum, it will continue evaporating until its
vapour reaches that pressure which will never happen it you allow the
atoms to escape to infinity.
>The question is not whether this happens anytime soon (it obviously
>doesn't), but whether it *ever* happens. If it did happen, maybe the
>spinning brick in intergalactic space would dissipate before it spun
>down. (The answer here might depend on the pressure of intergalactic
>gas.)
some partial pressure of the material the solid is made of. If so, the solid
will not completely evaporate. It is a question of chemical equilibrium.
Klaus Kassner
Douglas A. Singleton
[discussion on gravitational dispersion deleted]
>Once on sci.physics I noted that a spinning brick in the depths of
>intergalactic space would eventually slow to a halt due to the emission
>of gravitational radiation. To me this is fascinating simply because
>it's not true in classical mechanics. But I got some flack for it,
>because it would take a ridiculously long time to happen.
I missed the original discussion on this, and was wondering how
this works. If instead of a uniformly rotating brick one had
a uniformly charged sphere (or a spherical shell with uniform
charge) which rotated uniformly then there would be no E&M
radiation (right?), but there would be a static Coulomb E-field
and a dipole B-field. Why in the gravitational case would
there be radiation ? Does it have to do with the fact that the brick
does not have spherical symmetry ? It's not some Hawking or
Unruh radiation thing is it ? For example I can believe that
an isolated Kerr black hole will eventually spin down from
Hawking radiation.
Thanks in advance.
Doug
.
Patrick van Esch
: ba...@guitar.ucr.edu (john baez) wrote:
: >
: >Here's a silly question I just thought of. Say you have a brick in a
: >perfect vacuum, at some very low temperature, but not absolute zero.
: >Wouldn't the random motion of its molecules occaisionally concentrate
: >enough kinetic energy in one near the surface to make that molecule
: >break free and fly off? So, wouldn't the brick very very gradually
: >dissipate?
: Yes, it would. The solid is in thermodynamic equilibrium with its vapour
: at a certain small but nonzero pressure (as long as temperature is nonzero).
: So if it is in perfect vacuum, it will continue evaporating until its
: vapour reaches that pressure which will never happen it you allow the
: atoms to escape to infinity.
: >The question is not whether this happens anytime soon (it obviously
: >doesn't), but whether it *ever* happens. If it did happen, maybe the
: >spinning brick in intergalactic space would dissipate before it spun
: >down. (The answer here might depend on the pressure of intergalactic
: >gas.)
Hahaha, a funny and naughty remark: Given a quantum cosmologist,
and enough spacetime, all the rest of "normal physics" will
eventually follow :-)
Even day-by-day thermodynamics :-)
: Well, as long as there is intergalactic gas, it depends whether it contains
: some partial pressure of the material the solid is made of. If so, the solid
: will not completely evaporate. It is a question of chemical equilibrium.
Yes, but it is a dynamical equilibrium. So "pieces of brick" will form, but
the original brick will eventually dissipate,
no matter what the partial pressure of "brick"-atoms :-)
This is maybe related to a phase-transformation of the
universe in the (hopefully far) future:
"the wall" by Pink Floyd :-)
Matt McIrvin
da...@faraday.clas.Virginia.EDU (Douglas A. Singleton) wrote:
> Why in the gravitational case would
> there be radiation ? Does it have to do with the fact that the brick
> does not have spherical symmetry ?
Yes. A mass with an oscillating or rotating quadrupole moment will
emit gravitational radiation. A spinning sphere wouldn't do it.
--
Matt McIrvin Indent-o-Meter goes here, when I'm using trn.
Instead, you get a free URL. http://world.std.com/~mmcirvin/
--
Nntp-Posting-Host: world.std.com
Path: mmcirvin
Date: Sat, 30 Mar 1996 02:41:04 -0500
From: mmci...@world.std.com (Matt McIrvin)
john baez
>ba...@guitar.ucr.edu (john baez) wrote:
>>Here's a silly question I just thought of. Say you have a brick in a
>>perfect vacuum, at some very low temperature, but not absolute zero.
>>Wouldn't the random motion of its molecules occaisionally concentrate
>>enough kinetic energy in one near the surface to make that molecule
>>break free and fly off? So, wouldn't the brick very very gradually
>>dissipate?
>Yes, it would. The solid is in thermodynamic equilibrium with its vapour
>at a certain small but nonzero pressure (as long as temperature is nonzero).
>So if it is in perfect vacuum, it will continue evaporating until its
>vapour reaches that pressure which will never happen it you allow the
>atoms to escape to infinity.
That sounds right.
>>The question is not whether this happens anytime soon (it obviously
>>doesn't), but whether it *ever* happens. If it did happen, maybe the
>>spinning brick in intergalactic space would dissipate before it spun
>>down. (The answer here might depend on the pressure of intergalactic
>>gas.)
>Well, as long as there is intergalactic gas, it depends whether it contains
>some partial pressure of the material the solid is made of. If so, the solid
>will not completely evaporate. It is a question of chemical equilibrium.
That sounds right too. So: is the vapor pressure of brick (or ice, or
whatever folks actually know about!) at 3 degrees kelvin more, or less,
than the pressure of intergalactic gas?
I say 3 degrees kelvin because a brick in intergalactic space will be at
least that hot, due to the background radiation.
(I know I should say "3 kelvin" instead of "3 degrees kelvin", but I am
feeling in an especially rebellious mood today.)
Bill Rowe
van Esch) wrote:
>john baez (ba...@guitar.ucr.edu) wrote:
>: General relativity predicts a wee bit of dispersion, but nobody has ever
>: seen "gravity's rainbow", because the amount of dispersion caused by
>: something like the sun is very small. See Misner Thorne and Wheeler's
>: "Gravitation" for a nice discussion of this.
>
>Can you explain where this comes from ? I would have thought light
>folows ds = 0 geodesics and how can this depend on frequency ?
The geodesics are determined by the curvature of spacetime which in turn
is determined by the amount of energy/mass present. Photons of different
frequencies have different energies. So it follows the interaction between
spacetime curvature and photons will vary with photon frequency (energy).
--
"Against supidity, the Gods themselves contend in vain"
Patrick van Esch
: [discussion on gravitational dispersion deleted]
: >Once on sci.physics I noted that a spinning brick in the depths of
: >intergalactic space would eventually slow to a halt due to the emission
: >of gravitational radiation. To me this is fascinating simply because
: >it's not true in classical mechanics. But I got some flack for it,
: >because it would take a ridiculously long time to happen.
Actually, I'm not sure if it is not true in classical
mechanics. Ok, not via radiation, but
"tidal effects at a distance" ought to "lock in" the brick
with the "rotation of the remote stars". Like the moon is locked
with respect to the earth's rotation around the moon ( :-) )
: I missed the original discussion on this, and was wondering how
: this works. If instead of a uniformly rotating brick one had
: a uniformly charged sphere (or a spherical shell with uniform
: charge) which rotated uniformly then there would be no E&M
: radiation (right?), but there would be a static Coulomb E-field
: and a dipole B-field. Why in the gravitational case would
: there be radiation ? Does it have to do with the fact that the brick
: does not have spherical symmetry ? It's not some Hawking or
I think it is this. You have a rotating dipole, which, just
as in EM, emits radiation...
Cheers,
john baez
>In article <4l15hs$6...@guitar.ucr.edu>, john baez <ba...@guitar.ucr.edu> wrote:
>>perfect vacuum, at some very low temperature, but not absolute zero.
>>Wouldn't the random motion of its molecules occaisionally concentrate
>>enough kinetic energy in one near the surface to make that molecule
>>break free and fly off? So, wouldn't the brick very very gradually
>>dissipate?
>
>absurd amount of patience), though. Even in interstellar space, which
>is high vacuum by terrestrial standards, the density of stuff is high
>enough that it would probably accrete faster than it dissipated.
Okay, so I guess you are saying that the vapor pressure of a brick at 3 K
or so is less than the pressure in intergalactic space. I'm glad
SOMEONE around here knows about practical stuff like that.
>While we're on the subject of ridiculously negligible effects, won't
>it gradually change from whatever bricks are made of into iron?
>(Since iron is more tightly bound than anything else, and since there
>is a nonzero -- albeit minuscule -- rate for fusion events to happen.)
Well, if as you suggest the brick won't dissipate, and nothing else
weird happens, it would eventually turn to iron by quantum
tunneling-induced fusion. And then it might eventually turn into a
black hole for the same reason --- although recent work on black hole
thermodynamics has apparently overturned some previous beliefs about the
equilibrium state of stuff in a box. (Sorry I can't be more specific!
I think Steve Carlip knows about this stuff... he told me a bit about it
when I last saw him.)
Of course, the rates for these processes to occur are so slow, that I'm
sure all sorts of things we're forgetting about will happen first.
We're talking time periods that make the current age of the universe
pretty hard to tell from a millisecond.
Maybe the brick will accrete enough intergalactic gas to form a star!
john baez
>In article <4l15hs$6...@guitar.ucr.edu>, john baez <ba...@guitar.ucr.edu> wrote:
>>Once on sci.physics I noted that a spinning brick in the depths of
>>intergalactic space would eventually slow to a halt due to the emission
>>of gravitational radiation. To me this is fascinating simply because
>>it's not true in classical mechanics. But I got some flack for it,
>>because it would take a ridiculously long time to happen.
Here by "classical mechanics" I meant "as opposed to general
relativity", not "as opposed to quantum mechanics". "Classical" has
this annoying ambiguity to it.
>I missed the original discussion on this, and was wondering how
>this works. If instead of a uniformly rotating brick one had
>a uniformly charged sphere (or a spherical shell with uniform
>charge) which rotated uniformly then there would be no E&M
>radiation (right?), but there would be a static Coulomb E-field
>and a dipole B-field. Why in the gravitational case would
>there be radiation ?
I'm pretty sure there wouldn't be. Not unless you count quantum effects,
which are even MORE ridiculously negligible. I wasn't thinking about
those above.
>Does it have to do with the fact that the brick
>does not have spherical symmetry ?
Right. Classically, the main cause of gravitational radiation is a
time-dependent quadrupole moment of the mass density. A spinning sphere
or spherical shell would not have this, while the spinning brick I
mentioned would.
In general we expect time-depedent moments of charge, or mass, or
whatever, to create radiation. In electromagnetism and gravity,
time-dependent monopole moments are forbidden, by conservation of charge
and energy, respectively. (Here I'm talking about flat enough
spacetimes so that stuff like moments of the mass density and
conservation of energy make sense!) In gravity, unlike
electromagnetism, time-dependent dipole moments are also forbidden ---
by conservation of momentum. Time-dependent higher multipole moments
can also cause radiation, both for electromagnetism and gravity, but a
rotating spherically symmetric body has no time-dependent moments.
>It's not some Hawking or
>Unruh radiation thing is it ? For example I can believe that
>an isolated Kerr black hole will eventually spin down from
>Hawking radiation.
Right, that would eventually happen. This is a quantum effect.
Edward Green
>I have a certain
>fascination for issues of principle, so I like to point out effects that
>must exist even if they are much too small for any sane person to worry
>about.
eventually deform in response to applied stress, for much the same reasons
that the brick should evaporate, given below.
>Here's a silly question I just thought of. Say you have a brick in a
>perfect vacuum, at some very low temperature, but not absolute zero.
>Wouldn't the random motion of its molecules occaisionally concentrate
>enough kinetic energy in one near the surface to make that molecule
>break free and fly off? So, wouldn't the brick very very gradually
>dissipate?
>
>doesn't), but whether it *ever* happens.
>If it did happen, maybe the
>spinning brick in intergalactic space would dissipate before it spun
>down. (The answer here might depend on the pressure of intergalactic
>gas.)
gas", then the eventual result would be rounding into a spherical brick
globule to reduce surface effects. Of course this is only the equilibrium
shape, and with finite positive probability we would still experience
thermodynamic fluctuations; such as the one every 10^10^10... years or so
that turned the brick into a Snoopy statuette.
Other processes might dominate.
--
Ed Green / egr...@nyc.pipeline.com
Occam used a double-edged razor.
Edward Green
>I can't seem to find any discussion of
>what the dispersion of light around a massive object is like. I
>know for the above reasons that it must in principle exist, but I don't
>know what it's like in detail, and I also know that this effect is
>completely negligible in practice, unless one happens to be shining
>low-frequency radar at a very small black hole or something.
>
with garden variety dispersion in the solar atmosphere.
Emory F. Bunn
>perfect vacuum, at some very low temperature, but not absolute zero.
>Wouldn't the random motion of its molecules occaisionally concentrate
>enough kinetic energy in one near the surface to make that molecule
>break free and fly off? So, wouldn't the brick very very gradually
>dissipate?
I can't see why not. You'd need a mighty good vacuum (as well as an
absurd amount of patience), though. Even in interstellar space, which
is high vacuum by terrestrial standards, the density of stuff is high
enough that it would probably accrete faster than it dissipated.
While we're on the subject of ridiculously negligible effects, won't
it gradually change from whatever bricks are made of into iron?
(Since iron is more tightly bound than anything else, and since there
is a nonzero -- albeit minuscule -- rate for fusion events to happen.)
-Ted
Ray Tomes
>In article <4kr6n2$h...@usenet.ucs.indiana.edu> "henry l. barwood" <hbar...@indiana.edu> writes:
>>I know that the bending of light
>>near a massive body (the sun) has been measured. Does the amount of
>>deflection increase evenly as the light path nears the sun, or is it
>>anisotropic?
>I don't know what you mean by that.
I think that he wants the formula for the curvature as a function of
distance and angle between the light direction and the sun.
I don't know the formula but the curvature is greater when the light is
closer (it depends on M/r) and I also greater when travelling at right
angles to the direction of the sun (might be dependant on the sine of
the angle). Of course these two factors combine for a single ray.
>>Do all wavelengths deflect the same or are they dispersed?
>General relativity predicts a wee bit of dispersion, but nobody has ever
>seen "gravity's rainbow", because the amount of dispersion caused by
>something like the sun is very small. See Misner Thorne and Wheeler's
>"Gravitation" for a nice discussion of this.
I didn't know that. Do the waves have to have significant wavelength
relative to the distances involved for this to be relevant? Please tell
us more John (and save me a trip to the library).
-- Ray Tomes -- rto...@kcbbs.gen.nz -- Harmonics Theory --
http://www.vive.com/connect/universe/rt-home.htm
Geoffrey A. Landis
writes:
>Okay, so I guess you are saying that the vapor pressure of a brick at 3 K
>or so is less than the pressure in intergalactic space. I'm glad
>SOMEONE around here knows about practical stuff like that.
I posted a reply of the question on how long it will take a brick to
evaporate in a new thread, since it didn't seem that "bending light with
gravity" was the appropriate line. The answer is: a very long time.
In article <4l37of$h...@sulawesi.lerc.nasa.gov> Geoffrey A. Landis,
geoffre...@lerc.nasa.gov writes:
>...
>Say that the binding energy of an atom to the brick's surface is Eb.
>Call it 2 electron volts. Then the fraction of atoms with energy of Eb
>or greater is Exp[-Eb/kT]. If the brick is in thermal equilibrium with
>the cosmic background radiation of 3 K, then kT is 0.25 meV, so this
>fraction is Exp[-8000]. For reference, Exp[-8000] is about 10^-3478.
>Energy is redistributed in roughly the amount of time it takes a phonon
>to cross the atom, which is something like the phonon wavelength divided
>by the speed of sound v. Speed of sound will be on the order of a
>km/sec. lambda = hc/energy, so t = lambda/v = hc/vkT comes to something
>like ten to the minus 14 seconds, if I did the calculation correctly.
>(Actually, it's irrelevant whether I did the calculation correctly or
>not, since a factor of 10^-3500 trumps any possible algebra error except
>dividing by zero]. So the time constant for the brick to evaporate by a
>factor of e will look like Exp[-8000]*10^-14 seconds, or about 10^-3464
>seconds. That's 10^3457 years.
>...
Emory F. Bunn
>In article <4l41f1$p...@agate.berkeley.edu> t...@physics.berkeley.edu writes:
>>absurd amount of patience), though. Even in interstellar space, which
>>is high vacuum by terrestrial standards, the density of stuff is high
>>enough that it would probably accrete faster than it dissipated.
>
>or so is less than the pressure in intergalactic space. I'm glad
>SOMEONE around here knows about practical stuff like that.
I should point out two things:
1. I said "interstellar," not "intergalactic."
2. I was really just guessing anyway.
I think that what I said is probably true as far as interstellar
space (meaning space between the stars within a particular galaxy)
is concerned. The reason I think so is that the interstellar medium
in galaxies has got lots of "dust" in it. Interstellar dust is made
up of little grains of stuff like carbon. Not only do these grains
manage not to evaporate, but they actually *form*. That suggests
to me a vapor pressure that's high enough that bricks are probably
stable.
The density in intergalactic space is much less, and I wouldn't like
to guess whether dissipation or accretion would dominate for an
intergalactic brick. A real astronomer could probably make a good
guess.
>Of course, the rates for these processes to occur are so slow, that I'm
>sure all sorts of things we're forgetting about will happen first.
>We're talking time periods that make the current age of the universe
>pretty hard to tell from a millisecond.
Right. I took a general relativity class from Rich Gott when I was an
undergraduate, and he spent a good part of one lecture talking about
the distant future of the Universe. He mentioned that one particular
effect -- it may even have been the Earth turning into iron -- would
happen on a time scale of "ten to the ten to the seventieth" or
something. Someone asked him what the units were on that number, and
he correctly pointed out that it doesn't make any difference: that
number looks the same whether you're talking about Planck times or
Hubble times!
-Ted
john baez
>In article <4l4gb1$8...@guitar.ucr.edu>, john baez <ba...@guitar.ucr.edu> wrote:
>>Okay, so I guess you are saying that the vapor pressure of a brick at 3 K
>>or so is less than the pressure in intergalactic space. I'm glad
>>SOMEONE around here knows about practical stuff like that.
>1. I said "interstellar," not "intergalactic."
>2. I was really just guessing anyway.
>I think that what I said is probably true as far as interstellar
>space (meaning space between the stars within a particular galaxy)
>is concerned. The reason I think so is that the interstellar medium
>in galaxies has got lots of "dust" in it. Interstellar dust is made
>up of little grains of stuff like carbon. Not only do these grains
>manage not to evaporate, but they actually *form*. That suggests
>to me a vapor pressure that's high enough that bricks are probably
>stable.
>The density in intergalactic space is much less, and I wouldn't like
>to guess whether dissipation or accretion would dominate for an
>intergalactic brick. A real astronomer could probably make a good
>guess.
Gee, and you almost fooled me into thinking YOU were a real astronomer.
Okay, so I'm crossposting to sci.astro, where presumably such people
reside. I'm wondering:
1. What sort of densities are we talking about when we're talking about
interstellar space or intergalactic space? Pressures? I imagine the
pressure in interstellar space varies tremendously (see below on
Wolf-Rayet stars).
2. What sort of vapor pressures are we talking about for things like
dust grains in interstellar space? (Forget the brick; let's talk about
something that's actually out there in vast numbers!)
3. Does galactic dust eventually sublimate if it happens to get shot
out of the galaxy? Or is intergalactic space eventually going to become
as polluted as the air down here in Riverside, unless we slap some regulations
on those damn galaxies? I hear that Wolf-Rayet stars are really big
offenders when it comes to particulate emissions: those suckers
shoot out vast amounts of stuff like triply ionized carbon, at speeds of
around 4000 km/sec (as opposed to a wimpy 200 km/sec for the solar wind
around here).
If nobody answers I may have to go to the physics department library and
pull out some books on galactic dust.
john baez
>In article <4l4gb1$8...@guitar.ucr.edu> john baez, ba...@guitar.ucr.edu
>writes:
>>or so is less than the pressure in intergalactic space. I'm glad
>>SOMEONE around here knows about practical stuff like that.
>I posted a reply of the question on how long it will take a brick to
>evaporate in a new thread, since it didn't seem that "bending light with
>gravity" was the appropriate line. The answer is: a very long time.
Yes, I enjoyed your calculation! It's probably right up to an order of
magnitude of orders of magnitude, at least for a brick in a vacuum. I'm
not too worried about the last step, where somehow the answer went from
really small to really big:
>>.... Exp[-8000]*10^-14 seconds, or about 10^-3464 seconds. That's
>>10^3457 years.
The experts know how to get the right answer by making an even number of
mistakes. (Maybe you want something more like Exp[8000]*10^-14
seconds, but as you note that scarcely matters.)
But I am worried about the fact that it neglects the pressure of
intergalactic space. Your calculation implies that the vapor pressure
of a brick at 3 K is incredibly small, and if the pressure of
intergalactic space exceeds that, the brick won't ever sublimate.
Stefan Reisner
> Here's a silly question I just thought of. Say you have a brick in a
> perfect vacuum, at some very low temperature, but not absolute zero.
> Wouldn't the random motion of its molecules occaisionally concentrate
> enough kinetic energy in one near the surface to make that molecule
> break free and fly off? So, wouldn't the brick very very gradually
> dissipate?
Despite the amount of discussion that has already followed up this
post, I would like to add this:
Since John assumed the brick to be at some unspecific "very low"
temperature, I take it we are not assuming it to be in equilibrium
with the 3K background here.
Under this preposition I doubt that the brick would completely
dissipate if its total inner energy was less than the sum of portions
of energy required to remove each atom from the bulk.
In fact, the cooling of, I think, sodium atoms that led to
Bose-Einstein condensation recently was done by repeatedly letting
the hottest atoms evaporate from the trap, leaving the rest at a lower
temperature after thermalization.
This does not take the possibility of tunneling into account, of
course. But this way or another, in order for the dissipated atoms not
to interact with each other anymore, they would have to end up having
some finite amount of momentum and energy that carries them away from
each other and the brick. So I think for a sufficiently low
temperature it might just not work out energetically, although the
brick might end up being in equilibrium with a very thin "halo" of
atoms that tunnelled out and get re-adsorbed by van der Vaals forces.
Best regards,
Stefan Reisner.
Ilja Schmelzer
>That sounds right too. So: is the vapor pressure of brick (or ice, or
>whatever folks actually know about!) at 3 degrees kelvin more, or less,
>than the pressure of intergalactic gas?
>I say 3 degrees kelvin because a brick in intergalactic space will be at
>least that hot, due to the background radiation.
Before assuming 3K for the brick we have to verify that the
temperature equilibrium with the background radiation will be
established faster than the pressure equilibrium with intergalactic
gas. And we have to consider the color of the brick. As far as I
understand, the temperature of the brick will be 3K only if the brick
is a "black body", not necessary in general.
Ilja
--
My concept for the quantization of gravity: ~/PG/index.html
--------------------------------------------------------------------------
Ilja Schmelzer, D-10178 Berlin, Keibelstr. 38, <schm...@wias-berlin.de>
WWW: ~/index.html "~" means http://www.berlinet.de/schmelzer
--------------------------------------------------------------------------
Oz
<van...@jamaica.desy.de> writes
>
>Actually, I'm not sure if it is not true in classical
>mechanics. Ok, not via radiation, but
>"tidal effects at a distance" ought to "lock in" the brick
>with the "rotation of the remote stars". Like the moon is locked
>with respect to the earth's rotation around the moon ( :-) )
Right. An elastic brick.
Shouldn't that be 'remote galaxies'?
I bet that's got a long effective time too.
And I expect the brick will contain iron and other magnetic thingies.
And we haven't considered any photoelectric effects that may cause it to
be charged.
At this level of insanity, basically if you can think of it, it's got to
be considered. ......
-------------------------------
'Oz "When I knew little, all was certain. The more I learnt,
the less sure I was. Is this the uncertainty principle?"
Oz
writes
>
>But I am worried about the fact that it neglects the pressure of
>intergalactic space. Your calculation implies that the vapor pressure
>of a brick at 3 K is incredibly small, and if the pressure of
>intergalactic space exceeds that, the brick won't ever sublimate.
Oh I expect you just gotta wait a bit. After 10^1000 odd years the
pressure of intergalactic (or intergalacticmegaclustorial) space is
bound to have dropped significantly, or else increased "quite a lot" and
it'll still be the brick that sublimates.
Alan "Uncle Al" Schwartz
(snip)
>1. What sort of densities are we talking about when we're talking about
>interstellar space or intergalactic space? Pressures? I imagine the
>pressure in interstellar space varies tremendously (see below on
>Wolf-Rayet stars).
I understand the void averages a couple of atoms/m^3, about 240 photons
(cosmic background), and an undisclosed number of neutrinos.
>2. What sort of vapor pressures are we talking about for things like
>dust grains in interstellar space? (Forget the brick; let's talk about
>something that's actually out there in vast numbers!)
Vapor pressure assumes equilibrium. If the energy available to a surface
molecule or atom is less than its binding energy, then it only escapes by
tunneling or a stochastic coincidence at the tail of its energy
distribution. It is more likely to be eroded by intercepting energetic
radiation.
>3. Does galactic dust eventually sublimate if it happens to get shot
>out of the galaxy? Or is intergalactic space eventually going to become
>as polluted as the air down here in Riverside, unless we slap some regulations
>on those damn galaxies? I hear that Wolf-Rayet stars are really big
>offenders when it comes to particulate emissions: those suckers
>shoot out vast amounts of stuff like triply ionized carbon, at speeds of
>around 4000 km/sec (as opposed to a wimpy 200 km/sec for the solar wind
>around here).
Given the amount of stuff apparently available and the volume of space
available for its dispersal, an even dispersal would be an imperceptibly
changed thin gruel vs what we now have.
>If nobody answers I may have to go to the physics department library and
>pull out some books on galactic dust.
>
There is a question of whether dust is primarily primordial light
elements, or heavier stuff cycled through a star. With an equilibrium
radiation temperature of around 2.7K, anything heavier than hydrogen or
helium isn't going anywhere from its frozen lattice (except for
encountering energetic events like cosmic rays or the occasional UV
photon).
--
Alan "Uncle Al" Schwartz
Uncl...@ix.netcom.com ("zero" before "@")
http://www.netprophet.co.nz/uncleal/ (naughty beyond measure;
"Quis custudiet ipsos custodes?" The Net! funny beyond endurance)
Edward Green
>But I am worried about the fact that it neglects the pressure of
>intergalactic space. Your calculation implies that the vapor pressure
>of a brick at 3 K is incredibly small, and if the pressure of
>intergalactic space exceeds that, the brick won't ever sublimate.
If we have a pressure of intergalactic hydrogen that exceeds the brick's
total vapor pressure the brick may yet sublimate, because the brick is not
a lump of solid hydrogen, nor, persumably would a lump of solid hydrogen
be in equilibrium with the gas under those conditions...
Unless it is. Then we will plate out metallic hydrogen on the brick.
john baez
>>3. Does galactic dust eventually sublimate if it happens to get shot
>>out of the galaxy? Or is intergalactic space eventually going to become
>>as polluted as the air down here in Riverside, unless we slap some
>>regulations
>>on those damn galaxies? I hear that Wolf-Rayet stars are really big
>>offenders when it comes to particulate emissions: those suckers
>>shoot out vast amounts of stuff like triply ionized carbon, at speeds of
>>around 4000 km/sec (as opposed to a wimpy 200 km/sec for the solar wind
>>around here).
>Given the amount of stuff apparently available and the volume of space
>available for its dispersal, an even dispersal would be an imperceptibly
>changed thin gruel vs what we now have.
I was just joking about polluting intergalactic space with galactic dust
grains; obviously there is way too much room between the galaxies to
worry too much about that. My serious question here was: would a dust grain
sublimate in intergalactic space?
>There is a question of whether dust is primarily primordial light
>elements, or heavier stuff cycled through a star. With an equilibrium
>radiation temperature of around 2.7K, anything heavier than hydrogen or
>helium isn't going anywhere from its frozen lattice (except for
>encountering energetic events like cosmic rays or the occasional UV
>photon).
I think intergalactic dust contains lots of carbon and other crap shot
out of Wolf-Rayets and other stars in their dying final days. And I
indeed suspect this stuff "isn't going anywhere from its frozen lattice"
in any HURRY. But as a careful perusal of earlier posts in this thread
will disclose, we are interested in ridiculously slow effects here,
since we have eons of time at our disposal ---- UNLESS faster effects
win out. It's quite possible that cosmic-ray-induced fission will be
faster than the other effects we had been considering. (Mike Jones also
pointed out this effect, in email.)
john baez
>Before assuming 3K for the brick we have to verify that the
>temperature equilibrium with the background radiation will be
>established faster than the pressure equilibrium with intergalactic
>gas.
A brick at room temperature (say) will reach temperature equilibrium
with the background radiation long before it reaches pressure
equilibrium. It reaches temperature equilibrium by emitting infrared
and then microwave radiation, which it does easily. It reaches pressure
equilibrium by sublimating or accreting, which it does scarcely at all.
>And we have to consider the color of the brick. As far as I
>understand, the temperature of the brick will be 3K only if the brick
>is a "black body", not necessary in general.
A body at thermal equilibrium with its environment has the same
temperature as that of the environment, no matter what color it is.
Andrew Cooke
>: seen "gravity's rainbow", because the amount of dispersion caused by
>: something like the sun is very small. See Misner Thorne and Wheeler's
>: "Gravitation" for a nice discussion of this.
>
>folows ds = 0 geodesics and how can this depend on frequency ?
isn't it going to be some second order effect where the energy
density of the light itself is involved (hence it being only a
wee bit)?
just guessing,
andrew
--
work phone/fax: 0131 668 8356, office: 0131 668 8357
institute for astronomy, royal observatory, blackford hill, edinburgh
http://www.roe.ac.uk/ajcwww
Ben Weiner
>1. What sort of densities are we talking about when we're talking about
>interstellar space or intergalactic space? Pressures? I imagine the
>pressure in interstellar space varies tremendously (see below on
>Wolf-Rayet stars).
In the interstellar medium (ISM) of the Galaxy, there are several
phases, with pressure P/k = nT on the order of 1000 K cm^-3, as a
gross approximation (n is number density of atoms). Hot coronal gas
at T >= several x 10^5 K, warm ionized gas at T = 10^4 K, warm neutral
gas at 100 - few x 10^3 K, diffuse molecular gas at T ~ 60 K. You can
figure out ranges for n from nT ~ 1000, but allow at least an order of
magnitude variation.
Then there are molecular clouds, which are self-gravitating and not in
pressure equilibrium with the rest of the ISM, with T = 10-100 K and
n = 100 - 10^6 cm^-3.
Extended coronae of galaxies probably have T = few x 10^6 K and
n <= 10^-4 cm^-3.
Hot gas in rich clusters of galaxies has T = 10^7 to 10^8 K, n ~ 10^-4
cm^-3. (These numbers are all nominal and individual objects vary
considerably.)
There is probably some hot ionized gas between the galaxies but this
is pretty much speculation.
>2. What sort of vapor pressures are we talking about for things like
>dust grains in interstellar space? (Forget the brick; let's talk about
>something that's actually out there in vast numbers!)
You got me here. If it helps, dust - which ought to be called "soot" -
is probably grains about 0.5 - 250 nm in size, at temperatures something
like 10 - 50 K, made up of carbon, oxygen, silicon, magnesium, iron,
hydrogen, and what-all.
BTW, as far as Wolf-Rayet stars go, they have impressive winds but are
probably too hot to form a lot of dust. The conventional wisdom is
that dust is formed in outflows from cool stars like red giants.
Hence, soot.
>3. Does galactic dust eventually sublimate if it happens to get shot
>out of the galaxy? Or is intergalactic space eventually going to become
>as polluted as the air down here in Riverside, unless we slap some regulations
>on those damn galaxies?
Dust gets destroyed in shocks and by sputtering in hot gas. Same thing
really I guess - atoms moving at 100 - 1000 km/sec smack into the poor
little grains which were never built too solid to begin with. There's
also absorption of UV radiation. Draine & Salpeter (1979, Ap.J. 231, 438)
may be the canonical reference.
If something (like a supernova explosion) kicks gas out with enough
velocity to get far out of the galaxy, it probably destroys a lot of
the dust in the gas. OTOH, if a dust grain did get out of the galaxy,
I think it would probably cool to about 3 K and just sit there much
faster than it would sublimate.
By the way, it's too late as far as pollution control goes. There are
a lot of people who think that PAHs - Polycyclic Aromatic Hydrocarbons
- are present in the ISM and may be responsible for some dust-related
IR emission features. These are also a major ingredient of car
exhaust. And if it seems bad when you're in Pasadena and you can't
see the San Gabriels, just think - we're practically on top of the
Galactic Center, cosmologically speaking, yet there's 20 magnitudes of
extinction between it and us.
>If nobody answers I may have to go to the physics department library and
>pull out some books on galactic dust.
Try a book called "Dust in the Galactic Environment" by D. Whittet.
Amara Graps
>2. What sort of vapor pressures are we talking about for things like
>dust grains in interstellar space? (Forget the brick; let's talk about
>something that's actually out there in vast numbers!)
First of all, the dust grains can not form in interstellar space- they
must form in stellar atmospheres or other dense environments and then be
ejected into space.
Note: The grains can _evolve_ and _change_ in the interstellar medium,
but they can't _form_ there. The argument goes something like this:
given an observed typical grain diameter a, the time for a grain to
attain a, and given the temperature of interstellar gas, it would take
considerably longer than the age of Universe for interstellar grains to
form in the interstellar medium. (I can post the argument in "equation"
form, if you wish.)
For condensation from gas to solid to occur depends on the values of the
gas pressure P_gas and the vapour pressure P_vap. Once P_gas exceeds
P_vap, then condensation should occur. If one neglects curvature of the
grain surface (which is an effect that must be considered for tiny
grains), then
P_vap ~ P_0 exp[-T_0/T]
where P_0 and T_0 are pressure and temperature constants specfic to the
astronomical material. You can plug in the following numbers and get
some idea for the vapour pressure (from Anueurin Evans, _The Dusty
Universe_, page 85.):
Material P_0(N m^{-2}) T_0 (K)
Graphite 1.68E13 88880
Silicates 5.31E13 60560
Water ice 2.16E5 6160
Hydrogen 2.66E7 104
>3. Does galactic dust eventually sublimate if it happens to get shot
>out of the galaxy? Or is intergalactic space eventually going to become
>as polluted as the air down here in Riverside, unless we slap some regulations
>on those damn galaxies? I hear that Wolf-Rayet stars are really big
>offenders when it comes to particulate emissions: those suckers
>shoot out vast amounts of stuff like triply ionized carbon, at speeds of
>around 4000 km/sec (as opposed to a wimpy 200 km/sec for the solar wind
>around here).
Wolf-Rayet stars, hmm? WR stars all have in common, mass losses, and many
have thick, carbon-rich dust shells. But according to Abbott and Conti
(1987, Ann Rev of Astro Ap 25, 113) the average WR star wind conveys
2*10^{-5} solar masses per year to the interstellar medium. R.D. Gehrz
(in his chapter "Sources of Stardust in the Galaxy", IAU Symposium 135
_Interstellar Dust_, publ. by Kluwer, 1989) said that based on the
Galactic distribution of WR stars, the total mass input from WR stars is
~0.01 solars masses per year, with only about 10^{-4} solar masses per
year being in the form of dust. So, therefore, WR stars represent a
negligible amount of dust input as compared to that input by other
sources.
So what are some other sources?
I found an interesting table in Gehrz's chapter (pg 447) "Types of Dust
Grains in Stellar Outflows". (He breaks down the grains to composition
types, as well as gas-to-dust ratio by mass, but I'm not posting that
part of the table here.)
Stellar Type Input to Interstellar Medium, Relative to all Stars
M Stars (Miras) 35%
RLOH/IR stars 32%
Carbon stars 20%
Supernovae 8%
M supergiants 4%
WR stars 0.5%
Planetary Nebulae 0.2%
Novae 0.1%
RV Tauri stars 0.02%
O,B stars 0
Gehrz concludes in his last section titled: "The Ecology of Stardust in
the Galaxy" that:
1. M stars, RLOH/IR stars and M supergiants are the primary sources of
silicates, while carbon stars, WR stars and novae produce most of the
carbon and SiC. Novae, supernovae, and WR stars may be responsible for
most of the grains with chemical anomalies.
2. The current star formation rate implies that star formation is
depleting the interstellar medium (ISM) gas by some 3 to 10 solar
masses per year.
3. There is a deficit in stardust production/grain destruction.
Supernovae shock waves destroy ISM grains on very short time-scales
(Seab, 1987, _Interstellar Processes_, Hollenbach and Thronson ed.
Reidel) processing 10-30 solar masses per year and destroying 0.1-0.3
solar masses per year in dust. Gehrz estimates that 0.01-0.08 solar
masses per year of dust is returned to the ISM by stars. He feels that
grain growth in dark clouds is an attractive mechanism to make up the
dust deficit.
So it is pretty unlikely that the "intergalactic space is eventually
going to become as polluted as the air down here in Riverside"..
Amara
--
*************************************************************************
Amara Graps email: agr...@netcom.com
Computational Physics vita: finger agr...@best.com
Multiplex Answers URL: http://www.amara.com/
*************************************************************************
"If you gaze for long into the abyss, the abyss also gazes into
you." --Nietzsche
john baez
>ba...@guitar.ucr.edu (john baez) writes:
>
>>1. What sort of densities are we talking about when we're talking about
>>interstellar space or intergalactic space? Pressures? I imagine the
>>pressure in interstellar space varies tremendously (see below on
>>Wolf-Rayet stars).
>In the interstellar medium (ISM) of the Galaxy, there are several
>phases, with pressure P/k = nT on the order of 1000 K cm^-3, as a
>gross approximation (n is number density of atoms). Hot coronal gas
>at T >= several x 10^5 K, warm ionized gas at T = 10^4 K, warm neutral
>gas at 100 - few x 10^3 K, diffuse molecular gas at T ~ 60 K. You can
>figure out ranges for n from nT ~ 1000, but allow at least an order of
>magnitude variation.
>Then there are molecular clouds, which are self-gravitating and not in
>pressure equilibrium with the rest of the ISM, with T = 10-100 K and
>n = 100 - 10^6 cm^-3.
>Extended coronae of galaxies probably have T = few x 10^6 K and
>n <= 10^-4 cm^-3.
>Hot gas in rich clusters of galaxies has T = 10^7 to 10^8 K, n ~ 10^-4
>cm^-3. (These numbers are all nominal and individual objects vary
>considerably.)
Thanks for this and all the other fascinating information. Interstellar
space is lot more busy and variegated than one imagines from
popularizations that emphasize how vast and empty and boring it is.
Like most things in the universe, if you look at it at the right scale
it's quite interesting. Temperatures ranging from a chilly 60 K to a
roasting 10^5 K! Densities from 10^-4 to 10^6 atoms/cm^3! Wow!
>Try a book called "Dust in the Galactic Environment" by D. Whittet.
Will do.
john baez
>'ba...@guitar.ucr.edu (john baez)' wrote:
>>But I am worried about the fact that it neglects the pressure of
>>intergalactic space. Your calculation implies that the vapor pressure
>>of a brick at 3 K is incredibly small, and if the pressure of
>>intergalactic space exceeds that, the brick won't ever sublimate.
>Chemistry counts.
>If we have a pressure of intergalactic hydrogen that exceeds the brick's
>total vapor pressure the brick may yet sublimate, because the brick is not
>a lump of solid hydrogen, nor, persumably would a lump of solid hydrogen
>be in equilibrium with the gas under those conditions...
Damn! Partial pressures! They fool you (I mean me) every time!
Thanks.
Emory F. Bunn
>Gee, and you almost fooled me into thinking YOU were a real astronomer.
Nah. I work on astrophysics problems, but I'm definitely a physicist,
not an astronomer. There are big differences between the two in
training and temperament. I think the biggest difference is that
astronomers know a bunch of stuff and physicists don't. Physicists
just know how to calculate things or build things, but astronomers
actually know things! They remember what the differences are between
Seyfert I and Seyfert II galaxies, and how to tell early-type stars
from late-type ones, and what a carbonaceous chondrite is, and all
kinds of stuff. I forget that kind of thing as soon as anyone tells
me, which proves I'm a physicist rather than an astronomer.
-Ted
Oz
<t...@physics12.Berkeley.EDU> writes
I hate to say it but I think the word 'mathematical', 'theoretical' or
even 'not a chemical' should go in somewhere here.
Ilja Schmelzer
>A brick at room temperature (say) will reach temperature equilibrium
>with the background radiation long before it reaches pressure
>equilibrium.
May be. If you know the interaction rates and the densities, you can
estimate this, but you have to estimate the order of magnitude (I
haven't). I have interpreted the usual big bang descriptions with the
disconnection of the background radiation some time after the big bang
that the background radiation does not interact often enough with
matter to be in equilibrium.
>A body at thermal equilibrium with its environment has the same
>temperature as that of the environment, no matter what color it is.
Yes, sorry. But the color has an influence how fast the equilibrium
will be reached.
Geoffrey A. Landis
>gas", then the eventual result would be rounding into a spherical brick
>globule to reduce surface effects.
Actually, this will happen even if you don't assume sublimation. I think
it was Dyson, in his long-term evolution of the universe article in
_Reviews of Modern Physics_, who noted that over long enough time scales,
all matter is liquid. Basically, even in a solid, the atoms have some
mobility, and diffuse around. This happens even if the solid is at
absolute zero, due to zero-point motion. Gravity-gradient force and
surface-tension will tend to turn the brick into a sphere. For a
spinning brick, it will tend to turn it into an ellipsoid.
Geoffrey A. Landis
writes:
>Thanks for this and all the other fascinating information. Interstellar
>space is lot more busy and variegated than one imagines from
>popularizations that emphasize how vast and empty and boring it is.
>Like most things in the universe, if you look at it at the right scale
>it's quite interesting. Temperatures ranging from a chilly 60 K to a
>roasting 10^5 K! Densities from 10^-4 to 10^6 atoms/cm^3! Wow!
Yes, but do keep in mind that over a time scale which is small compared
to 10^1000 years, there *are* no Wolf-Rayet, no extended galactic
coronae, etc. Even the cosmic rays lose energy by scattering. It *all*
evens out to a uniform temperature.
Emory F. Bunn
Oz <O...@upthorpe.demon.co.uk> wrote:
>>I forget that kind of thing as soon as anyone tells
>>me, which proves I'm a physicist rather than an astronomer.
>
>I hate to say it but I think the word 'mathematical', 'theoretical' or
>even 'not a chemical' should go in somewhere here.
Agreed. I wasn't trying to imply that physicists necessarily *don't*
know about this sort of thing, just that astronomers necessarily *do*
and physicists need not necessarily.
-Ted
john baez
>ba...@guitar.ucr.edu (john baez) writes:
>>offenders when it comes to particulate emissions: those suckers
>>shoot out vast amounts of stuff like triply ionized carbon, at speeds of
>>around 4000 km/sec (as opposed to a wimpy 200 km/sec for the solar wind
>>around here).
>Wolf-Rayet stars, hmm? WR stars all have in common, mass losses, and many
>have thick, carbon-rich dust shells. But according to Abbott and Conti
>(1987, Ann Rev of Astro Ap 25, 113) the average WR star wind conveys
>2*10^{-5} solar masses per year to the interstellar medium.
Ah, nothing like a show of bogus expertise to draw the true experts from
the woodwork. But I swear my misinformed remarks on Wolf-Rayet starts
weren't a ploy... somehow I'd gotten it into my head that they emitted
lots of dust!
>Stellar Type Input to Interstellar Medium, Relative to all Stars
>
>M Stars (Miras) 35%
>RLOH/IR stars 32%
>Carbon stars 20%
>Supernovae 8%
>M supergiants 4%
>WR stars 0.5%
>Planetary Nebulae 0.2%
>Novae 0.1%
>RV Tauri stars 0.02%
>O,B stars 0
Cool. I'll have to learn more about Miras, RLOH/IR stars and carbon
stars. I checked out a few books on interstellar dust: The Dusty
Universe, Cosmic Dust, and Dusty Objects in the Universe (which has a
nice picture of my dining room table on the front cover). One article
in the last one says infrared emissions M giants fit a model where they
have a spherical envelope of "dirty silicate grains".
Oz
<t...@physics12.Berkeley.EDU> writes
Beware. You are catching the quotable quote syndrome too. :-)
I particularly like the 'physicists need not necessarily' bit.