From: Amara Graps (amara@amara.com)
Date: Sun Feb 17 2002 - 05:40:40 MST
Extropes,
Might I ask to those proposing wild-ass schemes, to please spend
some time doing some background reading about the objects for which
you are embedding in your engineering feat ? Not spending time
on those basic pieces (including doing your own math) makes the
whole shebang look like hand-waving silliness. Probably I'm being
grumpy, but alot of this black hole stuff can be found in basic
introductory astronomy texts.
From: Eugene Leitl <Eugene.Leitl@lrz.uni-muenchen.de>, Fri, 15 Feb 2002
>On Thu, 14 Feb 2002, Amara Graps wrote:
>> This equation assumes a hydrogen gas sphere in hydrostatic equilibrium,
>> with the total energy transport via radiation.
>
>Actually, it would probably make sense to keep a 10 kK hole in an opaque
>sphere pressurized with hydrogen. What is the power output at that
>blackbody maximum, about that of a nuke?
Main sequence stars balance radiation pressure with gravity. That's
what the above physical scenario looks like to me. Not a black hole.
Black holes in real life suck in matter around it, which become
ultra hot accretion disks.
>You're the resident astrophysicist here.
(who doesn't feel motivation these months to spend my limited
off-hours on science activities. I'm sorry about that, Eugene.)
I have no idea if "nano-sized black holes" scale like star-sized or
galactic-sized black holes (I'm not a black hole expert). The
pre-collapse state would be pretty wierd for a nano-sized black
hole, though. I'm not saying that it's not possible, but whoever is
proposing it should have a physically plausible description.
To power the energy output of a quasar (10^{47} erg/sec), assuming
an efficiency mass conversion via a swirling accretion disk of 10%,
would require swallowing more than 10 M_solar per year.
It's useful to examine the density of the object becoming a black hole.
For a pre-collapse state (using Euclidean geometry), the mean density of
the pre-black-hole object of mass M is: ~ ( 3 c^6 ) / (32 pi G^3 M^2).
[assumine a volume of a sphere, with R equal to the Schwarzschild radius
2GM/c^2]
Looking at stellar-sized (1 M_solar object) black hole and
galactic-sized 10^9 M_solar object black holes:
for a 1 M_solar object, the density is ~10^{16} gr/cm^3 (greater than
the density of a typical neutron star).
for a 10^(9) M_solar object, the density is ~10^{-2} gr/cm^3 (like
the density of a gas)
Some black hole pointers:
Black Hole Snacks
http://science.nasa.gov/headlines/y2001/ast05sep_1.htm
Accretion Disks (and Jets)
http://cpht.polytechnique.fr/cpht/amari/pages/accretionpages/accretion0.html
Black Holes: The Inside Story
http://www-theorie.physik.unizh.ch/~droz/inside/InsideStory.html
[from Astronomy 202, The Galactic Center
www.astro.ubc.ca/courses/astr202/GalCen.html]
Black Hole Basics (equations)
http://www.astro.ubc.ca/courses/astr202/GalCen/GalBH01.GIF
Black Hole Accretion Disk (equations <--- luminsity given here)
http://www.astro.ubc.ca/courses/astr202/GalCen/GalBH01.GIF
Graphic of Black Hole Accretion Disk
http://www.astro.ubc.ca/courses/astr202/GalCen/MBHoles.GIF
Black Holes in Galaxies
http://www.astro.ubc.ca/courses/astr202/GalCen/MDOs.html
More black hole details here:
Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler.
Gravitation San Francisco: W.H. Freeman, 1973.
Black Holes and Time Warps: Einstein's Outrageous Legacy, Kip S.
Thorne, New York : W.W. Norton, 1994
Gravity's fatal attraction: Black holes in the universe, Mitchell
Begelman, Martin Rees, New York : Scientific American Library :
W.H. Freeman, 1996
MSW's Gravitation might be the best place to start for 'harnessing a
cosmic generator'. They have a scenario of an advanced civilization
which has constructed an enclosed bubble five million miles in
diameter around a 10 M_Sun black hole and rotating in a
counterclockwise direction at about .94c. A space capsule hauling a
garbage barge is launched at 2/3 c, fast enough to allow a close
approach and escape. Whipped into an inward-spiraling orbit, the
vehicle enters the ergosphere in the black hole's equatorial plane,
where the ergosphere (region where frame-dragging can no longer
resist) is widest. At a given point, the capsule ejects the garbage
barge backward with with enormous force. The barge spirals down into
the black hole while the capsule picks up rotational energy and
flies back out to the bubble's inner surface, where it strikes a
flywheeel that powers an electrical generator.
This idea was proposed in early 70s.
>Would feeding the nanohole with dust at all make sense?
I didn't read the beginning and intermediate posts regarding this
problem, Eugene, so I don't know the conditions. I would guess that
the lifetime of the dust particle would not be very long though,
because you're immersing the dust in a high-energy shocked plasma
(i.e. the accretion disk around the black hole)
The below text is for a hot plasma from supernova remnants,
which is not as hot as an accretion disk, but the same arguments
should apply regarding short lifetimes.
======================
>From Dwek, E. chapter "Infrared Emission From Dust In Supernovae and
Supernova Remnants", IAU Symposium 135: Interstellar Dust, Kluwer,
1989
\subsection{Dust Temperature in a Hot Gas}
[...]
So far, I have assumed that the dust temperature can be
characterized by its equilibrium value, obtained by balancing the
dust heating rate by particle collisions to its cooling rate by IR
emission. However, below a given grain size, (approximately 200
angstrom in most remnants), the temperature of a dust particle will
fluctuate with time. This effect is a natural consequence of the
heat capacity and cross section of these small dust particles:
individual electron hits raise the grain temperature well above its
equilibrium value, and the grain cooling time at these temperatures
is significantly faster than the time between electronic collisions.
\subsection{Evidence for Very Small Dust Particles in a Shocked Gas}
The results described above suggest that in young supernova remnants
such as Cas A, Tycho, and Kepler, characterized by gas temperatures
in excess of 2~x~10^7 K, the infrared spectrum should be well
described by a single-temperature dust model. Yet, the observed IR
spectra of these remnants (Braun, 1987; Dwek \etal, 1987) show a
significant excess of 12micron emission above that expected from
dust particles radiating at the equilibrium temperature. Simply
extending the grain size distribution to very small particles (a ~3
Angstroms) will not cause a broadening in the infrared spectrum,
since the equilibrium dust temperature is essentially constant with
grain size. The 12micron flux from these remnants can only be
explained if the temperature of these dust particles fluctuates,
reaching values of ~300 K for brief intervals of time. The observed
12micron excess in these remnants therefore provides solid proof
for the existence of dust particles with sizes between ~10--200
angstroms in the remnant, and for the stochastic nature of their
heating mechanism. Furthermore, the lifetime of these remnants is
short ( <400 yrs), so these very small particles could not have been
created by the destruction of larger (a ~250 angstrom) particles in
the shocked gas (see below). This suggests that the grain size
distribution in the pre-shocked gas must have contained the very
small dust particles needed to explain the excess 12micron emission
in the spectrum of these remnants.
\subsection{Evidence for Grain Destruction}
In a hot gas, dust particles are destroyed by sputtering on a
timescale given by t(yr) ~10^6 a(micron)/n, where n is the gas
density in cm^{-3} and a is the radius in microns (Draine and
Salpeter, 1979; Seab, 1987). The lifetime of a 0.1micron dust
particle embedded in a 10 cm^{-3} gas is ~10^4 yrs, longer than the
shock crossing time of all bright x-ray remnants observed with the
IRAS. It should therefore not be surprising to find dust particles
in supernova remnants, a fact clearly demonstrated by the IRAS
observations. Sputtering, will, however, reduce the relative number
of small dust particles in the size distribution. This effect will
suppress the short wavelength infrared emission from the dusty
plasma.
To demonstrate that dust destruction is taking place in the remnant,
one must assume knowledge of the initial grain size distribution.
[...] The amount of sputtering needed to improve the fit to the
observed fluxes determines the residence time of the dust in the hot
gas, or the time since the gas was swept up by the expanding SN
blast wave. For region C in Puppis A, ADP found that the grain
residence time in the shocked gas is 300 +- 150 yrs.
Seab, C. G. 1987, in Interstellar Processes, eds. D.
Hollenbach, and H. A. Thronson, Jr., (Dordrecht: Reidel), p. 491.
Draine, B. T., and Salpeter, E. E. 1979, ApJ, 231, 77.
Dwek, E. 1987, ApJ, 322, 812.
Dwek, E., Dinerstein, H. L., Gillett, F. C., Hauser, M. G., and
Rice, W. L. 1987, ApJ, 315, 571.
And this abstract from the same book
======================
>From C. F. McKee chapter "Dust Destruction in the Interstellar
Medium", IAU Symposium 135: Interstellar Dust, Kluwer, 1989
\begin{abstract}
Grains are injected into the interstellar medium (ISM) from evolved
stars and supernovae; in addition, supernova ejecta may condense
onto pre--existing grains before becoming well--mixed with the
interstellar gas. Once in the ISM, grains can grow by accretion, but
are also subject to destruction by interstellar shocks. The current
status of the theory of shock destruction of interstellar grains is
reviewed briefly. Small grains are destroyed by thermal sputtering
in fast, nonradiative shocks; large grains are destroyed by
grain--grain collisions and eroded by nonthermal sputtering in
radiative shocks. The dominant shocks in the ISM are from supernova
remnants (SNRs), and the mass of grains destroyed is proportional to
the energy of the SNR. In a multiphase ISM, these shocks destroy the
grains at a rate proportional to the volume filling factor of the
phase; since the density of the hot phase is too low for efficient
grain destruction, most of the destruction occurs in the warm phase.
Not all SNRs are effective at destroying grains, however: some are
above the gas disk, and some ---Type II's in associations---are
highly correlated in space and time. The galactic SN rate is
observed to about 2.2 per century (van den Bergh, 1983), but the
{\it effective supernova rate} for grain destruction is estimated to
be only about 0.8 per century. As a result, the timescale for the
destruction of a typical refractory grain in the ISM is inferred to
be about 4x10^8 yr for either a two--phase or a three--phase
ISM. Most of the refractory material in the ISM (other than carbon)
is injected by supernovae, not evolved stars; the net injection
timescale is estimated as about 1.5x10^9 yr. Comparison of
the destruction and injection timescales indicates that the fraction
of grains injected by stars which survive in the ISM is only about
20%. Most of the refractory material in interstellar grains must,
therefore, have accreted onto the grains in the ISM. Nonetheless, a
significant fraction of dust formed in stars survives in the ISM and
may be detectable in meteorites and interplanetary dust particles.
\end{abstract}
======================
Amara
************************************************************************
Amara Graps, PhD | Max-Planck-Institut fuer Kernphysik
Heidelberg Cosmic Dust Group | Saupfercheckweg 1
+49-6221-516-543 | 69117 Heidelberg, GERMANY
Amara.Graps@mpi-hd.mpg.de * http://www.mpi-hd.mpg.de/dustgroup/~graps
************************************************************************
"We came whirling out of Nothingness scattering stars like dust." --Rumi
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