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From: richmond@spiff.Princeton.EDU (Stupendous Man)
Subject: Brief discussion of physics of SN light curves
Summary: first HOT, then BIG
Originator: news@nimaster
Nntp-Posting-Host: spiff.princeton.edu
Organization: Princeton University
Date: Fri, 9 Apr 1993 03:31:06 GMT
So, why is SN 93J getting bright again after an initial
fading? Let me try to explain things briefly, partly as
an exercise for my own understanding.
There are two ways to make a star really bright: it can
get very HOT, or it can get very BIG. Recall that luminosity
increases as temperature to the fourth power (for a black body),
and as radius squared.
Now, 93J's initial rise from 20'th mag to about 10'th was
caused by its outer layers getting really HOT. When the star's
core collapsed and then rebounded, it initiated a shock wave
that began to travel outwards through the star. As the shock
front travelled, it deposited large amounts of energy with
the material through which it passed (my earlier guess
at neutrino heating of the envelope was dead wrong - oops).
The outermost layers, for example, which were probably at around
4000K or so, were heated to something like 40,000K in a matter
of hours or, at most, days. An increase in T by a factor of 10 means
an increase in luminosity L by 10^4 = 10,000 = 10 magnitudes.
Bingo - from 20'th to 10'th apparent mag. However, after
the initial "shock breakout", the envelope began to cool.
The shock wave, and the super-heated material in the
star's interior, also began to blow material outwards
at very high speeds, greater than 10,000 km/s.
So, we have two competing processes: the envelope is
getting cooler (hence dimmer), but is growing in size
very rapidly (hence brighter). For several days, the
cooling from 40,000 K to, say, 10,000 K happened so
rapidly that the net effect was a fading; in fact, a rapid
fading.
However, the material becomes less efficient at radiating
away energy as it cools, and so eventually, the increase in
surface area began to dominate. We're in that stage now,
and the SN is getting brighter even though it's cooling down.
Note that 10,000 km/s times two weeks(~1,000,000 sec) comes
to 10^10 km radius, which is larger than the initial red giant
(radius ~ 10^8 km) by a factor of 100. Thus, the surface
area is about 10,000 times larger, and so, even though the
SN is now not much hotter than it was as a red giant, it's
again about 10 magnitudes brighter. Note that the SN's
photosphere is already much larger than the orbit of Pluto!
Eventually, the energy of the shock wave will completely
radiate away. However, as the ejecta cools to 3,000 K,
the hydrogen ions re-combine and become atoms. In the process
of doing so, they emit lots of Balmer radiation, including
H-alpha at 6563 Angstroms. As atoms, they are optically
transparent (well, more so than ions), and so a "window" forms
in the ejecta shell. Just behind this "window" is an opaque
screen of hydrogen ions, which act as a "curtain" and
forms a photosphere.
We are just beginning to see the H-alpha with strong P-Cygni
profile of such a photosphere now in 93J.
Although the ejecta is expanding, the radius of the
"curtain" of atoms is shrinking - because as each layer
of ions re-combines, it allows the energy of the
next-innermost layer of material to escape outwards
easily. Again, we have two competing processes,
an expansion outwards and a "recombination wave"
heading inwards. In another coincidence, for many
supernovae, the two processes tend to cancel each other
out, and the radius at which material re-combines
into neutral atoms remains relatively constant for
several weeks or months. And, since the material
there must have roughly the same temperature - 3,000 K,
the temperature at which H re-combines - the SN's
brightness remains ROUGHLY CONSTANT. We call
SNe which follow this pattern of development "type II
plateau", for the extended plateau of brightness
that occurs some time after the initial rise to
brightness.
So, IF 93J is a type IIP - and we don't know for sure
yet - we can look forward to it remaining brighter than,
say, 12'th magnitude for at least a month, probably two.
The more massive the progenitor's envelope at the
time of explosion, the longer it takes for the energy
to work its way through to the surface and the longer
the SN will remain bright. A few unusual SNe, such
as SN 1988Z, SN 1961V (if it was a SN) and, perhaps,
Eta Carinae (which exhibited some SN-like properties)
have remained in a plateau state for periods of a year
or more. They must have had VERY massive (M > 25 solar?)
envelopes, or some large amount of circumstellar material.
Brian Schmidt of CfA guessed that 93J would become
a type IIP several days ago. I would say that he's
got a very good chance of being bright. Way to go,
Brian!
Michael
--
----- Michael Richmond
"This is the heart that broke my finger." richmond@astro.princeton.edu
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