Calculating supernova yield

[marcus]

fire.biol.wwu.edu/trent/alles/Origin_of_Elements.pdf

In this source Alles gives a detailed description of the mechanism underlying Type Ia supernovas----so that one sees why they always release about the same amount of energy and can be used as standard candles for measuring distance. But he does not give the yield in joules.

Can anyone calculate the yield from the assumptions on page 13 of Alles "Origin of the Elements" essay?

A white dwarf consisting of carbon----no longer actively fusing----is being augmented by a red giant companion. When the dwarf reaches Chandra mass half of the carbon undergoes
fusion to elements such as chromium, manganese, iron, cobalt, and nickel. The problem is to estimate how much energy this fusion yields.

A more realistic assumption is that the white dwarf consists of a mixture of carbon and oxygen but this doesn't make much difference in rough calculation----anything around carbon merging to anything around iron gives about the same result.

 

[marcus]

quote from David Alles

If Alles picture needs correction or clarification please post same! There is some ambiguity about what fraction of the mass of the star undergoes fusion during the explosion. Here is page 13 from his essay

http://www.fire.biol.wwu.edu/trent/alles/Origin_of_Elements.pdf [Broken]

The Evolution of Double Stars and Supernovae of Type Ia

Almost half the stars in the sky are double or multiple. If the two stars are close together then they can have dramatic effects on each other. The more massive of the two stars will evolve faster and when it becomes a red giant it may be so big that gravity draws its outer atmosphere across to the companion star. The transfer of material can lead to all kinds of interesting and exciting effects, depending on the properties of the two stars.
Stars that have lost their atmospheres to their companions are identical to the white dwarves in the center of planetary nebulae. The less massive companion star, assisted by the extra mass it has gained, eventually becomes a red giant and starts to transfer material back onto its white dwarf companion. This can have the
effect of increasing its mass beyond a critical limit of 1.4 times the mass of the Sun, known as the Chandrasekhar limit. When this happens the carbon-oxygen core can suddenly explode, converting half the mass by nuclear fusion into elements like chromium, manganese, iron, cobalt and nickel. This is called a Type Ia supernova. Because they are very bright and we think they always explode releasing about the same amount of energy, they are used as standard brightness light sources. The recent discovery that the expansion of the universe is accelerating, was made by observing these supernovae in galaxies 5,000 million
light years away. Type Ia supernovae are also a major source of iron and other heavy elements.

 

[marcus]

supernova yield in natural units

I am exploring natural units for possible use in textbook and other curriculum material

In this case I assume we know the distance to the sun 93E44 and the Earth's orbit speed E-4.
So the sun's mass is given by RV² = 93E36 and the Chandrasekhar mass,
since it is 1.4 solar, is therefore 1.3E38.

(We know from other contexts that 1.3E38 is right for the mass limit expressed in natural units.)

A quick look at the atomic mass 55.935 of Iron-56 shows that going from carbon to iron releases about 0.1 percent of the mass as energy.

Assuming half the star fuses, we get the yield simply by
multiplying 1.3E38 by 0.05 percent, to get 6.5E34 energy units.

This actually provides a better way to get the yield in joules
(quicker than a calculation restricted to metric units) because the Planck energy is known to be 2 Gigajoules.

Therefore the energy release of 6.5E34 translates easily to
13E34 Gigajoules, assuming that one wanted it in metric in the first place.

 

[Labguy]

Originally posted by marcus
If Alles picture needs correction or clarification please post same! There is some ambiguity about what fraction of the mass of the star undergoes fusion during the explosion. Here is page 13 from his essay

http://www.fire.biol.wwu.edu/trent/alles/Origin_of_Elements.pdf [Broken]

The Evolution of Double Stars and Supernovae of Type Ia

Almost half the stars in the sky are double or multiple. If the two stars are close together then they can have dramatic effects on each other. The more massive of the two stars will evolve faster and when it becomes a red giant it may be so big that gravity draws its outer atmosphere across to the companion star. The transfer of material can lead to all kinds of interesting and exciting effects, depending on the properties of the two stars.
Stars that have lost their atmospheres to their companions are identical to the white dwarves in the center of planetary nebulae. The less massive companion star, assisted by the extra mass it has gained, eventually becomes a red giant and starts to transfer material back onto its white dwarf companion. This can have the
effect of increasing its mass beyond a critical limit of 1.4 times the mass of the Sun, known as the Chandrasekhar limit. When this happens the carbon-oxygen core can suddenly explode, converting half the mass by nuclear fusion into elements like chromium, manganese, iron, cobalt and nickel. This is called a Type Ia supernova. Because they are very bright and we think they always explode releasing about the same amount of energy, they are used as standard brightness light sources. The recent discovery that the expansion of the universe is accelerating, was made by observing these supernovae in galaxies 5,000 million
light years away. Type Ia supernovae are also a major source of iron and other heavy elements.

I am not sure of the point of this thread. Are you thinking out loud, or are you looking for something specific.

Either way, I feel compeled to "clarify" a point or two that always gets oversimplified. I hope writers (and websites) do this to keep things "basic" or more for the layman. Alles' information was interesting, but again it just mentioned the "Chandrasekhar limit, assuming that we all know that number, or may all think about the 1.44 Solar Masses (M_s) we read so much about and learned in school..

Chandrasekhar calculated the 1.44 M_s limit having in mind a small star, such as our sun, that had burned most Hydrogen in the core and then ignighted He as it swelled and expelled mass. Such a star would not have enough mass (= gravity) to create a core of elements heavier than He, so the core simply remained as a White Dwarf, no more nuclear reactions going on. If an He core had more than 1.44 M_s, the gravity would overcome the electron degeneracy pressure and the dwarf would collapse to a more compressed state. That is why it is called a LIMIT, no more than 1.44 M_s to stay a White Dwarf. But, this is only for a Helium core. Chandrasekhar also calculated other "limits", later confirmed by many other physicists. For example, if a star has an Iron core, the limit is 1.79 M_s, not 1.44. Chandrasekhar also calculated an upper limit for any star/material of 3.2 M_s above which any object (Neutron Star) would further collapse; Black Hole I suppose.

So, the point is that there are different "Chandrasekhar limits" for accumulations of matter, each based on the composition of whatever the hell it may be. It has often been stated that "a White Dwarf that accumulates (by accretion) matter and exceeds the "Chandrasekhar limit" will explode as a Type Ia Supernova". That statement is about 95% total bunk!

If your (anyone's) goal is to calculate the energy output of a supernova, you would have to know the chemical conditions necessary to cause the supernova in the first place, and you would need the mass of the matter involved in the explosion/fusion process that makes the "heavier elements" we are made of. It was calculated as early as 1956 (I think) that a Type Ia supernova, the topic of this discussion, can only occur in a White Dwarf with an initial composition of mainly Carbon and Oxygen. It has also been known that the Chandrasekhar limit for a carbon-oxygen core is not 1.44 M_s, it is 1.39 M_s.

Also, most White Dwarfs that form do not have the correct chemical composition, or in correct proportions, to go supernova whether accumulating more mass by accretion or not. A Type Ia is a very, very rare end for any White Dwarf. Most of them do nothing but cool, or if there is infalling matter, they flare-off in a surface nuclear reaction commonly known as a NOVA, not supernova.

As of now, the most common problem (question) confronting physics with respect to Type Ia supernovae, is whether the carbon-oxygen "core" detonates or propogates, by what is known as Carbon deflagration (burning). The energy output by which Type Ia supernovae is used as a "standard candle" is all in the visable part of the EM spectrum. Debate still survives as to the far larger energy output by way of neutrinos.

Marcus; I am not trying to dump water on your campfire, it is just that it has bugged me for years that the "Chandrasekhar limit" is always referred to as 1.44 M_s, and that so many people think (and are taught) that any old White Dwarf will explode as a biggie if more mass is dumped on it. Even the most active boys in the field, Wheeler, and especially J.C. Niemeyer and S.E. Woosley, don't call the 1.39 M_s a "Chandrasekhar limit", they call it the Chandrasekhar mass.

 

[marcus]

Originally posted by Labguy
I a, the topic of this discussion, can only occur in a White Dwarf with an initial composition of mainly Carbon and Oxygen. It has also been known that the Chandrasekhar limit for a carbon-oxygen core is not 1.44 M_s, it is 1.39 M_s.

Even the most active boys in the field, Wheeler, and especially J.C. Niemeyer and S.E. Woosley, don't call the 1.39 M_s a "Chandrasekhar limit", they call it the Chandrasekhar mass.

I'm happy with this clarification. I often call it the Chandrasekhar mass myself----the "Chandrasekhar limit" is just the phrase people are more apt to recognize----but let's do our part to gradually improve the language.

My source was in fact talking about a Carbon/Oxygen core and used the figure 1.4 solar (which looks like your 1.39 solar rounded off). So my source seems consistent with your clarification----which adds clarity, rigor and confirmation to the discussion.

So I am happy and my campfire is not damp but doing fine!

I still want to be able to make a very rough back-of-envelope estimate of the thermonuclear energy involved in a Type Ia explosion. Any factors you could supply that would help hone the estimate would be welcome.

A lot of gravitational energy is released as well as thermonuclear, but I would be satisfied to get a handle on the latter, say, to within a factor of two.

Of course there is always "ask an expert" and take someone's say-so. But it would be nice to have a rough and ready guesstimate that does not involve a web-search or trip to the library.

 

[Labguy]

No, the 1.39 M_s is not a rounding of 1.44. It is a specific mass for that particular matter composition. I suppose that is why they now refer to "Chandrasekhar mass" instead of limit. With all the different stellar types and evolution processes, there would now be many different Chandrasekhar masses to reference, so I think that the word "limit" is being used less. Same as for the 1.79 M_s for an Iron core. It isn't a rounded 1.44 any more than the 1.39 is a rounded 1.44.

 

[marcus]

Originally posted by Labguy
No, the 1.39 M_s is not a rounding of 1.44. It is a specific mass for that particular matter composition. I suppose that is why they now refer to "Chandrasekhar mass" instead of limit. With all the different stellar types and evolution processes, there would now be many different Chandrasekhar masses to reference, so I think that the word "limit" is being used less. Same as for the 1.79 M_s for an Iron core. It isn't a rounded 1.44 any more than the 1.39 is a rounded 1.44.

I think we are talking at cross purposes. I never used the 1.44 figure here and my source certainly did not say 1.44!
Yet you keep referring to 1.44-----could you be misreading.

My source uses the correct figure of 1.39 (at least according to you it is correct for carbon/oxygen and I ALSO believe this) and therefore, we have rounded the number 1.39 to 1.4

But this has nothing to do with the number 1.44, which you brought up.

So let's agree that 1.39 (or rounded 1.39 to two figures) is good
and not argue about this!

Be well

 

[marcus]

Labguy,
is it OK with you if I round off my figure of 1.39 to two
figures and write 1.4?
I round numbers to the nearest 2 or 3 figures a lot when
writing for non-tech audience---in an informal spirit.
But I don't want to offend you.
If you have some reason you don't want to see this
number rounded to the nearest two signif. figures, then
by all means tell me!
I will do everything in my power to oblige you in this little matter.

 

[marcus]

experts seem to differ about iron core mass pre-collapse

Labguy I see for iron cores your figure is 1.79 solar masses. As you say in a couple of different recent posts:
"...Same as for the 1.79 Ms for an Iron core. "
"...star has an Iron core, the limit is 1.79 Ms, "

and another expert says 0.98 solar masses for iron cores
so there is some variation, which is always interesting:

[[ Maximum Stellar Iron Core Mass Just Prior to Core Collapse
F.W. Giacobbe (Chicago Research Center/American Air Liquide, Inc.)

http://www.aas.org/publications/baas/v31n3/aas194/265.htm [Broken]

An analytical method of estimating the mass of a stellar iron core, just prior to core collapse, is described in this paper. The method employed depends, in part, upon the true relativistic mass increase experienced by electrons within a highly compressed iron core, just before core collapse, and is significantly different from a more typical Chandrasekhar mass limit approach. This technique produced a maximum stellar iron core mass value of 1.95 x 10^30 kg which is only slightly less than one solar mass. This mass value is very near the minimum mass found for neutron stars in a recent survey of actual neutron star masses. Although higher neutron star masses may be more typical, these higher mass neutron stars are believed to be formed as a result of fallback or accretion of additional non-ferrous matter after an initial collapse event involving an iron core having a mass no greater than 1.95 x 10^30 kg. ]]

solar is 1.989E30 and this is 1.95E30 so divide and get that this is 0.98 solar masses

from the proceedings of a 1999 American Astronomical Society (AAS) conference on white dwarfs, neutron stars, and pulsars.

We should check out the variation in people's estimates!

 

[Labguy]

Originally posted by marcus
Labguy,
is it OK with you if I round off my figure of 1.39 to two
figures and write 1.4?
I round numbers to the nearest 2 or 3 figures a lot when
writing for non-tech audience---in an informal spirit.
But I don't want to offend you.
If you have some reason you don't want to see this
number rounded to the nearest two signif. figures, then
by all means tell me!
I will do everything in my power to oblige you in this little matter.

Ok with me??

Of course, you or anyone sure don't need my permission to do some "matherizing" (new word) about any of the properties of any subject anywhere on PF. Also, no way I am offended, it is just that sometimes things get different results from different models and present their papers. I also mis-typed the 1.79 M_s figure several times because I hadn't opened the book for awhile. The correct number for a carbon-oxygen core is 1.76 M_s, not the 1.79 I was using. Bad memory.. .. From Supernovae by Paul Murdin, Royal Greenwich Observatory, Cambridge University Press, he states on page 120 that:

"The Chandrasekhar Limit lies between 1.44 and 1.76 solar masses, depending on precisely which nuclei the star is made of. If it is composed of helium nuclei, the maximum possible mass is 1.44 solar masses, and if of iron nuclei, 1.76 solar masses." (Damn, I hate quoting from books, haven't read one in quite some time).

Notice the phrase "maximum possible mass". I should have mentioned earlier that the "Chandrasekhar Limits" are just that; upper limits. I don't recall anything I have seen that states that an object must reach that number, just that anything over that number cannot exist without further collapse. A good example of this would be the "limit" of 3.2 M_s for a neutron star, above which it would collapse. That does not mean that all neutron stars are at or over 3.2 M_s, in fact most that have been measured come in at ~ 2 M_s. Rebounds, shock waves, excess mass ejection, etc. can, and probably do, account for the observed masses of white dwarfs and neutron stars at numbers below the "limit".

Please don't take any of my garbage as an "arguement", I just want to point out some things and sometimes get involved in threads exactly like this one. But, answering is tough because I can't type worth a X$%&!. For some specifics on Type Ia's, go to:

http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v475n2/33428/33428.html [Broken]

But, my friend, anyone looking this URL over must read the whole thing from end to end. This is because it is the style that explains various concepts, in detail with matherizing, and then goes on to say why it won't work that way. Anyway, keep up the long posts because mine will have to get much shorter than this batch...

Labguy;
Observatory at:
Lon. 82*28' W.
Lat. 28*03' N.

 

[marcus]

Tampa Florida area!

Labguy;
Observatory at:
Lon. 82*28' W.
Lat. 28*03' N.

Interesting sig, Labguy!

also interesting discussion of the variation
in masses, wish that book was online

 

[Labguy]

Originally posted by marcus
Labguy;
Observatory at:
Lon. 82*28' W.
Lat. 28*03' N.

Interesting sig, Labguy!

also interesting discussion of the variation
in masses, wish that book was online

I made another BAD typo in my last post. I said 1.76 for carbon-oxygen core when I should have said Iron core.

Recap of M_s number maximums:
A. 1.39 for carbon-oxygen core.
B. 1.44 for helium core.
C. 1.76 for iron core.
D. 3.2 for anything, any chemical composition.

also interesting discussion of the variation in masses, wish that book was online

I have never been able to find it, so I just keep the hardcopy on the desk.

 

[marcus]

Your list in Planck terms

Originally posted by Labguy
.
Recap of M_s number maximums:
A. 1.39 for carbon-oxygen core.
B. 1.44 for helium core.
C. 1.76 for iron core.
D. 3.2 for anything, any chemical composition.

Fascinating. It is nice to see it in the form of a small table like that.

What metric equivalent people use for the solar mass changes a bit. Allen says 1.989E30 kg

But CRC handbook says 1.991E30 kg

If I just use 1.99E30 kg then a solar mass is (temporarily avoiding roundoff)
91.423E36

(this just uses the National Institute of Standards etc website figure of 21.767 microgrms for the Planck mass)

So then your table reappears in E38 Planck mass units as

A. 1.27 for carbon-oxygen core.
B. 1.32 for helium core.
C. 1.61 for iron core.
D. 2.9 for anything, any chemical composition.

I have tended to use 1.3E38 as a ballpark figure, which I see might be considered a compromise between your figures for carbon-oxygen on one side and helium core on the other.

I will check out Paul Murdin's book on supernovae at the next opportunity! His figure for iron is interesting and rather different from the one calculated by Giacobbe in 1999 and shown here:
http://www.aas.org/publications/baa.../aas194/265.htm [Broken]

 

[marcus]

I found plenty of references to Murdin's writings on web
and, for example, this beautiful onion diagram of
a pre-collapse state, taken from a book by Murdin
called "End in Fire"

http://home.earthlink.net/~rarydin/supernovae.htm

there is also a Hans Bethe SciAm article "How Supernovae Explode" from sometime back 1980?

the above URL has an account of what it says is the
commonly accepted model of type II explosion
probably gleaned from Murdin.

at the heart of the onion, iron photodissociates
into alpha particles (helium nuclei) and collapse
begins...and so on (you probably have the same
story in Murdin on your desk)

interestingly the storm of neutrinos plays an
important role in blowing the outer layers away
in this "commonly accepted" model of the explosion

apparently the UV flash wouldn't even be seen if the
neutrinos didnt help blow off the outside

I wish you didnt hate typing so much.
I would love it if you would type in a few sentences
from Murdin giving a thumbnail sketch of
the orthodox view of what happens in a Type II explosion.

 

[marcus]

http://cosmos.colorado.edu/cw2/courses/astr1120/text/chapter6/lesson6.html [Broken]

Hi Labguy,

This chapter on SN for a university course may be helpful.
It is short and to the point.
And has a table comparing "thermonuclear SN" with
"core collapse SN"

If you take a look at it, let me know if its information seems reliable to you. Could I recommend this page to a HS or college freshman wanting to learn something about SN?

 

[Labguy]

Originally posted by marcus
I found plenty of references to Murdin's writings on web
and, for example, this beautiful onion diagram of
a pre-collapse state, taken from a book by Murdin
called "End in Fire"...<snip>...
I wish you didnt hate typing so much.
I would love it if you would type in a few sentences
from Murdin giving a thumbnail sketch of
the orthodox view of what happens in a Type II explosion.

What I can do is spend a few hours, little at a time, and type something in MS Word and then paste the whole thing under this thread. It may be awhile, I have been ill and get "surgeried" on June 5th..

I had (?) a great graphic with good detail on the size and reactions in the "burning shells" going on in a larger star just before the Type II supernova, but I can't remember if it was on the web or in a book. I'll find it eventually and URL the graphic, or list, in table form, the shells starting out from the core.

If you have one, send me the URL so I don't have to hunt, please.

 

[marcus]

See if you agree. I don't want to say anything wrong here.

Typical luminosity for Type Ia (thermonucl.) is ten billion suns
for Type II (core collapse) it is apt to be less, like a billion suns.

The original classification was that type I didnt have a hydrogen line.

Type II comes from very massive short-lifetime stars mostly in spiral arms of galaxies-----young populations of stars

Type I mostly comes from old populations (consistent with idea that the exploding star is a carbon/oygen core white dwarf)

Type I the hypothesized mechanism is that carbon/oxygen fuse to nickel-56 which decays to cobalt-56 and then to iron-56
the decay process is fairly protracted so it creates a plateau
in the light curve.

Type II does not have this plateau.

Type I leaves no remnant. Type II leaves something behind such as, for example, a neutron star.


A puzzle about Type Ia is this: in a binary system with a white dwarf accreting material from a red giant partner, what one would expect is periodic "nova" flashes as the layer of hydrogen building up on the white dwarf got thick enough to fuse to helium.
Why, instead of just a string of nova events, do you sometimes
get a supernova from this situation? I can think of several answers but it still should be recognized as a problem.

Do you see anything to find fault with here, or that needs further clarification?

*******footnote added later*******

JUST SAW YOUR POST sorry to hear you must have surgery. My wife must have surgery soon and i am worried about this.
Dont worry about research under stressful conditions unless you just feel like it.
I tried to get back to that onion picture at the "earthlink" address and the darned thing crashed my computer twice. So I regret to say I cannot offer you the diagram----it was from a Muldin book.

 

[Labguy]

Originally posted by marcus
http://cosmos.colorado.edu/cw2/courses/astr1120/text/chapter6/lesson6.html [Broken]

Hi Labguy,

This chapter on SN for a university course may be helpful.
It is short and to the point.
And has a table comparing "thermonuclear SN" with
"core collapse SN"

If you take a look at it, let me know if its information seems reliable to you. Could I recommend this page to a HS or college freshman wanting to learn something about SN?

I think that it, and the links, are excellent. Very handy to see the summary tables to compare differences side-by-side on one page. I am still going to find the more detailed graphic with specifics on the shells surrounding the core before a Type II explosion. Thanks for the lead.

 

[marcus]

Originally posted by Labguy
I think that it, and the links, are excellent. Very handy to see the summary tables to compare differences side-by-side on one page. I am still going to find the more detailed graphic with specifics on the shells surrounding the core before a Type II explosion. Thanks for the lead.

You are most welcome! I am looking forward to seeing whatever you get on this.

 

[IMVeridical]

Maximum Stellar Iron Core Mass

In reply to ref. originally posted by "Marcus" re. Maximum Stellar Iron Core Mass - See full published (and corrected) article by F.W. Giacobbe by downloading the PDF article at: http://www.iisc.ernet.in/pramana/v60/v60no3.htm [Broken]

Maximum Stellar Iron Core Mass (just prior to Core Collapse) is about 1.35 Solar Masses. It cannot be any larger than this before initial collapse leading to a supernoava event. The resulting neutron star can only get larger by adventitious accretion after the initial collapse event.

Write back to my yahoo email address if you want any detail or have trouble in downloading the PDF file.

WBR,
IMVeridical
2003/12/29