Pressure at the core

Does anyone have a reference for values of P_c (pressure) for the centers of
various stars, including the sun?

I need a reference value of P_c (sun or otherwise) to calculate the constant K
in certain polytropes:

http://en.wikipedia.org/wiki/Polytrope

Wiki does not mention what the constants are in its expression for K. I assume
that T is temp in Kelvins, k_b probably is Boltzmann's constant and rho is
density. What are N_A and mu?

Many thanks,
--
I.N. Galidakis

"I.N. Galidakis" wrote in message
news:1224507902.533497@athprx04...
Does anyone have a reference for values of P_c (pressure) for the centers
of
various stars, including the sun?

I need a reference value of P_c (sun or otherwise) to calculate the
constant K
in certain polytropes:

http://en.wikipedia.org/wiki/Polytrope

Wiki does not mention what the constants are in its expression for K. I
assume
that T is temp in Kelvins, k_b probably is Boltzmann's constant and rho is
density. What are N_A and mu?

Many thanks,
--
I.N. Galidakis

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

"I.N. Galidakis" wrote in message
news:1224507902.533497@athprx04...
Does anyone have a reference for values of P_c (pressure) for the centers
of
various stars, including the sun?

I need a reference value of P_c (sun or otherwise) to calculate the
constant K
in certain polytropes:

http://en.wikipedia.org/wiki/Polytrope

Wiki does not mention what the constants are in its expression for K. I
assume
that T is temp in Kelvins, k_b probably is Boltzmann's constant and rho is
density. What are N_A and mu?

As it's based on the equation of state for an ideal gas I would expect them
to be
N_A, Avogadro's number
and
mu, mean atomic mass

Have you found this set of lecture notes (Queen's University, Belfast)?
http://star.pst.qub.ac.uk/~sjs/teaching/stellarevol/

"OG" wrote in message
...

"I.N. Galidakis" wrote in message
news:1224507902.533497@athprx04...
Does anyone have a reference for values of P_c (pressure) for the centers
of
various stars, including the sun?

I need a reference value of P_c (sun or otherwise) to calculate the
constant K
in certain polytropes:

http://en.wikipedia.org/wiki/Polytrope

Wiki does not mention what the constants are in its expression for K. I
assume
that T is temp in Kelvins, k_b probably is Boltzmann's constant and rho
is
density. What are N_A and mu?

As it's based on the equation of state for an ideal gas I would expect
them to be
N_A, Avogadro's number
and
mu, mean atomic mass

Have you found this set of lecture notes (Queen's University, Belfast)?
http://star.pst.qub.ac.uk/~sjs/teaching/stellarevol/

You can get PDFs with more details for some of the lectures at
http://star.pst.qub.ac.uk/~sjs/teach...ecture%201.pdf
through
http://star.pst.qub.ac.uk/~sjs/teach...ecture%209.pdf

OG wrote:
"OG" wrote in message
...

"I.N. Galidakis" wrote in message
news:1224507902.533497@athprx04...
Does anyone have a reference for values of P_c (pressure) for the centers
of
various stars, including the sun?

I need a reference value of P_c (sun or otherwise) to calculate the
constant K
in certain polytropes:

http://en.wikipedia.org/wiki/Polytrope

Wiki does not mention what the constants are in its expression for K. I
assume
that T is temp in Kelvins, k_b probably is Boltzmann's constant and rho
is
density. What are N_A and mu?

As it's based on the equation of state for an ideal gas I would expect
them to be
N_A, Avogadro's number
and
mu, mean atomic mass

Many thanks a second time to you and Sam. Sam's reference contained P_c, but I
somehow oversaw it.

Have you found this set of lecture notes (Queen's University, Belfast)?
http://star.pst.qub.ac.uk/~sjs/teaching/stellarevol/

You can get PDFs with more details for some of the lectures at
http://star.pst.qub.ac.uk/~sjs/teach...ecture%201.pdf
through
http://star.pst.qub.ac.uk/~sjs/teach...ecture%209.pdf

Thanks. I think I am past the basic understanding of stellar evolution, as I've
had an excellent course of AP in college, over 22 years ago. My current interest
is mathematical modelling of various AP phenomena, hence my questions.

Thanks again for taking the time to dig these links up.
--
I.N. Galidakis

OG wrote:
[snip]

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

Sorry for nitpicking, but is your "Log(P)" meant to be base 10? We (the
abominable mathematicians) usually denote by "Log(x)" the natural logarithm
(base e).

If I use log base 10 for P as per the page, the polytrope n=3 model seems to
agree with the data fairly well. If I use the natural log, the results are awry.
--
I.N. Galidakis

"I.N. Galidakis" wrote in message
news:1224527030.287674@athprx03...
OG wrote:
[snip]

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

Sorry for nitpicking, but is your "Log(P)" meant to be base 10? We (the
abominable mathematicians) usually denote by "Log(x)" the natural
logarithm
(base e).

If I use log base 10 for P as per the page, the polytrope n=3 model seems
to
agree with the data fairly well. If I use the natural log, the results are
awry.
--
I.N. Galidakis



Unless otherwise specified, in astrophysics log means base 10, and ln means
base e. The Sun's basic structure isn't all that different (in order of
magnitude terms) from an n=3 polytrope, as I recall from dim and distant
stellar structure courses.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

Mike Dworetsky wrote:
"I.N. Galidakis" wrote in message
news:1224527030.287674@athprx03...
OG wrote:
[snip]

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

Sorry for nitpicking, but is your "Log(P)" meant to be base 10? We (the
abominable mathematicians) usually denote by "Log(x)" the natural
logarithm
(base e).

If I use log base 10 for P as per the page, the polytrope n=3 model seems
to
agree with the data fairly well. If I use the natural log, the results are
awry.
--
I.N. Galidakis


Unless otherwise specified, in astrophysics log means base 10, and ln means
base e. The Sun's basic structure isn't all that different (in order of
magnitude terms) from an n=3 polytrope, as I recall from dim and distant
stellar structure courses.

It looks like even the magnitudes can be adjusted to a pretty good match. I was
able to extract some results which agree fairly well with the data in the links
OG and Sam provided. For those interested:

http://ioannis.virtualcomposer2000.c...Polytrope.html

Many thanks to all who replied.
--
I.N. Galidakis

"I.N. Galidakis" wrote in message
news:1224581136.871203@athprx04...
Mike Dworetsky wrote:
"I.N. Galidakis" wrote in message
news:1224527030.287674@athprx03...
OG wrote:
[snip]

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

Sorry for nitpicking, but is your "Log(P)" meant to be base 10? We (the
abominable mathematicians) usually denote by "Log(x)" the natural
logarithm
(base e).

If I use log base 10 for P as per the page, the polytrope n=3 model
seems
to
agree with the data fairly well. If I use the natural log, the results
are
awry.
--
I.N. Galidakis


Unless otherwise specified, in astrophysics log means base 10, and ln
means
base e. The Sun's basic structure isn't all that different (in order of
magnitude terms) from an n=3 polytrope, as I recall from dim and distant
stellar structure courses.

It looks like even the magnitudes can be adjusted to a pretty good match.
I was
able to extract some results which agree fairly well with the data in the
links
OG and Sam provided. For those interested:

http://ioannis.virtualcomposer2000.c...Polytrope.html

Many thanks to all who replied.
--

Can I nitpick in return and point out the lack of units in your discussion
:-)

Well done otherwise.

Did you look at the detailed working in the QUB notes ?
http://star.pst.qub.ac.uk/~sjs/teach...ecture%208.pdf

OG wrote:
"I.N. Galidakis" wrote in message
news:1224581136.871203@athprx04...
Mike Dworetsky wrote:
"I.N. Galidakis" wrote in message
news:1224527030.287674@athprx03...
OG wrote:
[snip]

Page updated to include Mass distribution, Luminosity and Pressure,
Units for density updated to SI units.
http://www.astd60.dsl.pipex.com:80/structure_of_sun.htm

Sorry for nitpicking, but is your "Log(P)" meant to be base 10? We (the
abominable mathematicians) usually denote by "Log(x)" the natural
logarithm
(base e).

If I use log base 10 for P as per the page, the polytrope n=3 model
seems
to
agree with the data fairly well. If I use the natural log, the results
are
awry.
--
I.N. Galidakis


Unless otherwise specified, in astrophysics log means base 10, and ln
means
base e. The Sun's basic structure isn't all that different (in order of
magnitude terms) from an n=3 polytrope, as I recall from dim and distant
stellar structure courses.

It looks like even the magnitudes can be adjusted to a pretty good match.
I was
able to extract some results which agree fairly well with the data in the
links
OG and Sam provided. For those interested:

http://ioannis.virtualcomposer2000.c...Polytrope.html

Many thanks to all who replied.
--

Can I nitpick in return and point out the lack of units in your discussion
:-)

Hehe! Added now.

Well done otherwise.

Thanks.

Did you look at the detailed working in the QUB notes ?
http://star.pst.qub.ac.uk/~sjs/teach...ecture%208.pdf

No, but now that I looked, I see that my assumption to normalize the radius with
respect to the point xi where the density falls to 0, was on the reasonable
side.

I better collect all those links and add them as refs at the end of the article.
I think it would look better that way.

I assume that since you changed the contents of ref [6], this web resource is
yours, but I cannot find any other data except "Owen's Spare Webpages". If you'd
like me to put something more meaningful there (for ref [6]), please tell me so.

Again, my many thanks.
--
I.N. Galidakis