From lonnie at outstep.com Thu Dec 13 08:11:59 2007 From: lonnie at outstep.com (Lonnie Cumberland) Date: Thu, 13 Dec 2007 08:11:59 -0500 Subject: [Webnucleo-public] Polytrope Tool vs Standard Solar Model (BP2004) Message-ID: Greetings All, I have only recently come across the Polytrope Tool and want to compare various data against the Standard Solar Model (BP2004) data. In particular, the standard solar model lists various data fields like: astro-ph/0402114 Columns in the Standard Model table (below) represent: 1) Mass fraction in units of the solar mass 2) Radius of the zone in units of one solar radius 3) Temperature in units of deg (K) 4) Density in units of g/cm^3 5) Pressure in units of dyn/cm^2 6) Luminosity fraction in units of the solar luminosity 7) X(^1H): the hydrogen mass fraction 8) X(^4He): the helium 4 mass fraction 9) X(^3He): the helium 3 mass fraction 10) X(^12C): the carbon 12 mass fraction 11) X(^14N): the nitrogen 14 mass fraction 12) X(^16O): the oxygen 16 mass fraction The Table begins here. M/Msun R/Rsun T Rho P L/Lsun X Y He3 C12 N14 O16 0.0000298 0.00649 1.570e+07 1.531e+02 2.351e+17 0.00027 0.33984 0.64034 7.30e-06 2.41e-05 5.47e-03 8.65e-03 0.0000312 0.00659 1.570e+07 1.531e+02 2.350e+17 0.00028 0.33989 0.64030 7.30e-06 2.41e-05 5.47e-03 8.65e-03 . . . 0.9996899 0.94548 3.010e+05 9.078e-03 3.650e+11 1.00000 0.73963 0.24335 1.00e-04 2.88e-03 8.54e-04 7.91e-03 0.9996986 0.94591 2.984e+05 8.953e-03 3.567e+11 1.00000 0.73963 0.24335 1.00e-04 2.88e-03 8.54e-04 7.91e-03 0.9997074 0.94633 2.957e+05 8.831e-03 3.486e+11 1.00000 0.73963 0.24335 1.00e-04 2.88e-03 8.54e-04 7.91e-03 0.9997162 0.94676 2.931e+05 8.710e-03 3.407e+11 1.00000 0.73963 0.24335 1.00e-04 2.88e-03 8.54e-04 7.91e-03 Lsun 3.8418E+33 Rsun 6.9598E+10 since I have only just started using the Polytrope Tool, (which I think is VERY good by the way), I was not sure of the out data from the tool as it did not seem to compare to the tables in the BP2004 data file. I am wondering if someone might be able to tell me if I am missing some scaling or something? Thanks and have a great day, Lonnie T. Cumberland Email: Lonnie at outstep.com Lonnie_Cumberland at yahoo.com Lonnie.Cumberland at gmail.com "Helping our national economy and global environment, community by community......" -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.ces.clemson.edu/pipermail/webnucleo-public/attachments/20071213/8e1ff209/attachment.html From mbradle at CLEMSON.EDU Thu Dec 13 09:40:10 2007 From: mbradle at CLEMSON.EDU (Bradley S. Meyer) Date: Thu, 13 Dec 2007 09:40:10 -0500 (EST) Subject: [Webnucleo-public] Polytrope Tool vs Standard Solar Model (BP2004) In-Reply-To: References: Message-ID: <50022.68.159.112.167.1197556810.squirrel@wm.clemson.edu> On Thu, December 13, 2007 8:11 am, Lonnie Cumberland wrote: > [snip] since I have only just started using the Polytrope Tool, (which I think is > VERY good by the way), I was not sure of the out data from the tool as it > did not seem to compare to the tables in the BP2004 data file. > > I am wondering if someone might be able to tell me if I am missing some > scaling or something? > No, Lonnie, you are not missing something. Remember a polytrope is only an approximation to a real stellar model. To construct a polytrope, you assume the pressure P is a constant K time the density rho raised to the (1+1/n) power. K and n are constant throughout the model. This particular relationship allows you to solve for the structure of the star via the Lane-Emden equation. For a real star such as the Sun, the relationship between the pressure and density will vary depending on the equation of state, the detailed relationship between the pressure, density, temperature, and chemical composition. Since you have the BP2004 data, try plotting the logarithm of the Pressure versus the logarithm of the density. Unlike for the polytrope, where this plot will be a straight line, you will find a more complicated plot. If you can extract those data, try using the curve fitting tool at http://www.webnucleo.org/home/online_tools/curve_fit/0.3/ to fit log rho vs. log P to a line. The slope of the fitted line will give an estimate for the "overall" n of the BP2004 model. It should be reasonably close to n = 3. Without a detailed equation of state, it is not possible to obtain the temperature T from a polytrope. You can use the usual gas law P = N k T, where N is the number density and k is Boltzmann's constant. N would be rho times Avogadro's number divided by the average mass number of nuclear species present. A polytrope also doesn't follow energy generation and abundance changes. You have to use much more complicated models (like BP2004) to get that information. What's remarkable is how well polytropes work. You can see why people used them to study stellar structure in the days before fast computers. Best wishes. Brad Meyer -- Bradley S. Meyer Department of Physics and Astronomy Clemson University Clemson, SC 29634-0978 mbradle at clemson.edu http://nucleo.ces.clemson.edu