Explanations for solar physics computing page

Computing solar internal structure and evolution relies heavily on plasma physics, including equation of state and opacity. Since equation of state and opacity are not easy to calculate they are usually used in the form of tables which are interpolated. OPAL opacity and EOS tables can be obtained from Livermore Lavoratories web page.

Equation of state tables

is040423.etf: SAHA-S tables, interpolation values: T, rho, X, Z. Gryaznov V.K., Ayukov S.V., Baturin V.A., Iosilevskiy I.L., Starostin A.N., Fortov V.E.: In: Equation-of-State and Phase-Transition Issues in Models of Ordinary Astrophysical Matter, Eds. V.Celebonovic, W.Dappen, D.Gough. AIP Conference Proceedings, 731, New York, 147 (2004)

is040423.ete: SAHA-S tables, interpolation values: T, rho, X. Z is fixed at 0.02. See reference above.

opal2005.etf: OPAL EOS, interpolation values: T, rho, X, Z. Downloaded from OPAL site, marked there as "2005", seems to be unpublished.

opal2001.etf: OPAL EOS, interpolation values: T, rho, X, Z. Rogers F.J., Nayfonov A. Astrophys. J., 576, 1064 (2002).

opal1996.etf: OPAL EOS, interpolation values: T, rho, X, Z. Rogers, F.J., Swenson, F.J., Iglesias, C.A.: Astrophys. J., 456, 902 (1996)

mhd5.ete: MHD equation of state, interpolation values: T, rho, X. Z is fixed at 0.02. Provided by W.Dappen. References are: Hummer, D.G., and Mihalas, D. 1988, Astrophys. J., 331, 794; Mihalas, D., Dappen W., and Hummer, D.G. 1988, Astrophys. J., 331, 815; Dappen, W., Mihalas, D., Hummer, D.G., and Mihalas, B.W. 1988, Astrophys. J., 332, 261.

Opacity tables

`Mixture' is a set of relative abundances of chemical elements. Since H and He cannot be reliably determined from observations the term mixture in solar physics is related to elements heavier than helium. The chemical composition is a part of input data for opacities and equation of state; it can be either pair of X and Z; X, ZCNO, ZNe, ZFeSi; X and 19 individual Z components (see Input data below). When heavy element contents is specified as single Z value or ZC/ZN/ZF combo the mixture is used to compute individual element abundances. However not all EOS/opacity tables take into account individual element abundances. Right now only opal_f2005.otg table uses 19 heavy element abundances as input (this may change in the future). All other tables ignore mixture and use only total Z as input. Note that every table assumes some mixture internally but this mixture cannot be changed. Again if one specifies all 19 Zi for opal_f2005.otg table then mixture is also not used. So mixture is only used for opal_f2005.otg opacity when one Z or three groups ZCNO, ZNe, ZFeSi are specified.

The following mixtures are available: AG89, GN93, GS98, AGS05, LPG09, AGSS09.

The following values can be calculated:

Value	Symbol	Formulae	Unit, notes
Pressure	P		dyn/cm^2; includes radiative pressure
Reduced pressure	PI
Specific internal energy	U		erg/g
Logarithmic partial derivative	hi_t		dimensionless
Logarithmic partial derivative	hi_rho		dimensionless
Logarithmic partial derivative	hi_x		dimensionless
Expansion coefficient	Q		dimensionless
Specific heat at constant volume	Cv		erg/(g*K)
Specific heat at constant pressure	Cp		erg/(g*K)
Logarithmic partial derivative	ksi_rho	dlogU/dlogRHO	dimensionless
Adiabatic exponent Gamma3	G3		dimensionless
Adiabatic temperature gradient	nabla		dimensionless
Adiabatic exponent Gamma1	G1		dimensionless
Sound speed	cs		cm/sec
Rosseland opacity	K		cm^2/g
Nuclear energy generation rate	eps		erg/(gram*sec); PP-chain and CNO cycle. He3 is in equilibrium
Hydrogen burning rate	dXdt		1/sec

The following values must be input: temperature T (in Kelvin degrees), density rho (g/cm3), hydrogen mass fraction X and heavy element mass fraction Z. Helium mass fraction is assumed to be equal to 1-X-Z.

Formal limits for lgT are 3.0...9.0, for lgQ -- (Q=rho/(T/1e6)^3) -8.0...2.0, for X -- 0.0...0.9, for Z -- 0.0...0.025. However most tables are not rectangular, and data is missing in some points (T, rho, X, Z). When data is missing, execution stops and nothing is printed.

Heavy elements can be also specified as three components (CNO, Ne, FeSi) or 19 components (C, N, O, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Ti, Cr, Mn, Fe, Ni). These formats are not very useful with current EOS/opacity tables as most tables cannot be interpolated by individual element abundances. See Tables above on tables interpolation capabilities.