Abstract
The cesam code is a consistent set of programs and routines which perform calculations of 1D quasi-hydrostatic stellar evolution including microscopic diffusion of chemical species and diffusion of angular momentum. The solution of the quasi-static equilibrium is performed by a collocation method based on piecewise polynomials approximations projected on a B-spline basis; that allows stable and robust calculations, and the exact restitution of the solution, not only at grid points, even for the discontinuous variables. Other advantages are the monitoring by only one parameter of the accuracy and its improvement by super-convergence. An automatic mesh refinement has been designed for adjusting the localisations of grid points according to the changes of unknowns. For standard models, the evolution of the chemical composition is solved by stiffly stable schemes of orders up to four; in the convection zones mixing and evolution of chemical are simultaneous. The solution of the diffusion equation employs the Galerkin finite elements scheme; the mixing of chemicals is then performed by a strong turbulent diffusion. A precise restoration of the atmosphere is allowed for.
Similar content being viewed by others
References
Adelberger, E., et al.: Solar fusion rates. Rev. Mod. Phys. 70, 1265–1291 (1998)
Alécian, G., Michaud, G.: About diffusivity, radiative viscosity and particles transport. Astron. Astrophys. 431, 1–4 (2005)
Alexander, D.R., Ferguson, J.W.: Low-temperature Rosseland opacities. Astrophys. J. 437, 879 (1994)
Anders, E., Grevesse, N.: Abundances of the elements—meteoritic and solar. Geochim. Cosmochim. Acta 53, 197–214 (1989)
Angulo, C., Arnould, M., Rayet, M., The NACRE collaboration: A compilation of charged-particle induced thermonuclear reaction rates. Nucl. Phys. A 656, 3–183 (1999)
Asplund, M., Grevesse, N., Sauval, A.J.: In: Barnes, T.G. III, Bash, F.N. (eds.) Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis. ASP Conf. Ser., vol. 336, p. 25 (2005)
Bahcall, J.N., Pinsonneault, M.H., Wasserburg, G.J.: Solar models with helium and heavy-element diffusion. Rev. Mod. Phys. 67, 781 (1995)
Basu, S., Antia, H.M.: Seismic measurement of the depth of the solar convection zone. Mon. Not. R. Astron. Soc. 287, 189 (1997)
Basu, S., Antia, H.M.: Constraining solar abundances using helioseismology. Astrophys. J. Lett. 606, L85 (2004)
Basu, S., Pinsonneault, M.H., Bahcall, J.H.: How much do helioseismological inferences depend on the assumed reference model? Astrophys. J. 529, 1084 (2000)
Böhm-Vitense, E.: Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Z. Astrophys. 46, 108 (1958)
Boothroyd, A.I., Sackmann, I.-J.: Our Sun. IV. The standard model and helioseismology: Consequences of uncertainties in input physics and in observed solar parameters. Astrophys. J. 583, 1004 (2003)
Burgers, J.M.: Flow Equations for Composite Gases. Academic Press, New York (1969)
Canuto, V.M., Mazzitelli, I.: Stellar turbulent convection—a new model and applications. Astrophys. J. 370, 295–311 (1991)
Canuto, V.M., Goldman, I., Mazzitelli, I.: Stellar turbulent convection—a self-consistent model. Astrophys. J. 473, 550 (1996)
Caughlan, G.R., Fowler, W.A.: Thermonuclear reaction rates V. At. Data Nucl. Data Tables 40, 284–334 (1988)
Chaboyer, B., Demarque, P., Guenther, D.B.: The pulsation properties of Procyon A. Astrophys. J. 525, L41–L44 (1999)
Christensen-Dalsgaard, J.: Computational procedures for GONG solar model project. Astronomisk Institut, Aarhus Universitet (1988)
Christensen-Dalsgaard, J., Dappen, W.: Solar oscillations and the equation of state. Astron. Astrophys. Rev. 342, 267–361 (1992)
Clayton, D.D.: Principles of Stellar Evolution and Nucleosynthesis. McGraw-Hill, New York (1968)
Cox, A.N.: Allen’s Astrophysical Quantities. Springer, Berlin (2000)
Cox, A.N., Guzik, J.A., Kidman, R.B.: Oscillations of solar models with internal element diffusion. Astrophys. J. 342, 1187–1206 (1989)
Cox, J.P., Giuli, R.T.: Principles of Stellar Structure, vols. I & II. Gordon & Breach, New York (1968)
De Boor, C.: A Practical Guide to Splines, 3rd edn. Springer, Berlin (1978)
Di Mauro, M.P.: Theoretical aspects of asteroseismology: small steps towards a golden future. In: Danesy, D. (ed.) Helio and Asteroseismology, Toward a Golden Future, New Haven, Connecticut, 14–16 July. Proceedings of the SOHO 14/GONG 2004 Workshop (ESA SP-559), p. 186 (2004)
Eggenberger, P., Carrier, F., Bouchy, F.: Models of Procyon A including seismic constraints. New Astron. 10, 195–208 (2005)
Eggleton, P.P.: The evolution of low mass stars. Mon. Not. R. Astron. Soc. 151, 351 (1971)
Eggleton, P.P., Faulkner, J., Flannery, B.P.: An approximate equation of state for stellar material. Astron. Astrophys. 23, 325 (1973)
Ferguson, J.W., Alexander, D.R., Allard, F., et al.: Low-temperature opacities. Astrophys. J. 623, 585 (2005)
Gabriel, M.: Influence of heavy element and rotationally induced diffusions on the solar models. Astron. Astrophys. 327, 771–778 (1997)
Grevesse, N., Noels, A.: Cosmic abundances of the elements. In: Prantzos, N., Vangioni-Flam, E., Casse, M. (eds.) Origin and Evolution of the Elements, p. 14. Cambridge University Press, Cambridge (1993)
Grevesse, N., Sauval, A.J.: Standard solar composition. Space Sci. Rev. 85, 161–174 (1998)
Hairer, E., Wanner, G.: Solving Ordinary Differential Equations, vol. II. Springer, Berlin (1991)
Henyey, L.G., Vardya, M.S., Bodenheimer, P.L.: Studies in stellar evolution. III. The calculation of model envelopes. Astrophys. J. 142, 841 (1965)
Iben, I.: Stellar evolution I. The approach to the main sequence. Astrophys. J. 141, 993–1018 (1965)
Iben, I., MacDonald, J.: The effect of diffusion due to gravity and due to composition gradients on the rate of oxygen burning in a cooling degenerate dwarf. Astrophys. J. 296, 540–553 (1985)
Iglesias, C.A., Rogers, F.J.: Updated opal opacities. Astrophys. J. 464, 943 (1996)
Kippenhahn, R., Weigert, A.: Stellar Structure and Evolution. Springer, Berlin (1991)
Kurucz, R.L.: Atomic and molecular data for opacity calculations. Rev. Mex. Astron. Astrofís. 23, 45 (1992)
Lebreton, Y., Monteiro, M.J.P.F.G., Montalbán, J., Baglin, A., Michel, E.: The CoRoT evolution and seismic tools activity. In: Astrophys. Space Sci. (CoRoT/ESTA Volume). Springer, Berlin (2007)
Lide, D.R., et al.: CRC Handbook of Chemistry and Physics, 75th edn. CRC Press, Boca Raton (1994)
Mathis, S., Zahn, J.P.: Transport and mixing in the radiation zones of rotating stars. I. Hydrodynamical processes. Astron. Astrophys. 425, 229–242 (2004)
Mathis, S., Palacios, A., Zahn, J.P.: On shear-induced turbulence in rotating stars. Astron. Astrophys. 425, 243–247 (2004)
Michaud, G., Proffitt, C.R.: Particle transport processes. In: Baglin, A., Weiss, W.W. (eds.) Inside the Stars, San Francisco. ASP Conf. Ser., vol. 40, pp. 246–249 (1993)
Mihalas, D.: Stellar Atmospheres. Freeman, New York (1978)
Mihalas, D., Weibel-Mihalas, B.: Foundations of Radiation Hydrodynamics. Oxford University Press, Oxford (1984)
Mihalas, D., Dappen, W., Hummer, D.G.: The equation of state for stellar envelopes. II. Algorithm and selected results. Astrophys. J. 331, 815–825 (1988)
Mitler, H.E.: Thermonuclear ion–electron screening at all densities. I. Static solution. Astrophys. J. 212, 513–532 (1997)
Morel, P.: CESAM a code for stellar evolution calculations. Astron. Astrophys. Suppl. Ser. 124, 597–614 (1997)
Morel, P., Thévenin, F.: Atomic diffusion in stellar models of type earlier than G. Astron. Astrophys. 390, 611–620 (2002)
Morel, P., van’t Veer, C., Provost, J., Berthomieu, G., Castelli, F., Cayrel, R., Lebreton, Y.: Incorporating the atmosphere in stellar structure models: the solar case. Astron. Astrophys. 286, 91–102 (1994)
Morel, P., Pichon, B., Provost, J., Berthomieu, G.: Solar models and NACRE thermonuclear reaction rates. Astron. Astrophys. 350, 275 (1999)
Palacios, A., Talon, S., Charbonnel, C., Forestini, M.: Rotational mixing in low mass stars. I. Effects of the μ gradient in main sequence and sub-giant Pop I stars. Astron. Astrophys. 399, 603–617 (2003)
Paquette, C., Pelletier, C., Fontaine, G., Michaud, G.: Diffusion coefficients for stellar plasmas. Astrophys. J. Suppl. Ser. 61, 177–195 (1986)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes. Cambridge University Press, Cambridge (1986)
Proffit, C.R., Michaud, G.: Diffusion and mixing of lithium and helium in population II dwarfs. Astrophys. J. 371, 584–601 (1991)
Provost, J., Berthomieu, G., Morel, P.: Low frequency p- and g-mode solar oscillations. Astron. Astrophys. 353, 775 (2000)
Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer, Berlin (1994)
Rogers, F.J., Nayfonov, A.: Updated and expanded OPAL equation-of-state tables: Implications for helioseismology. Astrophys. J. 576, 1064 (2002)
Salpeter, E.E.: Energy and pressure of a zero-temperature plasma. Astrophys. J. 134, 669 (1961)
Samadi, R., Kupka, F., Goupil, M.J., Lebreton, Y., van’t Veer-Menneret, C.: Influence of local treatments of convection upon solar p-mode excitation rates. Astron. Astrophys. 445, 233–242 (2006)
Schumaker, L.: Spline Functions: Basic Theory. Wiley, New York (1981)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, Berlin (1979)
Talon, S., Zahn, J.P., Maeder, A., Meynet, G.: Rotational mixing in early-type stars: the main-sequence evolution of a 9M ⊙ star. Astron. Astrophys. 322, 209–217 (1997)
Thomas, L.H.: The radiation field in a fluid in motion. Q. J. Math. 1, 239 (1930)
Thoul, A.A., Bahcall, J.N., Loeb, A.: Element diffusion in the solar interior. Astrophys. J. 421, 828–842 (1994)
Turcotte, S., Richer, J., Michaud, G.: Consistent evolution of F stars: diffusion, radiative accelerations, and abundance anomalies. Astrophys. J. 504, 559 (1998)
van’t Veer-Menneret, C., Megessier, C.: Effective temperature of A and F stars from Balmer line profiles, and the Infrared Flux Method. Astron. Astrophys. 309, 879 (1996)
Zaatri, A., Provost, J., Berthomieu, G., Morel, P., Corbard, T.: Sensitivity of the low degree solar oscillations to the change of solar abundances. Astron. Astrophys. 269, 1145 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Morel, P., Lebreton, Y. CESAM: a free code for stellar evolution calculations. Astrophys Space Sci 316, 61–73 (2008). https://doi.org/10.1007/s10509-007-9663-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-007-9663-9