# Further details for Pisa Models

We are grateful to Emanuele Tognelli and the Pisa group for supplying versions of their isochrones which are an improvement on those in Tognelli et al. (2011) and Tognelli et al. (2012).

The adopted input physics is as described in Tognelli et al. (2011) and Tognelli et al. (2012).

The updates are as follows.

Equation of State:

OPAL EOS 2006 for M >= 0.2 Msun (Rogers & Nayfonov 2002)
Saumon, Chabrier & VanHorn (1995) for M < 0.2 Msun

Radiative Opacity: OPAL EOS 2005 for log T[K] >= 4.5 (Iglesias & Rogers 1996)
Ferguson et al. (2005) for log T[K] > 4.5

Both the opacity tables have been computed for the recent Asplund et al. (2009) heavy elements solar distribution.

Atmosphere models:
Allard et al. 2011 for Teff < 2000 K
Brott & Hauschildt (2005) for 2000 K <= Teff < 10000 K
Castelli & Kurucz (2003) for Teff >= 10000 K

Mixing length parameter:
Solar calibrated value ML = 1.74 (using the Brott & Hauschildt 2005 models)

Core overshooting:
Lambda_over=0.2 for M > 1.1 Msun

References:
Allard, F.,Homeier, D., & Freytag, B. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 448, 16th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, ed. C. Johns-Krull, M. K. Browning, & A. A. West, 91
Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
Brott, I. & Hauschildt, P. H. 2005, in ESA Special Publication, Vol. 576, The Three- Dimensional Universe with Gaia, ed. C. Turon, K. S. O'Flaherty, & M. A. C. Perry- man, 565
Castelli, F. & Kurucz, R. L. 2003, in IAU Symposium, Vol. 210, Modelling of Stellar Atmospheres, ed. N. Piskunov, W. W. Weiss, & D. F. Gray, 20P
Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, ApJ, 623, 585
Iglesias, C. A. & Rogers, F. J. 1996, ApJ, 464, 943
Rogers, F. J. & Nayfonov, A. 2002, ApJ, 576, 1064
Saumon, D., Chabrier, G., & van Horn, H. M. 1995, ApJS, 99, 713
Tognelli, E., Prada Moroni, P. G., & Degl'Innocenti, S. 2011, A&A, 533, A109
Tognelli, E., Degl'Innocenti, S., & Prada Moroni, P. G. 2012, A&A, 548, A41

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