Fine Print

This collection of model grids is meant to allow users to explore the consequences to integrated light indices (colors, line strengths, M/L ratios, SFB magnitudes) as stellar population parameters (age mix, metal mix, IMF, helium abundance) are varied.

The basic reference is G. Worthey 1994 ApJS, 95, 107, and, until something better comes along, that is the paper you should reference if you use Web page results. The impetus for making this page came from the organizers of the conference `From Stars to Galaxies: The Impact of Stellar Physics on Galaxy Evolution' Claus Leitherer, Uta Fritze-von Alvensleben, and John Huchra, because they made these data available on AAS CD-ROM volume 7 (1996, PASP, 108, 996).

If occasional Web use is not sufficient for your needs, I would be happy to make the interpolation program and grids available for installation on your machine. The package occupies about 105 MB. If you get the program from the AAS CD-ROM, there is a mild bug in the getmodel subroutine that you should fix. See the note at the end of this page.

The Models

Population models of this kind are flawed from the start by bad input physics. Garbage in = garbage out. For selected reasonable models differences in predicted colors lead to age estimates that differ by 35% from model to model (See Charlot, Worthey, Bressan, ApJ, Feb. 1). The uncertainties are even worse for ages less than a few Gyr. I would also urge the reader to read the "caveats & cautions" section in W94. Nevertheless, "basic correctness" has been demonstrated, and especially differential results can be trusted to the 35%-in-age level or maybe a little better.

For this Web page, some changes have been made to the original W94 models. First, for metal-poor populations, the morphology of the horizontal branch now follows the behavior of the Galactic globulars, becoming extended toward the blue. M3 and M92 were used as models for this behavior as in Aaronson et al. (1978), the M3 horizontal branch extending to log Te=4, and the M92 horizontal branch extending from log Te=3.9 to log Te=4.1. The switch to M3 morphology happens below [Fe/H] = -0.95; the switch to M92 morphology happens below [Fe/H] = -1.55. This scheme is discussed in Worthey (1993).

Second, the M/L ratios are slightly less arbitrary. The lower mass-cutoff of the power-law IMFs was kept at 0.1 Mo (and the upper at 100 Mo), but remnants were tracked using the Weidemann (1987) initial-to-final mass relation. The normalization of the mass follows W94: the initial mass of the system, obtained by integrating under the IMF, is normalized to be a million Mo. The mass of the population changes somewhat as stars are converted into remnants, and it is this reduced mass which is used to calculate the M/L ratios.

Third, quite a lot of new output was added as of February 2011. Synthetic magnitudes are now given in a wide variety of photometric systems. The Worthey & Ottaviani (1997) H gamma and H delta indices are there, on the Lick system. All lick indices plus H alpha plus the indices from Serven et al. (2005) are added, modeled at 200 km/s resolution. The higher-resolution synthetic fluxes are available, too, as an output option.

Explanation of Model Flavors

(a) Vanilla (default)
"Vanilla" has a Salpeter IMF integrated from 0.1 to 100 solar masses, stellar remnants, a horizontal branch that (crudely) varies its shape as a function of metallicity, helium abundance that rises smoothly with heavy element abundance. Colors are calculated from the Kurucz-Bessell-Brett-Scholz-Wood collection of synthetic spectra used by W94.
(b) Power-law IMFs plus Miller & Scalo (1979).
The lower mass cutoff is 0.1 Mo for the Miller & Scalo (1979) 3-piece power-law IMF, otherwise is given by the table above. The upper mass cutoff is 100 Mo in all cases.
(c) Helium abundance (Y)
Helium abundance is a free parameter in the W94 models. It is allowed to affect stellar lifetimes and temperatures through the helium flash. It affects later stage lifetimes through modulation of the helium core mass, but any temperature effects are neglected for later stages.
The minimum_Y and maximum_Y flavors are set by the helium abundances chosen by VandenBerg in the input evolutionary isochrones. He chose Y=0.20 and Y=0.30 below Z=0.008, and Y=0.25 and Y=0.35 above that value. (In the near-solar-Z regime some interpolation was needed. See W94.)
The shallow_Y scheme is that Y = 0.228 + 6*Z below Z=0.0077 and Y = 0.274 above that value. The Z=0.0077 corresponds to [Fe/H] = -0.34. (VandenBerg solar Z = 0.0169. See W94.) The default scheme in "vanilla" is Y = 0.228 + 2.7*Z at all Z.
(d) No late stages.
All stages of stellar evolution beyond the helium flash are truncated.
(e) More recent colors
Colors in the last case are calculated using high-resolution fluxes (300-1000 nm, plus low-resolution blue and red tails) computed for new work on detailed chemical abundances (e.g. Poole et al. 2010, Worthey et al. 2011).

Aaronson, M., Cohen, J. G., Mould, J. R., Malkan, M. 1978, ApJ, 223, 824
Leitherer, C. et al.
Miller, G. E., & Scalo J. M. 1979, ApJS, 41, 573
Poole, V., Worthey, G., Lee, H.-c., & Serven, J. 2010, AJ, 139, 809
Serven, J., Worthey, G., & Briley, M. M. 2005, ApJ, 627, 754
Weidemann, 1987, A&A, 188, 74
Worthey, G. 1993, ApJL, 415, L91
Worthey, G. 1994, ApJS, 95, 107; W94
Worthey, G., & Ottaviani, D. L. 1997, ApJS, 111, 377
Worthey, G., Ingermann, B. A., & Serven, J. 2011, ApJ, 730, in press

Explanatory blurb from the Leitherer et al. (1996) PASP Paper

Worthey (1994, ApJS, 95, 107) models

The Worthey (1994) evolutionary population models give integrated UBVRcIcJHKLL'M colors and magnitudes, SBF magnitudes, spectral energy distributions, and Lick/IDS spectral index strengths for populations of arbitrary age, and (assumed scaled-solar) abundance [Fe/H]. The ages range from 1 to 18 Gyr, and abundances from -2.0 to +0.5 dex. Helium abundance Y is a free parameter. The underlying stellar evolution is that of VandenBerg (VandenBerg 1985, VandenBerg & Bell 1985, VandenBerg & Laskarides 1987). The stellar fluxes used to compute integrated flux are mostly theoretical (Kurucz 1992, Bessell et al. 1989, 1991), and explicitly include the effects of metallicity on the spectral shape and colors. Please see Worthey (1994) for details.

The distribution on the CD-ROM includes several ``flavors'' of model grid: (1) Five power-law IMFs plus Miller \& Scalo (1979) are provided. For the power-law IMFs the lower mass cutoff was chosen so that M/L_V=2.5 for globular cluster-like populations (with a reasonable accounting of stellar remnants; Worthey 1996, in preparation), so output M/L values differ from the tabulation in Worthey (1994) by a constant factor plus a small perturbation caused by the fact that a small amount of low-mass starlight is missing. (2) Also included are four schemes for how helium abundance tracks overall abundance. (3) One model grid without helium-burning and later stages of stellar evolution is included for those interested in adding HB-, AGB-, EAGB-, PAGB-stages, or other stages of evolution by themselves. (4) The models as tabulated in Worthey (1994) are also included unaltered.

Each model (at one age and [Fe/H]) is stored in a FITS file with ascii table extensions. One ``flavor'' is made of a grid of FITS files covering the range of age and [Fe/H]. A fortran program is provided that reads the data using William Pence's FITSIO routines (also included), interpolates in the model grid to arbitrary age and metallicity, and combines populations in any combination the user specifies. Multicolor color-magnitude diagrams are also available in the FITS file ascii extensions.

If the reader is but an occasional consumer of population models, he or she would probably best be served by the web page which contains a form-driven version of the interpolation/addition program on this CD-ROM.

Bessell, M. S., Brett, J. M., Scholz, M., \& Wood, P. R. 1989, A&AS, 77, 1
Bessell, M. S., Brett, J. M., Scholz, M., \& Wood, P. R. 1991, A&AS, 89, 335
Kurucz, R. L. 1992, private communication
Miller, G. E., \& Scalo J. M. 1979, ApJS, 41, 573
VandenBerg, D. A. 1985, ApJS, 58, 561
VandenBerg, D. A., \& Bell, R. A. 1985, ApJS, 58, 561
VandenBerg, D. A., \& Laskarides, P. G. 1987, ApJS, 64, 103
Worthey, G. 1994, ApJS, 95, 107


Users of the CD-ROM software might want to fix a bug in the "getmodel.f" subroutine: replace line 70 with two lines:

if ( ja.eq.5 .and. ) ja=6
if ( .and. jz.eq.5 ) jz=6

The unchanged program did not choose grid points exactly correctly in the region of young age and low metallicity that is missing in the parameter space of the models. This caused a mild mismatch between published and interpolated values for [Fe/H]=-0.225 and ages younger than 8 Gyr. The error only shows up if the user chooses exactly [Fe/H]=-0.225: any lower and an error message appears; any higher and the grid points are chosen correctly.