ADMINISTRACIÓN GUBERNAMENTAL DE INGRESOS PÚBLICOS DIRECCIÓN GENERAL DE RENTAS

Phoenix incorporates the subroutines to read in and use data for planetary nebula options from G05 and vdH&G97, and SSP results from T04 that were originally written by the present author for the GCE model. For further details on these subroutines, see 2.2.3 and 2.2.4 above.

4.3.2 Evolve the galaxy

Details of the subroutine EVOLVE are given in figure 12. The user can select which yield options to use within the subroutines PNYIELDS (RV81, vdH&G97 or G05, whether to use results from WW95 or the Geneva group for large stars (between 8 and 40 M

), and the rates to use for SNIa evolution (Timmes 1995 or

Scannapieco and Bildsten 2005) via the file ‘values.in’. The model creates massbins (in steps of 0.1 M
up to 10 M
, thereafter in steps of 1 M
) of the new stars formed, calculating the mass held in that bin, the average star size, the chemical content of these stars, their main sequence lifetime, and, when calculated, the indices, weighted and unweighted, of these stars at the end of each timestep between them being formed and being fully evolved.

At each stage during this subroutine, the total mass and the mass fractions of hydrogen, helium and metals in stars and in gas, together with the masses of 14 selected elements, are updated. The evolutionary steps are calculated in series but of course in practice would occur in parallel. As planetary nebula events for higher metallicity stars can result in a reduction in oxygen, the model may in early timesteps temporarily appear to have “negative oxygen” or “negative carbon”, because this process is calculated before the oxygen and carbon- enriching processes of SNII. A check is built in to ensure that by the end of the timestep, this has been corrected to a net positive figure.

Subroutines called

GETFRAC

SNIA YIELDS

PN YIELDS

SNII G YIELDS Update star/gas masses and mass

fractions - from primordial if first timestep, otherwise as per end of previous timestep

If applicable, flow gas in

Calculate galaxy dimensions and current gas density and hence star formation rate

Calculate mass of new stars created, and allocate into massbins, with details of the stars (metallicity, main sequence lifetime etc)

SNII WW YIELDS or SNII G YIELDS, as selected by user

Separate off any stars that are so large they'd form black holes, or so small they'd form brown dwarves.

Evolve any remnants as SNIA, using user-selected rate (Timmes 1995 or Scanapeico and Bildsten 2005), update galaxy

Evolve any stars < 8Mo and reaching the end of their main sequence life in this timestep as planetary nebula. Update galaxy

Evolve any stars between 8Mo and 40Mo and reaching the end of their main sequence life in this timestep as SNII. Update galaxy

F o r e a c h t im e s te p

Evolve any stars between 40 Mo and 120Mo and reaching the end of their main sequence life in this timestep as SNII. Update galaxy

If applicable, flow gas out of the galaxy

Check for rounding errors, update galaxy

4.3.3 Produce synthetic indices and colours

The process for creating the synthetic Lick indices and colours at the end of each timestep is given in figure 13 below.

Lick indices for each stellar combination of age and metallicity at the end of each timestep can be obtained by looking up (and interpolating where necessary) this information from the SSP selected by the user. However, the mass of the individual stars is important because larger stars will be more luminous and consequently the indices from these stars are more important when calculating the overall integrated indices of the modelled galaxy; the luminosity of the stars in each mass bin is used to appropriately weight the synthetic indices.

Isochrones give the luminosity for a given age, mass and metallicity of a star. Isochrones from Bertelli et al. (1994) (also known as the Padova isochrones) (hereafter B94) were chosen as they cover a wide range of ages, masses and metallicities, and in addition to the luminosity give values for the colours, which can be used where the SSP data set does not include this information.

The source data first needs to be sorted, as the interpolation subroutine within Phoenix requires the data to be monotonically increasing, however, the data within each table was presented in order of reducing age, and within each age broadly, but not consistently in order of increasing mass. Code within the READBERTELLI subroutine therefore re-orders the data within each table to have increasing order of age and within each age, increasing order of mass. The READBERTELLI subroutine also converts [age] to actual age, Mbol to luminosity

using the relation (Ridpath 1997):

Mbol – 4.72 = 2.5 log(L/ L
) (21)

The Phoenix model does not distinguish between stars of different temperatures, so where several isochrones are provided for one stellar mass at a given age and metallicity, the average is taken. The isochrone tables are of different lengths, which the code adjusts for, and, as elsewhere, where the data required is outside the range available, the nearest value is used and a warning sent to file.

The massbin is then updated with the absolute luminosity of those stars in that timestep, and the colours from the appropriate interpolated isochrone. Once all the massbins for that timestep have this data, the total luminosity for the galaxy can be obtained, enabling the luminosity contribution of the stars in that mass bin to the overall luminosity be calculated, and hence the indices can be weighted, enabling the total integrated Lick indices and total integrated colours of the galaxy at the end of that timestep to be output.

Calls to other subroutines

B94ISOCHRONES Take each mass bin which contains

stars (some may be empty where stars have fully evolved)

Find the isochrone for these stars (at their age, Z and mass) and store the

appropriate luminosity

Add the luminosity to the tally of total luminosity

Once have gone through all the stars that exist at this timestep, calculate the luminosity weighting to be applied to each mass bin (luminosity of stars

in bin/total luminosity)

Apply the luminosity weighting to the indices, adjusting for those held as

magnitudes

Sum the luminosity weighted indices for all stars at the end of this timestep

W94INDICIES plus GV98INDICES or V99INDICES or T04INDICES

Find the SSP for these stars (at their age and Z) using SSP source selected

by user

Go to next mass bin.