Mg-sigma Generator

Produces an artificial simulation of an observed Mg-index versus (central) velocity dispersion diagram.

Major Parameters:

- N_merger = Number of mergers during each galaxy's lifetime.
- F_initial = Fraction of galaxy that forms immediately at z=z_formation.
- F_gas = fraction of gas/total mass in each merger.
- Mg_boost = additional metals added to each gas merger.
- Envelope = Merger probability envelope exponent n, in (1+z)n. Probability constant in time: enter n=-1.

Minor Parameters:


- z_view = redshift at which user views the simulated Mg-sigma diagram.
- N_masses = Number of logarithmically evenly-spaced galaxy masses to consider.
- N_repeat = Number of Monte Carlo realizations of each mass. (N_tot=N_repeat x N_masses)
- M_low = Lowest-mass galaxy. In 108 Mo.
- M_high = Highest-mass galaxy. In 1012 Mo.
- zformation = redshift at which first gas collapses occur.
- H0 = Hubble constant in km/s/Mpc.
- Omega = mass density parameter.
- Omega_R = space curvature parameter.
- Omega_lambda = cosmological constant. The three omegas must sum to one.
- Sigma_low = lower limit on velocity dispersion - for statistics only.
- Sigma_upp = upper limit on velocity dispersion - for statistics only.

Output Options:

- Index-sigma data and summary statistics are always output.
- Mg_2 - sigma plot.
- Mg b - sigma plot.
- Tables of merging histories for each galaxy. Can get lengthy . . .

Guide to Mg indices

There are 3 "Lick" Mg indices and one commonly used variant, all exploring the Mg I and MgH around 5100 angstroms. Beware the subtle typographic conventions that distiguish between them!
  1. Mg1 and
  2. Mg2 are very broad indices that share pseudocontinuum passbands but have different central passbands. The indices are expressed in magnitudes. See Worthey et al. and Trager et al. for definitions. Nonspectrophotometric data may suffer small systematic offsets from the Lick system. The indices are virtually unaffected by the velocity dispersion of the galaxy.
  3. Mg b is expressed in angstroms of equivalent width, and spans a much narrower wavelength range centered on the Fraunhofer b line due to the Mg I "triplet". Although this index is affected by the galaxies velocity dispersion more than the broader definitions, it is sometimes preferred because it is easier to put precisely on the original system.
  4. < Mg2> : This is a nonlinear combination of Mg1 and Mg2 defined in Davies et al. (7 Samurai) by the two equations: Mg2' = 0.03 + 2.10 Mg1 - 62 Mg14 and < Mg2> = 0.6 Mg2 + 0.4 Mg2'. There may be a few thousandths of a magnitude systematic offset between the Lick version, and the version adopted by the 7 Samurai, but nothing too alarming (Trager et al.).

References:

  1. Davies, R. L. et al. 1987, ApJS, 64, 581 - definition of < Mg2> .
  2. Trager, S. C. et al. 1998, ApJS, 116, 1 - Lick indices for galaxies
  3. Worthey, G. et al. 1994, ApJS, 94, 687

Guy Worthey