Predicting HCN, HCO+, multi-transition CO, and dust emission of
  star-forming galaxies From local spiral and ultraluminous infrared galaxies
  to high-z star-forming and submillimeter galaxies
  (abridged) In this work we have a closer look at the gas content or fraction
and the associated star formation rate in main sequence and starburst galaxies
at z=0 and z~1-2 by applying an analytical model of galactic clumpy gas disks
to samples of local spiral galaxies, ULIRGs, submillimeter (smm), and high-z
starforming galaxies. The model gas and dust temperatures are determined by the
heating and cooling equilibrium. Dense clouds are heated by turbulent
mechanical and cosmic ray heating. The molecular abundances of individual gas
clouds are determined by a detailed chemical network involving the cloud
lifetime, density, and temperature. Molecular line emission is calculated with
an escape probability formalism. The model calculates simultaneously the total
gas mass, HI/H_2 mass, the gas velocity dispersion, IR luminosity, IR spectral
energy distribution, CO spectral line energy distribution (SLED), HCN(1-0), and
HCO+(1-0) emission of a galaxy given its size, integrated star formation rate,
stellar mass radial profile, rotation curve, and Toomre Q parameter. The model
reproduces the observed CO luminosities and SLEDs of all sample galaxies within
the model uncertainties (~0.3 dex). Whereas the CO emission is robust against
the variation of model parameters, the HCN and HCO+ emission is sensitive to
the chemistry of the interstellar medium. The CO and HCN mass-to-light
conversion factors including CO-dark H_2 are given and compared to the values
found in the literature. Both, the HCN and HCO+ emission trace the dense
molecular gas to a factor of ~2 for the local spiral galaxies, ULIRGs and
smm-galaxies. About 80% of the molecular line emission of compact starburst
galaxies originates in non-selfgravitating gas clouds. The integrated
Kennicutt-Schmidt law has a slope of ~1 for the local spirals, ULIRGs, and
smm-galaxies, whereas the slope is 1.7 for high-z starforming galaxies.
