Star mass, orbit, albedo and greenhouse against liquid water.
-Stellar luminosity (Lsun)
-Star temperature (K)
-Zone inner edge (AU)
-Zone outer edge (AU)
-Flux at the planet (Earth = 1)
-Equilibrium temperature (K)
-Surface temperature (K)
-Orbital period (years)
-Main-sequence lifetime (Gyr)
-Verdict
The science
A star of mass M has luminosity L ~ M^4 (roughly, in solar units), radius R ~ M^0.8 and effective temperature T = 5772 K (L / R^2)^(1/4). The flux at distance d falls as S = L / d^2 (inverse-square law).
Kopparapu et al. (2013) fitted 1D climate-model results for the flux limits as a polynomial in temperature: S_eff = S_sun + aT + bT^2 + cT^3 + dT^4 with T = T_eff - 5780 K. The edges are at d = sqrt(L / S_eff). This page uses the moist-greenhouse (inner) and maximum-greenhouse (outer) limits for the green band; for the Sun that is 0.99 to 1.70 AU.
The planet's equilibrium temperature balances absorbed and radiated power: T_eq = T_star sqrt(R_star / 2d) (1 - A)^(1/4). A greenhouse offset (about 33 K for Earth) raises the surface temperature. The orbital period follows Kepler's third law P^2 = d^3 / M.
Honest simplifications: the zone edges include the star's spectrum (red dwarfs emit mostly infrared, which ice and clouds absorb, so their planets have a lower albedo than Earth); the surface temperature here uses one albedo slider instead. A single planet-wide albedo and greenhouse offset instead of a climate model, main-sequence mass-luminosity fits, no tidal locking (important around red dwarfs), no stellar flares and no stellar evolution. The lifetime is the rough scaling 10 Gyr M / L.