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Habitable zone boundaries

Habitable zone boundaries are computed following Kopparapu et al. (2013) 1 using stellar luminosities and effective temperatures from the Spada models 2 (physicalmodel.aOrbHZ). Six boundaries are returned:

Boundary Key
Recent Venus RecentVenus
Runaway Greenhouse RunawayGreenhouse
Moist Greenhouse MoistGreenhouse
Maximum Greenhouse MaximumGreenhouse
Early Mars EarlyMars
Midpoint (Moist + maximum Greenhouse) HZ

All distances are in AU and computed by default at 5000 Myr (params['AgeHZ']).

The HZ boundary is defined as the midpoint between the moist and maximum greenhouse limits:

\[a_\mathrm{HZ} = \frac{1}{2}\left(a_\mathrm{MoistGreenhouse} + a_\mathrm{MaximumGreenhouse}\right)\]

Each boundary distance is computed from the stellar flux factor \(S_\mathrm{eff}\) following Kopparapu et al. (2013), eq. 3 1:

\[a = \left(\frac{L_\mathrm{bol}}{L_\odot \cdot S_\mathrm{eff}}\right)^{1/2} \quad (\mathrm{AU})\]

where \(S_\mathrm{eff}\) depends on the stellar effective temperature \(T_\mathrm{eff}\) via a fourth-order polynomial anchored to solar values.

Fluxes in the habitable zone

\(F_X\), \(F_\mathrm{EUV,1}\), \(F_\mathrm{EUV,2}\), \(F_\mathrm{EUV}\), and \(F_\mathrm{Ly\alpha}\) are all computed at the HZ orbital distance and stored as standard quantities on every evolutionary track:

Track quantity Description
FxHZ X-ray flux at \(a_\mathrm{HZ}\)
Feuv1HZ EUV1 (10–36 nm) flux at \(a_\mathrm{HZ}\)
Feuv2HZ EUV2 (36–92 nm) flux at \(a_\mathrm{HZ}\)
FeuvHZ Total EUV (10–92 nm) flux at \(a_\mathrm{HZ}\)
FlyHZ Ly-\(\alpha\) flux at \(a_\mathrm{HZ}\)

These are computed as \(F = L / (4\pi a_\mathrm{HZ}^2)\) for each band.

Note

The habitable zone boundaries are calculated once at instantiation using stellar properties at params['AgeHZ'] (default 5 Gyr) and held fixed throughout the evolutionary track. This reflects the interest in planets that spend billions of years in the habitable zone, for which the main-sequence stellar properties are the appropriate reference.

  1. Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. (2013). Habitable zones around main-sequence stars: new estimates. The Astrophysical Journal, 765(2), 131. https://doi.org/10.1088/0004-637X/765/2/131 ↩↩

  2. Spada, F., Demarque, P., Kim, Y.-C., & Sills, A. (2013). The radius discrepancy in low-mass stars: single versus binaries. The Astrophysical Journal, 776(2), 87. https://doi.org/10.1088/0004-637X/776/2/87 ↩