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Calculating the Habitable Zone

A General Method for Approximating the Habitable Zone around a Main Sequence Star

by Tom E. Morris
Division of Natural Sciences
Fullerton College, Fullerton, CA, USA
http://planetarybiology.com
tmorris@fullcoll.edu
October 2010

Two stages of calculations

Stage 1: Estimate the absolute luminosity based on the star’s apparent visual magnitude

First Step – Calculate the absolute visual magnitude of the star based on the star’s apparent magnitude.

M_v = m_v – 5 log(d/10)

Where:

M_v = Absolute magnitude of the star

m_v = apparent magnitude of the star (visual spectrum)

d = distance from Earth to the star in parsecs

Second Step – Calculate bolometric magnitude of the star.

M_bol = M_v + BC

Where:

M_bol = bolometric magnitude of the star

M_v = the absolute magnitude of the star

BC = bolometric correction constant

Use the following table for general bolometric correction values [generalized from Habets and Heintz (1981)]

Spectral class	BC
B	-2.0
A	-0.3
F	-0.15
G	-0.4
K	-0.8
M	-2.0

Third Step – Calculate the absolute luminosity of the star

L_star/L_sun =

Where:

L_star/L_sun = the absolute luminosity of the star in terms of the absolute luminosity of the sun

M_{bol star} = the bolometric magnitude of the star

M_{bol sun} = the bolometric magnitude of the sun = 4.72

 

Stage 2: Approximate the radii of the boundaries of the star’s habitable zone

Where:

This method approximates habitable zone radii using stellar luminosity and stellar flux following methods presented by Whitmire et al., 1996, cited below.

r_i = the inner boundary of the habitable zone in astronomical units (AU)

r_o = the outer boundary of the habitable zone in astronomical units (AU)

L_star is the absolute luminosity of the star

1.1 is a constant value representing stellar flux at the inner radius (based on Kasting et al., 1993, cited below; Whitmire et al., 1996, cited below)

0.53 is a constant value representing stellar flux at the outer radius (based on Kasting et al., 1993, cited below; Whitmire et al., 1996., cited below)

Example

Star Gl 581
m_v = 10.55
Spectral type = M3
BC = -2.0 (based on M class star, and approximated using value in above table)
Distance = 6.26 parsecs

Calculate absolute visual magnitude

M_v = 10.55 – 5log(6.26/10) = 11.57

Calculate bolometric magnitude

M_bol = 11.57 + (-2.0) = 9.57

Calculate absolute luminosity

L_{Gl 581}/L_sun =  = 0.012

Approximate the boundaries of the habitable zone for this star

 = 0.1 AU

 = 0.15 AU

For more information on the development of this methodology, please see the chapter entitled "Astronomical Circumstances" by Tom Morris, available here at planetarybiology.com.

References
Fogg, Martyn J., (1992). An estimate of the prevalence of biocompatible and habitable planets. Journal of the British Interplanetary Society, 45: 3-12.
Habets, G.M.H.J.; Heintze, J.R.W., (1981). Empirical bolometric corrections for the main sequence. Astron. Astrophys. Suppl. Ser. 46: 193-237.
Kasting, James; Whitmire, Daniel; and Reynolds, Ray (1993). Habitable zones around main sequence stars. Icarus 101: 108-128.
Kasting, James F. (1996). Habitable zones around stars: An update. In: Doyle, Laurence (ed.). Circumstellar Habitable Zones, 117-142. Travis House Publications, Menlo Park.
Lang, Kenneth (1992). Astrophysical Data: Planets and Stars. Springer-Verlag, New York.
Whitmire, Daniel; Reynolds, Ray, (1996). Circumstellar habitable zones: astronomical considerations. In: Doyle, Laurence (ed.). Circumstellar Habitable Zones, 117-142. Travis House Publications, Menlo Park.