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

Get this procedure in *.pdf format.


Two stages of calculations

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

First Step (stage 1)  – Calculate the absolute visual magnitude of the host star based on the star’s apparent magnitude.

Mv = mv – 5 log(d/10)

Where:

Mv = Absolute magnitude of the star

mv = apparent magnitude of the star (visual spectrum)

d = distance from Earth to the star in parsecs

Second Step (stage 1)  – Calculate bolometric magnitude of the host star.

Mbol = Mv + BC

Where:

Mbol = bolometric magnitude of the star

Mv = 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 (stage 1) – Calculate the absolute luminosity of the host star

Lstar/Lsun = equation

Where:

Lstar/Lsun = the absolute luminosity of the host star in terms of the absolute luminosity of the sun

Mbol star = the bolometric magnitude of the host star

Mbol sun = the bolometric magnitude of the sun = 4.72

2.5 is a constant value used for comparing stellar luminosities -- known as "Pogson's Ratio."

 

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

equation
equation

Where:

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

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

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

Lstar 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

1. Calculate absolute visual magnitude

Mv = 10.55 – 5log(6.26/10) = 11.57

2. Calculate bolometric magnitude

Mbol = 11.57 + (-2.0) = 9.57

3. Calculate absolute luminosity

LGl 581/Lsun  =  equation  =  0.012

4. Approximate the boundaries of the habitable zone for this star

equation  =   0.1 AU

equation  =   0.15 AU

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

References

An alternative approach has been proposed by:

"Habitable Zones Around Main-Sequence Stars: New Estimates" by Kopparapu et al.(2013), Astrophysical Journal, 765, 131    arXiv link

Try the online habitable zone caclulator based on this alternative approach at:

University of Washington Virtual Planetary Laboratory