User talk:EvenGreenerFish

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Re: Habitable zone diagram for solar system

Thanks for the question!

In the description of the HD 85512 diagram I link to the paper on arXiv [1] which gives the formulae, it also tabulates the value for a 5700K G2 star. The Sun at 5780 K is somewhat hotter.

The incident fluxes in units of the solar flux at the Earth's orbit of the six habitable zone boundaries (three inner, three outer) are given by:

Limit	Formula
Recent Venus	$S=2.286\times 10^{-8}\,T_{\mathrm {e} }^{2}-1.349\times 10^{-4}\,T_{\mathrm {e} }+1.786$
Runaway greenhouse	$S=4.190\times 10^{-8}\,T_{\mathrm {e} }^{2}-2.139\times 10^{-4}\,T_{\mathrm {e} }+1.268$
Water loss	$S=1.429\times 10^{-8}\,T_{\mathrm {e} }^{2}-8.429\times 10^{-5}\,T_{\mathrm {e} }+1.116$
CO2 cloud condensation	$S=5.238\times 10^{-9}\,T_{\mathrm {e} }^{2}-1.424\times 10^{-5}\,T_{\mathrm {e} }+0.4410$
Maximum greenhouse	$S=6.190\times 10^{-9}\,T_{\mathrm {e} }^{2}-1.319\times 10^{-5}\,T_{\mathrm {e} }+0.2341$
Early Mars	$S=5.714\times 10^{-9}\,T_{\mathrm {e} }^{2}-1.371\times 10^{-5}\,T_{\mathrm {e} }+0.2125$

Note the above expressions are based on interpolating points at 3700 K (M0 star), 5700 K (G2 star) and 7200 K (F0 star) so are not valid outside this range.

The flux can then be converted to distance using:

$d={\sqrt {\frac {L}{S}}}$

Where distance d is in AU, luminosity L is in solar luminosities and the incident flux S is in units of the solar flux at Earth.

The tabulated and interpolated values are as follows:

Limit	5700 K (table)		5780 K (interpolated)
	Flux	Dist	Flux	Dist
Recent Venus	1.76	0.75	1.77	0.75
Runaway greenhouse	1.41	0.84	1.43	0.84
Water loss	1.10	0.95	1.11	0.95
CO2 cloud condensation	0.53	1.37	0.53	1.37
Maximum greenhouse	0.36	1.67	0.36	1.66
Early Mars	0.32	1.77	0.32	1.76

As you can see, moving from 5700 K to 5780 K does not make much difference!

Incidentally I would recommend you make the diagram as an SVG file rather than a PNG, this allows it to be scaled to any resolution and is ideal for diagrams. You can also put descriptive metadata into the files. Icalanise (talk) 21:00, 17 November 2012 (UTC)