# How realistic is this orange dwarf star?

For my world building project, I have an (on the large side) orange dwarf star with these parameters:

• Mass: 0.75 solar masses
• Luminosity: 0.36 solar luminosities
• Surface temperature: 5000 Kelvin (0.86 X solar surface temperature)

How realistic is this model, what changes would I need to make to make this star more realistic (as a K-type star) and what would its inner limit, outer limit, habitable zone and frost line be?

• You could probably google up some astronomical catalog and find out if there are such stars. Commented Nov 3, 2020 at 15:42
• Temp, mass, and radius check out, but Luminosity is lower than expected. Lifetime of an average orange dwarf star is supposed to be 15-45x the sun's lifetime. Commented Nov 3, 2020 at 15:43

Astronomer Eric Mamajek has a table of handy typical properties of main sequence stars (see Pecaut & Mamajek 2013), spread out across each spectral type. We can see that a star with a mass of $$M=0.75M_{\odot}$$ should be a K3V dwarf with . . .

• A radius of $$0.73R_{\odot}$$
• A luminosity of $$0.18L_{\odot}$$
• A temperature of 4830 Kelvin

We can extrapolate from this that the main sequence lifetime should be 2.1 times the length of the Sun's. Using Wien's law, we see that the emission should peak at 600 nm - fairly orange.

This is pretty close to what you're looking for. If we we increase the mass to roughly $$M=0.8M_{\odot}$$ solar masses, we fall between a K1.5V and K2V star. Extrapolating from the models, I'd expect a radius of $$0.78R_{\odot}$$, a luminosity of $$0.36L_{\odot}$$, a temperature of 5090 Kelvin, a main sequence lifetime 1.75 times the Sun's, and peak emission at 570 nm.

Therefore, increasing the mass to $$0.8M_{\odot}$$ makes the other properties of the star better match what you're looking for.

Habitable zones are notoriously tricky to calculate, and there's no consensus as to where the Sun's lies. You can probably convince yourself that the inner and outer limits should scale as $$\sqrt{L}$$. Kopparapu et al. 2013 found that the solar habitable zone's inner and outer boundaries lie near 0.95 AU and 1.62 AU. Scaling this by the square root of your orange dwarf's luminosity gives us new boundaries of 0.57 AU and 0.97 AU.