Close the door on your way out - Life lit by a blue dwarf star

Yes, it can happen.

For this to be possible, you first have to put the planet far enough away that it can become totally icy. Then, after the temperature rises as the red dwarf transitions into a blue dwarf, the habitable zone must encompass the planet's orbit, melting the ice and making it a better place for life. We can easily calculate whether or not the final habitable zone can ever extend far enough for this to be possible.

Your initial goal is to place the planet "well outside the [initial] habitable zone". That's fine. We can find the initial inner and outer boundaries of the habitable zone using the formulae found here. The outer radius of the initial habitable zone is $$r_o=\sqrt{\frac{L_*}{0.53}}\text{ AU}$$ Let's take the example of the 0.1-M$_\odot$ red dwarf used in the blog post. Its initial (i.e. pre-blue dwarf) luminosity is ~1/2400 L$_\odot$, or ~1.595$\times$10²³ watts. Plugging this in, we get $$r_o\approx2.80\times10^{-2}\text{ AU}$$ Now, this is for a very dim red dwarf (I would think about an M5V class or an M6V class dwarf), so it's not surprising that this is so small.¹

You say you want to have an ice planet. We can estimate the inner radius at which it can form by calculating the distance of the initial frost line. If we use the model attributed to Hayashi (1981) by Ida & Lin (2005), then $$r_f=2.7\left(\frac{L_*}{L_{\odot}}\right)^{\frac{1}{2}}\text{ AU}\approx5.50\times10^{-2}\text{ AU}$$ Now, it is clear that $L_*$ will change with time even before the transition to the blue dwarf stage. Kennedy & Kenyon (2008) model these changes on various stars and compare them to earlier results, including those of Ida & Lin.² The differences are drastic, in some cases. See their Figure 1:

For lack of more information, though, I'm going to have to stick to the original estimate.

Your article states that the initial surface temperature of the star is ~2230 K, prior to entering the blue dwarf phase. It then rises to ~5810 K, a change of a factor of about 2.5 The luminosity of a blackbody is proportional to its temperature to the fourth power (see the Stefan-Boltzmann law), so the inner and outer radii of the habitable zone are proportional to the temperature squared. This means that the final outer edge will be ~6 times as far out as it originally was - way beyond the initial frost line, about three times as far out.

This seems pretty good, but what about the inner edge of the final habitable zone. Where will that be? According to the same site that provided the formula for the outer edge, the inner edge will be $$r_i=\sqrt{\frac{L_*}{1.1}}\text{ AU}\approx0.70r_0$$ This is about twice as far out as the frost line originally was.

So, yes, from at least these estimates, the scenario is quite plausible.

^{1 Some results state that the habitable zone should be even smaller, although others disagree and say that it should be bigger.
2 Even more drastic changes are shown in Martin & Livio (2012).}

posted over 8 years ago

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