What would be the effects on a planet orbiting a shedding red giant?

Atmosphere loss

As you've suggested in your question, once a Sun-like star leaves the main sequence, it begins losing mass through a strong stellar wind, a stream of charged particles driven by photons. For a few hundred million years, it's a true red giant, expanding a bit and reaching luminosities of a few thousand solar luminosities. After spending some time on the horizontal branch, where its luminosity is constant, it ascends the asymptotic giant branch, or AGB, staying there for about 100,000 years; it then becomes a planetary nebula.

The wind should be strongest during the AGB phase, but it's also significant while the star is on the red giant branch. If we make certain assumptions about the structure of the wind, we can calculate the ablation rate for a planet - how quickly it loses material. An old paper that does this is Soker 1999, which I used in an answer to a related question. It's applicable mostly in the planetary nebula phase of a star's life. A planet orbiting the star will lose mass at a rate¹ $$\dot{M}=1.05\times10^{-11}\left(\frac{L_*}{5000L_{\odot}}\right)^{1/2}\left(\frac{R_p}{3\times10^4\text{ km}}\right)^{3/2}\left(\frac{a}{20\text{ AU}}\right)^{-1}M_J\text{ yr}^{-1}$$ where $L_*$ is the luminosity of the star, $R_p$ is the radius of the planet, and $a$ is its semi-major axis.

This relationship is only valid for stars with temperatures of $\sim10^5\text{ K}$, and as the relationship between the number of photons emitted per second is (roughly) inversely proportional to the star's temperature.² Therefore, for an AGB star or red giant, with $T\simeq3000\text{ K}$, the coefficient should instead be $3.15\times10^{-13}$.

Take the case of an Earth-like planet, with radius $R_P\simeq6300\text{ km}$. We can then calculate mass-loss rates (and total mass-loss) for the planet during different phases of the star's life.

• During the red giant phase for a Sun-like star, $L_*\simeq2000L_{\odot}$; the phase lasts for about 600 million years. For the planet to survive the subsequent evolution, it may be desirable to have it far out - say, $30\text{ AU}$. Then $\dot{M}\approx1.3\times10^{-14}M_J\text{ yr}^{-1}$, and the total mass lost should be 0.2% the mass of Earth. I use 30 AU because a planet like the one you're talking about - habitable like Earth while the star is on the main sequence - runs a strong risk of being engulfed when the star expands.
• During the AGB phase, $L\simeq10000L_{\odot}$, but this phase only lasts for 100,000 years. Then $\dot{M}\approx2.91\times10^{-14}M_J\text{ yr}^{-1}$, and the total mass lost should be $9.25\times10^{-7}$ Earth masses - about 1.1 times the mass of Earth's atmosphere.

I think the mass-loss rates for Earth in the red giant phase are actually really, really optimistic, even for a planet at 30 AU. However, the AGB mass-loss rates are much more realistic, and even if we disregard mass loss during the red giant phase, but it's very likely that it will entirely be stripped by the end of the AGB phase. Any planet previously in the habitable zone of the star while it was on the main sequence will certainly have lost its atmosphere.

Surface temperature

Red giants and AGB stars are extremely large, reaching sizes of 100 to 200 solar radii. Therefore, even though they're only about half as hot as the Sun, they're much more luminous, because of their large surface areas. This is why life on a planet orbiting a red giant has it tough. When the Sun becomes a red giant, life on Earth as we know it will not be able to survive. On planets further away, though, it might be able to.

Paradoxically, the range of orbits where a planet could survive atmospheric stripping (say, 30 AU outwards) is beyond the star's habitable zone for the vast majority of cases late in a star's life. The habitable zone should be around 5 - 10 AU, but planets there would likely lose their atmospheres during the AGB phase. It's possible that on the red giant branch itself, planets might be habitable and able to retain their atmospheres at those orbital radii. I assume there's only a narrow range of orbits where this is likely.

¹ The formula is given in Jupiter masses/year because that paper is from 1999, when the vast majority of exoplanets we knew about were massive gas giants, thanks to observational bias.

² For a star of temperature $T$, Wien's law tells us that the wavelength of peak emission is $\lambda=b/T$, where $b$ is Wien's constant. The energy per photon is $E=hc/\lambda$, where $c$ and $h$ are the speed of light and Planck's constant, and so the number of photons per second is just $$N_*=\frac{L_*}{E}=\frac{L_*}{hc/\lambda}=\frac{L_*}{hc}\frac{b}{T}=\frac{L_*b}{hc}\frac{1}{T}$$ It turns out that as Soker says, for $T\sim10^5\text{ K}$, this scales as $$N_*\approx2\times10^{47}\left(\frac{L_*}{5000L_{\odot}}\right)\text{ s}^{-1}$$ but for $T\simeq3000\text{ K}$, the proportionality constant is about two orders of magnitude lower.

posted over 5 years ago

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