<p>Habitable zones have a width that scales as the square root of the luminosity. So a 10000 solar luminosity star will have a zone about 100 times wider.</p>

<p>However, the temporal width is another thing: the luminosity changes relatively fast, so planets will not be in the zone over long timescales. </p>

<p>(The reason for the square root dependence is that a piece of surface at semimajor axis <span class="math-container">$a$</span> gets <span class="math-container">$L/4\pi a^2$</span> Watt of incoming energy, and if a blackbody with emissivity <span class="math-container">$\epsilon$</span> radiates away <span class="math-container">$\sigma \epsilon T^4$</span>. Energy balance gives <span class="math-container">$L/4\pi a^2 = \sigma \epsilon T^4$</span>, or rearranged, <span class="math-container">$a = \sqrt{L/4\pi \sigma \epsilon T^4}$</span>, proportional to <span class="math-container">$\sqrt{L}$</span>. The life zone is given by the range where <span class="math-container">$T$</span> allows liquid water. In practice this is more complex and fuzzy since it all depends on complex atmospheric properties, but as a first approximation it feels OK.)</p>

CC BY-SA 4.0
2019-08-28T07:55:39.903Z
2019-08-28T09:05:13.853Z
2019-08-28T09:05:13.853Z
Anders Sandberg
<p>Astrobiologists looking for signs of life outside Earth usually take excitement over planets orbiting red giant stars because a larger, brighter star usually means a farther-away but still wider habitable zone, a slice of space where liquid water would be possible.</p>

<p>To put this in perspective, a single red giant can have a luminosity ranging anywhere between 1,000 and 10,000 times brighter than our sun.  Would that mean that a habitable zone in a solar system orbiting only one red giant would be 1,000 to 10,000 times as wide as our own?</p>

<luminosity><habitable-zone><red-giant>
How Wide Would the Habitable Zone Be in a Singular Red Giant System?
JohnWDailey
# How Wide Would the Habitable Zone Be in a Singular Red Giant System?

(Asked by: username_0 on 2019-08-28)

Astrobiologists looking for signs of life outside Earth usually take excitement over planets orbiting red giant stars because a larger, brighter star usually means a farther-away but still wider habitable zone, a slice of space where liquid water would be possible.

To put this in perspective, a single red giant can have a luminosity ranging anywhere between 1,000 and 10,000 times brighter than our sun. Would that mean that a habitable zone in a solar system orbiting only one red giant would be 1,000 to 10,000 times as wide as our own?

**Tags:** luminosity, habitable-zone, red-giant

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## 1 answers

### Answer by username_1 on 2019-08-28. Score: 1

Habitable zones have a width that scales as the square root of the luminosity. So a 10000 solar luminosity star will have a zone about 100 times wider.

However, the temporal width is another thing: the luminosity changes relatively fast, so planets will not be in the zone over long timescales.

(The reason for the square root dependence is that a piece of surface at semimajor axis $a$ gets $L/4\pi a^2$ Watt of incoming energy, and if a blackbody with emissivity $\epsilon$ radiates away $\sigma \epsilon T^4$. Energy balance gives $L/4\pi a^2 = \sigma \epsilon T^4$, or rearranged, $a = \sqrt{L/4\pi \sigma \epsilon T^4}$, proportional to $\sqrt{L}$. The life zone is given by the range where $T$ allows liquid water. In practice this is more complex and fuzzy since it all depends on complex atmospheric properties, but as a first approximation it feels OK.)


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