<p>I've been interested in exomoons for a while as well, and having read multiple studies (I admit I only fully read about two), I don't recall seeing any mention of Van-Allen belts being an issue. The most commonly mentioned threat to life was a runaway greenhouse due to extra heating from the host, whether from tidal forces, planetshine (the heat from the star reflecting from its surface), or both. It seems generally agreed that:</p>
<ol>
<li>A moon must orbit about a distance of 10 times the host's radius in order to be safe from additional tidal heating;</li>
<li>The moon's orbit must not be too eccentric, or it will slowly spiral into its host due to tidal braking.</li>
<li>The habitable zone around the actual star will be slightly larger. This moon-habitable zone (which I like to arbitrarily name &quot;MHZ&quot;) varies depending on the study, but one from July 2022 (&quot;A target list for searching for habitable exomoons&quot;) refers to &quot;Pierrehumbert 2010, Chapter 4&quot; for the inner limit, and &quot;Kopparapu et al. 2014&quot; for the outer limit. I should add that it doesn't seem like the greenhouse potential of hydrogen (and thus a larger habitable zone) is considered here.</li>
</ol>
<blockquote>
<p>An exomoon is considered habitable, if the global heating flux of
the moon is between the runaway greenhouse (RG) and maximum
greenhouse fluxes (MG). The runaway greenhouse flux was calculated with a method that is dependent on the surface gravity of the
exomoon (Pierrehumbert 2010, Chapter 4). The advantage of this
method is that the runaway greenhouse flux scales with the radius
and the mass of the body. This is in contrast to the standard calculation method described by Kopparapu et al. (2014), in which the
calculations only apply to certain masses and radii. It was shown,
however, that the outer boundary of the circumstellar habitabile zone
has a weak dependence on the mass of the exomoon (Kopparapu et al.
2014), and for this reason, the maximum greenhouse limit described
by Kopparapu et al. (2014) was used as a lower limit for habitability.</p>
</blockquote>
<p><a href="https://i.sstatic.net/57dwt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/57dwt.png" alt="&quot;Contours of summed absorbed stellar irradiation and tidal heating (in logarithmic units of W/m2) as a function of semimajor axis aps and eccentricity eps on an Earth-like (upper row) and a Super-Ganymede (lower row) exomoon. In the left panels, the satellite orbits a Jupiter-like planet, in the right panels a Neptune-mass planet, in both cases at 1 AU from a Sun-like host star. In the white area at the right, tidal heating is negligible and absorbed stellar flux is 239 W/m2. The right-most contours in each panel indicate Io's tidal heat flux of 2 W/m2, a tidal heating of 10 W/m2, and the critical flux for the runaway greenhouse (295 W/m2 for the Earth-like moon and 243 W/m2 for the Super-Ganymede).&quot; - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/" /></a></p>
<p>EDIT: looks like the description I gave for the image above hasn't been included. This is from a DIFFERENT study.</p>
<blockquote>
<p>&quot;Contours of summed absorbed stellar irradiation and tidal heating (in
logarithmic units of W/m2) as a function of semimajor axis aps and
eccentricity eps on an Earth-like (upper row) and a Super-Ganymede
(lower row) exomoon. In the left panels, the satellite orbits a
Jupiter-like planet, in the right panels a Neptune-mass planet, in
both cases at 1 AU from a Sun-like host star. In the white area at the
right, tidal heating is negligible and absorbed stellar flux is 239
W/m2. The right-most contours in each panel indicate Io's tidal heat
flux of 2 W/m2, a tidal heating of 10 W/m2, and the critical flux for
the runaway greenhouse (295 W/m2 for the Earth-like moon and 243 W/m2
for the Super-Ganymede).&quot; -
<a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/" rel="nofollow noreferrer">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/</a></p>
</blockquote>

CC BY-SA 4.0
2023-09-19T17:17:11.010Z
I am sorry, but this ultimately doesn't answer my question as it is mostly saying "a range does exist", without supplying a said range, or giving me a way for me to find it myself. Can you please try to provide how I would find it? I have the mass and radius of both bodies. Those graphs are also very poorly labled, but that is more of a criticism of the people maing the paper. Edit: Wait, I missed the 10x the host radius.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T17:23:36.407Z
But also everything I find says even Europa is so close to Jupiter that it would recieve a very strong dose of radiation. To the extent that it literally glows.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T17:40:54.050Z
@DanceroftheStars I know, I saw that too. I think it's just because Europa is already below the 10-radius limit, *and* it's not massive enough to host *surface* life (which is normally what's being considered). I imagine the 10r limit is meant to account for radiation belts as well.
Kazon
CC BY-SA 4.0
2023-09-19T17:43:56.893Z
I see, thank you for your help. It is much appreciated.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T17:44:22.777Z
@DanceroftheStars As for your first comment (and I am grateful for the courtesy there!), I agree that it's not easy to understand if you don't know what you're looking at. 

The graph is logarithmic in both axes: basically, the bars between 1 and 10 are 2, 3, 4, etc., but after 10, it's 20, 30, 40 (or, with Y, 0.001, 0.002, etc., then 0.01...). "Rp" is the distance from the host in parent radii (Radius planet). 

The Y axis is the flux that the moon will experience, which can be understood as how much heat it will get.
Kazon
CC BY-SA 4.0
2023-09-19T17:50:26.210Z
Note, I actually looked it up, Europa's orbital radius is 15.44x the radius of Jupiter. So I feel that R should be more than 10x. As even 15x doesn't seem to be enough.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T17:52:37.380Z
@DanceroftheStars Where did you find that? Europa's orbit is an average of about 670,000km, whereas Jupiter's radius is 69,911km.
Kazon
CC BY-SA 4.0
2023-09-20T01:42:26.350Z
I meant Ganymede, I think. Which is around 15.31x doing the math again. Ganymede would still kill you in a few months at 50-80 mSv (5-8 rem) a day. Despite being 15.31 Jupiter radii. Which leaves me concerned by moon at 10x would be even deadlier.
DanceroftheStars
CC BY-SA 4.0
2023-09-20T01:53:31.207Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/148637/discussion-between-dancerofthestars-and-kazon).
DanceroftheStars
CC BY-SA 4.0
2023-09-19T17:06:10.440Z
2023-09-19T17:06:10.440Z
Kazon
<p>I am woring on creating a fictional star system, and I need to find an answer to a question to find an accurate way to depict this.</p>
<p>I am aware that Gas Giants create a dangerous field of radiation around themselves that would be harmful to anyone within a certain radius. I now my moon has to be within the Hill Sphere, which sets a solid outer boundary. But my question is, how would I find how far away my moon should be in order to properly maintain an atmosphere and be habitable, not being effected by the radiation to a harmful degree.</p>
<p>I don't need an exact number given, I moreso just need help finding out how I would calcualte the required distance to be able to remain safe. If any sort of formula or way to calculate it exists at all. But it would also be helpful and appreciated if you would do more help to find the numbers as well.</p>
<p>My parametres currently are around 5.9441197891 Jupiter Masses and 1.81 Jupiter Radii -1. (Please tell me if this isn't reasonable). How would I be able to find how far a moon would have to be in order to be habitable, have a atmosphere, and not be basked in deadly radiation.</p>
<p>Your help is much appreciated.</p>
<ol>
<li>I found these numbers by just choosing a radius of 1.81, and
finding what mass it would have to be to have the same density as
Jupiter. And found it was ~5.9441197891. This is likely wrong as
density of larger gas giants likely changes. Although it could also
be reasonable as, looking at lists, density seems to have a very
large range. It also likely would be different as it is closer to
the star than Class I gas giants.</li>
</ol>

CC BY-SA 4.0
2023-09-19T15:57:01.707Z
There is no general theory about the radiation belts of gas giants.
ProfRob
CC BY-SA 4.0
2023-09-19T16:19:29.223Z
I'd expect that the strength of the radiation field and belt depends a lot on the gas giant's magnetic field which very likely is tied to its rotation speed. Assuming a slow rotator (for whatever reason) might make an assumption of a small or less harmful radiation belt more likely
planetmaker
CC BY-SA 4.0
2023-09-19T18:29:34.140Z
Cold gas giants don't get much larger in radius than Jupiter, they just get denser. (Hot gas giants are a bit less dense). See https://astronomy.stackexchange.com/q/15066/16685
PM 2Ring
CC BY-SA 4.0
2023-09-19T18:36:17.803Z
There are a lot of particles in [Jupiter's magnetosphere](https://en.wikipedia.org/wiki/Magnetosphere_of_Jupiter) because of Io. (Of course, it also grabs a lot of material from the solar wind). However, it seems reasonably likely that a planet more massive than Jupiter will have a similar tidally stressed moon that spews out particles.
PM 2Ring
<mathematics><magnetic-field><gas-giants><radiation>
On the Radiation Field of large Gas Giants
DanceroftheStars
# On the Radiation Field of large Gas Giants

(Asked by: username_0 on 2023-09-19)

I am woring on creating a fictional star system, and I need to find an answer to a question to find an accurate way to depict this.

I am aware that Gas Giants create a dangerous field of radiation around themselves that would be harmful to anyone within a certain radius. I now my moon has to be within the Hill Sphere, which sets a solid outer boundary. But my question is, how would I find how far away my moon should be in order to properly maintain an atmosphere and be habitable, not being effected by the radiation to a harmful degree.

I don't need an exact number given, I moreso just need help finding out how I would calcualte the required distance to be able to remain safe. If any sort of formula or way to calculate it exists at all. But it would also be helpful and appreciated if you would do more help to find the numbers as well.

My parametres currently are around 5.9441197891 Jupiter Masses and 1.81 Jupiter Radii -1. (Please tell me if this isn't reasonable). How would I be able to find how far a moon would have to be in order to be habitable, have a atmosphere, and not be basked in deadly radiation.

Your help is much appreciated.

1. I found these numbers by just choosing a radius of 1.81, and
   finding what mass it would have to be to have the same density as
   Jupiter. And found it was ~5.9441197891. This is likely wrong as
   density of larger gas giants likely changes. Although it could also
   be reasonable as, looking at lists, density seems to have a very
   large range. It also likely would be different as it is closer to
   the star than Class I gas giants.

**Tags:** mathematics, magnetic-field, gas-giants, radiation

> **Comments:**
> **username_1**: There is no general theory about the radiation belts of gas giants.  
> **username_2**: I'd expect that the strength of the radiation field and belt depends a lot on the gas giant's magnetic field which very likely is tied to its rotation speed. Assuming a slow rotator (for whatever reason) might make an assumption of a small or less harmful radiation belt more likely  
> **username_3**: Cold gas giants don't get much larger in radius than Jupiter, they just get denser. (Hot gas giants are a bit less dense). See https://astronomy.stackexchange.com/q/15066/16685  
> **username_3**: There are a lot of particles in [Jupiter's magnetosphere](https://en.wikipedia.org/wiki/Magnetosphere_of_Jupiter) because of Io. (Of course, it also grabs a lot of material from the solar wind). However, it seems reasonably likely that a planet more massive than Jupiter will have a similar tidally stressed moon that spews out particles.  

---

## 1 answers

### Answer by username_4 on 2023-09-19. Score: 3

I've been interested in exomoons for a while as well, and having read multiple studies (I admit I only fully read about two), I don't recall seeing any mention of Van-Allen belts being an issue. The most commonly mentioned threat to life was a runaway greenhouse due to extra heating from the host, whether from tidal forces, planetshine (the heat from the star reflecting from its surface), or both. It seems generally agreed that:

1. A moon must orbit about a distance of 10 times the host's radius in order to be safe from additional tidal heating;
2. The moon's orbit must not be too eccentric, or it will slowly spiral into its host due to tidal braking.
3. The habitable zone around the actual star will be slightly larger. This moon-habitable zone (which I like to arbitrarily name "MHZ") varies depending on the study, but one from July 2022 ("A target list for searching for habitable exomoons") refers to "Pierrehumbert 2010, Chapter 4" for the inner limit, and "Kopparapu et al. 2014" for the outer limit. I should add that it doesn't seem like the greenhouse potential of hydrogen (and thus a larger habitable zone) is considered here.

> An exomoon is considered habitable, if the global heating flux of
> the moon is between the runaway greenhouse (RG) and maximum
> greenhouse fluxes (MG). The runaway greenhouse flux was calculated with a method that is dependent on the surface gravity of the
> exomoon (Pierrehumbert 2010, Chapter 4). The advantage of this
> method is that the runaway greenhouse flux scales with the radius
> and the mass of the body. This is in contrast to the standard calculation method described by Kopparapu et al. (2014), in which the
> calculations only apply to certain masses and radii. It was shown,
> however, that the outer boundary of the circumstellar habitabile zone
> has a weak dependence on the mass of the exomoon (Kopparapu et al.
> 2014), and for this reason, the maximum greenhouse limit described
> by Kopparapu et al. (2014) was used as a lower limit for habitability.

[!["Contours of summed absorbed stellar irradiation and tidal heating (in logarithmic units of W/m2) as a function of semimajor axis aps and eccentricity eps on an Earth-like (upper row) and a Super-Ganymede (lower row) exomoon. In the left panels, the satellite orbits a Jupiter-like planet, in the right panels a Neptune-mass planet, in both cases at 1 AU from a Sun-like host star. In the white area at the right, tidal heating is negligible and absorbed stellar flux is 239 W/m2. The right-most contours in each panel indicate Io's tidal heat flux of 2 W/m2, a tidal heating of 10 W/m2, and the critical flux for the runaway greenhouse (295 W/m2 for the Earth-like moon and 243 W/m2 for the Super-Ganymede)." - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/](https://i.sstatic.net/57dwt.png)](https://i.sstatic.net/57dwt.png)

EDIT: looks like the description I gave for the image above hasn't been included. This is from a DIFFERENT study.

> "Contours of summed absorbed stellar irradiation and tidal heating (in
> logarithmic units of W/m2) as a function of semimajor axis aps and
> eccentricity eps on an Earth-like (upper row) and a Super-Ganymede
> (lower row) exomoon. In the left panels, the satellite orbits a
> Jupiter-like planet, in the right panels a Neptune-mass planet, in
> both cases at 1 AU from a Sun-like host star. In the white area at the
> right, tidal heating is negligible and absorbed stellar flux is 239
> W/m2. The right-most contours in each panel indicate Io's tidal heat
> flux of 2 W/m2, a tidal heating of 10 W/m2, and the critical flux for
> the runaway greenhouse (295 W/m2 for the Earth-like moon and 243 W/m2
> for the Super-Ganymede)." -
> <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/>

> **Comments:**
> **username_0**: I am sorry, but this ultimately doesn't answer my question as it is mostly saying "a range does exist", without supplying a said range, or giving me a way for me to find it myself. Can you please try to provide how I would find it? I have the mass and radius of both bodies. Those graphs are also very poorly labled, but that is more of a criticism of the people maing the paper. Edit: Wait, I missed the 10x the host radius.  
> **username_0**: But also everything I find says even Europa is so close to Jupiter that it would recieve a very strong dose of radiation. To the extent that it literally glows.  
> **username_4**: @username_0 I know, I saw that too. I think it's just because Europa is already below the 10-radius limit, *and* it's not massive enough to host *surface* life (which is normally what's being considered). I imagine the 10r limit is meant to account for radiation belts as well.  
> **username_0**: I see, thank you for your help. It is much appreciated.  
> **username_4**: @username_0 As for your first comment (and I am grateful for the courtesy there!), I agree that it's not easy to understand if you don't know what you're looking at.   The graph is logarithmic in both axes: basically, the bars between 1 and 10 are 2, 3, 4, etc., but after 10, it's 20, 30, 40 (or, with Y, 0.001, 0.002, etc., then 0.01...). "Rp" is the distance from the host in parent radii (Radius planet).   The Y axis is the flux that the moon will experience, which can be understood as how much heat it will get.  
> **username_0**: Note, I actually looked it up, Europa's orbital radius is 15.44x the radius of Jupiter. So I feel that R should be more than 10x. As even 15x doesn't seem to be enough.  
> **username_4**: @username_0 Where did you find that? Europa's orbit is an average of about 670,000km, whereas Jupiter's radius is 69,911km.  
> **username_0**: I meant Ganymede, I think. Which is around 15.31x doing the math again. Ganymede would still kill you in a few months at 50-80 mSv (5-8 rem) a day. Despite being 15.31 Jupiter radii. Which leaves me concerned by moon at 10x would be even deadlier.  
> **username_0**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/148637/discussion-between-username_0-and-username_4).  

---

