<p>I know ordinarily a star's mass and radius tend to be proportional, so a 0.5 solar masses star tends to be about 0.5 solar radii and have a density of 4.82 g/cm³, 3.42 or about three and a half times the Sun's.</p>
<p>But, is it theoretically possible to have a main sequence star with 0.77 solar masses while still only being 0.54 solar radii?  This comes out to a density of 6.88 g/cm³, 4.88 or about five times the Sun's.</p>
<p>This represents a density 1.43 or about one and a half times denser than &quot;usual&quot;.</p>
<p>Can this happen in nature?</p>

CC BY-SA 4.0
2021-02-25T07:38:55.367Z
Is there any context to this question? Have such measurements been published, or is this purely hypothetical?
ProfRob
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2021-02-25T09:34:18.723Z
A stars mass and radii aren't quite proportional.   Also, the age of the star affects size.   The ratio is somewhat close, but I think it's inaccurate to think of it as proportional.   As for your scenario, a convective 0.77 solar mass star might in enough time, convert enough hydrogen to helium to shrink to that comparatively smaller size, while avoiding expansion at the end of the main sequence like our sun, but .77 might be a little high for that scenario. A little less mass and there's not enough time in the age of the universe. I think you're a bit outside the boundary of what's possible.
userLTK
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2021-02-25T21:52:22.870Z
@ProfRob The data points are purely hypothetical, but the concept of higher mass ratio than radius is the core of why I came up with those particular data points.
Xi-K
CC BY-SA 4.0
2021-02-25T21:54:47.940Z
@userLTK Interesting.. since stars are almost completely composed of hydrogen and helium, is there any known relationship between amount of hydrogen fuel used up as a percent of mass and temperature decline?  Like, is it a linear "half hydrogen used, half temperature decline" or is it less extreme?
Xi-K
CC BY-SA 4.0
2021-02-25T22:35:27.397Z
@userLTK main sequence stars of 0.77 solar masses get larger as they age. I think the answer is no.
ProfRob
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2021-02-26T01:31:42.053Z
@ProfRob Do you know what the mass threshold at which stars shrink as they age instead of grow is?
Xi-K
CC BY-SA 4.0
2021-02-26T08:18:51.157Z
I would think they need to be fully convective ($<0.3 M_{\odot}$) and the changes would take $10^{11}+$ years.
ProfRob
<star><mass><size><density>
Is is possible for a main sequence star to have 0.77 solar masses yet only be 0.54 solar radii?
Xi-K
# Is is possible for a main sequence star to have 0.77 solar masses yet only be 0.54 solar radii?

(Asked by: username_0 on 2021-02-25)

I know ordinarily a star's mass and radius tend to be proportional, so a 0.5 solar masses star tends to be about 0.5 solar radii and have a density of 4.82 g/cm³, 3.42 or about three and a half times the Sun's.

But, is it theoretically possible to have a main sequence star with 0.77 solar masses while still only being 0.54 solar radii? This comes out to a density of 6.88 g/cm³, 4.88 or about five times the Sun's.

This represents a density 1.43 or about one and a half times denser than "usual".

Can this happen in nature?

**Tags:** star, mass, size, density
> **Comments:**
> **username_1**: Is there any context to this question? Have such measurements been published, or is this purely hypothetical?  
> **username_2**: A stars mass and radii aren't quite proportional.   Also, the age of the star affects size.   The ratio is somewhat close, but I think it's inaccurate to think of it as proportional.   As for your scenario, a convective 0.77 solar mass star might in enough time, convert enough hydrogen to helium to shrink to that comparatively smaller size, while avoiding expansion at the end of the main sequence like our sun, but .77 might be a little high for that scenario. A little less mass and there's not enough time in the age of the universe. I think you're a bit outside the boundary of what's possible.  
> **username_0**: @ProfRob The data points are purely hypothetical, but the concept of higher mass ratio than radius is the core of why I came up with those particular data points.  
> **username_0**: @userLTK Interesting.. since stars are almost completely composed of hydrogen and helium, is there any known relationship between amount of hydrogen fuel used up as a percent of mass and temperature decline?  Like, is it a linear "half hydrogen used, half temperature decline" or is it less extreme?  
> **username_1**: @userLTK main sequence stars of 0.77 solar masses get larger as they age. I think the answer is no.  
> **username_0**: @ProfRob Do you know what the mass threshold at which stars shrink as they age instead of grow is?  
> **username_1**: I would think they need to be fully convective ($<0.3 M_{\odot}$) and the changes would take $10^{11}+$ years.  

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## 0 answers

