<p>The contraction timescale of protostars towards a stable configuration where they &quot;burn&quot; hydrogen (the zero age main sequence, ZAMS) is governed by the rate at which the released gravitational potential energy can be radiated.
Thus the timescale is of order
<span class="math-container">$$\tau \sim \frac{GM^2}{RL}\ ,$$</span>
where <span class="math-container">$M$</span>, <span class="math-container">$R$</span>, <span class="math-container">$L$</span> are the mass, radius and luminosity of the protostar.</p>
<p>For a protostar of fixed mass, the radius and luminosity will only decline with time, so the overall formation time is dominated by the final stages of contraction.</p>
<p>For a high mass star, the interior becomes so hot that it becomes more transparent to photons and the transfer of energy out of the centre is dominated by radiation. The star contracts at an almost constant luminosity, that is similar to it's luminosity at the ZAMS, with <span class="math-container">$L\propto M^{3.5}$</span>. The high mass dependence of the luminosity ensures that at any given radius, a higher mass protostar is contracting much more quickly <span class="math-container">$(\tau \propto M^{-1.5})$</span>.</p>
<p>Lower mass protostars are cooler inside and more opaque. The rate at which energy can be transported outwards is limited by convection. The protostars contract at almost constant surface temperature, which means their luminosities fall and the contraction timescales lengthen considerably. As they approach the ZAMS they have <span class="math-container">$L\propto M^{-3.5}$</span> like higher mass main sequence stars and <span class="math-container">$R \propto M$</span> and thus contraction timescales that go as <span class="math-container">$M^{-0.5}$</span> and thus lower mass objects reach the ZAMS later.</p>

CC BY-SA 4.0
2024-05-13T07:40:04.890Z
2024-05-13T07:40:04.890Z
ProfRob
<p>I understand that larger mass stars form faster than lower mass stars. After doing research, I found it was because they got heated faster. But wouldn't this slow down the process as the higher luminosity would blow the material away? Is there another reason I didn't find?</p>

<star><star-formation>
Why do larger mass stars form quicker?
Astrovis
# Why do larger mass stars form quicker?

(Asked by: username_0 on 2024-05-13)

I understand that larger mass stars form faster than lower mass stars. After doing research, I found it was because they got heated faster. But wouldn't this slow down the process as the higher luminosity would blow the material away? Is there another reason I didn't find?

**Tags:** star, star-formation

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## 1 answers

### Answer by username_1 on 2024-05-13. Score: 10 | Accepted answer

The contraction timescale of protostars towards a stable configuration where they "burn" hydrogen (the zero age main sequence, ZAMS) is governed by the rate at which the released gravitational potential energy can be radiated.
Thus the timescale is of order
$$\tau \sim \frac{GM^2}{RL}\ ,$$
where $M$, $R$, $L$ are the mass, radius and luminosity of the protostar.

For a protostar of fixed mass, the radius and luminosity will only decline with time, so the overall formation time is dominated by the final stages of contraction.

For a high mass star, the interior becomes so hot that it becomes more transparent to photons and the transfer of energy out of the centre is dominated by radiation. The star contracts at an almost constant luminosity, that is similar to it's luminosity at the ZAMS, with $L\propto M^{3.5}$. The high mass dependence of the luminosity ensures that at any given radius, a higher mass protostar is contracting much more quickly $(\tau \propto M^{-1.5})$.

Lower mass protostars are cooler inside and more opaque. The rate at which energy can be transported outwards is limited by convection. The protostars contract at almost constant surface temperature, which means their luminosities fall and the contraction timescales lengthen considerably. As they approach the ZAMS they have $L\propto M^{-3.5}$ like higher mass main sequence stars and $R \propto M$ and thus contraction timescales that go as $M^{-0.5}$ and thus lower mass objects reach the ZAMS later.


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