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When stars run out of hydrogen, they explode (though they also use heavier elements for some time) and form nebulae. In the nebulae, new stars are born which use hydrogen as their fuel.

So, my question is from where do these new stars get hydrogen for their fuel?

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Stars only burn hydrogen in their core, where the temperature gets high enough for nuclear reactions to occur. They end their lives when they run out of fuel in the core, but lots of hydrogen still exists in their envelopes.

The Sun will burn 5-10% of its mass before exhausting its core. When this happens, the core will contract due to the radiation pressure disappearing. It then starts to burn hydrogen in a shell around the core. Eventually, when the Sun dies, it will have burned less than half of its hydrogen. Larger stars burn an even smaller fraction.

This means that, when stars die they still leave hydrogen behind for the next generation.

Galaxies can still run of of gas, though. Since after all, each $M_\odot$ of star formed burns of the order of $1\,M_\odot$, if a galaxy isn't fueled with new gas it will become depleted on a timescale of order $1$ over its specific star formation rate sSFR, which is its star formation rate SFR measured in Solar masses per year, divided by its stellar mass $M_*$ in Solar masses: $$ t_\mathrm{depl} \sim \frac{1}{\mathrm{sSFR}}=\frac{M_*/M_\odot}{\mathrm{SFR}/M_\odot\,\mathrm{yr}^{-1}}. $$ For instance, a $10^9\,M_\odot$ galaxy with a star formation rate of $10\,M_\odot\,\mathrm{yr}^{-1}$ will become depleted of gas in roughly $10^8$ years.

Gas-depleted galaxies do exist, and the more depleted they are, the lower the star formation rate is (e.g. Rose et al. 2010), but in general the timescale is longer than the above, since galaxies also accrete gas from the surrounding circumgalactic medium.

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  • $\begingroup$ got this one, but still have a bit of confusion. When stars run out of hydrogen in their core, why don't they simply exchange heavier gases with the envelope, like simple diffusion? $\endgroup$ – another 'Homo sapien' Feb 10 '16 at 13:32
  • $\begingroup$ I think this should be posted as a separate question, but briefly: They do to some extend. Stellar interiors are divided into regions of energy transport dominated by radiation and convection, respectively. Depending on their mass, the relative size of these regions differ, and will also change during their life. For the Sun, the inner ~2/3 have radiative transport, whereas the outer ~1/3 has convection. When it has depleted its core of hydrogen, the convection zone will start reaching deep into the radiative zone, resulting in the so-called "dredge-up" which mixes gas from the zone. $\endgroup$ – pela Feb 10 '16 at 14:23
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    $\begingroup$ @aayushsrivastav Simple diffusion results in heavier elements sinking to the core and thus does not provide more hydrogen fuel - quite the opposite. $\endgroup$ – Rob Jeffries Feb 10 '16 at 14:36

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