# How much mass is lost in the red giant phase of a star?

The red giant phase of stars are relatively fast. How will this impact a star's total mass? Are there significant mass losses taking place when this happens? If so, do we know how much? The sizes of red giants varies a lot so there obviously can't be an exact value, but maybe there is a specific percentage figure - say, 30% mass lost during the red giant phase.

• What do you mean by "mass loss"? Are you asking about the mass lost to fusion, or about the mass lost due to material being expelled by the star? Nov 3, 2021 at 8:58
• @David Hammen. Any kind of loss I suppose. But wouldn’t it more apply to the latter. I am not sure if fusion still is taking place. Is it? Nov 3, 2021 at 9:01
• main sequence and later stars undergo nuclear fusion throughout their lives. Stars also lose mass due to stellar winds throughout their lives. Stars can also lose mass due to mass transfer. You'll want to think about what you want to know first, then you'll know better what you need to ask here. Nov 3, 2021 at 9:39
• @Constantthin Unlike neutron stars, white dwarfs, and black holes, which in my mind are ex-stars that are pining for the fjords, red giants are stars in the sense that fusion is still occurring within them. This fusion can occur in several forms. Stars on the red giant branch fuse hydrogen into helium in a thin shell surrounding a non-fusing helium core. Stars on the red clump branch and the horizontal branch have a core that fuses helium into carbon and oxygen, surrounded by a shell that fuses hydrogen into helium. And now I'm out of my league and am awaiting ProfRob's definitive answer. Nov 3, 2021 at 9:57
• Regarding my use of "pining for the fjords", I suggest you google that term, or the related term "Norwegian Blue". Nov 3, 2021 at 9:57

The exact amount is not known - because the details of mass-loss in the later stages of a star's life are not well understood - but about $$0.47M_\odot$$.

Details

We can still attempt to answer the question by asking what is the relationship between the initial mass of a (low-mass) star and the white dwarf that it leaves behind at the end of its life. Most of the difference between these two numbers is mass lost during the first ascent and asymptotic red giant branches. The mass lost due to nuclear fusion and the solar wind during the main sequence phase should be a relatively small adjustment to this (see below).

The plot below is the "initial-final mass relation" derived by observing white dwarfs in clusters (with known age) and using cooling calculations to work out how long they have been cooling and therefore how long their main sequence progenitor spent on the main sequence, and hence the progenitor mass.

From this we see that the Sun is likely to leave a $$0.53 \pm 0.03 M_\odot$$ white dwarf. It must therefore lose about $$0.47 M_\odot$$ during its time as a red giant, minus the mass it loses as a main sequence star between now and when it becomes a red giant.

We can get a rough estimate of the mass lost on the main sequence by talking the current solar luminosity and mass loss and assuming they are reasonable averages over the 12 billion years or so that the Sun is on the main sequence. Converting the solar luminosity to a mass loss rate and multiplying by 12 billion years we get $$8\times 10^{-4}M_\odot$$. The current solar mass-loss rate via its wind is about $$3\times 10^{-14} M_\odot$$ per year, so over 12 billion years the Sun would lose just $$4\times 10^{-4}M_\odot$$. Thus $$<0.01 M_\odot$$ is lost during main sequence evolution.

Thus the basic answer is $$0.47M_\odot$$ with an uncertainty of perhaps 10%.

The plot can be used in a similar way to estimate how much mass is lost during the red giant phase of stars of higher mass too. The fraction of mass lost in evolving to the white dwarf stage is much higher for larger initial masses.