# Old star vs New star

We know that with the passage of time, hydrogen inside (near or at the core) a star is converted to helium and other heavy elements via fusion. We can then deduce that the old sun contains heavier elements in comparison to the new one. Does that mean that the mass of the old sun is more than the new sun?

• I think you mean "fusion" not "fission" – Steve Linton Jul 9 '18 at 19:32
• Not clear what you mean by "mean mass"? – ProfRob Jul 9 '18 at 22:40
• Is "mean" the "average"? Please edit to say either "Does that mean that the mass of the old sun...." or "Is the average mass of the particles of the old sun". – James K Jul 11 '18 at 6:11
• A star loses its total mass when evolves from many channels. Fusion combine light elements to heavier ones, implying that the total mass decreases. Stars also have stellar wind, or eruption, which expels some mass. In a binary system, a star can lose mass if its companion pulls the gas envelope. Or, it can gain the mass by accretion. – Kornpob Bhirombhakdi Jul 13 '18 at 14:05

The Sun's luminosity is about $L_{\odot}=4\times10^{26}\text{ J/s}$. Now, if we assume that the majority of that energy comes from nuclear fusion, we have $$L_{\odot}=\frac{dE}{dt}=\frac{d(mc^2)}{dt}=c^2\frac{dm}{dt}=c^2\dot{M}_{\text{nuc}}$$ Therefore, we can write the mass-loss due to nuclear fusion as $\dot{M}_{\text{nuc}}=L_{\odot}/c^2\sim4\times10^{9}\text{ kg/s}$.

Now, the Sun also loses mass via the solar wind. I believe the mass loss rate is a few times about $\dot{M}_{\text{wind}}\sim3\times10^{-14}M_{\odot}/\text{yr}\sim2\times10^9\text{ kg/s}$. Coronal mass ejections, solar flares and similar phenomena are often accounted for in this figure; at any rate, they don't add a significant amount.

This figure should increase as the Sun moves into the red giant (and especially asymptotic giant branch) phase of its life; it winds will increase to become much more significant that they are today. However, fusion will also increase, and the Sun's luminosity will increase by a factor of 1000 or 10000; therefore, the mass loss due to fusion will also increase. However, I think mass loss due to winds will increase more significantly, possibly by a factor of $\sim10^6$ - but I'll check that.

At any rate, an older star will have a lower mass than a younger star. For a Sun-like star, this would be hard to measure over the span of a human lifetime - remember that it only loses about $10^{-13}$ solar masses each year. Long-term records could make it possible, though, through various observations of the Sun and its effects. Centuries or millennia of data-gathering do tend to yield results.

• I changed "a few times $10^{14}$ solar masses each year" to "about $10^{-13}$ solar masses each year". If the Sun did indeed lose a few times $10^{14}$ solar masses each year, it would cease being the Sun in a few tens of nanoseconds. – David Hammen Jul 10 '18 at 8:45
• I've read elsewhere that the Sun is estimated to lose about $9.1\times10^{-14}$ solar masses per year, which comports nicely with this answer. This should be observable (or close to observable) due to the extremely high precision solar system ephemerides developed since the start of the space age, the moderately high precision solar system ephemerides developed since Kepler's time, and the records of solar eclipses that span almost three millennia. – David Hammen Jul 10 '18 at 8:55
• @DavidHammen Thanks for the edit; such timescales would not be consistent with our modern understanding of stellar evolution! I've also made my last paragraph slightly clearer, thanks to what you said. – HDE 226868 Jul 10 '18 at 13:21
• You say a newer star would have a lower mass... I think you mean higher – Steve Linton Jul 10 '18 at 16:59

The main fusion reaction converts four atoms of hydrogen into one atom of helium. The total mass of for hydrogen atoms is a little more than the mass of one helium atom, the difference being converted to energy. Thus the mass of the star goes down a bit as it fuses hydrogen. It actually goes down more due to matter being lost in the stellar wind, but both effects reduce the mass over time