# Are stars getting more metal-rich, less massive and shorter-lived with cosmic time?

A star produces energy through nuclear fusion with the 2H and 3H isotopes to create 4He for example. I read that there is a mass loss of 0.018884 (in atomic mass units).

Of course this mass loss is turned into energy ($E=Mc^2$). So, the amount of mass when the star was young and its mass when it is about to die are different. So, when this star does eventually die and disperse all its matter there is less matter than when the star started with, and in other words this means there is less 'material' or building blocks to form other stars.

Wouldn't this point towards the idea that stars are getting smaller with the slowly decreasing matter count in the universe to make them? I would also predict that stars would be getting more and more 'metal rich' and it can be seen with the patterns of population star groups: http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/pop12.html

Lastly, if stars are getting more and more 'metal rich' does this mean they die younger and are ever increasingly dying younger until they are too unstable at birth to 'live' any significant life?

## 3 Answers

There are lots of questions here, let's take them one at a time.

Are star getting less massive as a result of nuclear fusion?

Yes. If a star has a luminosity $L$ then this corresponds to a mass change $c^2 dM/dt$. For the Sun $L = 3.83\times10^{26}$ W, so the Sun is getting less massive at a rate of 4 million tonnes per second. However, over the Sun's main sequence lifetime of $10^{10}$ years, this amounts to a decrease of only $6.7\times 10^{-4}$ solar masses. Later stages of nuclear burning result in a more luminous Sun, but these phases are also much shorter, so the overall effect on the Sun's mass is similar.

In contrast, the solar wind has a mass loss rate of $\sim 2 \times 10^{-14}$ $M_{\odot}$/yr (but may have been much stronger in the past). This means that the mass lost in a wind and the mass lost by nuclear fusion are comparable over the main sequence lifetime. However, in later stages of the Sun's life it will lose some tenths of a solar mass during the red giant and asymptotic giant branch phases due to a radiatively driven dusty wind.

Something similar is true for most stars: averaged over their lives the mass lost in nuclear fusion is negligible compared to the mass loss they experience as a result of direct loss from stellar winds, and is also a very small fraction (less than 0.1%) of the original mass of the star.

Are stars getting less massive on average with time

Possibly, but it is very difficult to tell. When we look at old populations of stars then they do not contain massive stars because they have lived their lives and died. But I guess what you mean is whether the mass spectrum at star birth is shifted towards lower masses?

There is certainly theoretical evidence that the earliest metal-poor stars could be built to have very high masses - the so-called population III stars. Once metals are present in the gas then radiation pressure due to the gas opacity prevents the construction of very massive ($>200 M_{\odot}$) stars.

Further down the mass spectrum the evidence for any variations in the so-called "Initial mass function" with time is weak or absent. The conclusion of a big review by Bastian, Covey & Meyer (2010) is that there is no evidence for any variation "over cosmic time".

Are stars getting more metal rich?

Yes. All elements heavier than He (bar traces of Li and Be) are mostly produced inside stars. Therefore the stellar "ecological cycle" of birth and death results in an overall increase in the metal-richness of the interstellar medium and hence the stars that are then produced. To understand exactly the rate at which this occurs requires a complex "galactic chemical evolution model".

It turns out that most of the increase in metallicity (in our Galaxy) occurred very early on - between 8 and 12 billion years ago; when the star formation rate was much higher and the rate of production of massive stars and supernovae was probably an order of magnitude higher than it is now. As a result, the rate of increase of metallicity now is much smaller. The 4.5 billion year old Sun has a similar metallicity to stars that are being produced in the solar neighbourhood right now.

Let's also put this into context. Even after about 12 billion years of star formation and stellar death, the metallicity of the interstellar medium still only consists of order 2% by mass of elements heavier than helium.

Do more metal-rich star die younger?

No, quite the contrary. At a fixed mass one can show that the luminosity on the main sequence relates to metal mass fraction $Z$, as $L \propto Z^{-1/6}$. i.e. High metallicity stars have a lower luminosity than more metal-poor stars of the same mass. As the fuel supply is dominated by hydrogen, and as a mass fraction this is very similar in both metal-rich and metal-poor stars, then the lifetimes of metal-rich stars are longer. e.g. see Figs 1 and 2 of this paper by Bazan & Mathews (1990).

• Wow i always assumed that metal-rich stars die younger. My initiation idea/question that new stars are smaller because of less 'materials' to create them seems to be answered thank you. Would this lack of materials maybe point towards a decreasing rate of star formations in the universe though? – Hatmix5 Nov 20 '14 at 6:04
• @Hatmix5 There isn't a lack of materials. The decrease in star formation rate in our Galaxy (and others) is more to do with the metallicity and density of the ISM. – Rob Jeffries Nov 20 '14 at 7:18

Firstly, you are correct in assuming that the stars will lose mass as time passes. However, a star's density will be nowhere near constant in their stellar timeline. The size of a star depends on several factors: temperature, density, composition, etc. So it would be hard to answer your question given no constraints. Secondly, you are also correct in asserting that stars will be more 'metal-rich'. Astronomers have found both by observation and calculation that stars will become more metal-rich (i.e. their metallicity will increase) as time passes.

• I always thought that the size of a star is determined by the force of gravity pulling in trying to make the star as small as possible and the outward force from the radiation created in the core of the sun trying to 'swell it up' in a way. And i just assumed the more matter used in creating the star would effect both of these forces.. – Hatmix5 Sep 6 '14 at 9:14
• @NickI: yes, but the amount of radiation the star produces changes during its lifetime. – John Rennie Sep 6 '14 at 9:48
• So what would the radiation be dependent on? – Hatmix5 Sep 6 '14 at 9:50
• @Nikki The amount of radiation depends on what is reacting, temperature, density, composition, etc. BTW, our sun will eventually expand out to near the Earth's orbit in about 5 billion years. – LDC3 Sep 6 '14 at 14:06
• Hmm, yes the Red giant. I wouldn't like to include this into the question seeing it is only in the special case when He is fueling the star when this happens (well i think). I do have the last question or idea: Will the life span of newly born stars slowly get smaller and smaller with it getting more and more metal rich. Thus in a very long time stars will be too metal rich to function properly for a significant amount of time? – Hatmix5 Sep 6 '14 at 23:17

Well, stars do loose mass over the course of their lifetime. And during the course of a star's lifetime it will go through several stages generating heavier materials.

However there is a minimum mass for a star. Below this mass the star does not achieve high enough temperaturs to ignite nuclear fusion. Objects below this critical mass are called "brown dwarves".

I'm not aware of any studies that have shown a general decrease in stellar mass as the universe ages. I would wager that there is enough hydrogen and helium left to ignite pretty massive stars.