Red dwarf stars are by far the most common stars in the galaxy and they have masses ranging from 0.08 to 0.4 times the mass of the Sun. 0.08 times the mass of the Sun is just about the lowest possible mass a star can have and still be able to sustain hydrogen fusion within its core. The least massive red dwarf stars shine at only 0.01 percent the luminosity of the Sun while the most massive ones do not exceed 10 percent the luminosity of the Sun.
Assuming that the lifespan of a star is the total duration in which it is able to sustain nuclear fusion reactions, the lowest mass red dwarf stars can have lifespans that exceed 10 trillion years. In comparison, the current age of the universe is a mere 13.7 billion years and the estimated lifespan of the Sun is just 12 billion years. At the current age of 13.7 billion years, all the red dwarf stars in the universe have only just begun their seemingly eternal existence.
One reason why red dwarf stars have such incredibly long lifespans when compared to more massive stars is because red dwarf stars have fully convective interiors and this means than almost all of the hydrogen within such stars is available for sustaining nuclear fusion within the cores of these stars. A more massive star such as the Sun has a mostly radiative interior and this means that only the hydrogen within the core of the Sun is available for nuclear fusion due to the absence of any convective mixing between the matter in the core with the matter in the overlying layers. The other reason for the longevity of red dwarf stars is that such stars burn their hydrogen via nuclear fusion at a much smaller rate than more massive stars.
In this article, we shall follow the evolution of a red dwarf star that has 0.1 times the mass of the Sun. It takes an estimated 2 billion years for this red dwarf star to contract from an initial cool cloud of hydrogen and helium to the point where is able to sustain hydrogen fusion within its core. At the onset of stable hydrogen fusion within its core, the newly formed red dwarf star will have a surface temperature of 2200 Kelvin and shine at 0.04 percent the luminosity of the Sun. Since the red dwarf star has a fully convective interior, almost all of its hydrogen is available to sustain the fusion reactions within its core. With 0.1 times the mass of the Sun, this red dwarf star is estimated to have a nuclear burning lifespan of over 6 trillion years. In fact, the current age of the universe is not even a quarter of a percent of the multi-trillion year lifespan of this red dwarf star.
At age zero, the mass of the red dwarf star is three quarters hydrogen and one quarter helium. Over the subsequent trillions of years, the red dwarf star will fuse hydrogen into helium within its core, gradually converting more of its fraction by mass into helium. The steady rise in the helium mass fraction of the red dwarf star increases the rate at which energy is being generated by nuclear fusion in the core of the star, causing the surface temperature and the overall luminosity of the star to also increase.
After 3.1 trillion years, the red dwarf star’s fraction of mass that is helium surpasses the fraction of mass that is hydrogen. At this point, the red dwarfs star will have a surface temperature of 2500 Kelvin and shine at 0.1 percent the luminosity of the Sun. As the red dwarf star crosses the age of 5.7 trillion years, over 85 percent of its mass will now be in the form of helium and this is the point where radiative transport of energy replaces convection in the core of the star. At this stage, the red dwarfs star will have a surface temperature of 3500 Kelvin and shine at 0.3 percent the luminosity of the Sun.
The creation of the radiative core within the red dwarfs star signifies the closing stages of its near eternal lifespan as the evolution of the star begins to accelerate. The core of the red dwarf star increases in mass via the buildup of helium as the remaining hydrogen undergoes fusion into helium in a shell surrounding the core which gradually moves outward through the star. During this process, the surface temperature and luminosity of the red dwarf star continues to increase until it eventually reached a maximum surface temperature of 5800 Kelvin and shines with just under one percent the luminosity of the Sun. In fact, the surface temperature of the red dwarf star is now slightly greater than the surface temperature of the Sun even though its overall luminosity is much lower due to its vastly smaller size compared to the Sun. At this stage, the red dwarf star is a far cry compared to what it initially was.
After the red dwarf star attains its maximum surface temperature, it beings to turn around and evolves towards a lower surface temperature and a lower luminosity. At this point, the red dwarf star is still producing energy by burning hydrogen into helium in a shell surrounding a large and inert helium core. The rate at which energy is being generated by the fusion of hydrogen into helium in the shell gradually diminishes and it is eventually extinguished at 540 billion years after the red dwarf star first develops its radiative core. At this point in time, the red dwarf star has a surface temperature of 1700 Kelvin and shines with 0.0005 percent the luminosity of the Sun, 80 times dimmer than its luminosity at birth. Since the onset of the radiative core occurs 5.7 trillion years into the lifespan of the red dwarf star, the total duration of nuclear burning within the star adds up to just over 6 trillion years.
The red dwarf star now ends its life as a low mass helium white dwarf star with a final mass fraction where 99 percent of it is helium with the remaining 1 percent being hydrogen. This final mass fraction shows the extraordinary efficiency in which the red dwarf star generates energy by burning its hydrogen into helium through nuclear fusion. In comparison, the Sun burns only 10 percent of its hydrogen throughout its entire lifespan.
A 6 trillion year lifespan is not the longest a red dwarf star can possibly have. In fact, a red dwarf star with 0.08 times the mass of the Sun has an estimated lifespan of 12 trillion years, making it twice as long as a red dwarf star with 0.1 times the mass of the Sun. In this incredibly distant future universe, the red dwarf star with 0.1 times the mass of the Sun has finally evolved into a white dwarf star. After many trillions of years of further cooling, this white dwarf star will eventually become a black dwarf where its surface temperature gets ever nearer to absolute zero.
Given that red dwarf stars make up the vast majority of stars in a galaxy and that these stars can live for trillions of years, most of the stellar evolution that will occur has yet to occur. In the far future universe, red dwarf stars will play an increasingly important role in contributing to the total luminosity of a galaxy as the rate of star formation decreases and as the more massive stars in the galaxy age and fade away. This is because the gradual increase in the luminosities of red dwarf stars nearly compensates the loss in luminosity as the rate of star formation declines and as the more massive stars fade away. This ultimately causes the total luminosity of the galaxy to remain fairly constant over trillions of years.