Frozen Stars

“As one great furnace flamed; yet from those flames

No light; but rather darkness visible”

- Paradise Lost by John Milton

In 1997, two astrophysicists, Fred Adams and Gregory Laughlin from the University of Michigan published a paper titled “A Dying Universe: The Long Term Fate and Evolution of Astrophysical Objects”. The paper outlines the long term fate of the universe based on what is currently known about the universe. In it, the authors investigate the evolution of planets, brown dwarfs, stars, black holes, galaxies and other astrophysical objects on timescales that vastly exceed the current age of the universe.

One particularly interesting type of astrophysical object mentioned in the paper is the idea of “frozen” stars. In the paper, the concept is described as follow: “The forthcoming metallicity increases may also decrease the mass of the minimum mass main sequence star as a result of opacity effects. Other unexpected effects may also occur. For example, when the metallicity reaches several times the solar value, objects with 0.04 solar mass may quite possibly halt their cooling and contraction and land on the main sequence when thick ice clouds form in their atmospheres. Such “frozen stars” would have an effective temperature of around ~273 K, far cooler than the current minimum mass main sequence stars. The luminosity of these frugal objects would be more than a thousand times smaller than the dimmest stars of today, with commensurate increases in longevity”.

In astronomy, the metallicity of an object is the proportion of its material that is comprised of elements heavier than hydrogen and helium. Basically, all elements heavier than hydrogen and helium are termed “metals”, a term that encompasses even elements such as carbon, oxygen, nitrogen and silicon. The Sun for example, has a metallicity of 0.02, implying that 2 percent of its mass is in the form of “metals”. In the beginning, the universe started out with only hydrogen (75 percent) and helium (25 percent). All “metals” found in the Sun were formed through nuclear fusion processes by generations of stars that preceded the Sun. The demise of these stars enriched the interstellar medium with “metals”. Subsequently, the Sun formed from one of these enriched interstellar clouds and acquires a higher metallicity than its predecessors.

Generations of stars come and go, steadily increasing the concentration of “metals” in the interstellar medium. A consequence of this is stars that form in the far future would have a much higher metallicity than stars today. The increase in metallicity lowers the minimum mass required for an object to sustain nuclear fusion in its core and become a star. Today, a star needs to have at least ~8 percent the Sun’s mass. Short of that, and it would be termed a brown dwarf instead of a star.

However, in the far future, objects formed from the interstellar medium can have several times the Sun’s metallicity. Such an object can sustain nuclear fusion in its core and become a star even if its mass is as low as 4 percent the Sun’s mass. The idea behind this is that the high metallicity makes the core an insulator (i.e. less able to radiate energy), allowing a smaller core and hence, a less massive star to support the temperature required to sustain hydrogen fusion. The rate of hydrogen fusion in the core of such a star is believed to be so low that the star can have a surface temperature of around zero degrees Celsius, cold enough for ice clouds to form in the star’s atmosphere. In their paper, Fred Adams and Gregory Laughlin termed them “frozen” stars.

In the present universe, the least massive stars have surface temperatures around 2000 K and lifespans exceeding 10 trillion years. A “frozen” star like is unlike any found in the present universe. The low rate of hydrogen fusion means a “frozen” star would be able to sustain hydrogen fusion for a much longer period of time, giving it a vastly greater longevity. A star’s lifespan is the amount of time it can sustain hydrogen fusion in its core. For comparison, the present age of the universe is 13.8 billion years, while the Sun has a lifespan of 10 billion years.

“Frozen” stars in the far future of the universe would be orders of magnitude dimmer than the dimmest stars known today. Nevertheless, such objects are clearly considered stars, since, like the Sun, they produce energy via nuclear fusion in their cores. A “frozen” star would be roughly the size of Jupiter. Yet, it is by no means like Jupiter. With 4 percent the Sun’s mass, which is approximately 40 times Jupiter’s mass, the gravity on the surface of a “frozen” star would be a crushing ~100g’s. Still, such exotic stars are interesting astrophysical objects to think about.

Reference:

Fred Adams and Gregory Laughlin (1997), “A Dying Universe: The Long Term Fate and Evolution of Astrophysical Objects”, arXiv:astro-ph/9701131