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After the sun becomes a white dwarf, how long will it take to cool to a black dwarf whose internal temperature is a max of 70 degrees Fahrenheit?
Thanks,
Green
Answer Hello Green:
Thanks for your question on dwarf stars!
Extract from Wikipedia:
"Radiation and cooling of stars...
The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type main sequence star to the red of a M-type red dwarf.[51] White dwarf effective surface temperatures extend from over 150,000K[25] to under 4,000K.[52][53] In accordance with the Stefan-Boltzmann law, luminosity increases with increasing surface temperature; this surface temperature range corresponds to a luminosity from over 100 times the Sun's to under 1/10,000th that of the Sun's.[53] Hot white dwarfs, with surface temperatures in excess of 30,000K, have been observed to be sources of soft (i.e., lower-energy) X-rays. This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations.[54]
A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.Unless the white dwarf accretes matter from a companion star or other source, this radiation comes from its stored heat, which is not replenished. White dwarfs have an extremely small surface area to radiate this heat from, so they remain hot for a long period of time.[1] As a white dwarf cools, its surface temperature decreases, the radiation which it emits reddens, and its luminosity decreases. Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time. A white dwarf may cool from a surface temperature of 20,000K to one of 5,000K in approximately the same amount of time it takes to cool from one of 5,000K to one of 4,000K.[55], eq. (2.3). Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star.[56] The crystal structure is thought to be a body-centered cubic lattice.[57][5] In 1995 it was pointed out that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,[58] and in 2004, Travis Metcalfe and a team of researchers at the Harvard-Smithsonian Center for Astrophysics estimated, on the basis of such observations, that approximately 90% of the mass of BPM 37093 had crystallized.[56][59][60][61] Other work gives a crystallized mass fraction of between 32% and 82%.[62]
Most observed white dwarfs have relatively high surface temperatures, between 8,000K and 40,000K.[63][26] A white dwarf, though, spends more of its lifetime at cooler temperatures than at hotter temperatures, so we should expect that there are more cool white dwarfs than hot white dwarfs. Once we adjust for the selection effect that hotter, more luminous white dwarfs are easier to observe, we do find that decreasing the temperature range examined results in finding more white dwarfs.[64] This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000K[65], and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K.[52] The reason for this is that, as the Universe's age is finite, there has not been time for white dwarfs to cool down below this temperature. The white dwarf luminosity function can therefore be used to find the time when stars started to form in a region; an estimate for the age of the Galactic disk found in this way is 8 billion years.[64]
A white dwarf will eventually cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. However, no black dwarfs are thought to exist yet.[7]"
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So it seems that the time required is close to infinity for a white dwarf to cool down to a 70 degree temperature as a black dwarf!
