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What is the projected temperature of the sun as white dwarf?

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newtonian

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What is the projected core and surface temperature of our sun's core and surface during white dwarf stage:<br /><br />100 billion years from now?<br />1 trillion years from now?<br />10 trillion years from now?<br />100 trillion years from now?<br />1 Quadrillion years from now?<br /><br />When will the surface of our sun lower to 100C at white [black!] dwarf stage?<br /><br />Can we construct a solid that would float on the surface of our sun at white dwarf stage [er -actually black dwarf]?<br /><br />Say a solid with vacuum holes within it?<br /><br />Ditto any black dwarf? <br /><br />What is the lightest solid currently manufactured?
 
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kyle_baron

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From The Night Sky Observers Guide Vol. 1, Introduction page xix:<br />The typical white dwarf packs nearly the mass of the sun into a sphere the size of the earth. For any stellar remanent less than 1.25 solar masses no further contraction is possible. So the white dwarf has no further energy source and simply radiates its residual energy away. These objects have such small surface areas, that billions of years must pass before a white dwarf with a surface temperature of an O star (25,000K) will cool down to a white dwarf with a surface temperature of a yellow G-type star (6000K). Given sufficient time a white dwarf will cool down to the 3K ambient temperature of interstellar space. <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>
 
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newtonian

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kyle_baron - thank you for a ball-park estimate! But how many billions of years until a white dwarf reaches 6,000 K? Also, isn't a red giant surface temperature cooler than that - namely: 3,000 K?<br /><br />I suspect quadrilions of years before reaching 100K on the surface - but what I really need, I guess, is some math (physics) formula to calculate the temperature curve!<br /><br />Better yet, a source that already did the approximate calculations.<br /><br />BTW - this all assumes the star stays a closed system thermodynamically and does not merge with another star in those quadrillions or years, let alone enter another universe.
 
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newtonian

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Another question: what will the core temperature of our sun as a black dwarf with a surface temperature lowered to 100 C be?<br /><br />I assume much hotter than earth's core since earth is less massive and has a surface temperature much lower than 100C.
 
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priusguy

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According to this page, it takes 10 billion years for a white dwarf to cool from its original temperature of 100,000 K to 5,000 K. Now, the radiative heat flux from any hot object is inversely proportional to the fourth power of temperature -- so whatever time C it took to go from temperature T to T/X, it will take C * X^4 to go from T/X to T/X^2. IOW, if it something took 1 year to cool from 1000 K to 500 K, it will take 16 years to cool from 500 K to 250 K.<br /><br />In case of white dwarfs, 10 billion years (keep in mind, this is all at "one order of magnitude" precision!) takes to drop initial temperature 20-fold. Thus dropping another 20-fold (to 250 K) would take astonishing:<br /><br />10 billion * (20^4) = <b>160 trillion</b> years<br /><br />Closer to home, a young white dwarf goes from 100,000 K to 50,000 K in:<br /><br />1. If halving initial temperature took X years then lowering it by 2^n took X * 2^(4 * (n-1))<br />2. log base 2 of 20 is approximately 4.3<br />3. 10 billion = X * 2^(4 * (4.3-1)) = X * 2^(13.2) = X * 9410<br />4. X = 10 billion / 9410 = approximately 1 million<br /><br />So it takes 1 million years for a white dwarf to halve its initial temperature. Next halving takes about 15 million years, the one after that about 250 million, then 4 billion, etc.<br /><br />And, Newtonian, your guess about reaching 100 K was correct. If it takes 160 trillion years to reach 250 K, 125 K is reached after:<br /><br />160 trillion * 16 = about 2.5 quadrillion years.
 
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vogon13

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Even now (although grossly swamped by larger effects such as fusion and gravitational contraction) the sun is radiating (IIRC) >400 watts per second due to proton decay.<br /><br />In the extreme future, this will be the suns dominant energy producing reaction.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>
 
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newtonian

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Priusguy - Thank heavenly hash! I guessed right! See my heavnely hash thread (not visible yet).
 
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