How long will the sun remain a white dwarf?

Hi:

When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?


Thanks,

Radium

On Fri, 13 Jul 2007 19:45:36 -0000, Radium wrote:

Hi:

When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?

That would take forever. But a few tens of billions of years should be
long enough that the temperature drops low enough that no photons in the
visible range are produced, which is generally what defines a black
dwarf.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Jul 13, 1:16 pm, Chris L Peterson wrote:

That would take forever. But a few tens of billions of years should be
long enough that the temperature drops low enough that no photons in the
visible range are produced, which is generally what defines a black
dwarf.

Approximately how long until this white drawf [which used to be the
sun] cools to around 70 degrees Fahrenheit? Will the universe exist
long enough for this to happen?

On Fri, 13 Jul 2007 21:42:41 -0700, Radium wrote:

Approximately how long until this white drawf [which used to be the
sun] cools to around 70 degrees Fahrenheit? Will the universe exist
long enough for this to happen?

The temperature falls off somewhat exponentially... looks like it would
take hundreds of billions of years to get that cool, maybe trillions.
But it has all the time in the world (or the Universe), since it seems
likely the Universe will not ever cease to exist, but will just keep
cooling down and expanding forever.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Fri, 13 Jul 2007 19:45:36 -0000, Radium
wrote:

When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?

It takes a solar type star about 100 billion years, which is more than
the presently estimated age of the universe.

Bud
--
The night is just the shadow of the Earth.

In article .com,
Radium wrote:

When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?

SInce the cooloff is pretty much exponential, it will take forever and
the rediated energy will never drop to exactly zero. SO you should
rephrase your question as:

# When the sun becomes a white dwarf, approximately how long will it
# take for it to cool off to a cold black dwarf that does not emit
# any significant anounts of heat or light [or other energies] than
# the surrounding space?

That time span will depend a lot on your precise definition of
"significant". But it will probably take hundreds of billion years,
or more.

Let me give you one concrete example: suppose the outside temperature
is exactly freezing, i.e. 0 deg C. You boil a pot of water, then
bring it outside. How long time will it take until the pot has
cooled down so there's no temperature difference between the pot
of water and the surroundings?

At the start, the temperature difference is 100 deg C of course.
Let's say after one hour the temperature difference is 10 degrees.
After two hours it's 1 degree, after three hours 0.1 degrees, after
four hours 1E-2 degrees. After a day+night the temperature difference
is 1E-22 degrees, after a week 1E-166 degrees, after a year 1E-8764
degrees, and after 15 billion years 1E-131490000000000 degrees. The
temperature difference will never ever go all the way to zero!

Of course a temperature difference of 1E-6 degrees or smaller is
indistinguishable from zero - we call such a difference insignificant.

But where do you draw the line between "significant" and
"insignificant" here? In the example above, do you consider the
temperature of the pot of water to be "the same" as the surroundings
when the temperature difference drops below one degree? If so, it
will happen after two hours. Or do you require a temperature
difference of less than 0.01 degrees to consider the temperatures "the
same"? If so, the cooldown will require four hours.

The situation is similar with a white dwarf: no internal fusion gives
any energy anymore, so the white dwarf just cools down. OK, there's
one internal energy source remaining: gravitational contraction: the
white dwarf can contract somewhat under its own gravitation, and that
will release some energy, keeping it warmer for some time(*). But
still the white dwarf cools off more or less exponentially. Now,
since the white dwarfs are faint stars, they don't radiate that much
energy out into space, and that's one major reason they can "live" for
so long.


(*) Before astronomer's realized that the Sun's energy source was nuclear
fusion, other sources of energy were suggested. If the Sun had been
a huge coal fire, it would be able to shine only for a few centuries,
maybe a millennium. A more efficient energy source was gravitational
contraction, which would be able to keep the Sun hot for approximately
a million years. Back then, geologists suggesting that the Earth is
some 5 billion years old had an obvious difficulty: what energy source
could have kept the Sun shining for those five billion years? The
answer is of course nuclear fusion - but it wasn't until well into the
1900's that astronomers realized this.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/

In article ,
Chris L Peterson wrote:

On Fri, 13 Jul 2007 19:45:36 -0000, Radium wrote:

Hi:

When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?

That would take forever. But a few tens of billions of years should be
long enough that the temperature drops low enough that no photons in the
visible range are produced, which is generally what defines a black
dwarf.

That would take forever too!!! According to the Planck blackbody
radiation curve, any blackbody hotter than absolute zero radiates
photons over all wavelengths. Yes, you and I radiate visible light,
X-rays and even gamma rays, although at an extremely low rate - but
still at a rate slightly above zero. And if a cool body would emit,
say, one gamma ray photon over a billion years, is that "no gamma
radiation" or not?

So if you say "that would take forever" about cooling down until no
more energy is radiated, you must say the same about radiation at
visible wavelengths, or any other wavelength rate. Only if you set some
level near but above sero as "insignificant" you can assign a finite
cooldown time span.


Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/

On Sat, 14 Jul 2007 09:42:19 GMT, (Paul Schlyter) wrote:

That would take forever too!!!

That's true. I meant until the level of visible photons drops below
detectability (which is, of course, a moving target). As you say, all
that can be done is to set a threshold, or a specific target
temperature.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

Don'tforget about fluctuation theory, sometimes known as Statistical
Mechanics. You will et a time (in that time range) where the
probability is that once heated water is colder than the ice.


On Jul 14, 5:42?am, (Paul Schlyter) wrote:
In article .com,

Radium wrote:
When the sun becomes a white dwarf, approximately how long will it
take for it to cool off to a cold black dwarf that does not emit
anymore heat or light [or other energies] than the surrounding space?

SInce the cooloff is pretty much exponential, it will take forever and
the rediated energy will never drop to exactly zero. SO you should
rephrase your question as:

# When the sun becomes a white dwarf, approximately how long will it
# take for it to cool off to a cold black dwarf that does not emit
# any significant anounts of heat or light [or other energies] than
# the surrounding space?

That time span will depend a lot on your precise definition of
"significant". But it will probably take hundreds of billion years,
or more.

Let me give you one concrete example: suppose the outside temperature
is exactly freezing, i.e. 0 deg C. You boil a pot of water, then
bring it outside. How long time will it take until the pot has
cooled down so there's no temperature difference between the pot
of water and the surroundings?

At the start, the temperature difference is 100 deg C of course.
Let's say after one hour the temperature difference is 10 degrees.
After two hours it's 1 degree, after three hours 0.1 degrees, after
four hours 1E-2 degrees. After a day+night the temperature difference
is 1E-22 degrees, after a week 1E-166 degrees, after a year 1E-8764
degrees, and after 15 billion years 1E-131490000000000 degrees. The
temperature difference will never ever go all the way to zero!

Of course a temperature difference of 1E-6 degrees or smaller is
indistinguishable from zero - we call such a difference insignificant.

But where do you draw the line between "significant" and
"insignificant" here? In the example above, do you consider the
temperature of the pot of water to be "the same" as the surroundings
when the temperature difference drops below one degree? If so, it
will happen after two hours. Or do you require a temperature
difference of less than 0.01 degrees to consider the temperatures "the
same"? If so, the cooldown will require four hours.

The situation is similar with a white dwarf: no internal fusion gives
any energy anymore, so the white dwarf just cools down. OK, there's
one internal energy source remaining: gravitational contraction: the
white dwarf can contract somewhat under its own gravitation, and that
will release some energy, keeping it warmer for some time(*). But
still the white dwarf cools off more or less exponentially. Now,
since the white dwarfs are faint stars, they don't radiate that much
energy out into space, and that's one major reason they can "live" for
so long.

(*) Before astronomer's realized that the Sun's energy source was nuclear
fusion, other sources of energy were suggested. If the Sun had been
a huge coal fire, it would be able to shine only for a few centuries,
maybe a millennium. A more efficient energy source was gravitational
contraction, which would be able to keep the Sun hot for approximately
a million years. Back then, geologists suggesting that the Earth is
some 5 billion years old had an obvious difficulty: what energy source
could have kept the Sun shining for those five billion years? The
answer is of course nuclear fusion - but it wasn't until well into the
1900's that astronomers realized this.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/

"Chris L Peterson" wrote in message
...
On Sat, 14 Jul 2007 09:42:19 GMT, (Paul Schlyter) wrote:

That would take forever too!!!

That's true. I meant until the level of visible photons drops below
detectability (which is, of course, a moving target). As you say, all
that can be done is to set a threshold, or a specific target
temperature.

I think the OP asked about 70F with the idea of having
some humans around. His question is really whether there
could be habitable planets around at a time when the
galaxies were evaporating rather than how long it would
take for a white dwarf to cool to 290K.

One can imagine a time when gathering hydrogen to keep
their brown dwarf running was a civilisation's main
occupation, but I guess that's another story.

George