What is theorized to be the coldest white dwarf in the Universe?

[swampwiz]

Yes, I understand that once white dwarfs get cold enough, they aren't luminous enough to get observed, so my question could be interpreted as "when did the earliest white dwarf evolve, and how cold is it now"?

This is the article that motivated this question:
https://public.nrao.edu/news/cold-white-dwarf/

 

[Vanadium 50]

I typed "when did the earliest white dwarf evolve, and how cold is it now" word for word into Google and here is what it said:

The white dwarfs born from the earliest generations of stars are still cooling off, 14-billion-years later. So the coolest white dwarfs we know of, with temperatures around 4,000 degrees Celsius (7,000 degrees Fahrenheit), may also be some of the oldest relics in the cosmos.

It gived as a reference https://earthsky.org/astronomy-essentials/white-dwarfs-are-the-cores-of-dead-stars/

 

[Ken G]

And note it is not obvious how to calculate the coolest possible white dwarf. For sure you want to take the oldest possible stars, so 13.8 billion years old, but the question is, what mass? You have to take a mass that has evolved to the white dwarf phase, so it can't be too low, but white dwarfs start pretty hot, so you actually want a larger mass so it will have been a white dwarf for a long time. But if you take too high of a mass, such that it was almost a neutron star, then it will fuse past carbon and might be what is called an ONeMg white dwarf (fusing up to magnesium), or even an iron white dwarf. Those will be white dwarfs the longest because of how fast they evolve into white dwarfs, but they will also have higher mass, so might need a longer time to cool down. Hence it is not obvious the "sweet spot" in mass for maximum cooling. My guess is, the coolest white dwarf will depend on physics that we don't really quite know yet, because the final evolution stages will be crucial, but its mass might be fairly close to a solar mass.

(Watch out for the Bad Astronomy in the linked source, where it says "But eventually, a star will run out of hydrogen in its center. At this point, it shifts to fusing helium into carbon and oxygen, and hydrogen fusion moves to a shell surrounding the core. The star inflates and becomes a red giant. " No, the star inflates and becomes a red giant before helium fusion begins; when helium fusion initiates the star shrinks back down and is no longer a red giant, becoming a "red clump" or "horizontal branch" star instead, which is quite a bit smaller, maybe 10 times the solar radius instead of 100 times. But that's not really what the article is about, and otherwise it is good.)

 

[swampwiz]

And note it is not obvious how to calculate the coolest possible white dwarf. For sure you want to take the oldest possible stars, so 13.8 billion years old, but the question is, what mass? You have to take a mass that has evolved to the white dwarf phase, so it can't be too low, but white dwarfs start pretty hot, so you actually want a larger mass so it will have been a white dwarf for a long time. But if you take too high of a mass, such that it was almost a neutron star, then it will fuse past carbon and might be what is called an ONeMg white dwarf (fusing up to magnesium), or even an iron white dwarf. Those will be white dwarfs the longest because of how fast they evolve into white dwarfs, but they will also have higher mass, so might need a longer time to cool down. Hence it is not obvious the "sweet spot" in mass for maximum cooling. My guess is, the coolest white dwarf will depend on physics that we don't really quite know yet, because the final evolution stages will be crucial, but its mass might be fairly close to a solar mass.

(Watch out for the Bad Astronomy in the linked source, where it says "But eventually, a star will run out of hydrogen in its center. At this point, it shifts to fusing helium into carbon and oxygen, and hydrogen fusion moves to a shell surrounding the core. The star inflates and becomes a red giant. " No, the star inflates and becomes a red giant before helium fusion begins; when helium fusion initiates the star shrinks back down and is no longer a red giant, becoming a "red clump" or "horizontal branch" star instead, which is quite a bit smaller, maybe 10 times the solar radius instead of 100 times. But that's not really what the article is about, and otherwise it is good.)

All good points. Perhaps this would be a good project for an astrophysics thesis?

 

[snorkack]

And note it is not obvious how to calculate the coolest possible white dwarf. For sure you want to take the oldest possible stars, so 13.8 billion years old, but the question is, what mass? You have to take a mass that has evolved to the white dwarf phase, so it can't be too low, but white dwarfs start pretty hot, so you actually want a larger mass so it will have been a white dwarf for a long time. But if you take too high of a mass, such that it was almost a neutron star, then it will fuse past carbon and might be what is called an ONeMg white dwarf (fusing up to magnesium), or even an iron white dwarf. Those will be white dwarfs the longest because of how fast they evolve into white dwarfs, but they will also have higher mass, so might need a longer time to cool down. Hence it is not obvious the "sweet spot" in mass for maximum cooling. My guess is, the coolest white dwarf will depend on physics that we don't really quite know yet, because the final evolution stages will be crucial, but its mass might be fairly close to a solar mass.

Probably less.
What is 13,8 milliards? The age of whole universe?
First stars formed some hundreds of millions years later. Not sure how many hundreds. Deep fields tend to diminish that number.
From first stars in a cluster to first white dwarf and last supernova takes how long? Less than 100 million years, but is it 70 millions? 30 millions?
The 6 nearest white dwarfs, in order of temperature, are:

1. Sirius B. 25 000 K, +11,18. 1,02 solar mass, 0,0084 solar radii. Has been a white dwarf about 120 million years, star for 100 million years before that. Guestimated as 5 solar masses on main sequence.
2. Keid B. 16 500 K, +11,02. 0,57 solar mass, 0,014 solar radii. Colder than Sirius B but brighter because lighter and therefore bigger.
3. Gliese 440. 8500 K, +13,2. Mass 0,56 solar, radius 0,01 solar
4. Procyon B. 7700 K, +13,0. 0,60 solar mass, 0,012 solar radii. Has been a white dwarf about 1,2 milliard years, a star about 700 million years before that.
5. Gliese 169 B. 7100 K, +13,72. 0,67 solar mass, 0,011 solar radii
6. van Maanen´s star. 6100 K, +14,21. 0,67 solar mass, 0,011 solar radii. Estimated to have been a white dwarf for 3,5 milliards of years, a star 900 millions of years before that.

Note how most nearby white dwarfs cluster in 0,56...0,67 solar masses an 0,01...0,014 solar radii. Sirius B is unusually heavy and small.
What precisely does the white dwarf branch of a globular cluster Hertzsprung-Russell diagram look like?
Most white dwarfs are black bodies of nearly the same radius and different temperatures, so they should form a narrow band whose kinks are dictated by eye sensitivity and spectral class spacing. In the early end, it of course goes into O (the planetary nebula nuclei). But how does the late end act? van Maanen´s star, at 6100 K and late F is just 3,5 milliards of years and globular clusters are 13 milliards. Even stars which were 1 milliard years in main sequence will have been 12 milliards years white dwarfs.
When you approach heavy and small white dwarfs, they will be dimmer for the same temperature than lighter white dwarfs. But will they also be hotter for the same age? Does the late-class end of globular cluster white dwarf series actually turn to hotter and dimmer ones?

 

[Ken G]

All good points. Perhaps this would be a good project for an astrophysics thesis?

I agree, one could try to find the surface T of a set of stars that are 13.7 billion years old, starting from a range of masses, and look for a minimum. One could even include some binary evolution, that might help speed up the evolution by giving a star mass, then make a faster cooling white dwarf by taking some mass away in the later stages. What is the coolest such a white dwarf can get?

 

[Ken G]

Probably less.
What is 13,8 milliards? The age of whole universe?
First stars formed some hundreds of millions years later. Not sure how many hundreds. Deep fields tend to diminish that number.
From first stars in a cluster to first white dwarf and last supernova takes how long? Less than 100 million years, but is it 70 millions? 30 millions?
The 6 nearest white dwarfs, in order of temperature, are:

1. Sirius B. 25 000 K, +11,18. 1,02 solar mass, 0,0084 solar radii. Has been a white dwarf about 120 million years, star for 100 million years before that. Guestimated as 5 solar masses on main sequence.
2. Keid B. 16 500 K, +11,02. 0,57 solar mass, 0,014 solar radii. Colder than Sirius B but brighter because lighter and therefore bigger.
3. Gliese 440. 8500 K, +13,2. Mass 0,56 solar, radius 0,01 solar
4. Procyon B. 7700 K, +13,0. 0,60 solar mass, 0,012 solar radii. Has been a white dwarf about 1,2 milliard years, a star about 700 million years before that.
5. Gliese 169 B. 7100 K, +13,72. 0,67 solar mass, 0,011 solar radii
6. van Maanen´s star. 6100 K, +14,21. 0,67 solar mass, 0,011 solar radii. Estimated to have been a white dwarf for 3,5 milliards of years, a star 900 millions of years before that.

Note how most nearby white dwarfs cluster in 0,56...0,67 solar masses an 0,01...0,014 solar radii. Sirius B is unusually heavy and small.
What precisely does the white dwarf branch of a globular cluster Hertzsprung-Russell diagram look like?
Most white dwarfs are black bodies of nearly the same radius and different temperatures, so they should form a narrow band whose kinks are dictated by eye sensitivity and spectral class spacing. In the early end, it of course goes into O (the planetary nebula nuclei). But how does the late end act? van Maanen´s star, at 6100 K and late F is just 3,5 milliards of years and globular clusters are 13 milliards. Even stars which were 1 milliard years in main sequence will have been 12 milliards years white dwarfs.
When you approach heavy and small white dwarfs, they will be dimmer for the same temperature than lighter white dwarfs. But will they also be hotter for the same age? Does the late-class end of globular cluster white dwarf series actually turn to hotter and dimmer ones?

There are a lot of white dwarfs around 0.6 solar masses because the helium core builds up to about 0.5 solar masses when helium starts to fuse, even for much more massive stars than the Sun, and it only adds a little more carbon mass from helium shell burning by the time the star climbs the asymptotic giant branch and ejects its envelope. So more massive stars just eject more of their mass, they don't get a much higher mass carbon white dwarf. But that ceases to hold if you go to much larger mass stars, whose helium cores are already beyond 0.6 solar masses, they will make more massive white dwarfs. If you go to really high mass stars, almost to the masses that undergo core collapse, then the carbon starts to fuse to make ONeMg white dwarfs, and with various binary pathways thrown in, they can even go on to fuse to iron (without going enough past 1 solar masses to go supernova).

So we can expect a lot of white dwarfs to cap at maybe 0.7 solar masses, but there can be ones closer to the edge of supernova that are above 1 solar masses, and those form in less than the 10 billion years it takes for a solarlike star. There is even a binary pathway that leads to a type of supernova called a "kilonova", where it starts to try to explode its carbon but never really does it enough to destroy the white dwarf. So with all these different ways to make a white dwarf, there could be some massive star pathways that evolve to white dwarfs very quickly so cool for a long time, but then the question is do those white dwarfs cool more slowly (in part because they are small, as you say). So what's the best way to make a very cool white dwarf if you have 13.7 billion years? I suspect binary mass transfer would be the best way, and not a lot is known about how that works!

 

[snorkack]

An examination of M4:
https://arxiv.org/abs/astro-ph/0205087

 

[Ken G]

An examination of M4:
https://arxiv.org/abs/astro-ph/0205087

Sounds like M4 is almost as old as stars get, at least in the Milky Way. One wonders, though, if there are not leftovers from the "first stars" that could have had different properties (especially low metallicity and different masses and binarity), and could have made a rather different collection of white dwarf residue. So to ask "what is the coldest white dwarf in the universe today", one might need to look even older. Which will be pretty much impossible, I would think! So it likely remains a theoretical question, and our theories are probably not quite good enough to answer it, but M4 is a good place to start setting down the upper limit.

 

[Vanadium 50]

"first stars" that could have had different properties (especially low metallicity and different masses and binarity), and could have made a rather different collection of white dwarf residue. S

I am not sure you get white dwarfs from Population III stars. Zero out the metallicity and the opacity falls. With lower opacity, the energy trransfer falls, and the star formation process ends later - you get big, big stars. They do not typically evolve to white dwarfs.

Can you get some? Probably - if you start with a small enough gas cloud, I suppose. After all. your star can't be any bigger than the gas cloud it formed from. But these have to be incredibly rare.

 

[Ken G]

It is true that zero metallicity stars are thought to generally be more massive, but the fragmentation process that occurs as stars form will likely always make smaller stars along with the big monsters. (For one thing, high mass stars go supernova after only a few million years, which is a flash in the pan for lower mass stars that take much longer than that to even form in the first place. So even the very first generation of low mass stars will be byproducts of supernovae in their vicinity, and this may also help to promote fragmentation as well as increase metallicity.) So if we want to know the coolest white dwarf in the universe, we will likely always have some low mass stars to choose from, even from the very first era of star formation.

 

[Budgieye]

Here is a nice older white dwarf, cooled off so that it no longer emits UV or blue light.
253.503162621, 62.898839220
https://skyserver.sdss.org/dr16/en/tools/explore/Summary.aspx?id=1237671767467819214
https://www.galaxyzooforum.org/index.php?topic=278111.msg484589#msg484589

 

[swampwiz]

Here is a nice older white dwarf, cooled off so that it no longer emits UV or blue light.
253.503162621, 62.898839220
https://skyserver.sdss.org/dr16/en/tools/explore/Summary.aspx?id=1237671767467819214
https://www.galaxyzooforum.org/index.php?topic=278111.msg484589#msg484589

The first reference has it depicted as a green star. Could it be possible that unlike any other star, a post-fusion star (i.e., what is generally referred to as a "white dwarf") could be seen as having a greenish hue?

 

[Ken G]

Probably not, as even our own Sun has a spectrum that peaks in the green region (only slightly less blue than this white dwarf spectrum). Nevertheless, the Sun is classified as a yellow star, but you can easily see if you hold out a blank piece of paper in daylight that the human eye detects the color of the Sun as extremely white (even, definitively white, as we tend to appreciate color in contrast to the light we are used to seeing). There is also the issue that our eyes don't see color until the brightness is pretty high, so we'd have to be pretty close to this white dwarf to see it as having a color. If we were close enough that it looked as bright as our Sun, I suspect it would still look pretty much as white as the Sun does, perhaps the slightest bluer hue, but not green. (I believe a thermal spectrum is always too broad for us to see it as green; even that brilliant green light we sometimes see in the flame of a gas burner is not due to a thermal spectrum but to spectral lines from particular gaseous components like copper.)

 

[Ken G]

The article speculates that the white dwarf is a helium white dwarf, meaning that the stellar core never got hot enough to fuse helium into carbon. That means it has to have had a mass less than our Sun (which will fuse helium into carbon in another 5 billion years), perhaps a little below 0.8 solar masses. The age of hydrogen burning for sunlike stars scales with age something like mass to the minus 3 power, so 0.8 solar masses would take 20 billion years to be a white dwarf, so would not have happened yet. Hence it is surprising that any helium white dwarfs exist at all, most likely something would have needed to happen to speed up the process (I mentioned the possibility of binary mass transfer, that can start a star out with more mass than remove it by the time it would have otherwise begun burning helium into carbon). So maybe that happened to this star.

 

[Vanadium 50]

could be seen as having a greenish hue?

Ever see a green blackbody? (This ingot is hotter than red hot...it;s green hot!) So no.

 

[swampwiz]

OK, the depiction is just wrong. The other source has it as being blue.

 

[Budgieye]

The first reference has it depicted as a green star. Could it be possible that unlike any other star, a post-fusion star (i.e., what is generally referred to as a "white dwarf") could be seen as having a greenish hue?

 

[Budgieye]

SDSS skyserver uses false colours. The green channel assigned from RGB comes from red light. So the actual colour of the star is orange-red.
Not that it makes any difference to the premise that the star is a cooling white dwarf.

 

[swampwiz]

SDSS skyserver uses false colours. The green channel assigned from RGB comes from red light. So the actual colour of the star is orange-red.
Not that it makes any difference to the premise that the star is a cooling white dwarf.

Is there some sort of standard that is used for such false colorization?

 

[Vanadium 50]

Of course not, since different colorations are used to represent different things.

 

[swampwiz]

Of course not, since different colorations are used to represent different things.

So how is someone supposed to know what the colors represent?

 

[Vanadium 50]

Usually there is a legend. Or a statement like "false color is used to improve contrast"

 

[Hornbein]

I don't really know but I expect more massive white dwarfs have not only a higher initial temperature but also less surface area and higher density, so there is a triple whammy as far as cooling goes. Also it has been a very long time so even a slight difference in cooling rate should dominate. I'd guess the first light weight white dwarf would be the coolness winner by a considerable margin.

 

[Budgieye]

So how is someone supposed to know what the colors represent?

https://panoptes-uploads.zooniverse...age/2681d3a5-a9ea-4da2-a1ca-88ceb616799d.jpeg
https://www.zooniverse.org/projects/zookeeper/galaxy-zoo/talk/1268/582784?comment=967393
https://classic.sdss.org/dr7/instruments/imager/#filters

 

[Ken G]

I don't really know but I expect more massive white dwarfs have not only a higher initial temperature but also less surface area and higher density, so there is a triple whammy as far as cooling goes. Also it has been a very long time so even a slight difference in cooling rate should dominate. I'd guess the first light weight white dwarf would be the coolness winner by a considerable margin.

Yes, so to get the coolest one, you have a tradeoff. The most massive one will be the oldest, assuming they all form in first light, but it will cool slower so wouldn't be the coolest. So the best way is to start with higher mass so the star evolves quickly, but then rob it of mass via mass transfer to a companion in the late stages of evolution, to make a lower mass and larger white dwarf. That must be what happened to any helium white dwarf we see, they have too little mass to have had time to evolve to that stage by themselves. In that scenario, the coolest one would likely simply be one that has whatever mass we regard as the minimum mass of something we are calling a white dwarf, i.e., not a brown dwarf.

 

[swampwiz]

Yes, so to get the coolest one, you have a tradeoff. The most massive one will be the oldest, assuming they all form in first light, but it will cool slower so wouldn't be the coolest. So the best way is to start with higher mass so the star evolves quickly, but then rob it of mass via mass transfer to a companion in the late stages of evolution, to make a lower mass and larger white dwarf. That must be what happened to any helium white dwarf we see, they have too little mass to have had time to evolve to that stage by themselves. In that scenario, the coolest one would likely simply be one that has whatever mass we regard as the minimum mass of something we are calling a white dwarf, i.e., not a brown dwarf.

But a brown dwarf would not have spent its life fusing ¹H.

 

[Ken G]

Good point, it would be easy to tell the difference by the amount of H still there.