# B Surface Temperatures - White Dwarf vs Neutron Star

1. Feb 9, 2017

### Jimmy87

Hi,

My textbook has a multiple choice question about which stellar object has the highest surface temperature and the answer was a white dwarf. However, one of the options was a neutron star. Neutron stars are much denser and have been crushed by gravity even more plus they are rotating at immense speeds. So how can the surface temperature of a neutron star be less than a white dwarf? Can't find an answer anywhere,

Thanks for any help

2. Feb 9, 2017

### Helios

Likely, the white dwarf was the choice with the highest luminosity. The temperature is then evaluated by the Stephan-Boltzmann law of black body radiation.

3. Feb 12, 2017

### Chronos

A neutron star has a spectal peak of about 3 angstroms [re: https://www.cfa.harvard.edu/~pberlind/atlas/htmls/neutron.html], which corresponds to around 3 million K. White dwarfs peak much higher in the spectrum [e.g.,110 nm or 1100 angstroms for Sirius B,] and generally max out at a temperature of around 100,000 K [re: https://imagine.gsfc.nasa.gov/science/objects/dwarfs2.html]. According to Wiens law a shorter frequency spectral peak means a higher temperature. The textbook answer looks incorrect to me.

4. Feb 12, 2017

### Ken G

I agree with Chronos and your intuition-- I don't see how a white dwarf surface will be hotter than a neutron star. What's more, both are cooling, so it very much depends on how old they are. Most white dwarfs that we observe have cooled to something like 10,000 K at the surface, and I can't say how much the typical neutron star has cooled. In any event, it's a poor question if they intend the answer to be white dwarfs-- the only reasonable logic is to notice how much higher the energy scales are for neutron stars, so the natural association is that they should have the higher surface temperature also.

5. Feb 13, 2017

### sophiecentaur

It's much easier to write a half decent Text Book than to write a set of really good associated questions. I have been guilty of giving many Text Book questions as an assignment which have given students real problems. The secret is to give useful feedback to students afterwards. If a student has problems with a question they should always challenge the teacher (or come to PF); the student may sometimes be correct.

6. Feb 20, 2017

### Jimmy87

Yaaay, i'm right! Thanks for your help guys.

7. Feb 21, 2017

### stefan r

Neutron stars radiate neutrinos. That can add up to rapid energy loss. The cooling rate is much faster.

This question should depend on the definition of "stellar object" that you use. Does a collision count? You could rephrase the question to "known stellar objects currently measurable with a UV/visible light telescope".

Both the white dwarfs and neutron stars eventually cool off without changing to a different category of star. That will take so long that there are not any examples of cold white dwarfs. As a "category of stellar object" white dwarfs are reliably hot. Some dark matter could be old neutron stars.

8. Feb 22, 2017

### Ken G

Neutron stars only cool via neutrinos when they are very young and very hot. In the longer term, their cooling times seem vaguely similar to white dwarfs. So if the initial formation is the issue, neutron stars are much hotter, and if the long-term cooling is the issue, it depends on the age of the object in ways that go way beyond any simple question. So the question seems to be entirely bogus if the answer is supposed to be the white dwarf.