# What is the spectral reflection curve of cold white dwarfs and neutron stars?

Suppose that I got a white dwarf and a neutron star and after some trillions of years their temperature are down to just a few °K so cold that they don't emit any appreciable black body radiation.

Now, I send to each one, a robot/spaceship with a huge spotlight and shine a white light into them, possibly even making those old balls as illuminated as the Earth is, even if just for some seconds or minutes.

Also, the robots/spaceships takes photos to be presented as human eyes would see on a distance enough to see them roughly the same angular size that a basketball has in my hand when my arm is extended.

So, let's go to the actual questions.

What would be the color of the stars?

• Would they act like perfect spherical mirrors reflecting not just the spotlight, but everything else nearby?
• Or would they appear white by reflecting all that light diffusely?
• Or maybe pitch black because they would absorve all the light and reflect nothing?
• Perhaps gray, by partially reflecting and partially absorving the light diffusely equally in all wavelengths?
• Or silvery?
• Or perhaps, due to Doppler gravitational reddening, golden?
• Or, maybe I am missing something funny and they are pink, blue or green?

Bonus:

Could I distinguish them only by looking at the photos without measuring density, gravity, size or radiation, considering that the photos show them with the same angular diameter?

• Both types of object are usually assumed to be pretty close to blackbodies, so would absorb everything incident upon them. Of course that cannot be entirely true at some level; the problem is I doubt anyone has modelled the opacity/reflectivity of the atmospheres of white dwarfs and neutron stars at a few Kelvin because that can't happen. May 16, 2022 at 13:48
• You might not want to limit your illuminator to visible wavelengths. May 16, 2022 at 14:12
• victor, to clarify @ProfRob 's comment - long before these bodies cool to such levels they'll have collapsed or gone nova or other complete transformations. May 16, 2022 at 14:13
• Actually what I meant was that nobody will have bothered calculating atmospheres for ultracold white dwarfs and neutron stars because the coldest ones in our universe are $>3000$ K and they cannot cool to ultra-low temperatures because they will accrete material from the ISM. May 16, 2022 at 15:20
• different question but related and answers are potentially helpful here: What is the spectral reflectance of starlight in a close binary?
– uhoh
May 16, 2022 at 19:59

## 1 Answer

There doesn't seem to be much work done so far on truly cold white dwarfs; in particular, once the atmosphere starts condensing out the cooling models change in apparently awkward ways according to experts I talked to.

Still, we can make some educated guesses. The heavier degenerate matter will not be visible since the lightest components, helium and hydrogen, will tend to layer on top.

Under cold high pressure conditions hydrogen would tend to be metallic, but the 100,000g surface gravity of the star is not enough to force the top of a hydrogen layer to be metallic - it would presumably be one of the other molecular crystal forms that are transparent.

Helium on the other hand would also solidify at some 300 MPa, again a bit below the surface leaving it liquid. As far as I can tell it is denser than metallic hydrogen (which is fairly incompressible) at low temperatures, so it would likely form a layer below some hydrogen and be pressured solid (still, the density is temperature dependent, and gradual cooling might well cause some potential for odd cryotectonics driven by convection overturn).

How smooth is the surfacce? The scale of stable mountains is $$1/g$$, so we should expect height variations to be on the order of 0.1 m or less - the surface would be pretty smooth, but not necessarily shiny (especially if there had been cryovolcanism).

So my answer would be a crystalline and transparent, not necessarily smooth, layer overlaying a metallic hydrogen layer. I would expect young white dwarfs to have plenty of dislocations, making the crystals scatter light strongly. So a surface finish like imperfect quartz might not be too implausible. As they age the crystals slowly coarsen and become more transparent, until you get a nearly perfectly smooth layer overlaying the reflective metallic hydrogen.

Note that dislocations due to cosmic rays and polluting elements may have tricky color effects (electron beams make diamonds and glass turn brownish, for example). Accreting hydrogen may also keep the surface somewhat messy for a long bit of the degenerate era.

• The scale of stable mountains is $1/g$?? In what units? May 19, 2022 at 19:54