Neutron star: smoothest surface in the universe?

Catria

I wrote a paper in the physics department's student newspaper at my school, which described why, in my opinion, I considered a neutron star's surface as the smoothest surface in the universe, I considered the space between the particles at the surface (thousands of times smaller than at TPN conditions on Earth), the degeneracy pressure that makes such a surface possible and the fact that a body whose gravity at the surface makes for a relativistic escape speed wouldn't allow for much in the way of ruts. And I made an addendum pertaining to rotation, explaining that, with rotational factors added, it's actually the poles of a neutron star that are its smoothest points.

Of course I meant that as a joke but perhaps does it have some merit?

Perhaps am I completely off as I am no expert in condensed matter or astrophysics but what do you think?

mfb

Neutron stars can have mountains of the order of ~0.1mm (source) or maybe even ~1cm (article) with a width of maybe 100m-1km. Using the lower mountain height and the upper width, this corresponds to deviations of at least 10^-7.
This is similar to the Si-28-balls produced at the PTB (Physikalisch-Technische Bundesanstalt in Germany): Deviations smaller than 30nm on a sphere with 10cm diameter (maximal relative deviation 3*10^-7).

If you look at the atomic scale, things might be different. Is a perfect crystal lattice smooth?

Catria

Do neutron stars have perfect crystal lattices, especially when they are so close that the neutrons may as well be touching each other?

mfb

That was related to shapes on earth, but neutron stars have atoms there, too:
from here, given source there: V. S. Beskin (1999). "Radiopulsars". УФН. T.169, №11, p.1173-1174

ImaLooser

Neutron star cores are a very hot superfluid, which I have no intuition about. It's exotic. I would say it has nothing in common with a crystal.

ImaLooser

The magnetic field is so strong that the nuclei polymerize. Wild!

FiveWords

Interesting topic and very informative site...thank you all.

Wouldn't trying to claim something is the "smoothest" in the universe be akin to the coastline paradox? It would depend upon the method and scale used?

Catria

I mentioned neutron star cores nowhere. However, not all neutron stars have solid surfaces, so the ones that can actually be given the "smooth" qualifier are the ones with solid surfaces (i.e. the colder ones) Do they have perfect crystal lattices if the atoms and other particles may as well be touching each other?

And thus there are perhaps heavier atoms than hydrogen and helium in there...

Chronos

So, what 'color' would the sun be were it not a seethingly hot ball of plasma? Disregarding the laws of physics is not an acceptable option.

ImaLooser

There is a thin (like a few centimeters) atmosphere of carbon and possibly liquid carbon on the surface. Then there are iron nuclei, and possibly heavier nuclei deeper down.
The nuclei are several billion times denser than anything on Earth.

Hydrogen may accumulate on the surface, but tends to undergo fusion explosions that cover the entire star.

Catria

Is there anything smoother on Earth?

Chronos

The fuzed quartz gyroscopes they used in the gravity probe B experiment were pretty smooth. From http://einstein.stanford.edu/TECH/technology1.html:
"... the GP-B gyro rotors are now listed in the Guinness Database of World Records as being the roundest objects ever manufactured, topped in sphericity only by neutron stars."

Catria

I'm so tempted to say that a girl has smoother skin than a neutron star...

Not even a white dwarf? Like a neutron star, a white dwarf is very dense (much less so than a neutron star), prevented from collapsing with degeneracy pressure, small radius and a significant fraction of a solar mass contained within a ball Earth's size.

Chronos

The density difference between a white dwarf and neutron star is pretty significant. The typical white dwarf is about 1 solar mass and the size of earth. The typical neutron star is about 1.4 solar mass and the size of a city [~12km].

Lsos

The Hubble Space Telescope mirror (2.4 m diameter) was polished to within 10 nm of perfection. I didn't do the math, but I would guess this is smoother than anything mentioned so far?

ImaLooser

Sure, go ahead and tell her. She might like it. Just don't say that she's sexier than a white dwarf. That wouldn't go over very often.

ImaLooser

Maximum deviation on surface of a millisecond pulsar is 1mm or so. (As I recall, I wouldn't swear to it.) The diameter is about 20km. 1mm/20km = 5* 10-8.

Hubble: 10-8/2.4 = 4*10-8. It's a tie (within significant figures)! Amazing.

Unfortunately, I read that
The surface of the Hubble telescope's primary mirror has a total variance of less than 0.04 microinches (10 angstroms)
That's 100nm, or 10-7. So Hubble has 4*(10-7) and neutron star wins, but it is close. But what do they mean by variance? Standard deviation? According to the New York Times the maximum error was 2.5 um, so neutron star wins hands down if that's right.

I also found that Perkin-Elmer, the makers of the mirror, knew it was flawed before it was launched. Scandal! They agreed to pay 25 million dollars for this to avoid a court case. Read all about it! http://people.tamu.edu/~v-buenger/658/Hubble.pdf