Neutron star: smoothest surface in the universe?

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Discussion Overview

The discussion revolves around the characterization of neutron stars, specifically whether their surfaces can be considered the smoothest in the universe. Participants explore various aspects of neutron star surfaces, including their physical properties, the presence of mountains, and comparisons to other smooth objects, while delving into the implications of atomic structures and the effects of extreme conditions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that neutron stars have surfaces that could be considered the smoothest due to the small scale of particle spacing and the effects of degeneracy pressure.
  • Another participant cites that neutron stars can have surface irregularities, such as mountains measuring up to ~1cm, which raises questions about their overall smoothness.
  • There is a discussion about whether neutron stars have perfect crystal lattices, with some participants expressing skepticism about the existence of such structures under extreme conditions.
  • Some participants mention that neutron star cores are superfluid and exotic, suggesting that they may not resemble traditional crystals.
  • Comparisons are made between neutron stars and other objects, such as the Hubble Space Telescope mirror and fused quartz gyroscopes, with varying claims about their smoothness.
  • One participant humorously suggests that human skin could be smoother than a neutron star, prompting further light-hearted commentary.
  • Another participant discusses the density differences between neutron stars and white dwarfs, emphasizing the significant distinctions in their physical properties.
  • There are references to the methods used to measure smoothness and the implications of the coastline paradox in defining "smoothness."

Areas of Agreement / Disagreement

Participants express a range of views on the smoothness of neutron stars, with no consensus reached. Some argue for their smoothness based on theoretical considerations, while others point out physical irregularities and question the validity of such claims.

Contextual Notes

Participants note the dependence on definitions of smoothness and the scale at which measurements are made, highlighting the complexity of the topic. There are unresolved questions regarding the atomic structure of neutron star surfaces and the implications of extreme conditions on their properties.

Catria
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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?
 
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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?
 
Do neutron stars have perfect crystal lattices, especially when they are so close that the neutrons may as well be touching each other?
 
That was related to shapes on earth, but neutron stars have atoms there, too:
Wikipedia said:
On the basis of current models, the matter at the surface of a neutron star is composed of ordinary atomic nuclei crushed into a solid lattice with a sea of electrons flowing through the gaps between them.
from here, given source there: V. S. Beskin (1999). "Radiopulsars". УФН. T.169, №11, p.1173-1174
 
Catria said:
Do neutron stars have perfect crystal lattices, especially when they are so close that the neutrons may as well be touching each other?

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.
 
mfb said:
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

The magnetic field is so strong that the nuclei polymerize. Wild!
 
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?
 
ImaLooser said:
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.

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?

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

And thus there are perhaps heavier atoms than hydrogen and helium in there...
 
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.
 
  • #10
Catria said:
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...

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.
 
  • #11
mfb said:
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?

Is there anything smoother on Earth?
 
  • #12
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."
 
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  • #13
I'm so tempted to say that a girl has smoother skin than a neutron star...

Chronos said:
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."

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.
 
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  • #14
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].
 
  • #15
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?
 
  • #16
Catria said:
I'm so tempted to say that a girl has smoother skin than a neutron star...

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.
 
  • #17
Lsos said:
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?

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
 
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  • #18
ImaLooser said:
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.
0.04 microinch are 1nm = 10 Å.
This would be extremely good for a mirror.

I saw 10nm as value for its surface. The total shape deviates from a paraboloid, but that does not change the smoothness of the surface.
 
  • #19
mfb said:
0.04 microinch are 1nm = 10 Å.
This would be extremely good for a mirror.

I saw 10nm as value for its surface. The total shape deviates from a paraboloid, but that does not change the smoothness of the surface.


1nm = 10 Å is true. That would be ten atomic diameters, so I don't believe the mirror is that precisely ground.

0.04 microinches is quite close to 100nm.

With their having made such a gross error I don't trust that source. I'll go with the NY Times.
 
  • #20
1 inch = 0.025m
0.04µinch = 40ninch = 40*0.025nm = 1nm
 
  • #21
mfb said:
1 inch = 0.025m
0.04µinch = 40ninch = 40*0.025nm = 1nm

By golly you are right. I don't believe a mirror can be ground that accurately, though.
 
  • #22
it is predictable that many would support the notion that neutron stars have the smoothest surfaces in the universe...and yet the OP, nor anyone else, has bothered to define the term "surface" within the context of this thread. i don't know whether or not solidity and/or the ability to support a mass is a prerequisite for you guys and gals, but if we go by the traditional simplistic definition of a surface as a simple 2-dimensional manifold/barrier, then i would venture so far as to say that the surfaces of black holes (event horizons) are smoother than the surfaces of neutron stars, despite them not being surfaces that can physically support a mass...
 
  • #23
Lsos said:
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?
No, a neutron star is within a millirmeter of being perfectly spherical. Factor that over 12-20 kilometers.
 
  • #24
Chronos said:
No, a neutron star is within a millirmeter of being perfectly spherical. Factor that over 12-20 kilometers.

Isn't that what they did above? Turns out the Hubble IS slightly smoother, but within the same order of magnitude.
 
  • #25
does anyone care to argue that event horizons are not the smoothest surfaces in the universe? after all, if a surface is simply a 2-dimensional manifold or boundary, then event horizons qualify as surfaces, even if their properties are vastly different from the material surfaces of objects such as a rocky planet, white dwarf, or neutron star...
 
  • #26
Not all neutron stars are equally smooth. It depends on spin. Maximum spin is about 750 revolutions per second. In this case any "mountain" more than a millimeter high produces gravitational waves which dissipate a large amount of energy, so such a mountain is energetically unfavorable. For slowly rotating neutron stars the maximum mountain could be a few centimeters high.
 
  • #27
94JZA80 said:
does anyone care to argue that event horizons are not the smoothest surfaces in the universe? after all, if a surface is simply a 2-dimensional manifold or boundary, then event horizons qualify as surfaces, even if their properties are vastly different from the material surfaces of objects such as a rocky planet, white dwarf, or neutron star...

can anyone refute this?
 
  • #28
The surface of a sphere around an arbitrary point, with radius 1m, is perfectly smooth. Downside: It has no special physical meaning, as it is not made out of matter.
The event horizon has a physical meaning, but it is not an object, so it is somewhere in between the imaginary sphere and solid objects.
 
  • #29
goldsax said:
can anyone refute this?

Sure, an idealized mathematical surface can be smoother than an actual physical object. To me that is not an interesting case.
 
  • #30
A surface is a 2-dimensional manifold or boundary characterizing a material object for the purposes of this thread.
 

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