APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Comments and questions about the APOD on the main view screen.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by BDanielMayfield » Wed Dec 18, 2019 8:41 pm

neufer wrote:
Wed Dec 18, 2019 8:04 pm
BDanielMayfield wrote:
Wed Dec 18, 2019 7:36 pm
Because the gravitational lensing effect of neutron stars is so strong, J0300 displays more than half of its surface toward the Earth.
So photon paths are bent around the normal horizon of NSs, letting us see more than half of their surfaces!

I number crunched some stats to estimate the escape velocity for NSs in the mass range of 1.1 to 2.14 Solar masses and came up with a range of .54 to .73 c.

So, what percentage of a neutron star's surface are we able to see?
If the radius were 1.5 times its Schwarzschild radius then one would be able to see all of the neutron star's surface.

In this case the actual radius of this neutron star is ~1.8 times its Schwarzschild radius so perhaps ~10% of the neutron star's surface is unseen.
Thanks Art.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by TheOtherBruce » Thu Dec 19, 2019 1:42 am

MarkBour wrote:
Wed Dec 18, 2019 8:01 pm
Wouldn't Hawking radiation apply to these bodies just as well as it would to a black hole?
Can you get Hawking radiation if there isn't an actual event horizon?
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by Chris Peterson » Thu Dec 19, 2019 1:45 am

TheOtherBruce wrote:
Thu Dec 19, 2019 1:42 am
MarkBour wrote:
Wed Dec 18, 2019 8:01 pm
Wouldn't Hawking radiation apply to these bodies just as well as it would to a black hole?
Can you get Hawking radiation if there isn't an actual event horizon?
No.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by neufer » Thu Dec 19, 2019 4:04 am

Chris Peterson wrote:
Thu Dec 19, 2019 1:45 am
TheOtherBruce wrote:
Thu Dec 19, 2019 1:42 am
MarkBour wrote:
Wed Dec 18, 2019 8:01 pm

Wouldn't Hawking radiation apply to these bodies just as well as it would to a black hole?
Can you get Hawking radiation if there isn't an actual event horizon?
No.
For a solar mass black hole to evaporate by Hawking radiation would require at least 1064 years.

Solar mass neutrons stars may well have evaporated by other methods long before solar mass black holes disappear:
https://en.wikipedia.org/wiki/Proton_decay wrote:
<<According to the Standard Model, protons, a type of baryon, are stable because baryon number (quark number) is conserved. Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon. Some beyond-the-Standard Model grand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life of 1031 to 1036 years. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.>>
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by alter-ego » Thu Dec 19, 2019 6:18 am

neufer wrote:
Wed Dec 18, 2019 8:04 pm
BDanielMayfield wrote:
Wed Dec 18, 2019 7:36 pm
Because the gravitational lensing effect of neutron stars is so strong, J0300 displays more than half of its surface toward the Earth.
So photon paths are bent around the normal horizon of NSs, letting us see more than half of their surfaces!

I number crunched some stats to estimate the escape velocity for NSs in the mass range of 1.1 to 2.14 Solar masses and came up with a range of .54 to .73 c.

So, what percentage of a neutron star's surface are we able to see?
If the radius were 1.5 times its Schwarzschild radius then one would be able to see all of the neutron star's surface.

In this case the actual radius of this neutron star is ~1.8 times its Schwarzschild radius so perhaps ~10% of the neutron star's surface is unseen.
I don't get the same estimate.
First, rs for the 1.35 M neutron star = 4km which makes it's actual radius =13km/4km ~3 times Schwarzschild radius. Second, instead of ray trajectory plots, I chose to use the video which shows the changing view of the lat/long wire-frame neutron star as function of mass. I estimated the increase in latitude visible at 0.9, 1.3, 1.7, and 2.2 solar masses, then calculated the sphere area visible. I find that ~60% to 65% of the NS surface will be visible (or 35% to 40% is unseen).
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by BDanielMayfield » Thu Dec 19, 2019 1:18 pm

The escape velocities I had come up with were way off, according to this from the neutron star wikipedia article:
One measure of such immense gravity is the fact that neutron stars have an escape velocity ranging from 100,000 km/s to 150,000 km/s, that is, from a third to half the speed of light.
My errors arose because the radii I used where too small. How does one correctly calculate NS radius for given mass?
Last edited by BDanielMayfield on Thu Dec 19, 2019 3:08 pm, edited 1 time in total.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by Chris Peterson » Thu Dec 19, 2019 2:30 pm

neufer wrote:
Thu Dec 19, 2019 4:04 am
Chris Peterson wrote:
Thu Dec 19, 2019 1:45 am
TheOtherBruce wrote:
Thu Dec 19, 2019 1:42 am

Can you get Hawking radiation if there isn't an actual event horizon?
No.
For a solar mass black hole to evaporate by Hawking radiation would require at least 1064 years.

Solar mass neutrons stars may well have evaporated by other methods long before solar mass black holes disappear:
https://en.wikipedia.org/wiki/Proton_decay wrote:
<<According to the Standard Model, protons, a type of baryon, are stable because baryon number (quark number) is conserved. Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon. Some beyond-the-Standard Model grand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life of 1031 to 1036 years. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.>>
I wouldn't say "may well have evaporated", but rather, "there's a remote chance that neutrons decay, and that would result in evaporation on a much shorter timescale than that of the evaporation of small black holes".

(FWIW, I calculate that a neutron star contains about 1.8 x 1057 neutrons, or about 2190, so if neutrons decay with a half-life of 1034 years, that suggests a lifetime of about 1036 years.)
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by neufer » Thu Dec 19, 2019 3:03 pm

BDanielMayfield wrote:
Thu Dec 19, 2019 1:18 pm

My errors arose because the radii I used where too small. How does one correctly calculate NS radius for given mass?
One could ask a bystander:
https://asterisk.apod.com/viewtopic.php?t=40100 wrote:
<<Through very careful analysis of the X-ray variations from this neutron star, the NICER data
show that J0030+0451 is 40 percent more massive than the Sun, but only about 15 miles wide.>>
It is probably better to think visually in terms of photon spheres
rather than mathematically in terms of escape velocities:

https://en.wikipedia.org/wiki/Photon_sphere
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by neufer » Thu Dec 19, 2019 3:48 pm

Chris Peterson wrote:
Thu Dec 19, 2019 2:30 pm
neufer wrote:
Thu Dec 19, 2019 4:04 am

For a solar mass black hole to evaporate by Hawking radiation would require at least 1064 years.

Solar mass neutrons stars may well have evaporated by other methods long before solar mass black holes disappear:
https://en.wikipedia.org/wiki/Proton_decay wrote:
<<According to the Standard Model, protons, a type of baryon, are stable because baryon number (quark number) is conserved. Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon. Some beyond-the-Standard Model grand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life of 1031 to 1036 years. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.>>
I wouldn't say "may well have evaporated", but rather, "there's a remote chance that neutrons decay, and that would result in evaporation on a much shorter timescale than that of the evaporation of small black holes".
There's a remote chance that we are capable of accurately predicting
what will be going on in 1.67×1034 years (much less 1064 years).
Chris Peterson wrote:
Thu Dec 19, 2019 2:30 pm

(FWIW, I calculate that a neutron star contains about 1.8 x 1057 neutrons, or about 2190, so if neutrons decay with a half-life of 1034 years, that suggests a lifetime of about 1036 years.)
A neutron star doesn't have to lose a whole lot of mass before it devolves into a large & very unstable atomic nucleus.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by BDanielMayfield » Thu Dec 19, 2019 3:51 pm

neufer wrote:
Thu Dec 19, 2019 3:03 pm
BDanielMayfield wrote:
Thu Dec 19, 2019 1:18 pm

My errors arose because the radii I used were too small. How does one correctly calculate NS radius for given mass?
One could ask a bystander:
https://asterisk.apod.com/viewtopic.php?t=40100 wrote:
<<Through very careful analysis of the X-ray variations from this neutron star, the NICER data
show that J0030+0451 is 40 percent more massive than the Sun, but only about 15 miles wide.>>
That would make J0030+0451's radius only about 12.07 km. However, in trying to answer my own question about NS radii calculation I find no consensus yet:
The equation of state for a neutron star is not yet known. It is assumed that it differs significantly from that of a white dwarf, whose equation of state is that of a degenerate gas that can be described in close agreement with special relativity. However, with a neutron star the increased effects of general relativity can no longer be ignored. Several equations of state have been proposed (FPS, UU, APR, L, SLy, and others) and current research is still attempting to constrain the theories to make predictions of neutron star matter.[10][41] This means that the relation between density and mass is not fully known, and this causes uncertainties in radius estimates. For example, a 1.5 M☉ neutron star could have a radius of 10.7, 11.1, 12.1 or 15.1 kilometers (for EOS FPS, UU, APR or L respectively).[41]
The radii I had come up with were 11.24 and 12 km for 1.1 to 2.14 solar mass stars, so I was still inside the realm of possibly valid values I guess.
It is probably better to think visually in terms of photon spheres
rather than mathematically in terms of escape velocities:

https://en.wikipedia.org/wiki/Photon_sphere
In view of the radius uncertainties that makes sense.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by JohnD » Thu Dec 19, 2019 4:17 pm

I LOVE it! Proper science, educating me! Not hand wavey, isnt-it-beatiful!
Thanks, science guys!
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by sillyworm 2 » Fri Dec 20, 2019 12:12 am

I am also happy to enjoy envisioning a city sized neutron star spinning at the calculated speed...with and without the science.

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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by TheZuke! » Fri Dec 20, 2019 3:11 pm

neufer wrote:
Wed Dec 18, 2019 8:04 pm

In this case the actual radius of this neutron star is ~1.8 times its Schwarzschild radius so perhaps ~10% of the neutron star's surface is unseen.
[jaw drop]!

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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by alter-ego » Sun Dec 22, 2019 11:34 pm

After some thought, I decided that some might be interested a graphic showing surface visibility evaluation details.
Art - I pursued a hybrid empirical evaluation using both the YouTube wireframe and an accurate, family of ray-trajectories. The two approaches agreed very well, only because the wireframe has a 1.3M example and the actual mass is estimated at 1.35M.
  • Fraction of surface area visible = 68% to 70%
The left panel shows a large collection of parallel light-ray trajectories originating at right from infinity interacting with a Schwarzschild black hole. The right panel a screenshot from the video showing the actual and apparent size of a 1.3M NS. The two panels are scaled so that the NS actual sizes are equal.
 
 
Visible Surface Fraction Evaluation_2.JPG
→ The blue rays show a family of "plunge orbits", i.e. all rays that are captured by the black hole.
→ The red rays show trajectories that aren't captured
→ The smaller black circle is the BH event horizon of mass M, and
     radius = 1 Schwarzschild radius, RS
→ The larger green circle represents the NS actual size = 3.25 RS
→ Green shaded area represents visible NS surface.
→ The 2 black trajectory rays leave the NS from their tangent point
(furthest visible point on surface) and propagate to infinity

Note:The X and Y distance units in the left pane Are normalized by the quantity G/c2 . The Schwarzschild radius = 2M in GR-convenient units.
 
  • The indicator lines connecting the two panels show the very good agreement for the predicted apparent NS sizes.
    The apparent size difference between and 1.3M and1.35are within the accuracy of the evaluation techniques. (I was pleasantly surprised the agreement as this good)
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by BDanielMayfield » Mon Dec 23, 2019 2:33 am

alter-ego wrote:
Sun Dec 22, 2019 11:34 pm
After some thought, I decided that some might be interested a graphic showing surface visibility evaluation details.
Art - I pursued a hybrid empirical evaluation using both the YouTube wireframe and an accurate, family of ray-trajectories. The two approaches agreed very well, only because the wireframe has a 1.3M example and the actual mass is estimated at 1.35M.
  • Fraction of surface area visible = 68% to 70%
The left panel shows a large collection of parallel light-ray trajectories originating at right from infinity interacting with a Schwarzschild black hole. The right panel a screenshot from the video showing the actual and apparent size of a 1.3M NS. The two panels are scaled so that the NS actual sizes are equal.
 
 
Visible Surface Fraction Evaluation_2.JPG
→ The blue rays show a family of "plunge orbits", i.e. all rays that are captured by the black hole.
→ The red rays show trajectories that aren't captured
→ The smaller black circle is the BH event horizon of mass M, and
     radius = 1 Schwarzschild radius, RS
→ The larger green circle represents the NS actual size = 3.25 RS
→ Green shaded area represents visible NS surface.
→ The 2 black trajectory rays leave the NS from their tangent point
(furthest visible point on surface) and propagate to infinity

Note:The X and Y distance units in the left pane Are normalized by the quantity G/c2 . The Schwarzschild radius = 2M in GR-convenient units.
 
  • The indicator lines connecting the two panels show the very good agreement for the predicted apparent NS sizes.
    The apparent size difference between and 1.3M and1.35are within the accuracy of the evaluation techniques. (I was pleasantly surprised the agreement as this good)
Awesome analysis and graphics! Thanks alter-ego.
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by neufer » Mon Dec 23, 2019 10:11 am

BDanielMayfield wrote:
Mon Dec 23, 2019 2:33 am

Awesome analysis and graphics! Thanks alter-ego.
Indeed, and thanks alter-ego for the correction with the actual size of the neutron star.

Apparently, I struggle with the simplest of math of relating 15 mile wide neutron stars with 2.95 kilometer radius solar mass black holes. :oops:
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Re: APOD: A Hotspot Map of Neutron Star... (2019 Dec 18)

Post by BDanielMayfield » Mon Dec 23, 2019 11:12 am

neufer wrote:
Mon Dec 23, 2019 10:11 am
BDanielMayfield wrote:
Mon Dec 23, 2019 2:33 am

Awesome analysis and graphics! Thanks alter-ego.
Indeed, and thanks alter-ego for the correction with the actual size of the neutron star.

Apparently, I struggle with the simplest of math of relating 15 mile wide neutron stars with 2.95 kilometer radius solar mass black holes. :oops:
__it happens to us all. And hey, hasn't a simple unit conversion error even doomed a Mars mission? At least tens of millions weren't wasted here.
Just as zero is not equal to infinity, everything coming from nothing is illogical.