# Would a Neutron Star Stop a Neutrino?

by Islam Hassan
Tags: neutrino, neutron, star, stop
 P: 131 Like the question says, would a neutrino be stopped by the very high density matter in a neutron star? IH
 PF Patron Sci Advisor Emeritus P: 5,310 Googling shows that there are various people trying to calculate this, e.g., http://arxiv.org/abs/astro-ph/9806285 http://prola.aps.org/abstract/PR/v133/i4B/pB1046_1 Just as a first guess, I would have expected by default that a neutrino entering a neutron star would have about the same probability of being absorbed as a neutrino entering a main-sequence star, since they encounter about the same amount of mass. The abstract of the second paper talks about a mechanism that produces a deviation from this expectation, causing a neutron star to be completely transparent to neutrinos with low energies.
 Mentor P: 14,661 The first guess is pretty close. And since we know that probability is low, we know that neutron stars are largely transparent to neutrinos.
P: 131

## Would a Neutron Star Stop a Neutrino?

 Quote by bcrowell Googling shows that there are various people trying to calculate this, e.g., http://arxiv.org/abs/astro-ph/9806285 http://prola.aps.org/abstract/PR/v133/i4B/pB1046_1 Just as a first guess, I would have expected by default that a neutrino entering a neutron star would have about the same probability of being absorbed as a neutrino entering a main-sequence star, since they encounter about the same amount of mass. The abstract of the second paper talks about a mechanism that produces a deviation from this expectation, causing a neutron star to be completely transparent to neutrinos with low energies.
Funny, isn't density a factor at all? I would have thought that the sheer density of matter in a neutron star would significantly raise the probability of impact. After all, if you can precisely align a neutrino's trajectory with a nucleon, wouldn't impact be guaranteed? How would impact depend only on the magnitude of mass encountered and not on its spatial 'packing'?

IH
P: 1,262
 Quote by Islam Hassan Like the question says, would a neutrino be stopped by the very high density matter in a neutron star?
It is a fairly simple problem to estimate (in an order of magnitude sense), which is much better than guessing. The cross section for interaction between a neutrino and a nucleon (e.g. neutron) is about $$\sigma_{n \nu} \approx 10^{-42} \textrm{ cm}^2$$. If you assume a neutron star is ~1.4 solar masses, with a radius of about 10km, composed entirely of nucleons -- you can calculate the mean free path as $$l = (n \sigma)^{-1}$$, where n is the number density of nucleons.

The mean free path (l) is the average distance a neutrino will go before colliding. If the mean free path is smaller than 10km, you can expect the neutrino to collide; otherwise you would expect it to escape freely.

~~~~~

The exact answer depends on the details of neutron star structure which is still uncertain.
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P: 4,464
 Quote by Islam Hassan Funny, isn't density a factor at all? I would have thought that the sheer density of matter in a neutron star would significantly raise the probability of impact. After all, if you can precisely align a neutrino's trajectory with a nucleon, wouldn't impact be guaranteed? How would impact depend only on the magnitude of mass encountered and not on its spatial 'packing'? IH
I'm not sure this part has been answered. A nucleon is complex object (an acquaintance who assisted programming lattice QCD likened it to weather forecasting, only worse), consisting of quarks and gluons (mostly). From the perspective of a neutrino, it is mostly empty space. Thus, first order, squeezing a given mass into a smaller volume does not change the interaction cross section.

Given that it takes light years of lead to reach 50% chance of absorbing a neutrino, that is enough to conclude that neutrons stars have a small chance of stopping a neutrino.
P: 131
 Quote by PAllen I'm not sure this part has been answered. A nucleon is complex object (an acquaintance who assisted programming lattice QCD likened it to weather forecasting, only worse), consisting of quarks and gluons (mostly). From the perspective of a neutrino, it is mostly empty space. Thus, first order, squeezing a given mass into a smaller volume does not change the interaction cross section. Given that it takes light years of lead to reach 50% chance of absorbing a neutrino, that is enough to conclude that neutrons stars have a small chance of stopping a neutrino.
What if we assume that a good deal of the center of a neutron star is quark gluon plasma; would that enhance the chances of impact?

IH
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 Quote by Islam Hassan What if we assume that a good deal of the center of a neutron star is quark gluon plasma; would that enhance the chances of impact? IH
Not unless it were much denser than a neutron. In fact it is less dense.
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 Quote by zhermes It is a fairly simple problem to estimate (in an order of magnitude sense), which is much better than guessing. The cross section for interaction between a neutrino and a nucleon (e.g. neutron) is about $$\sigma_{n \nu} \approx 10^{-42} \textrm{ cm}^2$$. If you assume a neutron star is ~1.4 solar masses, with a radius of about 10km, composed entirely of nucleons -- you can calculate the mean free path as $$l = (n \sigma)^{-1}$$, where n is the number density of nucleons. The mean free path (l) is the average distance a neutrino will go before colliding. If the mean free path is smaller than 10km, you can expect the neutrino to collide; otherwise you would expect it to escape freely. ~~~~~ The exact answer depends on the details of neutron star structure which is still uncertain.
I verified the given cross section as ballpark (depends sensitively on neutrino energy). I also calculate that the nucleon density in the core of a neutron star is 5*10^38 nucleon/cm^3 (assuming I didn't make a mistake combining various published figures). This gives a rather short mean free path. This suggests both a neutron star and a normal star are likely to absorb a neutrino.

So, unless there is a flaw in the above, my previous answers were incorrect.
P: 1,262
 Quote by PAllen This gives a rather short mean free path.
From that calculation, I get l ~ 1000 cm. Extremely short indeed; neutron stars are definitely opaque to neutrinos.

 Quote by PAllen This suggests both a neutron star and a normal star are likely to absorb a neutrino.
A normal star is very unlikely to absorb a neutrino. The interaction probability is not dependent on only the total mass---as the above calculation indicates. The number density of nucleons scales like $$R^{-3}$$ while the path-length of interest only scales like R---thus a larger (less dense) distribution is far less effective at absorbing a neutrino.
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 Quote by zhermes From that calculation, I get l ~ 1000 cm. Extremely short indeed; neutron stars are definitely opaque to neutrinos. A normal star is very unlikely to absorb a neutrino. The interaction probability is not dependent on only the total mass---as the above calculation indicates. The number density of nucleons scales like $$R^{-3}$$ while the path-length of interest only scales like R---thus a larger (less dense) distribution is far less effective at absorbing a neutrino.
Right. Of course, since the cross section is proportional to neutrino energy squared, and the given figure is ballpark for 1 Mev neurtrinos, if you consider 1 ev neutrinos, you have mean free path of 10^15 cm, even through neutron star core material. So very low energy neutrinos are the ultimate ghost particles.
P: 14
 Quote by PAllen Right. Of course, since the cross section is proportional to neutrino energy squared, and the given figure is ballpark for 1 Mev neurtrinos, if you consider 1 ev neutrinos, you have mean free path of 10^15 cm, even through neutron star core material. So very low energy neutrinos are the ultimate ghost particles.
Based on what we think we knew last week. So when the recent studies in Japan are confirmed, it's either as we thought last week or we have to consider our model flawed in that we had thus far only considered neutrinos of a given type, but now with the possibility that some are linking to a higher state to become a charged particle, we would have to assume an impact; or something else that changes the environmental conditions.
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 Quote by quasi44 Based on what we think we knew last week. So when the recent studies in Japan are confirmed, it's either as we thought last week or we have to consider our model flawed in that we had thus far only considered neutrinos of a given type, but now with the possibility that some are linking to a higher state to become a charged particle, we would have to assume an impact; or something else that changes the environmental conditions.
I could be wrong, but the derivation and formula I reviewed purported to be independent of neutrino flavor, thus not affected by oscillation. Perhaps the extremely small magnetic moment that follows if the Japan results are confirmed would be relevant at low energies. Please explain what you mean by 'linking to a higher state to become a charged particle'. I don't know what that means or how it relates to recent findings.
P: 14
 Quote by PAllen I could be wrong, but the derivation and formula I reviewed purported to be independent of neutrino flavor, thus not affected by oscillation. Perhaps the extremely small magnetic moment that follows if the Japan results are confirmed would be relevant at low energies. Please explain what you mean by 'linking to a higher state to become a charged particle'. I don't know what that means or how it relates to recent findings.
Well, their finding suggested that they are registering hits by neutrinos with an electron, though that is not what they fired. To pick up an electron, it would have to hit something, or have some requirement satisfied as to allow it to take one from something else.
P: 14
 Quote by PAllen I could be wrong, but the derivation and formula I reviewed purported to be independent of neutrino flavor, thus not affected by oscillation. Perhaps the extremely small magnetic moment that follows if the Japan results are confirmed would be relevant at low energies. Please explain what you mean by 'linking to a higher state to become a charged particle'. I don't know what that means or how it relates to recent findings.
Oh, yeah, sorry. Not a charged particle, but a particle pair with charge.
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