30
M. C. Miller
1.5.2 Additional Neutrino Production Channels
and Suppression
As described in the lucid review of [172], hyperons can produce neutrinos via, e.g.,
Σ − → Λ + e − + ¯
ν e , Λ + e − → Σ − + ν e , and processes that involve both hyperons
and nucleons. If condensates form (the leading candidates are of pions or kaons)
then the condensate acts as an effectively infinite reservoir of momentum. This
produces channels such as n + +π − → n + e − + ¯
ν e and n + +K − → n + e − + ¯
ν e ,
where the angle brackets indicate the condensate. The kaon process involves a
strangeness change and is thus less efficient than the pion process, modulo effects
related to the medium [172]. If deconfined quarks are a significant degree of freedom
then other direct URCA-like processes can emerge, such as u + e − → d + ν e and its
inverse (e + could be present in negatively charged quark matter, but the processes
are the same), and u + e − → s + ν e and its inverse (suppressed by an order of
magnitude because of the strangeness change). All of these processes are orders of
magnitude more efficient than modified URCA, and all scale as T 6 .
A separate channel has the interesting property that it can both increase and
suppress cooling, depending on the details. This is the transition to a superfluid
state. This transition occurs via Cooper pairing of the neutrons, and the immediate
effect is the emission of a neutrino-antineutrino pair: n + n → [nn] + ν + ¯
ν. Given
that one fewer effective particle is involved than in modified URCA the emissivity
scales as T 7 instead of T 8 , so at T ∼ 10 9 K the emissivity of Cooper pairing can be
comparable to or greater than modified URCA. As the shell where the temperature
is less than the superfluid critical temperature moves inwards, this can therefore
enhance neutrino emission.
In the long term, however, the pairing produces an energy gap Δ ∼ kT c (where T c
is the superfluid critical temperature) at the Fermi surface that suppresses processes
by a factor of order e −Δ/kT for T T c , modulo details of the phase space
and the temperature dependence of Δ. The suppression can thus be extremely
dramatic. It occurs for both the neutrino emissivity and for the specific heat (with
different factors). See, e.g., Figure 5 of [172] for plots of some of the suppression
factors (called control functions there). The critical temperature and energy gap
are extremely difficult to calculate from first principles. Current estimates of the
3 P-F 2 gap suggest Δ ∼ 0.05 − 0.1 MeV [74, 169, 198], which corresponds to
T ∼ 5 × 10 8 − 10 9 K. This is comparable to the expected core temperatures and
thus could make a significant difference.
Cooper pairing can also occur in deconfined quark matter [6]. In that context it
is much more complicated than in ordinary matter because quarks have different
colors, flavors, and masses. Multiple types of condensation are therefore possible.
The color gap is estimated to be ∼50 − 100 MeV [172], which is huge compared to
internal temperatures and is thus potentially quite important.
M. C. Miller
1.5.2 Additional Neutrino Production Channels
and Suppression
As described in the lucid review of [172], hyperons can produce neutrinos via, e.g.,
Σ − → Λ + e − + ¯
ν e , Λ + e − → Σ − + ν e , and processes that involve both hyperons
and nucleons. If condensates form (the leading candidates are of pions or kaons)
then the condensate acts as an effectively infinite reservoir of momentum. This
produces channels such as n + +π − → n + e − + ¯
ν e and n + +K − → n + e − + ¯
ν e ,
where the angle brackets indicate the condensate. The kaon process involves a
strangeness change and is thus less efficient than the pion process, modulo effects
related to the medium [172]. If deconfined quarks are a significant degree of freedom
then other direct URCA-like processes can emerge, such as u + e − → d + ν e and its
inverse (e + could be present in negatively charged quark matter, but the processes
are the same), and u + e − → s + ν e and its inverse (suppressed by an order of
magnitude because of the strangeness change). All of these processes are orders of
magnitude more efficient than modified URCA, and all scale as T 6 .
A separate channel has the interesting property that it can both increase and
suppress cooling, depending on the details. This is the transition to a superfluid
state. This transition occurs via Cooper pairing of the neutrons, and the immediate
effect is the emission of a neutrino-antineutrino pair: n + n → [nn] + ν + ¯
ν. Given
that one fewer effective particle is involved than in modified URCA the emissivity
scales as T 7 instead of T 8 , so at T ∼ 10 9 K the emissivity of Cooper pairing can be
comparable to or greater than modified URCA. As the shell where the temperature
is less than the superfluid critical temperature moves inwards, this can therefore
enhance neutrino emission.
In the long term, however, the pairing produces an energy gap Δ ∼ kT c (where T c
is the superfluid critical temperature) at the Fermi surface that suppresses processes
by a factor of order e −Δ/kT for T T c , modulo details of the phase space
and the temperature dependence of Δ. The suppression can thus be extremely
dramatic. It occurs for both the neutrino emissivity and for the specific heat (with
different factors). See, e.g., Figure 5 of [172] for plots of some of the suppression
factors (called control functions there). The critical temperature and energy gap
are extremely difficult to calculate from first principles. Current estimates of the
3 P-F 2 gap suggest Δ ∼ 0.05 − 0.1 MeV [74, 169, 198], which corresponds to
T ∼ 5 × 10 8 − 10 9 K. This is comparable to the expected core temperatures and
thus could make a significant difference.
Cooper pairing can also occur in deconfined quark matter [6]. In that context it
is much more complicated than in ordinary matter because quarks have different
colors, flavors, and masses. Multiple types of condensation are therefore possible.
The color gap is estimated to be ∼50 − 100 MeV [172], which is huge compared to
internal temperatures and is thus potentially quite important.