Gap Bridging enhancement of modified Urca process in nuclear matter - - PowerPoint PPT Presentation

Gap Bridging enhancement of modified Urca process in nuclear matter

Kamal Pangeni

(in collaboration with Mark Alford)

Washington University in St. Louis

Nuclear Physics, Compact Stars, and Compact Star Mergers 2016 (NPCSM2016) YITP , Kyoto University.

October 27, 2016

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 1 / 24

Overview

In superfluid nuclear matter, transport properties (such as neutrino emissivity) are strongly suppressed as exp(−∆/T) by the gap ∆ in neutron or proton spectrum. Density oscillation of high enough amplitude can unsuppress the exponential suppression of certain transport propetries such as neutrino emissivity and bulk viscosity that are dominated by flavor changing weak processes. The mechanism is called “Gap Bridging”.

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 2 / 24

Overview

In superfluid nuclear matter, transport properties (such as neutrino emissivity) are strongly suppressed as exp(−∆/T) by the gap ∆ in neutron or proton spectrum. Density oscillation of high enough amplitude can unsuppress the exponential suppression of certain transport propetries such as neutrino emissivity and bulk viscosity that are dominated by flavor changing weak processes. The mechanism is called “Gap Bridging”. Some oscillation in neutron star can reach high amplitude.

1

StarQuakes

• L. Franco et. al APJ 543(2000) 987

2

Tidal forces in binary mergers

• D. Tsang et. al PRL 108 (2012)

3

Unstable oscillations of rotating compact stars such as r-modes

• N. Andersson, APJ 502 (1998) 708

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 2 / 24

Overview

In superfluid nuclear matter, transport properties (such as neutrino emissivity) are strongly suppressed as exp(−∆/T) by the gap ∆ in neutron or proton spectrum. Density oscillation of high enough amplitude can unsuppress the exponential suppression of certain transport propetries such as neutrino emissivity and bulk viscosity that are dominated by flavor changing weak processes. The mechanism is called “Gap Bridging”. Some oscillation in neutron star can reach high amplitude.

1

StarQuakes

• L. Franco et. al APJ 543(2000) 987

2

Tidal forces in binary mergers

• D. Tsang et. al PRL 108 (2012)

3

Unstable oscillations of rotating compact stars such as r-modes

• N. Andersson, APJ 502 (1998) 708

Consequences:

1

enhanced cooling via neutrino emission.

2

non-linear damping of r-mode itself.

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Compression drives the system out of beta equilibrium

Density compression leads to the change in Fermi momenta.

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Compression drives the system out of beta equilibrium

Density compression leads to the change in Fermi momenta. Under relatively fast compression the proton Fermi energy is µ∆ below the neutron Fermi energy. µ∆ = µn − µp − µe

Beta Equilibrium n p e µn µp+ µe n p e Compression µΔ n p e New Equilibrium

An increase in µ∆ increaes the reaction rate and neutrino emissivity.

• A. Reisenegger, APJ 442:749-757 (1995)

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 3 / 24

How does “Gap Bridging” work?

µn

p

µ e µe + ∆ p n 2

n

No Compression

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 4 / 24

How does “Gap Bridging” work?

µn

p

µ e µe + ∆ p n 2

n

No Compression

µ∆ e n p

Slight Compression

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 4 / 24

How does “Gap Bridging” work?

µn

p

µ e µe + ∆ p n 2

n

No Compression

µ∆ e n p

Slight Compression

µ∆ e p n

Strong Compression At strong compression n → p can go but n → n and p→ p are still pauli blocked. Gap Bridging is relevant to any reaction where nucleon or quark change flavor.

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 4 / 24

Previous work: 1S0 neutron pairing and direct Urca

T50 T25 T10 T5 T0 T100 1 2 5 10 20 50 100 1020 1015 1010 105 1 105

Μ

• T

RΕ

• M. Alford, S. Reddy and K. Schwenzer PRL 108 (2012)

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 5 / 24

Previous work: 1S0 neutron pairing and direct Urca

T50 T25 T10 T5 T0 T100 1 2 5 10 20 50 100 1020 1015 1010 105 1 105

Μ

• T

RΕ

• M. Alford, S. Reddy and K. Schwenzer PRL 108 (2012)

Direct Urca process (n↔ p+e+¯ ν) is forbidden in most of the neutron stars by energy momentum conservation.(pFn > pFp + pFe) In the inner regions of NS, neutrons pair in 3P2 channel not 1S0.

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 5 / 24

Plan

Previous Work:

1

Direct Urca process with 1S0 neutron pairing.

Current Work:

1

Modified Urca process with 1S0 neutron pairing

2

Modified Urca process with 3P2 neutron pairing

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Modified Urca process

p2 p1 p3 pe 𝒘 p4 p n2

n p

e

𝒘

n1 n3

n + n → n + p + e− + ¯ νe p + n + e− → n + n + νe n1 is “spectator” neutron. n2 is “protagonist” neutron. The‘spectator’ neutron, interacting via pion exchange, absorbs the extra momentum.

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Modified Urca process

p2 p1 p3 pe 𝒘 p4 p n2

n p

e

𝒘

n1 n3

n + n → n + p + e− + ¯ νe p + n + e− → n + n + νe n1 is “spectator” neutron. n2 is “protagonist” neutron. The‘spectator’ neutron, interacting via pion exchange, absorbs the extra momentum. No flavor change for spectator particle. What role does spectator neutron play?

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 7 / 24

Gap Bridging enhancement of neutrino emission.

Emissivity (ǫ): ǫ =  

4

• j=1

d3Pj (2π)3   d3Pe (2π)3 d3Pν (2π)3 (2π)4δ(Ef − Ei)× δ3( Pf − Pi)Eνf1f2(1 − f3)(1 − f4)(1 − fe)|Mfi|2 Rǫ = ǫ(µ∆/T, ∆/T) ǫ(0, 0) Rǫ is the modification function. Rǫ measures how much the emissivity is affected by nonlinear high amplitude effects and by Cooper pairing. Battle between exp(−∆/T) suppression and µ∆ enhancement.

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Emissivity with 1S0 pairing for neutrons and protons

n T 20 n T 40 n T 60 n T 80 p n

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n

RΕ

1S0 neutron and proton pairing

When µ∆ = 0, R¯

ǫ is roughly exp[−2∆/T]

When µ∆ = 4∆n, R¯

ǫ is of order 1. Cancels exp[−∆/T]

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Dominant processes at low and high µ∆

n p p e e n

⇒

n p p e e n

µ∆ = 0(exp(−2∆/T)) µ∆ > 0(exp(−2∆/T))

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 10 / 24

Dominant processes at low and high µ∆

n p p e e n

⇒

n p p e e n

µ∆ = 0(exp(−2∆/T)) µ∆ > 0(exp(−2∆/T))

n p p e e n

⇒

n p p e e n

µ∆ = 0(exp(−4∆/T)) µ∆ > 0(exp(−2∆/T))

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 10 / 24

3P2 neutron pairing

For the 3P2, there is still a choice of orientation of the condensate: Jz could be 0, ±1, ± 2. Microscopic calculations find that Jz = 0 is very slightly energetically favored over the other subchannels.

• T. Takatsuka and R. Tamagaki, PTP (1971),
• L. Amundsen and E. Ostgaard, NPA, (1985)

However this is not conclusive because of uncertainities in the microscpoic theory. We will consider neutron condensates with Jz = 0 and |Jz| = 2 as we expect these to show different dependencies of the emissivity

• n temperatue and oscillation amplitude.

1

For Jz = 0 all neutron states at fermi surface are gapped.

2

for |Jz| = 2 there are ungapped nodes at the poles.

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Modified Urca process with 3P2(Jz = 0) neutron pairing

The angular dependence of the neutron gap in this channel is : ∆n(θ) = ∆n0

• 1 + 3 cos2(θ)

2 n0 4 n0 Pn

The gap varies between a minimum of ∆n0 (around the equator) and 2∆n0 (at the poles) but does not vanish anywhere on the Fermi surface. We therefore expect that 3P2 pairing will be qualitatively similar to

1S0 pairing

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n0 T 20 n0 T 40 n0 T 60 n0 T 80 n0 p

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n0

RΕ

3P2Jz0 neutron pairing and 1S0 proton pairing

Emissivity in 3P2(Jz = 0) is about a factor of 40 less than the 1S0 case.

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 13 / 24

Modified Urca with 3P2(Jz = 2) neutron pairing

The angular dependence of the neutron gap in (Jz = 2) subchannel is: ∆n(θ) = ∆n0 sin(θ) The Neutron gap vanishes at the poles and has a maximum value of ∆n0 around the equator. n3 n2 n1

2 Δn0

60

• Kamal Pangeni (Wustl)

Gap Bridging October 27, 2016 14 / 24

n0 T 20 n0 T 40 n0 T 60 n0 T 80 n0 p

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n0

RΕ

3P2Jz2 neutron pairing and 1S0 proton pairing

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 15 / 24

n0 T 20 n0 T 40 n0 T 60 n0 T 80 n0 p

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n0

RΕ

3P2Jz2 neutron pairing and 1S0 proton pairing n0 T 20 n0 T 40 n0 T 60 n0 T 80 n0 p

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n0

RΕ

3P2Jz0 neutron pairing and 1S0 proton pairing

Lower suppression of 3P2(Jz = 2) subchannel is expected becuase

• f the node in the neutron fermi surface.

For low amplitudes the neutrino emissivity is exponentially suppressed by the gap, roughly as exp(−1.73∆n0/T), as compared with exp(−2∆n/T) for 1S0 neutron pairing . Complete gap bridging happens at µ∆ = 2.73∆n in the case of

3P2(Jz = 2)

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 15 / 24

Conclusions

We have shown that the exponential suppression of flavor-changing beta processes in superfluid/superconducting nuclear matter can be completely overcome, via the mechanism of gap bridging, by compression oscillations of sufficiently high amplitude, regardless of how low the temperature may be. In Jz = 0 subchannel of modified Urca process with 3P2 neutron pairing, the exponential suppression is overcome when µ∆ ∼ 4∆n In Jz = 2 subchannel of modified Urca process with 3P2 neutron pairing, the exponential suppression is overcome when µ∆ ∼ 2.73∆n The enhancement of transport properties, such as neutrino emissivity, will lead to enhanced cooling via neutrino emission.

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 16 / 24

Thank You!!

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Back Up Slides

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n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n n p p e e n Δp Δn 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 µn µe µp

16 different channels that fall under 5 classes. channels under same class have same response to compression

• scillation.

channels under class 3 dominates at low δµ while channel 1 dominates at high δµ

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Rules at zero compression (δµ=0)

For each arrow starting at energy +E (i.e. above the Fermi surface): a factor of exp(−E/T) For each arrow ending at energy −E (i.e. below the Fermi surface): a factor of exp(−E/T) n p p n

Δp Δn

e e

2

n p p e e n

3

exp(−3∆n) exp(−2∆n)

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n T

• P

T 60 1 2 3 4 5

1 2 3 4 5 1012 100 1020 1040 1060 1080 10100 Μ

• n

RΕ

1S0 neutron and proton pairing

n p p e e n

4 (ẟµ=0)

n p p e e n

4 (ẟµ>0)

e-3Δ/T e-3Δ/T

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 21 / 24

n T

• P

T 60 1 2 3 4 5

1 2 3 4 5 1012 100 1020 1040 1060 1080 10100 Μ

• n

RΕ

1S0 neutron and proton pairing

n p p e e n

2 (ẟµ=0)

n p p e e n

2 (ẟµ>0)

e-3Δ/T e-Δ/T

This explains the step structure

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n0 T 20 n0 T 40 n0 T 60 n0 T 80 n0 p

1 2 3 4 5 1012 100 1015 1030 1045 1060 1070 Μ

• n0

RΕ

3P2Jz2 neutron pairing and 1S0 proton pairing p e e n n n n

0.86 Δn0

p

Δp

Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 23 / 24

p p e e n n n n

0.86Δn0 Δp

p p e e n n n n

0.86Δn0 Δp

(ẟµ=0) (ẟµ=0.86Δn0) p p e e n n n n

0.86Δn0 Δp

(ẟµ=1.73Δn0)

Complete gap bridging happens at δµ = 2.73∆n

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