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. StarQuakes 1 L. Franco et. al APJ 543(2000) 987 Tidal forces in binary mergers 2 D. Tsang et. al PRL 108 (2012) Unstable oscillations of rotating 3 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. StarQuakes 1 L. Franco et. al APJ 543(2000) 987 Tidal forces in binary mergers 2 D. Tsang et. al PRL 108 (2012) Unstable oscillations of rotating 3 compact stars such as r-modes N. Andersson, APJ 502 (1998) 708 Consequences: enhanced cooling via neutrino emission. 1 non-linear damping of r-mode itself. 2 Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 2 / 24
Compression drives the system out of beta equilibrium Density compression leads to the change in Fermi momenta. Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 3 / 24
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 ∆ = µ n − µ p − µ e µ Δ µ n µ p+ µ e p p p n n n e e e Beta Equilibrium Compression 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? µ µ n p ∆ 2 n + µ e p n e No Compression Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 4 / 24
How does “Gap Bridging” work? µ ∆ µ µ n p ∆ 2 n + µ e p p n n e e Slight Compression No Compression Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 4 / 24
How does “Gap Bridging” work? µ ∆ µ ∆ µ µ n p ∆ 2 n + µ e p p p n n n e e e Slight Compression Strong Compression No 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: 1 S 0 neutron pairing and direct Urca 10 5 � � T � 0 � � T � 5 1 � � T � 10 10 � 5 R Ε � � � T � 25 10 � 10 10 � 15 � � T � 50 � � T � 100 10 � 20 1 2 5 10 20 50 100 � � � T Μ M. Alford, S. Reddy and K. Schwenzer PRL 108 (2012) Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 5 / 24
Previous work: 1 S 0 neutron pairing and direct Urca 10 5 � � T � 0 � � T � 5 1 � � T � 10 10 � 5 R Ε � � � T � 25 10 � 10 10 � 15 � � T � 50 � � T � 100 10 � 20 1 2 5 10 20 50 100 � � � T Μ 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.( p Fn > p Fp + p Fe ) In the inner regions of NS, neutrons pair in 3 P 2 channel not 1 S 0 . Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 5 / 24
Plan Previous Work: Direct Urca process with 1 S 0 neutron pairing. 1 Current Work: Modified Urca process with 1 S 0 neutron pairing 1 Modified Urca process with 3 P 2 neutron pairing 2 Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 6 / 24
Modified Urca process n + n → n + p + e − + ¯ ν e p 𝒘 p + n + e − → n + n + ν e 𝒘 pe e p4 p p3 n3 n n 1 is “spectator” neutron. n 2 is “protagonist” neutron. n2 n1 The‘spectator’ neutron, p1 p2 interacting via pion exchange, absorbs the extra momentum. Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 7 / 24
Modified Urca process n + n → n + p + e − + ¯ ν e p 𝒘 p + n + e − → n + n + ν e 𝒘 pe e p4 p p3 n3 n n 1 is “spectator” neutron. n 2 is “protagonist” neutron. n2 n1 The‘spectator’ neutron, p1 p2 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 ): � 4 d 3 P j d 3 P e d 3 P ν � ( 2 π ) 3 ( 2 π ) 4 δ ( E f − E i ) × ǫ = ( 2 π ) 3 ( 2 π ) 3 j = 1 δ 3 ( � P f − � P i ) E ν f 1 f 2 ( 1 − f 3 )( 1 − f 4 )( 1 − f e ) | M fi | 2 R ǫ = ǫ ( µ ∆ / T , ∆ / T ) ǫ ( 0 , 0 ) R ǫ is the modification function. R ǫ measures how much the emissivity is affected by nonlinear high amplitude effects and by Cooper pairing. Battle between exp ( − ∆ / T ) suppression and µ ∆ enhancement. Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 8 / 24
Emissivity with 1 S 0 pairing for neutrons and protons 1 S 0 neutron and proton pairing 10 12 10 0 � n � T � 20 10 � 15 � n � T � 40 R Ε 10 � 30 � n � T � 60 10 � 45 � n � T � 80 10 � 60 � p � � n 10 � 70 0 1 2 3 4 5 � Μ � � � n When µ ∆ = 0 , R ¯ ǫ is roughly exp [ − 2 ∆ / T ] When µ ∆ = 4 ∆ n , R ¯ ǫ is of order 1. Cancels exp [ − ∆ / T ] Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 9 / 24
Dominant processes at low and high µ ∆ n p n p e e n p n p e e ⇒ 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 n p e e n p n p e e ⇒ µ ∆ = 0 ( exp ( − 2 ∆ / T )) µ ∆ > 0 ( exp ( − 2 ∆ / T )) n p n p e e n n e e p p ⇒ µ ∆ = 0 ( exp ( − 4 ∆ / T )) µ ∆ > 0 ( exp ( − 2 ∆ / T )) Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 10 / 24
3 P 2 neutron pairing For the 3 P 2 , there is still a choice of orientation of the condensate: J z could be 0, ± 1, ± 2. Microscopic calculations find that J z = 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 J z = 0 and | J z | = 2 as we expect these to show different dependencies of the emissivity on temperatue and oscillation amplitude. For J z = 0 all neutron states at fermi surface are gapped. 1 for | J z | = 2 there are ungapped nodes at the poles. 2 Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 11 / 24
Modified Urca process with 3 P 2 ( J z = 0 ) neutron pairing The angular dependence of the neutron gap in this channel is : � ∆ n ( θ ) = ∆ n 0 1 + 3 cos 2 ( θ ) 4 � n0 P n 2 � n0 The gap varies between a minimum of ∆ n 0 (around the equator) and 2 ∆ n 0 (at the poles) but does not vanish anywhere on the Fermi surface. We therefore expect that 3 P 2 pairing will be qualitatively similar to 1 S 0 pairing Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 12 / 24
3 P 2 � J z � 0 � neutron pairing and 1 S 0 proton pairing 10 12 10 0 � n0 � T � 20 10 � 15 � n0 � T � 40 R Ε 10 � 30 � n0 � T � 60 10 � 45 � n0 � T � 80 � n0 � � p 10 � 60 10 � 70 0 1 2 3 4 5 � Μ � � � n0 Emissivity in 3 P 2 ( J z = 0 ) is about a factor of 40 less than the 1 S 0 case. Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 13 / 24
Modified Urca with 3 P 2 ( J z = 2 ) neutron pairing The angular dependence of the neutron gap in ( J z = 2 ) subchannel is: ∆ n ( θ ) = ∆ n 0 sin ( θ ) The Neutron gap vanishes at the poles and has a maximum value of ∆ n 0 around the equator. n 3 n 1 n 2 60 o 2 Δ n0 Kamal Pangeni (Wustl) Gap Bridging October 27, 2016 14 / 24
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