Neutrino flavor transformationfrom compact object mergers
Gail McLaughlin
North Carolina State University
Collaborators: Jim Kneller (NC State), Alex Friedland (SLAC), Annie Malkus (University of Wisconsin), Albino Perego (Darmstadt),
Rebecca Surman (Notre Dame), Daavid Väänänen (NC State), Yonglin Zhu (NC State)Why examine neutrino flavor transformation for mergers?
• Recent hints from astronomy that a rare event may be responsible
for the main r-process Frebel, Roderer. mergers?
• Current and upcoming radioactive beam experiments will reduce
uncertainties in nuclear masses, reactions for nucleosynthesis.
• Many new merger simulations currently being performed.
• Flavor transformation may affect not only nucleosynthesis but also
dynamics, jet formation in mergers.

Nucleosynthesis from neutron star mergers• tidal ejecta• disk/hypermassive NS outflow• collisional ejecta• outflow from viscous heating

fig. from Bauswein et al 2013
fig. from Perego et al 2014

Nucleosynthetic outflow influenced by neutrinos• tidal ejecta• disk/hypermassive NS outflow• collisional ejecta• outflow from viscous heating

fig. from Bauswein et al ’13fig. from Perego et al ’14

The influence of neutrinos
on tidal, collisional outflow

Fig. from Roberts et al 2016, for more collisional/tidal ejecta with neutrinos see also Wanajo et al ’14, Sekiguichi et al ’15, ’16, Just’15, Radice et al ’16, Lehner et al ’16

The influence of neutrinos
on wind outflow

Malkus et al ’16 For wind neutrino influence on nucleosynthesis/Ye see also Surman et al ’08, Wanajo et al ’12, Caballero et al ’14,Metzgeret al ’14, Perego et al ’14, Foucart et al ’15, Martin et al ’16, Wu et al ’16

Neutrinos influence nucleosynthesis
Neutrinos change the ratio of neutrons to protons
ν e + n → p + e−ν̄e + p → n + e−

Oscillations change the neutrinos
Neutrinos change the ratio of neutrons to protons
ν e + n → p + e−ν̄e + p → n + e−
Oscillations change the spectra of νe s and ν̄e s
νe ↔ νµ , ντν̄e ↔ ν̄µ , ν̄τ
Mergers have less νµ , ντ than νe and ν̄e→ oscillation reduces numbers of νe , ν̄e

Neutrino oscillations usually studied in free streaming limit
Usually calculated in a regime with few collisions, so above trapping
surfaces → free streaming approximation
Interesting flavor transformation behavior stems from the potentials
neutrinos experience. These potentials come from coherent forward
scattering from neutrons, protons, electrons, positrons, neutrinos.

Oscillations: scales

Modified wave equation
22δmabcos(2θ)
Ve + Vνν− δmV+dνν
4E
4E sin(2θ)
ψi~c ψν =22δmbadrsin(2θ)
Vνν+ δm−V+−V+eνν
4E4E cos(2θ)
Scales in the problem:•δm2vacuum scale 4E• matter scale Ve ∝ GF Ne (r)• neutrino self-interaction scaleVνν ∝ GF Nν ∗ angle − GF Nν̄ ∗ angle

Oscillations: vacuum

Modified wave equation

δm2
δm2ab
Ve + Vνν − 4E cos(2θ)
Vνν + 4E sin(2θ)
dψ
i~c ψν = 22δmbadrsin(2θ)
Vνν+ δm−V+−V+eνν
4E
4E cos(2θ)
Scales in the problem:•δm2vacuum scale 4E• matter scale Ve ∝ GF Ne (r)• neutrino self-interaction scaleVνν ∝ GF Nν ∗ angle − GF Nν̄ ∗ angle
δm24E >> Ve , Vνν → vacuum oscillations

e.g. atmospheric neutrinos, most terrestrial oscillation experiments

Oscillations: MSW

Modified wave equation22δmabVe + Vνν− δmcos(2θ)
V+sin(2θ)
dνν
4E4E
ψ
i~c ψν = 22δmbadrVνν+ δmsin(2θ)−V+−V+eνν
4E
4E cos(2θ)
Scales in the problem:•δm2vacuum scale 4E• matter scale Ve ∝ GF Ne (r)• neutrino self-interaction scaleVνν ∝ GF Nν ∗ angle − GF Nν̄ ∗ angle
δm24E ∼ Ve >> Vνν → MSW oscillations

e.g. sun, outer layers of supernova, outer layers of compact object
mergerOscillations: nutation/bipolar

Modified wave equation22δmabVe + Vνν− δmcos(2θ)
V+dνν
4E
4E sin(2θ)
ψi~c ψν =22δmbadrsin(2θ)
Vνν+ δm−V+−V+eνν
4E
4E cos(2θ)
Scales in the problem:•δm2vacuum scale 4E• matter scale Ve ∝ GF Ne (r)• ν self-interaction scale Vνν ∝ GF Nν ∗ angle − GF Nν̄ ∗ angle
δm24E ∼ Vνν → nutation/bipolar oscillations

e.g. supernova (100s of km), see e.g. Balantekin, Dighe, Duan, Carlson, Fuller, Kneller, Mirrizi, Pehlivan,Raffelt, Qian, Volpe, Yoshida, Yuksel, black hole accretion disks Dasgupta et al

Oscillations: matter neutrino resonance

Modified wave equation
22δmabVe + Vνν− δmcos(2θ)
V+sin(2θ)
dνν
4E4E
ψ
i~c ψν = 22δmbadrsin(2θ)
Vνν+ δm−V+−V+eνν
4E4E cos(2θ)
Scales in the problem:•δm2vacuum scale 4E• matter scale Ve ∝ GF Ne (r)• ν self-interaction scale Vνν ∝ GF Nν ∗ angle − GF Nν̄ ∗ angle
Ve ∼ Vνν → MNR oscillations
e.g. Mergers, black hole accretion disks, Malkus et al ’12, ’14, Duan, Frensel, Kneller, Malkus,GCM, Qian, Perego, Surman, Wu, Väänänen, Volpe, Zhu

Oscillations: nonlinear

Modified wave equationδm2δm2abVe + Vνν − 4E cos(2θ)
Vνν + 4E sin(2θ)
dψ
i~c ψν = 22δmbadrVνν+ δmsin(2θ)−V+−V+eνν
4E4E cos(2θ)
Whenever Vνν is important, the problem is very nonlinear. Vννdepends on the number density of each flavor of neutrino, which
depends how the neutrinos have oscillated.
multi-energy : each energy neutrino and antineutrino has its own
equation, solved simultaneously with the others
multi-angle : each emitted neutrino and antineutrino has its own
equation, solved simultaneously with the others**This means thousands of these coupled equations.**

Why are merger oscillations different
than supernova?
Potentials Vνν and Ve can have opposite sign
Capture some basic behavior with a toy model: single energy gas ofneutrinos and antineutrinos. More antineutrinos than neutrinos. Let
density of neutrinos and antineutrinos decline. Matter stays fixed.
Calculate survival probabilities: Pνe = |ψνe |2 , Pν̄e = |ψν̄e |2

MNR transition: single energy model

Survival Probability

Potentials Vνν and Ve can have opposite sign

10.8

Pν

0.6

Pν

0.4

Pνe, nume, nume, pred

0.2

Pνe, pred

3000|V(δm /2E)|

2500

Ve|Vνν|

2

2000
1500
1000
500
00

5

10

15

20

30

25
2

Distance (2E/δm )Fig. from Malkus et al 2014

3540

Matter neutrino resonance transitions
What is happening?
Explanations: Neutrinos stay “on resonance” Malkus et al ’14, instantaneousmass splitting stays “small” Väänännen et al ’16, neutrinos are “adiabatic” Wu et al’16, Väänännen et al ’16 all lead to same formula at zero orderPνe ≈Pν̄e ≈(α2 −1)µν (r)2 −Ve (r)24Ve (r)µν (r)(α2 −1)µν (r)2 +Ve (r)24αVe (r)µν (r)− 1/2+ 1/2

α is the asymmetry between antineutrinos and neutrinos and µν is thescale of the neutrino self interaction potentialMNR transition: single energy model

Survival Probability

Compare numerics to prediction

10.8

Pν

0.6Pν

0.4Pνe, nume, nume, pred

0.2Pνe, pred

3000

|V(δm /2E)|2500

Ve|Vνν|

22000
1500
1000
500
00510152030

25
2Distance (2E/δm )Fig. from Malkus et al 20143540

Now switch to a disk geometry
and a multi-energy calculation
Neutrino disk is 45 km, neutrinos have temperature 6.4 MeV
Antineutrino disk is 45 km, antineutrinos have temperature of 7.1 MeV
Launch a neutrino at 45 degrees to the disk.

Merger oscillations: potentials for

Potential (erg)same size νe and ν̄e disks
10-16

10-18

Ve
|Vν|
∆12
|∆32|

MNR
regionnutation
region10-20MSW
region

10-22
10-24
105

106

107
108
Position (cm)1091010

Merger oscillations: survival probabilities forsame size νe and ν̄e disks

Ve|Vν|
∆12
|∆32|

-16

10

MNR
regionPotential (erg)-1810Survival Probability Survival Probability

multi-energy, single angle calculations

nutation
region-20

10MSW
region

-22

10-24

10

5

10

6

10

7

8

10
10
Position (cm)10

fig. from Malkus et al 2016

910

10

1.4
1.2
10.8
0.6
0.4
0.2
01.4
1.2
10.8
0.6
0.4
0.2
0MNR
regionnutationregion

MSW
region810<P>-<P>

0λν /λνe0eλ-ν /λ-νe

510e

6

107

1010Position (cm)

91010fig. from Malkus et al 2016, see also Frensel et al 2016

Merger oscillations: potentials for

Potential (erg)different size νe and ν̄e disks
10-16

10-18

Ve
|Vν|
∆12
|∆32|

symmetric MNR
regionMNR
regionnutation
region10-20

MSW
region

10-22
10-24
105

106

107
108
Position (cm)1091010

Merger oscillations: survival probabilities fordifferent size νe and ν̄e disks-16MNR
region-18

Potential (erg)

Ve|Vν|∆12|∆32|

symmetric MNR
region1010Survival Probability Survival Probability

multi-energy, single angle calculations

nutation
region-20

10MSW
region-22

10-24105106107

81010Position (cm)

10fig. from Malkus et al 2016

910

10

1.4
1.2
10.8
0.6
0.4
0.2
0
1.4
1.2
10.8
0.6
0.4
0.2
0

symmetric MNR
regionMNR
regionnutation
regionMSW
region810<P>-<P>

0λν /λνe0eλ-ν /λ-νe510e61071010Position (cm)fig. from Malkus et al 2016

91010

Analytic survival probability prediction
also works for symmetric MNR transitions
Geometry causes Vνν to switch sign

Symmetric MNR Fig. from Väänänen ’16

How oscillations effect nucleosynthesis

Malkus et al ’16

Matter densities in a
dynamical merger calculation

Zhu et al ’16

Resonance locations, Ve ∼ Vνν , in the
dynamical merger remnant
350300νe of 10.67 MeV–

νe of 16.22 MeV–

νe of 24.66 MeV–

νe of 10.67 MeV
νe of 16.22 MeVνe of 24.66 MeVz (km)

250
200
150
100

3500-150-100-500y (km)Fig. from Zhu et al 2016

50100150

Potentials and survival probabilities alongSurvival Probability

1.4
1.2
10.8
0.6
0.4
0.2
0
10-17

Potential (erg)a sample trajectory

10-18
10-19
10-20
10-21
10-22
10-23

Pν ,nume
P–ν ,numePν ,predeP–ν ,prede

100

Ve-Vν(x,0)Vν(x,0)|Vν(x,t)|

5060

80

100120

Position (km)Fig. from Zhu et al 2016

140 160 180

Neutrino densities in a
dynamical merger remnant

Fig. from Zhu et al ’16

Conclusions
Rapid progress in last couple years:• Predictions of matter neutrino resonance transition behavior• Likely exists in mergers, caveat: multi-angle• Likely a significant impact on nucleosynthesis
What to do next?
• a little more theory work
• keep up with dynamical models as they advance transport• physical effects, general relativity
Long term• full multi-angle effects• decoupling regime, feedback into dynamical calculation