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Analysis of supernova neutrino fluxes and neutron star properties Andrea Gallo Rosso Gran Sasso Science Institute Astroparticule et Cosmologie (APC) Advisors: F. Vissani and C. Volpe 5 th April 2019 List of publications A. Gallo Rosso et al .

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SLIDE 1

Analysis of supernova neutrino fluxes

and neutron star properties

Andrea Gallo Rosso Gran Sasso Science Institute Astroparticule et Cosmologie (APC) Advisors: F. Vissani and C. Volpe 5th April 2019

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SLIDE 2

List of publications

  • A. Gallo Rosso et al. JCAP 1812 (2018) no.12, 006.
  • V. Gentile et al. JCAP 2018 (2018) no.08, 015.
  • A. Gallo Rosso et al. JCAP 1804 (2018) no.04, 040.
  • A. Gallo Rosso et al. JCAP 1711 (2017) no.11, 036.
  • A. Gallo Rosso et al. EPJ Plus 133 (2018) no.7, 267.
  • G. Fantini et al. [ISBN:9789813226081].
  • E. Aprile et al. Phys.Rev.Lett. 122 (2019) 071301.
  • E. Aprile et al. Phys.Rev.Lett. 121 (2018) no.11, 111302.
  • E. Aprile et al. Phys.Rev. D97 (2018) no.9, 092007.
  • E. Aprile et al. Phys.Rev. D96 (2017) no.12, 122002.
  • E. Aprile et al. Eur.Phys.J. C77 (2017) no.12, 881.
  • E. Aprile et al. Eur.Phys.J. C78 (2018) no.2, 132.
  • E. Aprile et al. Phys.Rev.Lett. 119 (2017) no.18, 181301.
  • E. Aprile et al. Phys.Rev. D96 (2017) no.4, 042004.
  • E. Aprile et al. Eur.Phys.J. C77 (2017) no.12, 890.

…

Theoretical Papers Theoretical Reviews XENON collaboration

1

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SLIDE 3

List of publications

  • A. Gallo Rosso et al. JCAP 1812 (2018) no.12, 006.
  • V. Gentile et al. JCAP 2018 (2018) no.08, 015.
  • A. Gallo Rosso et al. JCAP 1804 (2018) no.04, 040.
  • A. Gallo Rosso et al. JCAP 1711 (2017) no.11, 036.
  • A. Gallo Rosso et al. EPJ Plus 133 (2018) no.7, 267.
  • G. Fantini et al. [ISBN:9789813226081].
  • E. Aprile et al. Phys.Rev.Lett. 122 (2019) 071301.
  • E. Aprile et al. Phys.Rev.Lett. 121 (2018) no.11, 111302.
  • E. Aprile et al. Phys.Rev. D97 (2018) no.9, 092007.
  • E. Aprile et al. Phys.Rev. D96 (2017) no.12, 122002.
  • E. Aprile et al. Eur.Phys.J. C77 (2017) no.12, 881.
  • E. Aprile et al. Eur.Phys.J. C78 (2018) no.2, 132.
  • E. Aprile et al. Phys.Rev.Lett. 119 (2017) no.18, 181301.
  • E. Aprile et al. Phys.Rev. D96 (2017) no.4, 042004.
  • E. Aprile et al. Eur.Phys.J. C77 (2017) no.12, 890.

…

Theoretical Papers Theoretical Reviews XENON collaboration

1

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SLIDE 4

Introduction

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SLIDE 5

SN 1987A

Before After

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SLIDE 6

Introduction

SN H SN I SN II Si SN Ia He SN IIb SN IIL SN IIF SN IIpec SN IIP SN IIn SN Ib SN Ic

(linear) (faint) (peculiar) (plateau) (narrow) no yes yes no rich poor He dominant H dominant

CORE COLLAPSE THERMONUCLEAR

3

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SLIDE 7

Introduction

CORE-COLLAPSE SUPERNOVA EXPLOSION

  • Longstanding open question in astrophysics
  • ∼ 1053 erg gravitational binding energy
  • 99% emitted in neutrinos
  • ∼ 10 s signal
  • Delayed-accretion paradigm
  • From Wilson (1971) & Bethe and Wilson (1985)
  • To 2D & 3D numerical simulations

4

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SLIDE 8

Introduction

DELAYED EXPLOSION

  • 1. Instability & collapse
  • 2. Bounce & shock propagation
  • 3. Stallation & accretion
  • 4. Cooling
  • T. Totani et al., Astrophys. J. 496 (1998).

5

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SLIDE 9

Introduction

DELAYED EXPLOSION

  • 1. Instability & collapse
  • 2. Bounce & shock propagation
  • 3. Stallation & accretion
  • 4. Cooling
  • T. Totani et al., Astrophys. J. 496 (1998).

5

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SLIDE 10

Introduction

DELAYED EXPLOSION

  • 1. Instability & collapse
  • 2. Bounce & shock propagation
  • 3. Stallation & accretion
  • 4. Cooling
  • T. Totani et al., Astrophys. J. 496 (1998).

5

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SLIDE 11

Introduction

DELAYED EXPLOSION

  • 1. Instability & collapse
  • 2. Bounce & shock propagation
  • 3. Stallation & accretion
  • 4. Cooling
  • T. Totani et al., Astrophys. J. 496 (1998).

5

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SLIDE 12

Introduction

NEUTRINO MESSENGERS

  • Weakly interacting
  • 99% of binding energy emitted in neutrinos
  • 6 flavors: νe νµ ντ νe νµ ντ
  • Flavor transformation
  • Vacuum: determined with good accuracy
  • Matter conversion: Mikheyev-Smirnov-Wolfenstein effect (MSW) [1]
  • Self-interaction effects in dense media still studied
  • 1L. Wolfenstein, Phys. Rev. D17 (1978).

S.P. Mikheyev and A.Y. Smirnov, Sov. J. Nucl. Phys. 42 (1985).

6

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SLIDE 13

Introduction

WHAT CAN WE LEARN FROM SUPERNOVA NEUTRINOS?

  • Star properties
  • Pointing and alert (SNEWS)
  • Standard candle (νe burst)
  • Explosion mechanism
  • Particle properties
  • Flavor conversion in dense media
  • Non-standard properties

7

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SLIDE 14

Introduction

SN 1987A: THE ONLY NEUTRINO SIGNAL (SO FAR)

  • Large Magellanic Cloud (51.4 kpc)
  • Kamiokande-II, IMB, Baksan
  • About 25 νe neutrino events
  • Inverse Beta Decay Only
  • νe νµ ντ νµ ντ still missing
  • Good agreement with expectations
  • F. Vissani, J. Phys. G 42, 013001 (2015).
  • Radiated νe energy (4.8 + 2.3 − 1.0) × 1052 erg
  • νe temperature (3.9 + 0.5 − 0.3) MeV

8

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SLIDE 15

Introduction

Kamiokande-II

∼ 10×

Super-Kamiokande

∼ 10×

Hyper-Kamiokande

MANY DETECTION CHANNELS — ENERGY, TIME, FLAVOR

9

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SLIDE 16

Introduction

νe νe νx=νμ,νμ,ντ,ντ

10 20 30 40 0.0 0.5 1.0 1.5 2.0 2.5 Neutrino energy [MeV] Time integrated flux [1010 MeV-1 cm-2]

TIME INTEGRATED FLUX (FLUENCE) Total energy E ⇔ normalization Mean energy ⟨E⟩ ⇔ 1st moment Pinching α ⇔ width 3 PARAMETERS × 3 SPECIES = 9 D.O.F.

10

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SLIDE 17

Introduction

TIME INTEGRATED FLUX (FLUENCE) Total energy E ⇔ normalization Mean energy ⟨E⟩ ⇔ 1st moment Pinching α ⇔ width 3 PARAMETERS × 3 SPECIES = 9 D.O.F.

10

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SLIDE 18

Introduction

NUMBER OF PARAMETERS ARBITRARILY REDUCED

  • Lu et al. [2] JUNO detector
  • Importance of combining channels
  • Eνe up to 5% @ 90% C.L.
  • ⟨Eνe⟩ up to 1% @ 90% C.L.

with MSW transformation w/o equipartition (Etot ̸= Ei/6) Etot known up to 13% but for spectral shape (i.e. pinching) fully known

2Lu et al. Phys. Rev. D 94, 023006 (2016).

11

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SLIDE 19

Introduction

DIFFICULTY IN RECONSTRUCTING THE BINDING ENERGY

  • H. Minakata et al. [3]
  • Hyper-Kamiokande
  • only νe + p → e+ + n
  • If pinching unknown
  • Eνe acc. 50% @ 3σ
  • ⟨Eνe⟩ acc. 4% @ 3σ
  • Parameter degeneracy
  • 3H. Minakata et al., JCAP 0812, 006 (2008).

12

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SLIDE 20

WHAT CAN WE LEARN FROM SUPERNOVA NEUTRINOS?

  • How well can we reconstruct the neutrino fluxes

without any usual assumptions?

  • Will the uncertainty on the pinching compromise

the determination of key properties?

  • What is the impact of including other detection channels?
  • What can we infer on the neutron star properties?

13

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SLIDE 21
  • 1. FLUX RECONSTRUCTION AND M–R RELATION OF THE NEUTRON STAR
  • Monte Carlo based likelihood analyses
  • Without usual assumptions
  • Shape α unknown
  • Three detection channels (9 d.o.f.)
  • νe + p → e+ + n (IBD)
  • ν + e− → ν + e− (ES)
  • ν + 16O → ν + X + γ (OS)

REFERENCE PAPERS

  • A. Gallo Rosso, F. Vissani, M.C. Volpe, JCAP 1711 (2017) no.11, 036
  • A. Gallo Rosso, F. Vissani, M.C. Volpe, JCAP 1804 (2018) no.04, 040

14

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SLIDE 22
  • 2. LATE-TIME SIGNAL AND PROTO-NEUTRON STAR RADIUS
  • First analysis of its kind
  • Neutrino signal alone
  • Reference model
  • Exploration of extended theories of gravity

REFERENCE PAPER

  • A. Gallo Rosso, S. Abbar, F. Vissani, M.C. Volpe, JCAP 1812 (2018)

no.12, 006

15

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SLIDE 23
  • 1. Flux reconstruction
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SLIDE 24
  • 1. Flux reconstruction

Hypotheses and method

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SLIDE 25

Hypotheses and method

SUPERNOVA PARAMETERS

  • Distance D∗ = 10 kpc
  • Total energy E∗ = 3 × 1053 erg

DETECTORS

  • Super-Kamiokande
  • 22.5 kton (fiducial mass)
  • Hyper-Kamiokande
  • 374 kton (fiducial mass)
  • 5 MeV threshold
  • 100% efficiency

16

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SLIDE 26

Hypotheses and method

TIME-INTEGRATED FLUXES (FLUENCES)

  • Quasi-thermal alpha-fit [4]
  • 3 neutrino species (νe, νe, νx)
  • 3 parameters (E, ⟨E⟩, α)

d F0

i

d Eν = Ei 4πD2 (αi + 1)(αi+1) Γ(αi + 1) Eαi ⟨Ei⟩αi+2 exp [ −(αi + 1) E ⟨Ei⟩ ]

  • Agreement with SN 1987A data
  • Good description of simulations

νe νe νx=νμ,νμ,ντ,ντ 10 20 30 40 0.0 0.5 1.0 1.5 2.0 2.5 Neutrino energy [MeV] Time integrated flux [1010 MeV-1 cm-2]

4M.T. Keil et al., Astrophys. J. 590 (2003).

17

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SLIDE 27

Hypotheses and method

NEUTRINO FLAVOR TRANSFORMATIONS IN SUPERNOVAE

  • Normal mass hierarchy
  • Mikheyev-Smirnov-Wolfenstein (MSW) effect

{ Fνe = F0

x

Fνe = |Ue1|2 · F0

νe + (1 − |Ue1|2) · F0 x

  • Neutrino self-interaction neglected

18

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SLIDE 28

Hypotheses and method

TOTAL ENERGIES

  • E∗

i = 0.5 × 1053 erg

MEAN ENERGIES

  • ⟨Eνe⟩∗ = 9.5 MeV
  • ⟨Eνe⟩∗ = 12 MeV
  • ⟨Eνx⟩∗ = 15.6 MeV

PINCHING PARAMETERS

  • α∗

i = 2.5

Teun Hocks, Measuring

  • C. Lujan-Peschard et al., JCAP (2014).

19

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SLIDE 29

Hypotheses and method

— HYPER-KAMIOKANDE EXTRACTED EVENTS —

Expected distribution Extracted events 10 20 30 40 50 60 2 4 6 8 10

×103

Ee [MeV]

νe + p → e+ + n (76 × 103 expected events)

True distribution Extracted events 5 10 15 20 25 30 35 100 200 300 400 500 600 Ke [MeV]

ν + e− → ν + e− (4 × 103 expected events)

20

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SLIDE 30

Hypotheses and method

ν + 16O → ν + X + γ

  • γ within (4 ÷ 9) MeV
  • ∼ 800 OS
  • ∼ 8000 IBD+ES
  • Non-Gaussian smearing
  • No disentangling IBD+ES
  • Neutral-Current Region

֒ → NCR = IBD + ES + OS

1 2 5 10 15 20 25 3

Energy [MeV] Signal [a.u.]

  • K. Langanke et al., Phys. Rev. Lett. 76 (1996).

21

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SLIDE 31

Hypotheses and method

NEUTRINO-OXYGEN CROSS SECTION σOS(Eν) ≈ κ · σ0 · (Eν/MeV − 15)4 [5]

  • measurements expected [6]
  • 10% uncertainty (optimistic)
  • Systematic ∼ Gauss(κ∗ = 1, σκ = 0.1)
  • Results weakly concerned

10th parameter κ

5J.F. Beacom and P. Vogel, PRD 58 (1998) 053010.

  • 6K. Scholberg, talk at CNNP2017.

22

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SLIDE 32

Hypotheses and method

LIKELIHOODS Lj (param.) ∝

Nbin

∏

i=1

νni

i

ni e−νi with j = IBD, ES LNCR (param.) ∝ exp [ −(nNCR − NNCR)2 2NNCR − (κ − 1)2 2σ2

κ

] 3 ANALYSES IBD → L = LIBD IBD + ES → L = LIBD × LES IBD + ES + NCR → L = LIBD × LES × LNCR

  • R. Laha and J.F. Beacom, Phys. Rev. D89 (2014).

23

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SLIDE 33

Hypotheses and method

PRIOR 0.2 × 1053 erg ≤ Ei ≤ 1.0 × 1053 erg 5.0 MeV ≤ ⟨Ei⟩ ≤ 30 MeV 1.5 ≤ αi ≤ 3.5 0.8 ≤ κ ≤ 1.2 CONDITION log L ≥ log Lmax − 1 2Adof,CL with ∫ A χ2

dof(z)dz = C.L. 24

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SLIDE 34

Hypotheses and method

Comparison with Minakata et al. (2008): Good agreement

14.6 14.8 15.0 15.2 15.4 15.6 0.3 0.4 0.5 0.6 0.7

〈E(νe)〉 [MeV] ℰ(νe) [1053 erg]

2σ

log L(Pi) ≥ log Lmax − 1 2Adof,CL with ∫ A χ2

dof(z) dz = CL 25

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SLIDE 35
  • 1. Flux reconstruction

Results on neutrino fluxes

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SLIDE 36

Results on neutrino fluxes

— THE IMPORTANCE OF MANY DETECTION CHANNELS — Degeneracy broken for νe and νx total energies

26

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SLIDE 37

Results on neutrino fluxes

— THE IMPORTANCE OF MANY DETECTION CHANNELS — Degeneracy broken for νe and νx mean energies

27

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SLIDE 38

Results on neutrino fluxes

IBD

True spectrum Set of values P1 Set of values P2 10 20 30 40 50 50 100 150 200 e+ energy [MeV] Events spectrum [MeV-1] ES (νe+νx) True spectrum Set of values P1 Set of values P2 10 20 30 40 50 10 20 30 40 e– energy [MeV] Events spectrum [MeV-1]

P1 P2 E(νe) [1052erg] 6.65 2.94 E(νx) [1052erg] 2 10 ⟨E(νe)⟩ [MeV] 12.8 13.5 ⟨E(νx)⟩ [MeV] 9.3 11.9 α(νe) 2.08 2.08 α(νx) 2.16 2.16

28

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SLIDE 39

Results on neutrino fluxes

— STILL SOME RESIDUAL UNCERTAINTIES — νe species undetermined and almost all pinching parameters α

29

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SLIDE 40

Gravitational binding energy of the neutron star

— TOTAL NEUTRINO EMITTED ENERGY —

Prior IBD IBD+ES IBD+ES+NCR 2 3 4 5 6 0.00 0.02 0.04 0.06 0.08 0.10

ℰB reconstructed [1053 erg]

  • Prob. density [1053 erg]-1

EB

[1053 erg]

  • Acc. %

IBD

3.40 ± 0.86 25.1

IBD+ES

3.27 ± 0.37 11.2

IBD+ES+NCR

3.18 ± 0.35 11.0

Super-Kamiokande

IBD IBD+ES IBD+ES+NCR 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.00 0.02 0.04 0.06 0.08 0.10

ℰB reconstructed [1053erg] Probability

EB

[1053 erg]

  • Acc. %

IBD

3.64 ± 0.79 21.7

IBD+ES

3.10 ± 0.16 5.3

IBD+ES+NCR

3.07 ± 0.18 5.8

Hyper-Kamiokande

30

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SLIDE 41

Gravitational binding energy of the neutron star

— TOTAL NEUTRINO EMITTED ENERGY IN EQUIPARTITION (Etot = Ei/6) —

IBD IBD+ES IBD+ES+NCR 2.6 2.8 3.0 3.2 3.4 3.6 3.8 0.00 0.01 0.02 0.03 0.04

ℰB reconstructed [1053erg] Probability

EB

[1053 erg]

  • Acc. %

IBD

3.15 ± 0.25 7.9

IBD+ES

3.06 ± 0.10 3.4

IBD+ES+NCR

3.023 ± 0.095 3.1

Super-Kamiokande

IBD IBD+ES IBD+ES+NCR 2.90 2.95 3.00 3.05 3.10 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

ℰB reconstructed [1053erg] Probability

EB

[1053 erg]

  • Acc. %

IBD

3.13 ± 0.23 7.4

IBD+ES

3.130 ± 3.035 0.89

IBD+ES+NCR

3.015 ± 0.021 0.68

Hyper-Kamiokande

31

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SLIDE 42
  • 1. Flux reconstruction

Results on mass–radius relation

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SLIDE 43

Mass–radius relation of the neutron-star

EQUATION OF STATE [7] (0.60 ± 0.05)β 1 − β/2 = EB Mc2

  • Relation EB–β
  • β = GM/Rc2
  • EB ≈ Etot
  • 10% uncertainty

Fit T VII Inc Buch T IV WFF1 WFF2 WFF3 N4 AP4 AP3 MS0 MS1 GM3 ENG PAL6 GS1 GS2 PCL2 PS

0.10 0.15 0.20 0.25 0.30 0.35 0.05 0.10 0.15 0.20

Compactness β = GM/Rc2 ℰB/M

  • 7J. M. Lattimer and M. Prakash, Phys. Rept. 442 (2007) 109.

32

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SLIDE 44

Neutron star

M = √ EBR 0.6 G [√ 1 + ϵ2 − ϵ ] with ϵ = 1 4 √ EBG 0.6 R c4 Total energy Etot + Equation of state

  • M–R constraint8

ℰB ± 10% (SK) ℰB ± 1% (HK)

8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Radius [km] Gravitational mass [M⊙]

8An estimation of the baryonic mass may also be needed.

33

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SLIDE 45
  • 2. Late time signal and R of PNS
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SLIDE 46

EB–R relation

Solving Tolman-Oppenheimer-Volkoff (TOV) equations Standard and f(R) gravity: Ricci scalar R → f(R) = R + αGR2

10 12 14 0.0 0.1 0.2 0.3 0.4 B/M c2 GR = 1 = 2 = 20

R [km]

12 14 16

R [km]

16 APR SLy

— SENSITIVE TO EoS AND POTENTIALLY TO EXTENDED GR —

34

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SLIDE 47

Reference model for neutrino signal

— QUASI-STATIC COOLING (6 ÷ 10 s window) —

10−4 10−3 10−2 10−1 100 101 102 Lν (1052 erg s−1)

νe ¯ νe νx

4 6 8 10 12 14 16 e

ν (MeV)

10−1 100 101 102 tpost-bounce (s) 101 102

R (km)

Rpns Rν

10−1 100 101 102 tpost-bounce (s) 2 4 6 8 10 12 Tν−sphere (MeV)

Almost constant behavior

L.F. Roberts and S. Reddy (2017) arXiv:1612.03860.

35

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SLIDE 48

Proto-neutron star radius reconstruction

FERMI-DIRAC BLACK BODY Pinching parameter η(α) L = −24π2c (hc)3 Li4(−eη) R2 [⟨E ⟩ F2(η) F3(η) ]4 RADIUS RECONSTRUCTION

  • Measuring (L, ⟨E⟩, η) to get R
  • Hyper-Kamiokande
  • 6 ÷ 10 s window ⇒ theoretically clean but smaller dataset
  • 10 kpc ⇒ # events as Super-Kamiokande in previous project
  • 2 kpc ⇒ # events as Hyper-Kamiokande in previous project

36

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SLIDE 49

Proto-neutron star radius reconstruction

— CORRELATION BETWEEN R AND α — νe species νx species L ∝ Li4 ( −eη(α)) F2[η(α)] F3[η(α)]

37

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SLIDE 50

Proto-neutron star radius reconstruction

— RADII RECONSTRUCTED @ 10 kpc —

νe species νe species νx species 5 10 15 20 25 30 35 0.00 0.05 0.10 0.15

R reconstructed [km] Probability [km-1]

R R∗ [km]

  • Rec. [km]

% νe 11.9 19 ± 19 100 νe 11.5 7 ± 4 56 νx 11.4 11 ± 6 55 Default α ∈ [2.1, 3.5]

νe species νe species νx species 5 10 15 20 25 30 35 0.00 0.05 0.10 0.15

R reconstructed [km] Probability [km-1]

R R∗ [km]

  • Rec. [km]

% νe 11.9 24 ± 21 86 νe 11.5 9 ± 2 26 νx 11.4 14 ± 3 25 Tighter α ∈ [2.27, 2.47]

38

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SLIDE 51

Proto-neutron star radius reconstruction

— RADII RECONSTRUCTED @ 2 kpc —

νe species νe species νx species 5 10 15 20 25 30 35 0.00 0.02 0.04 0.06 0.08 0.10 0.12

R reconstructed [km] Probability [km-1]

R R∗ [km]

  • Rec. [km]

% νe 11.9 17 ± 16 97 νe 11.5 11 ± 4 34 νx 11.4 12 ± 5 40 Default α ∈ [2.1, 3.5]

νe species νe species νx species 5 10 15 20 25 30 35 40 0.00 0.05 0.10 0.15 0.20 0.25 0.30

R reconstructed [km] Probability [km-1]

R R∗ [km]

  • Rec. [km]

% νe 11.9 22 ± 18 81 νe 11.5 10 ± 1 12 νx 11.4 13 ± 2 14 Tighter α ∈ [2.27, 2.47]

39

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SLIDE 52

Inverting the perspective

USING R TO CONSTRAIN α

  • Realistic values
  • R ∈ [8, 16] km from the EoS
  • α(νe) from ∼ 14% to ∼ 5–7% @ 2–10 kpc
  • 10% accuracy
  • R ∈ [10.2, 13.1] km
  • α(νe) from ∼ 14% to ∼ 1–2% @ 2–10 kpc

40

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SLIDE 53

Conclusions and perspectives

slide-54
SLIDE 54

Conclusions

  • 1. NEUTRINO FLUX RECONSTRUCTION
  • Large datasets necessary but not sufficient
  • Elastic scattering is crucial to break the degeneracy
  • Hyper-Kamiokande
  • EB with few %
  • νe well determined (⟨E⟩, α ∼ %)
  • νe undetermined: prior constraint
  • NS mass at ∼ 30% for R known at ∼ 10%

41

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SLIDE 55

Conclusions

  • 2. LATE-TIME ANALYSIS
  • R sensitive to EoS and gravity
  • Radius determination from black body emission
  • R–α strong correlation
  • Poor accuracy if α is not strongly constrained
  • Pinching α constrained from physical values of R

42

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SLIDE 56

Perspectives

DEVELOPMENTS AND IMPROVEMENTS

  • Flavor conversion phenomena:
  • Neutrino self-interaction
  • Experimental apparatus:
  • Improving detector response
  • Likelihood analysis:
  • More detectors/channels
  • Determination of νe species

43