Diffuse Supernova Neutrinos

Diffuse Supernova Neutrinos Irene Tamborra von Humboldt Research Fellow at the MPI for Physics, Munich INT 2-2a, Nuclear and Neutrino Physics in Stellar Core Collapse University of Washington, Seattle July 6, 22

Outline Cosmological supernova rate Neutrino oscillations in supernovae Reference neutrino signal Diffuse supernova neutrino background (DSNB) Conclusions This talk is based on work in collaboration with Cecilia Lunardini, JCAP 7 (22) 2.

Why the DSNB? Galactic supernova maybe rare but supernova explosions are quite common. On average there is one supernova explosion every second somewhere in the universe and these produce a diffuse supernova neutrino background (DSNB). detection Beacom window & Vagins, PRL 93:7,24 Detectable ν e flux at the Earth mostly from redshift z ~ Test of supernova astrophysics New frontiers for neutrino astronomy * Beacom and Vagins, arxiv: hep-ph/393

DSNB Detection Perspectives The DSNB has not been observed yet, the most stringent limit is from Super-Kamiokande (SK): φ νe 2.8 3. cm 2 s computed for energies above 7.3 MeV. For details see: C. Lunardini, arxiv: 7.3252.

DSNB Detection Neutron tagging in Gd-enriched WC detector (Super-K with tons Gd to trap neutrons) ν e e ν e + p n + e + p e + n Gd p γ γ we received ull funding Positron and gamma ray ~$4,,) vertices are within ~5cm. or this effort. can be identified by delayed c ν e can be identified by delayed coincidence spatial and temporal separation between prompt positron Cherenkov light and delayed Gd neutron capture gamma cascade 24 5- few clean events/yr in Super-K with Gd c by yashi] Selective Water+Gd Filtration System *See talks by Vagins at Hanse 2 and by Beacom at Neutrino 22. 2 ton (6.5 m X 6.5 m) water tank (SUS34) Transparency Measurement

Ingredients cosmological supernova rate oscillated neutrino flux corrected by redshift [ E = E( + z) ] cosmology

Cosmological Supernova Rate

Cosmological Supernova Rate (SNR) R SN (z,m) = 25M 8M dm η(m) 25M.5M dmmη(m) ρ (z) initial mass function star formation rate (mass distribution of stars at birth) The initial mass function η(m) M 2.35. Therefore the flux is dominated by low mass stars. The DSNB is dominated by the contribution of the closest ( z ) and least massive ( M 8M ) stars and it depends only weakly on M max and z max 5.

Cosmological Supernova Rate (SNR) The redshift correction of energy is responsible for accumulating neutrinos of higher redshift at lower energies. Therefore the diffuse flux is dominated by the low z contribution ( z ) in the energy window relevant for experiments ( <E< 4 MeV). total detection energy window z=- z=2-3 z=-2 See for details Ando, Sato, PLB 559 (23) 3; Lunardini, arxiv: 7.3252.

SNR: Predictions From Star Formation Rate The SNR is proportional to the star formation rate (SFR), mass that forms stars per unit time per unit volume: ( + z) δ z< ρ ( + z) α <z<4.5 ( + z) γ 4.5 <z The most precise way to measure the SNR is from data on the SFR. The cosmic star formation history as a function of the redshift is pretty well known from data in the ultraviolet and far-infrared. Impressive agreement among results from different groups. See for details Horiuchi, Beacom, arxiv: 6.575; Hopkins, Beacom, arxiv: astro-ph/6463.

SNR: Measured Supernova Rate SNR [ -4 yr - Mpc -3 ]. mean local SFR (see Figure 2) Prediction from cosmic SFR Cosmic SNR measurements.2.4.6.8. Redshift z Li et al. (2b) Cappellaro et al. (999) Botticella et al. (28) Cappellaro et al. (25) Bazin et al. (29) Dahlen et al. (24) The SNR is also given by direct SN observations. Surprisingly, the normalization from direct SN observations is lower than that from SFR data by a factor ~ 2 and by a smaller factor at higher z. Why? There are missing SNe - they are faint, obscured, or dark. The existing measurements of the SNR and their uncertainties are dominated by normalization errors. See Horiuchi et al., arxiv: 2.977; Botticella et al., arxiv:.692.

Neutrino Mixing

Neutrino Masses and Neutrino Flavors Neutrino flavor eigenstates are linear combinations of mass eigenstates by means of three mixing angles and one CP-phase ν e ν µ ν τ = U(θ 2, θ 3, θ 23, δ) ν ν 2 ν 3 Neutrino mass eigenstates differ by two mass differences. The sign of the biggest one is still unknown [normal hierarchy: + m 2, inverted hierarchy: m 2 ]. For example, in inverted hierarchy: ν 2 ν ν e ν µ ν τ δm 2 solar mass difference m 2 atmospheric mass difference ν 3

Neutrino Masses and Mixing Angles 4 & 3 N# N # 2 NH IH solar mass difference 6.5 7. 7.5 8. 8.5 2 4 3 "m -5 / 2 ev 2. 2.2 2.4 2.6 2.8 2-3 2 $m / ev..5..5 2. "/% atmospheric mass difference N# 2 mixing angles.25.3.35 2 sin! 2.3.4.5.6.7..2.3.4 2 2 sin! 23 sin! 3 * G.L. Fogli et al., arxiv: 25.5254.

Neutrino Masses and Mixing Angles mass-mixing parameters. We remind that m is defined herein as m (m Parameter Best fit σ range δm 2 / 5 ev 2 (NH or IH) 7.54 7.32 7.8 sin 2 θ 2 / (NH or IH) 3.7 2.9 3.25 m 2 / 3 ev 2 (NH) 2.43 2.34 2.5 m 2 / 3 ev 2 (IH) 2.42 2.32 2.49 sin 2 θ 3 / 2 (NH) 2.45 2.4 2.79 sin 2 θ 3 / 2 (IH) 2.46 2.5 2.8 sin 2 θ 23 / (NH) 3.98 3.72 4.28 sin 2 θ 23 / (IH) 4.8 3.78 4.43 δ/π (NH).89.45.8 δ/π (IH).9.47.22 * G.L. Fogli et al., arxiv: 25.5254.

Neutrino Oscillations in Supernovae

Neutrino Interactions Neutrinos interact with matter and among themselves... all flavors e,µ, e,µ, Z Neutral current (NC) interactions with matter background fermion (p, n, e) e-flavor only e e W e-flavor has charged current (CC) interactions too electron ( ) ν ( ) ν ν ν interactions ( ) ν ( ) ν

Equations of Motion The equations of motion for neutrinos and antineutrinos describing the time evolution in a homogeneous medium for each energy mode E and angle ϑ are i E,ϑ =[H E,ϑ, E,ϑ ] and i E,ϑ =[ H E,ϑ, E,ϑ ] with the neutrino Hamiltonian defined as H E,ϑ = UM2 U 2E + 2G F N l +2π 2G F de ϑ d cos ϑ ( E,ϑ E,ϑ )( cos ϑ cos ϑ ) ϑ ϑ vacuum term matter term N (with opposite sign = diag(n e nē,n µ n µ,n τ n τ ) for antineutrinos) ν ν interaction term The Hamiltonian for antineutrinos has the vacuum term with opposite sign.

Neutrino Interactions with Matter (MSW) When the vacuum term is in resonance with the matter term maximal flavor conversions occur (MSW effect). Level-Crossing diagrams in a supernova Normal hierarchy Inverted hierarchy m 2 resonance for neutrinos δm 2 resonance for neutrinos m 2 resonance for antineutrinos δm 2 resonance for neutrinos * For details see: A. Dighe and A. Yu. Smirnov, arxiv: hep-ph/997423

Neutrino-neutrino Interactions The ν ν term is non linear and it depends on the relative angle between colliding neutrinos HE,ϑ 2 U UM2 U UM 2 2 UM U UM Ud cos ( ϑ = HE,ϑ = + 2GF N+l + 2π 2G 2G N + 2π de 2G de ϑ ( d cos ϑ ( ) cos )E,ϑ ( ϑ cos cos ) ϑ)cos ϑ cos ) ϑ ) HE,ϑ = 2GFF N+ 2GF2G NlF+ 2π de 2GFdE,ϑ cosde ϑ ( d cos ϑ E,ϑ ( )cos ( ( ϑ )cosϑϑ cos F = l F HE,ϑ + E,ϑ E,ϑ E,ϑ l + 2π E,ϑ E,ϑ 2E 2E 2E 2E We assume the bulb model *: the neutrino-sphere emits neutrinos of all flavors from each point in the forward solid angle uniformly and isotropically. Neutrino-sphere t θ Bulb model p Rν q q θpq ϕ Duan et al., PRD74,54(26) p r q of the angle among colliding neutrinos. Only lately, we are learning to appreciate the drole Hνν = 2GF * For details see: H. Duan et al., arxiv: astro-ph/6666. 3 (2π)3 (Pq Pq )( cos θpq ) For realistic angular distributions see S. Sarikas, G.G. Raffelt, L. Huedepohl, H.-T. Janka, arxiv: 9.36 Multi-angle effect: the interaction depends on the relative angle of the colliding neutrinos

Flux (a.u.)..8.6.4.2! e! x Initial neutrino and antineutrino fluxes! e! x Spectral Splits The immediate signature of collective effects is the spectral split : for energies above a critical value, a full flavor swap occurs*. non-oscillated fluxes. 2 3 4 5 2 3 4 5..8 Final fluxes in inverted hierarchy (multi-angle) E (MeV) E (MeV) Flux (a.u.).6.4.2! x! e. 2 3 4 5 E (MeV)! x! e 2 3 4 5 E (MeV) fluxes after collective effects in inverted hierarchy fluxes after collective effects = non-oscillated fluxes in normal hierarchy The appearance and the number of splits are strictly dependent on: the ratio among the fluxes of different flavors the geometry of the neutrino angular emission the neutrino mass hierarchy. * For details see: G.L. Fogli, E. Lisi, A. Marrone, A. Mirizzi, I. Tamborra arxiv: 77.998, 88.87 G.G. Raffelt and A. Yu. Smirnov, arxiv: 75.83, 79.464, H. Duan et al., arxiv: 76.4293

3ν =2ν ν approximation Typical supernova neutrino energies are below threshold for µ and τ production via CC. ν µ and ν τ behave in a similar way and are often denoted by ν x. Generally, one may use an effective 2-flavor approximation as far as δm 2 / m 2.* δm 2 m 2 3ν effective 2ν ν e ν µ ν τ ν 2 ν δm 2 / m 2 ν,2 ν e ν x another spectator + ν x ν 3 ν 3 The effects on collective oscillations induced by the third flavor are of the nature of a subtle correction, negligible for our purposes. In what follows, we will treat collective oscillations in the two flavor approximation and the only way the spectator ν x will affect the final spectra will be by MSW transitions. * B. Dasgupta, A. Dighe, arxiv: 72.3798 [hep-ph]

Oscillated Fluxes at the Earth neutrino-sphere R ν neutrino-neutrino interactions MSW R For large θ 3 the oscillated fluxes are: =sin 2 θ 2 [ P c (Fν c e,f c ν e,e)](fν e Fν y )+Fν y F ν NH e = cos 2 θ 2 Pc (Fν c e,f c ν e,e)(f ν e Fν y )+Fν y, F NH ν e F IH ν e =sin 2 θ 2 P c (F c ν e,f c ν e,e)(f ν e F ν y )+F ν y, F IH ν e = cos 2 θ 2 [ P c (F c ν e,f c ν e,e)](f ν e F ν y )+F ν y Since self-induced flavor conversions and MSW resonances occur in well separated regions in most of the cases, we choose to factorize both the effects and treat them separately.

Reference Neutrino Signal

accretion: large differences among the fluxes 54 Reference Neutrino Signal ν e 8 M 8 solar masses 54.8 solar masses.8 M 8.8 M 8.8 solar masses cooling: similar fluxes Lνβ (erg s ) Luminosity ergs s 53 52 5 ν x ν e Luminosity ergs s 53 52 5 Luminosity ergs s........ 2. times times times 5. Eνβ EMeV (MeV). 7. 5. 3.......... times t(s) t(s) t(s) Figure. Luminosities (on the top) and mean energies (on the bottom) in the observer frame for three progenitors with masses M = 8,.8, 8.8 M (from left to right) as a function of the postbounce time [3, 48]. In blue (red, black respectively) are plotted the quantities related to ν µ,τ and * Fisher et al. ν µ,τ (Basel denoted group), by ν x arxiv: ( ν e, ν98.87 e ). [astro-ph.he] We adopt SN simulations* consistently developed over s for three different SN masses.

Oscillations During the Accretion Phase

Accretion Phase Matter (right density panel) at different during post-bounce the times. accretion phase vs. neutrino density for a.8 M SN (Basel model). 5:.8 M progenitor mass. Radial evolution of the net electron density n e (left panel) and of the neutrino density rence n νe n νx During the accretion phase the matter density is always larger than the neutrino one. Then, one could expect multi-angle matter suppression of collective flavor conversions at small radii. Does this happen? [See talk by G. Raffelt]. 6:.8 M progenitor mass. Radial evolution of the ratio R between electron and neutrino densities at different -bounce times. The two dashed vertical strips delimit the position of r sync (left line) and r end (right line). * For details see: S. Chakraborty et al., arxiv: 4.43, arxiv: 5.3, S. Sarikas, G.G. Raffelt, arxiv: 9.36

Whenever the Accretion Phase: Flavor Evolution ) plane, i.e. essentially the density profile as a function of radius because µ r r 4. results agree with the numerical solutions of Ref. [3] for all models. al solutions find no flavor conversion, our SN trajectory indeed stays clear of the unstable Conversely, y analysis with whenthe it briefly numerical enterssolutions the unstable of Ref. regime [3] as in the left panel of Fig., we ce olution the onset for Stability aradius.8 Mfor partial model analysis flavor at various conversion post bounce of Ref. [3]. The linear stability analysis erexplains suppression [See the numerical of talk self-induced by G. results. Raffelt] flavor conversion, but r km r km ius for the models 2 ms t pb 3 ms. and monochromatic spectra, leading to the simple The integrals I t =.3 s n can now be evaluated analytically. each pair 3 (µ, λ). Figure shows the region 2 where isocontours. We also show the SN trajectory in rofile as 2 a function of radius because µ r r 4. Λ km 4 lutions of Ref. [3] for all models..2 our SN trajectory indeed stays.2 clear of the unstable e unstable regime as.5 2in the.5left panel of Fig., we 2.5 3 2 Μ km r km t =.4 s Λ km 3 Whenever the conversion of Ref. [3]. The linear stability analysis Matter suppression of collective effects during the accretion -only MSW- interesting that in principle the SN Κ km ry can enter the instability region matter suppression s a toy model we consider the density.2.43 µ with half-isotropic emission. S kmandµ r =7 4 km R 4 /2r 4..5 we show κ(r) and the.5evolution of 2 iagonal element S. Indeed 2 S oscild grows in 3 the 3 unstable 2 regime,. only 2 4 6 8 s when κ =, and then Μ km grows again r km he second instability crossing. It rebe of seen SN (thick if therered are line) realistic at density t = 3Figure ms (left) 2: FIG. Growth and7: rate.8κm and progenitor off-diagonal mass. ele- Radial evolution of the where odel discussed such a multiple in Ref. instability [3]. sitxists in practice. ment S survival for a toyprobability model (see text). P The high electron density suppresses collective ee for electron antineutrinos different flavor oscillations (no splits) during the post-bounce times for the multi-angle evolution in presence accretion phase for the three of considered matter effects (continuous progenitors curve) and ( P c for n e =(dashed ). Only MSW occurs. 2 curve). 3 2.2.5.5 3 2. Μ km : Contours of κ and the trajectory of SN (thick red line) at t = 3 ms (left) and 3 right) post bounce for a.8 M model discussed in Ref. [3]. n y n. Λ km 2 Κ km vacuum matter The angular distribution is crucial for the flavor-oscillation suppression!. partial conversions S Electron survival probability for one energy mode (IH,.8 M ) * For details see: S. Chakraborty et al., probability arxiv: 4.43, P ee for different arxiv: post-bounce 5.3, times, S. Sarikas obtained et al., arxiv:.5572 2 taking into account the effects of the SN matter profile

Oscillations During the Cooling Phase

Pee,t=9s Pee,t=6s Pee,t=3s.9 Cooling Phase: Flavor Evolution neutrinos 9 antineutrinos.8 M,IH IH,.8M.8 8 ee ee.7.6.5.4.3.2..8.6.4.2.9 2 4 6 8 2 4 6 8 7 6 5 4 3 2 2 4 6 8 8 6 4 2 2 4 6 8 9 During the cooling phase multiple spectral splits are expected. We numerically solve the evolution equations for discrete time slices. The spectral splits are smeared and their size is reduced due to similarity of the un-oscillated flavor spectra and due to multi-angle effects. Only partial conversion is realized. For NH, P c.6 for high energies and P c.3 for low energies with transition energy increasing with time for energies from 5 to 35 MeV. A similar behavior is observed for antineutrinos for E > 5 MeV..8 8 ee.7.6.5.4.3.2. 2 4 6 8 7 6 5 4 3 2 2 4 6 8 For IH, P c..3 for E < 5-2 MeV to P c >.6 at higher energies. For antineutrinos P c >.7 at all times and at all energies. E (MeV) E (MeV) E(MeV ) E(MeV ) * For details see: Fogli, Lisi, Marrone, Tamborra, arxiv: 97.555; Mirizzi and Tomàs, arxiv: 2.339.

Diffuse Supernova Neutrino Background

Time-integrated Neutrino Fluxes ( ).8 M.5 58 NH, ν e Normal hierarchy no osc. MSW MSW + ν ν Normal hierarchy NH, ν e E 2 Fνe, νe (MeV). 58 5. 57.5 58 IH, ν e Inverted hierarchy Inverted hierarchy IH, ν e E 2 Fνe, νe (MeV). 58 5. 57 2 3 4 5 6 2 3 4 5 6 E(MeV) E(MeV) The MSW effect is large and it generates hotter fluxes. Collective effects produce a slight hardening or softening of the fluxes depending on the mass hierarchy. No signature of the spectral splits. For details see: C. Lunardini and I. Tamborra, arxiv: 25.6292.

Diffuse Supernova Neutrino Background E 2 Φνe (MeVcm 2 s ). 4 NH 5. 2 NH,.8 M IH. IH,.8 M 5. 8 6..5 4 2 E 2 Φ νe (MeVcm 2 s ). 2 3 4 5. 4 5. 2. 5. 8 6..5 4 2. 2 3 4 5 2 25 3 35 4 E(MeV) E(MeV) region of interest for Super-Kamiokande detection A maximum variation of -2% (at E 2 MeV) is related to the mass hierarchy. For details see: C. Lunardini and I. Tamborra, arxiv: 25.6292.

Estimate of the Different Contributions Φtot(cm 2 s ).4.3.2.. ν e a b c neutrinos d e f NH IH 4 3 2 ν e a b antineutrinos c d e f Compared to static spectra (a), the effect of time-dependence of the spectra over s is responsible for a variation of 6% (b). The MSW effects (c) are the largest source of variation of the DSNB with respect to the case without oscillations and it is 5-6%. Neutrino-neutrino interactions (d) are responsible for a variation of 5-%. The stellar population (e) is responsible for a variation of 5-% due to the more luminous fluxes of the massive stars. Φ ν e,nh tot Φ ν e,nh tot =.3 cm 2 s and Φ ν e,ih tot =.26 cm 2 s and Φ ν e,ih tot =.27 cm 2 s =.32 cm 2 s For details see: C. Lunardini and I. Tamborra, arxiv: 25.6292.

Conclusions The inclusion of time-dependent neutrino spectra is responsible for colder neutrino spectra in the DSNB (error ~5%). The largest effect of flavor oscillations is due to MSW resonances (~5-6%), neutrino-neutrino interactions contribute at 5-%. No energy-dependent signature of collective oscillations. The dependence on the mass hierarchy is ~-2% and it is stronger for antineutrinos. Combining results for different progenitor stars (instead of using.8m spectra for all stars), increases the DSNB by 5-%. The DSNB is mainly affected by MSW effects and it can be used to extract astrophysical quantities. The forthcoming detection of the DSNB will be an excellent benchmark to test models of neutrino spectra/emission and SNR.

!ank y" for y"r a#ention!