Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg Core-Collapse Supernova

0.17 MB·English

by  Huaiyu Duan

INTPUB 07-23
LA-UR-07-6726
Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg
Core-Collapse Supernova
Huaiyu Duan,1 George M. Fuller,2,1 J. Carlson,3 and Yong-Zhong Qian4
1Institute for Nuclear Theory, University of Washington, Seattle, WA 98195
2Department of Physics, University of California, San Diego, La Jolla, CA 92093
3Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545
4School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455
Wepresentresultsof3-neutrinoflavorevolutionsimulationsfortheneutronizationburstfroman
O-Ne-Mg core-collapse supernova. We find that nonlinear neutrino self-coupling engineers a single
spectralfeatureofstepwiseconversionintheinvertedneutrinomasshierarchycaseandinthenormal
mass hierarchy case, a superposition of two such features corresponding to the vacuum neutrino
8 mass-squareddifferencesassociatedwithsolarandatmosphericneutrinooscillations. Theseneutrino
0 spectralfeaturesofferauniquepotentialprobeoftheconditionsin thesupernovaenvironmentand
0 may allow us to distinguish between O-Ne-Mgand Fecore-collapse supernovae.
2
n PACSnumbers: 14.60.Pq,97.60.Bw
a
J
In this Letter we suggest an exciting new neutrino neutrino flavor state ψ in matter is described by the
8
| i
1 signal-basedprobeofconditionsdeepinsideasupernova. Schr¨odinger-like equation,
We do this by performing the first fully self-coupled 3-
d
] neutrino flavor (3 3) evolution calculations. Stars of i ψ =Hˆ ψ , (1)
h × dt| i | i
p 8–11M⊙ develop degenerate O-Ne-Mg cores, at least
∼
- someofwhicheventuallycollapseto producesupernovae where t is an Affine parameter along the neutrino
o (e.g., Refs. [1, 2, 3]). The matter density falls off so worldline, and the Hamiltonian Hˆ is composed of two
r
t steeply in the regionbetween sucha coreand the hydro- pieces: Hˆ = Hˆ +Hˆ . The matter contribution is
s vac matt
a genenvelopethatthereislittlehindrancetotheoutgoing να Hˆmatt νβ = √2GFneδαβδeα, where GF is the Fermi
[ supernova shock. Consequently, O-Ne-Mg core-collapse hcon|stant,n| iis the electronnumber density, and ν de-
2 supernovae are the only case where neutrino-driven ex- notes a puree flavor state with α = e,µ,τ. The |vaαciuum
v plosionhasbeendemonstratedbyseveralgroups[4,5,6]. piece of Hˆ is να Hˆvac νβ = (2Eν)−1(UMU†)αβ, where
h | | i
1 Suchsupernovaemaybethe site forproducingthe heav- E is the neutrino energy. The transformation U re-
ν αi
7 iest elements by rapid neutron capture [7] and may also lates pure flavor state ν to vacuum mass eigenstate
α
2 | i
explain the observed subluminous supernovae [5]. They ν (seeChap.13ofRef.[15]forourconvention): ν =
1 | ii | αi
0. areexpectedtoberelativelycommonbecausetheknown i=1,2,3Uα∗i|νii. The mass matrix is diagonal in the
progenitors of most core-collapse supernovae lie in the vPacuum mass basis, M =diag(0,∆m2 ,∆m2 +∆m2 ),
1 21 21 32
7 mass range ∼8–20M⊙ (e.g., Ref. [8]). wherethemass-squareddifferencesare∆m2ij =m2i−m2j.
0 The region of steeply-falling matter density immedi- In calculations presented here we take the three mix-
: ately above an O-Ne-Mg core provides an extremely in- ing angles and the CP violating phase to be θ = 0.6,
v 12
i terestingenvironmentforstudyingneutrinoflavorevolu- θ23 = π/4, θ13 = 0.1, δ = 0, respectively. We take
X tion. For the vacuum neutrino mass-squared differences ∆m2 = 8 10−5eV2 ∆m2 and ∆m2 = 3
ar ∆m2atm and∆m2⊙ associatedwith atmosphericandsolar 10−321eV2 ≃ ±×∆m2atm, whe≃re the⊙plus (minus3)2sign±is fo×r
neutrino oscillations, respectively, the two correspond- the normal (inverted) mass hierarchy.
ing conventionalMikheyev-Smirnov-Wolfenstein(MSW) In pure matter-driven MSW evolution, for small θ ,
13
[9, 10] resonances occur with very small radial separa- the ν survival probability P = ν ψ 2 can be fac-
e νeνe |h e| i|
tion in this region. As the neutrino number density de- torized [11]: P = PH PL , where PH and PL
νeνe νeνe νeνe νeνe νeνe
creases much more gently with radius than the matter arethe ν survivalprobabilitiesin2-flavor(2 2)mixing
e
×
density, neutrino self-coupling can affect flavorevolution processesatthe∆m2 and∆m2 scales,respectively. In
atm ⊙
associatedwith both ∆m2atm and ∆m2⊙, and a full treat- otherwords,thefull3 3MSWresultisthesuperposition
×
ment of3 3 mixing appearsto be required. To identify oftwoindependent 2 2MSW scenarios,one foreachof
× ×
clearly any new physics, we study the relatively simple the solar and atmospheric mass-squareddifferences.
case of the neutronization burst, which consists of pre- Using the n profile for the O-Ne-Mg core model of
e
dominantly νe emitted when the shock breaks through Refs. [1, 2] and the neutrino mixing parameters given
the neutrino sphere. above, we show P as a function of E in Fig. 1 as-
νeνe ν
Traditional analyses of flavor evolution of supernova suming pure matter-driven MSW evolution. The results
neutrinos are based on the pure matter-driven MSW ef- shown are for radius r = 5000 km, where the vacuum
fect (see, e.g., Refs. [11, 12, 13, 14]). The evolution of Hamiltonian dominates for most neutrino energies. The
2
1 nos emitted in all directions from the neutrino sphere
havethesameflavorevolutionhistoriesasthosewiththe
0.8 same energies but propagating along a radial trajectory.
With this approximation we have
0.6
Pννee n D(r/Rν) Lνe dE f (E ), (3)
0.4 ν,λ −→ 2πR2 E Z ν νe ν
Xλ ν h νei
0.2 where D(ξ)= 1(1 1 ξ−2)2. In our calculations for
2 − −
the neutronization buprst we assume ν is the only neu-
e
0
0 10 20 30 40 trinospeciesemittedfromthe neutrinosphere(atradius
Eν(MeV) R =60km)andtaketheν luminositytobeL =1053
ν e νe
erg/s. The ν energy distribution function f (E ) is
FfuInGc.ti1o:n(sCooflonreuotnrliinnoe)eNneerugtyriEnoνsfuorrvpivuarlepmroabtatebri-lditriievsePnνMeνeSWas takentobe ofeFermi-Diracformwithdegeneracνyepaνram-
evolution. The2×2flavormixingcaseswith ∆m2≃∆m2atm eter η = 3 and with an average νe energy hEνei = 11
and ∆m2 are shown as the dashed and dotted lines, respec- MeV. Full 2 2 multi-angle simulations show that the
tively. T⊙he 2×2 flavor mixing case with ∆m2 ≃ −∆m2atm single-angle a×pproximation appears to be adequate for
(not shown) corresponds to Pνeνe ≃ 1 for all energies. The qualitative studies of the collectiveflavortransformation
solid linegivesPνeνe(Eν)forfull3×3flavormixingwiththe phenomena of interest here [19, 20, 21].
normal mass hierarchy. The 3×3 inverted mass hierarchy
Fig. 2 shows the results of single-angle simulations of
case (not shown) is almost identical to thedotted line.
full 3 3 neutrino flavor evolution including nonlinear
×
neutrino self-coupling for the neutrino mixing and emis-
sion parameters given above. Results for both the in-
dashed and dotted lines in this figure show the 2 2
× verted(upperpanels)andnormal(lowerpanels)neutrino
flavor mixing cases with the normal mass hierarchy for
∆m2 = 3 10−3eV2 ( ∆m2 ) and 8 10−5eV2 mass hierarchies are presented, again at radius r =5000
( ∆m2), ×respectively. ≃In thesaetmcases we t×ake the ef- km as in Fig. 1. The left-hand panels show the proba-
≃ ⊙ bility a 2 = ν ψ 2 for neutrinos to be in each of the
fective 2 2 vacuum mixing angles to be θ = 0.1 and | νi| |h i| i|
× masseigenstates ν ,andtheright-handpanelsshowthe
0.6, respectively. We note that in either case MSW fla- i
| i
probability a 2 = ν ψ 2 for neutrinos to be in each
vor transformation for neutronization burst neutrinos of | να| |h α| i|
of the flavor states ν .
averageenergy E =11MeVisneitherfullyadiabatic α
(P = sin2θ)hnoνerifully non-adiabatic (P = cos2θ) Theinvertedneut|riniomasshierarchyproducesastep-
νeνe νeνe wiseν /ν conversionatenergyE 11MeV[Fig.2(a)].
due to the rapid decrease of matter density ρ with ra- 2 1 ν
≃
dius in the region of interest (d(lnρ)/dr & 0.04km−1). This spectral swap feature can be understood in a 2 2
×
The spike in PνHeνe(Eν) (dashe|d line) at |Eν ≃ 8 MeV is mInixtihnigs sscchheemmeewthitehfl∆amvo2r≃ev∆olmut2⊙ion(seoef,ae.gn.e,uRtreifn.o[2c2a])n.
caused by a sharp change in n at the base of the hy-
e
be represented as the precession of a spin or polariza-
drogen envelope, where the electron fraction Y jumps
e
tion vector in flavor isospace, in analogy to a magnetic
from 0.5 to 0.85. The 2 2 inverted mass hierarchy
case with ∆m∼2 ∆m2 h×as P 1 for all energies spin (e.g., Ref. [18]). When neutrino number fluxes
≃− atm νeνe ≃ are large, the neutrino self-coupling is strong and the
(i.e., no MSW resonance). In the complete 3 3 mixing
× “magnetic spins” representing neutrinos can rotate col-
case with the normal mass hierarchy, P is given by
νeνe lectively in the region where a neutrino with a represen-
the solid line. This case corresponds closely to a succes-
tative energy would experience a resonance in the pure
sion of two independent 2 2 mixing schemes, with the
× matter-drive MSW evolution [23]. This corresponds to
solid line being approximately the product of the values
ofthe dashed(PH )anddotted(PL )lines. The3 3 a neutrino-background-enhancedMSW-like flavor trans-
νeνe νeνe × formation [22, 23, 24, 25]. Subsequently, the “magnetic
inverted mass hierarchy case gives P nearly identical
νeνe spins” will enter a collective precession mode. As neu-
to the dotted line.
trinofluxesbecomesmallatlargeradiiandthecollective
In supernovae, where neutrino luminosities are large,
precession mode dies out, a mass-basis spectral swap is
neutrino-neutrinoforwardscatteringcontributesanother
established [26, 27]. The swap point in the neutrino en-
term for the Hamiltonian [16, 17, 18]
ergy spectrum is determined by conservation of a mass-
Hˆ =√2G n ψ ψ , (2) basis “lepton number” [27, 28]. In fact, the result of
νν F ν,λ λ λ
X | ih | the full 3 3 calculation agrees very well with that of
λ ×
the 2 2 calculation with ∆m2 ∆m2. In contrast to
× ≃ ⊙
where sumsoverallbackgroundneutrinostates ψ thepure-matterdrivenMSWevolution,neutrinosonthe
λ | λi
with nPumber density n . To simplify the problem, we two sides of the swap point appear to have experienced
ν,λ
adopt the “single-angle approximation” in which neutri- almostfullyadiabaticorfully non-adiabaticflavortrans-
3
1 1
(a) (b)
0.8 0.8
0.6 0.6
2aνi| 2aνα|
|0.4 |0.4
0.2 0.2
0 0
0 10 20 30 40 0 10 20 30 40
Eν(MeV) Eν(MeV)
1 1
(c) (d)
0.8 0.8
0.6 0.6
2aνi| 2aνα|
|0.4 |0.4
0.2 0.2
0 0
0 10 20 30 40 0 10 20 30 40
Eν(MeV) Eν(MeV)
FIG. 2: (Color online) Probabilities as functions of neutrino energy Eν for neutrinos to be in each vacuum mass eigenstate
(|aνi|2, left panels) and flavor eigenstate (|aνα|2, right panels), respectively. The solid, dashed and dotted lines represent the
ν1,ν2,andν3 statesintheleftpanelsandtheνe,νµ,andντ statesintherightpanels. Top(bottom)panelsshowtheinverted
(normal) mass hierarchy case.
formation with those in the low (high) mass eigenstate tures, reminiscent of the factorization property of pure
endingupontheright(left)handsideoftheswappoint. matter-drivenMSW evolution. The ν /ν swap at E
3 2 ν
≃
We note that no neutrino-background-enhanced MSW- 12.7 MeV and the ν /ν swap at E 15 MeV corre-
2 1 ν
≃
like flavor transformation occurs at the ∆m2 scale in spondto those in the 2 2 schemeswith ∆m2 ∆m2
atm × ≃ atm
theinvertedmasshierarchycase. Thisisanalogoustothe and ∆m2, respectively. This result seems to justify
⊙
pure matter-driven MSW evolution. We also note that the 2 2 approximation used in previous work (e.g.,
×
conservation of the mass-basis lepton number prohibits Refs.[19, 20, 21, 23, 25, 29, 30, 31, 32]), but is some-
the formation of a spectral swap in the corresponding what surprising given the nonlinear nature of neutrino
2 2 mixing scheme with ∆m2 ∆m2 because all self-coupling and the fact that the regions of collective
× ≃ − atm
neutrinos start as ν in our calculation [38]. flavor transformationfor ∆m2 and ∆m2 overlapwith
e atm ⊙
Because θ12 is large, Pνeνe(Eν) exhibit a large oscil- eachother. Wenotethattheν3/ν2 swapismuchsharper
latory feature in the transition region near the stepwise than the ν2/ν1 swap. We also note that the dip (bump)
νO2u/tνs1idceonthveisrsrieogniopno,instpeacttrEaνl s∼wa1p1 cMaenVal[ssoeebFeigse.e2n(bf)o]r. itno |tahνe3|a2b(r|uapν2t|2c)hacnengteerinednaetaEtνth≃e 5b.a2seMoefVthceorhryesdproongedns
0th.3e2n(euUtrin2oflav0o.6r7s)tafoters.EFo.rex9aMmepVle,(PEνeν&e ≃16|UMe2e|2V≃). efincvieenlocpyeo.fTthheisnfeeuattruinreo-ibnactkhgeronuenpdr-oenfihleanrecdeducMesStWhe-liekfe-
e1 ν ν
Nerogtyert|ehgaitm||eaν≃Eµ|2 i&s la1r3geMre(Vsm(aEller).th1a0nM|aeνVτ|)2.iTnhtihseisena- ttruarnesifsoramlsoatpiornesoenftνeinatthtehpeu∆remm2atamttsecra-dler.ivAensMimSiWlarefveao--
ν ν
consequence of setting the CP-violating phase to δ = 0. lution, but in a different energy range (see Fig. 1).
Asδ isincreased,|aντ|2 increases(decreases)forEν &13 As in the inverted mass hierarchy case, the spectral
MeV (Eν . 10 MeV), and |aνµ|2 = |aντ|2 for δ = π/2. swaps are also present in the flavor basis [see Fig. 2(d)].
pFloarcδes=. π,the|aνµ|2 and|aντ|2 curvesinFig.2(b)switch EMxecVep,tnfeoarrlytheallmνod’esraatreebturmanpsfocremnteedred(waitthEPν ≃ 5.2
e νeνe ≃
Fig. 2(c) shows that the normal neutrino mass hierar- U 2 0.01) below the ν /ν swap energy E 12.7
e3 3 2 ν
| | ≃ ≃
chy produces a superposition of two spectral swap fea- MeV. In contrast, there is less significant ν depletion
e
4
above the ν2/ν1 swap energy Eν 15 MeV, for which [3] C. Ritossa, E. Garc´ıa-Berro, and I. J. Iben, Astrophys.
energy range P U 2 0.6≃7 would be expected. J. 515, 381 (1999).
The bump in Pνeνe (≃E|)ea1t| E≃ 5.2 MeV corresponds [4] R. Mayle and J. R. Wilson, Astrophys. J. 334, 909
to the feature inνeνae 2νat theνsa≃me energy as explained (1988).
| ν2| [5] F.S.Kitaura, H.-T.Janka, andW.Hillebrandt,Astron.
above. On the other hand, we note that the apparent
Astrophys. 450, 345 (2006), astro-ph/0512065.
peak of Pνeνe(Eν) in Eν ≃15.5MeV is part of the same [6] L. Dessart et al., Astrophys. J. 644, 1063 (2006), astro-
oscillation feature discussed above for Fig. 2(b). This ph/0601603.
oscillation feature will disappear at very large distances [7] H.Ning,Y.Z.Qian,andB.S.Meyer,Astrophys.J.667,
where coherence has been lost. L159 (2007), arXiv:0708.1748 [astro-ph].
[8] W.-D. Li et al., Astrophys. J. 641, 1060 (2006), astro-
Thespectralswapfeaturesillustratedherefortheneu-
ph/0507394.
tronization burst from an O-Ne-Mg core-collapse super- [9] L. Wolfenstein, Phys. Rev. D17, 2369 (1978).
nova are not expected to be present for an Fe-core col- [10] S. P. Mikheyev and A. Y. Smirnov, Yad. Fiz. 42, 1441
lapse supernova. This is because at the neutronization (1985), [Sov.J. Nucl.Phys. 42, 913 (1985)].
burstepoch,thereisanextendedregionofhighn above [11] T.-K. Kuo and J. T. Pantaleone, Phys. Rev. D37, 298
e
(1988).
an Fe core. So in this case high neutrino fluxes are al-
[12] A.S.DigheandA.Y.Smirnov,Phys.Rev.D62,033007
ways accompanied by high n , which inhibits neutrino-
e (2000), hep-ph/9907423.
background-enhanced MSW-like flavor transformation. [13] C. Lunardini and A. Y. Smirnov, JCAP 0306, 009
ThestudiesofneutrinosfromFecore-collapsesupernovae (2003), hep-ph/0302033.
based on pure matter-driven MSW evolution show that [14] J. P. Kneller and G. C. McLaughlin, Phys. Rev. D73,
the ν survival probability is P sin2θ 0.32 056003 (2006), hep-ph/0509356.
or leses for either mass hierarchyνeν(esee≃, e.g., T⊙ab≃le I in [15] W.-M. Yaoet al., J. Phys. G33, 1 (2006).
Ref. [33]). If enough high-energy (E & 15 MeV) neu- [16] G. M. Fuller, R. W. Mayle, J. R. Wilson, and D. N.
ν Schramm, Astrophys.J. 322, 795 (1987).
trino events are collected from the neutronization burst
[17] J. T. Pantaleone, Phys. Rev. D46, 510 (1992).
of a future Galactic supernova in both the charged- [18] G. Sigl and G. Raffelt, Nucl. Phys. B406, 423 (1993).
currentandneutral-currentchannels,theprogenitormay [19] H.Duan,G.M.Fuller,J.Carlson,andY.-Z.Qian,Phys.
be identified as having an O-Ne-Mg or Fe core based on Rev. D74, 105014 (2006), astro-ph/0606616.
whether or not ν is the dominant species in the burst. [20] A. Esteban-Pretel, S. Pastor, R. Tomas, G. G. Raf-
e
Because the total neutrino fluence over the 10 ms du- felt, and G. Sigl, Phys. Rev. D76, 125018 (2007),
∼ arXiv:0706.2498 [astro-ph].
rationoftheneutronizationburstisonlyasmallfraction
[21] G. L. Fogli, E. Lisi, A. Marrone, and A. Mirizzi (2007),
of that emitted during the first several seconds after the
arXiv:0707.1998 [hep-ph].
onset of core collapse, collection of the required number [22] H.Duan,G.M.Fuller,andY.-Z.Qian,Phys.Rev.D76,
of events from the neutronization burst may be beyond 085013 (2007), arXiv:0706.4293 [astro-ph].
the capabilities of existing detectors but could be within [23] S. Pastor and G. Raffelt, Phys. Rev. Lett. 89, 191101
the reach of proposed megaton water Cherenkov detec- (2002), astro-ph/0207281.
tors [33, 34, 35] and liquid argondetectors like ICARUS [24] Y. Z. Qian and G. M. Fuller, Phys. Rev. D51, 1479
[36, 37]. The low-energy (. 10 MeV) neutrino signals (1995), astro-ph/9406073.
[25] G. M. Fuller and Y.-Z. Qian, Phys. Rev. D73, 023004
in the O-Ne-Mg core-collapse supernova neutronization
(2006), astro-ph/0505240.
burst, though even more difficult to detect, carry infor-
[26] H.Duan,G.M.Fuller,J.Carlson,andY.-Z.Qian,Phys.
mationthatpotentiallycandistinguishbetweentheneu- Rev. D75, 125005 (2007), astro-ph/0703776.
trino mass hierarchies [see Figs. 2(b) and (d)]. [27] G. G. Raffelt and A. Y. Smirnov, Phys. Rev. D76,
081301(R) (2007), arXiv:0705.1830 [hep-ph].
We thank K. Nomoto for providing the electron num-
[28] S.Hannestad,G.G.Raffelt,G.Sigl,andY.Y.Y.Wong,
berdensityprofileinhisO-Ne-Mgcoremodel. Weappre- Phys. Rev.D74, 105010 (2006), astro-ph/0608695.
ciate the hospitality of the Institute for Nuclear Theory [29] A. B. Balantekin and H. Yu¨ksel, New J. Phys. 7, 51
at the University of Washington during the completion (2005), astro-ph/0411159.
of this work. This work was supported in part by NSF [30] H.Duan,G.M.Fuller,andY.-Z.Qian,Phys.Rev.D74,
grant PHY-04-00359 at UCSD, DOE grants DE-FG02- 123004 (2006), astro-ph/0511275.
87ER40328 at UMN, DE-FG02-00ER41132 at INT, an [31] H.Duan,G.M.Fuller,J.Carlson,andY.-Z.Qian,Phys.
Rev. Lett.97, 241101 (2006), astro-ph/0608050.
IGPP/LANL mini-grant, and by the DOE Office of Nu-
[32] H.Duan,G.M.Fuller,J.Carlson,andY.-Z.Qian,Phys.
clear Physics, the LDRD Programand Open Supercom- Rev.Lett.99,241802(2007),arXiv:0707.0290[astro-ph].
puting at LANL. [33] M. Kachelriess et al., Phys. Rev. D71, 063003 (2005),
astro-ph/0412082.
[34] Y. Itow et al. (The T2K) (2001), hep-ex/0106019.
[35] M. Goodman et al., UNO whitepaper (2001),
PREPRINT-SBHEP01-3.
[1] K.Nomoto, Astrophys.J. 277, 791 (1984). [36] I. Gil-Botella and A. Rubbia, JCAP 0310, 009 (2003),
[2] K.Nomoto, Astrophys.J. 322, 206 (1987). hep-ph/0307244.
5
[37] C. Vignoli, D. Barni, J. M. Disdier, D. Rampoldi, and [38] A. Mirizzi (2007), private communication.
G. Passardi (ICARUS), AIP Conf. Proc. 823, 1643
(2006).