Colliders to Cosmic Rays 2007 , Lake Tahoe, CA

The Diffuse Flux of Supernova Neutrinos

Cecilia LunardiniInstitute for Nuclear Theory

University of Washington - Seattle

Abstract

• Diffuse neutrinos from supernovae

• O(1) question: Seen? – Not yet – BUT: will be seen

• O() question: What can we learn?– original spectrum (at emission)

How do stars die? Supernovae

• Massive stars (M>8Msun) gravitational instability–Collapse to nuclear density core–Shock and explosion

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A neutrino phenomenon

• 99% of the gravitational energy in neutrinos– GN M2

f/rf - GN M2i/rI ~ 1053 ergs

• Diffusion from thermal surface e, , , anti-e, anti-, anti-

– Time : (size2)/(mean free path) ~ 10 s

– h E i : ~9 – 22 MeV, h Eei < h Eanti-e i < h Exix=,

The diffuse flux

• Cosmological SN rate: RSN(0) 10-4 Mpc-3yr-1

ddE

c

H0

RSN (z)dNw ( E )

d E we,,

0

zmax Pwe (E,z)dz

m (1 z)3

E (1 z)E

H0 70Km /(sMpc), m 0.3, 0.7, zmax 5

RSN (z) RSN (0) (1 z) z 1, 3

RSN (0)2 z 1

Fit to core collapse SN data only, C.L., astro-ph/0509233 Star Formation fit,

Beacom & Hopkins, astro-ph/0601463

Data: Cappellaro et al., A&A 430, 2005; Dahlen et al., APJ 613 2004 (3 extinction-corrected, 1 not corrected)Confidence levels: 68.3,90,95.4%

• “Effective” neutrino spectrum after oscillations:– (“pinching”) 2-4 , E0 12 - 20 MeV

SN1987A-motivated, Mirizzi & Raffelt, PRD72, 2005

Predictions

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rtm

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SK limit

(E

>19

.3 M

eV)/

(cm

-2 s

-1)

Seen? Not yet! Limits: anti-e, e

KamLAND

SuperKamiokande

(E

)/(M

eV-1cm

-2 s

-1)

Zhang et al. (Kamiokande) PRL61, 1988; Eguchi et al. (KamLAND), PRL92, 2004; Malek et al. (SK), PRL90, 2003; Aharmim et al., (SNO), PRD70, 2004; Aglietta et al. (LSD), Astrop. Phys. 1, 1992, Aharmim et al., (SNO), hep-ex/0607010, 2006

Atmospheric , invisible

SK+oscillations, Lunardini, PRD73, 2006

SNO

BUT: will be seen at Mton detectors

Fogli et al., hep-ph/0412046

Beacom & Vagins, PRL93, 2004

Anti-e + p n + e+

Most conservative, C.L., astro-ph/0509233

See also Ando & Sato, New J. Phys., 2004; Fogli et al., JCAP, 2005; Marrodan Undagoitia et al., Prog. Part. Nucl. Phys. 57, 2006 ; Cocco et al. JCAP 0412:002,2004

UNO/HyperK:Water, 0.4 Mton fiducial, E > 19.3 MeV

GADZOOKSWater+Gd, 20 Kt fiducial, E>11.3 MeV

Anti-e + p Events/4 yr (99% CL, from SN1987A)

7 - 60 1.1 - 6.4

What can we learn?

• Spectrum of e+:– E0 , (“pinching”), (SNR power)

• Number of e+ events: – Le , RSN(0), E0, ,

• Original spectrum?– Yes!– Useful observable:

(bin 1)/(rest)

• Supernova Rate?– No/difficult

Water only

C.L., astro-ph/0612701

Normalized to 60 events

Spectral sensitivity

Water+Gd

Normalized to 150 events

C.L., astro-ph/0612701

To understand: analytics

• Approximations: dominated by z<1 at high energy (redshift):– RSN=0 z>1

– z<<1 & m + = 1:

ddE

c

H0

RSN (z)dNw ( E )

d E we,,

0

zmax Pwe (E,z)dz

m (1 z)3

• Result: = + - (3/2)m , zmax=1

• Cruder : neglect upper integration limit– = E0/(1+), only in the polynomial part!

• Crudest: “fitted” exponential: = 0 e-E/<E>

• Exact• Result• Cruder (20%

accuracy above 20 MeV)– neglect upper

integration limit

• Crudest– “fitted”

exponential

R(0)=10-4 Mpc-1yr-1 , Le=5 1052 ergs, b = 3.28 , a=2.6 E0 =15 MeV

Numbers of events

add information

• events/4 year• (bin 1)/(rest)

R(0)=10-4 Mpc-1yr-1 , Le=5 1052 ergs, 0.4 Mt, 4 yr

Conclusions: likely scenario

• Gadzooks and/or LENA and/or HyperK/UNO/MEMPHYS will see the DF

• known from SN surveys (SNAP, JWST)

• DF spectrum -> E0 , – Test of SN numerical models

• DF number of events -> break degeneracy between E0, , L, RSN(0)

http://snap.lbl.gov/ http://www.jwst.nasa.gov/,

Backup slides

Original spectrum? YES!

Normalized to 60 events, =3.28 Total error, no GdTotal error, with Gd

C.L., astro-ph/0612701

Original spectrum? YES!

• Depends on = E0/(1+)

Normalized to 60 events, =3.28

/MeV=2 (E0/MeV=12, =5)

/MeV=4.2 (E0/MeV=15, =2.6)

/MeV=6.7 (E0/MeV=20, =2)

Original spectrum? YES!

• Useful observable: first bin/rest of data

Normalized to 60 events, =3.28

SN population? ..no..

Normalized to 60 events, E0/MeV=15, =2.6

=2

=3.28

=5

Number of events add information

=3.28 E0/MeV=11 E0/MeV=15 E0/MeV=20

=2 21.6 71.6 163

=4 7.4 37.5 110

R(0)=10-4 Mpc-1yr-1 , Le=5 1052 ergs, 0.4 Mt, 4 yr, Eth=18 MeV

7

=5 E0/MeV=11 E0/MeV=15 E0/MeV=20

=2 34 129 326

=4 10 59 200