1. The Diffuse Flux of Supernova Neutrinos
F n
Cecilia Lunardini
Institute for Nuclear Theory
University of Washington - Seattle
Colliders to Cosmic Rays 2007 , Lake Tahoe, CA

2. Abstract Diffuse neutrinos from supernovae O(1) question: Seen?
Not yet
BUT: will be seen
O(e) question: What can we learn?
original n spectrum (at emission)

3. How do stars die? Supernovae
Massive stars (M>8Msun) gravitational instability
Collapse to nuclear density core
Shock and explosion
Mention adiabatic index, say that mass is the factor. Split the slide? Make it less boring? Write some reactions?

4. A neutrino phenomenon 99% of the gravitational energy in neutrinos
GN M2f/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 Exi
Give numbers for density and radius.. Think if condition is right.. Say it’s basically the same as the early universe.. Say it’s the only modern site with thermalized neutrinos!!
x=,

5. The diffuse flux Cosmological SN rate: RSN(0) ~ 10-4 Mpc-3yr-1
add plot of SNR from my paper, with reference to Beacom

6. Fit to core collapse SN data only,
C.L., astro-ph/
Star Formation fit,
Beacom & Hopkins, astro-ph/
Data: Cappellaro et al., A&A 430, 2005; Dahlen et al., APJ (3 extinction-corrected, 1 not corrected)
Confidence levels: 68.3,90,95.4%

7. “Effective” neutrino spectrum after oscillations:
a (“pinching”)~ 2-4 , E0 ~ MeV
Check values used… keep in mind that Mirizzi-Raffelt find smaller values of alpha possible
SN1987A-motivated,
Mirizzi & Raffelt, PRD72, 2005

8. Predictions Ando & Sato SK limit Kaplinghat et al. Strigari et al.
F(E>19.3 MeV)/(cm-2 s-1)
Hartmann
& Woosley
Kaplinghat et al.
Strigari et al.
Lunardini
Say that: 1. requiring compatibility with SN1987A and SN observations gives low flux 2. makes the case for UNO

9. Seen? Not yet! Limits: anti-ne, ne
KamLAND
SNO
SK+oscillations, Lunardini, PRD73, 2006
F(E)/(MeV-1cm-2 s-1)
SuperKamiokande
Atmospheric n, invisible m
Add ref to SNO
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/ , 2006

10. BUT: will be seen at Mton detectors
Anti-e + p  n + e+
Beacom & Vagins, PRL93, 2004
Add plot from Lisi and citation , update reference to my paper
Fogli et al., hep-ph/

11. Anti-ne + p Events/4 yr (99% CL, from SN1987A) 7 - 60 1.1 - 6.4
UNO/HyperK:
Water, 0.4 Mton fiducial, En > 19.3 MeV
GADZOOKS
Water+Gd, 20 Kt fiducial, En>11.3 MeV
Anti-ne + p Events/4 yr (99% CL, from SN1987A)
7 - 60
update reference to my paper, cite Ando-Sato and others, mention LENA, SNO+, etc…
Most conservative, C.L., astro-ph/
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

12. What can we learn? Spectrum of e+: Number of e+ events:
E0 , a (“pinching”), b (SNR power)
Number of e+ events:
Le , RSN(0), E0, a , b
Say: spectrum interesting because less degenerate… in principle it’s very interesting to probe beta, but you’ll see that’s very hard.. Somewhere, say that the variables describe the spectrum after conversion. Give indicative value of R_SN(0)

13. Spectral sensitivity Original  spectrum? Supernova Rate? Water only
Yes!
Useful observable: (bin 1)/(rest)
Supernova Rate?
No/difficult
Normalized to 60 events
C.L., astro-ph/

14. Water+Gd
Normalized to 150 events
C.L., astro-ph/

15. To understand: analytics
Approximations: dominated by z<1 at high energy (redshift):
RSN=0 z>1
z<<1 & Wm + WL = 1:

16. Result: h = a + b - (3/2)Wm , zmax=1
Cruder : neglect upper integration limit
e = E0/(1+a), b only in the polynomial part!
Crudest: “fitted” exponential: F = F0 e-E/<E>

17. Cruder (20% accuracy above 20 MeV)
R(0)=10-4 Mpc-1yr-1 ,
Le= ergs, b = 3.28 , a=2.6 E0 =15 MeV
Exact
Result
Cruder (20% accuracy above 20 MeV)
neglect upper integration limit
Crudest
“fitted” exponential
Explain why the crudest works better! Say that analytics is useful to understand how <E> and Phi_0 are related to the original spectral parameters

18. Numbers of events add information
events/4 year
(bin 1)/(rest)
Motivate the beta=5 with my results , and the 3.28 with beacom’s ones , check value of R_0
R(0)=10-4 Mpc-1yr-1 ,
Le= ergs,
0.4 Mt, 4 yr

19. Conclusions: likely scenario
Gadzooks and/or LENA and/or HyperK/UNO/MEMPHYS will see the DF
b known from SN surveys (SNAP, JWST)
DF spectrum -> E0 , a
Test of SN numerical models
DF number of events -> break degeneracy between E0, a, Ln, RSN(0)
Improve conclusions, less boring!

20. Backup slides

21. Original n spectrum? YES!
C.L., astro-ph/
Normalized to 60 events, b=3.28
Total error, no Gd
Total error, with Gd
say that figure was produced varying only original spectrum, so if we know \beta we can distinguish… Cite beacom-hopkins for 3.28?

22. Original n spectrum? YES!
Normalized to 60 events, b=3.28
Depends on e = E0/(1+a)
e/MeV=2 (E0/MeV=12, a=5)
e/MeV=4.2 (E0/MeV=15, a=2.6)
e/MeV=6.7 (E0/MeV=20, a=2)
“results are smowhat intuitive… some of you might have an understanding of them, already… however, In a minute I will show… analytics..” emphasize the ratio method more??

23. Original n spectrum? YES!
Normalized to 60 events, b=3.28
Useful observable: first bin/rest of data
“results are smowhat intuitive… some of you might have an understanding of them, already… however, In a minute I will show… analytics..” emphasize the ratio method more??

24. SN population? ..no.. Normalized to 60 events, E0/MeV=15, a=2.6 b=5
Say that even if we don’t know beta, we don’t have to worry, because the beta dependence is very small, say it’s bad if you want to test beta, but good if you want to learn about neutrino spectrum

25. Number of events add information
R(0)=10-4 Mpc-1yr-1 , Le= ergs, 0.4 Mt, 4 yr, Eth=18 MeV
b=3.28
E0/MeV=11
E0/MeV=15
E0/MeV=20
a=2
21.6
71.6
163
a=4
7.4
37.5
110
e ~ 7
Motivate the beta=5 with my results , and the 3.28 with beacom’s ones , check value of R_0
b=5
E0/MeV=11
E0/MeV=15
E0/MeV=20
a=2 34
129
326
a=4 10 59
200