Temporal Structure of the Supernova Neutrino Signal
Neutron Stars, Supernova & Phases of Dense Quark Matter Seeking observable signatures for dense quark matter in astrophysics Sanjay Reddy Theoretical Division, LANL Observables: (sensitive to the high density physics) Mass and Radius Supernova Neutrinos Surface Temperature and Age Spin period ( and d/dt)dt) Gravity Waves Hard Physics: E ~ 400 MeV Soft Physics: E ~ T 10-3-50 MeV Neutron Star Mass
Origin of the clustering at MNS~1.4 Msolar ? Physics issue : EoS at high density - what is the heaviest neutron stars one can make ? Courtesy: J. Lattimer Radius: L =F d2 =4 R2 T4 R = R 1- GM/Rc/RcRc 2 T = 1- GM/Rc/RcRc 2 T ( 1- GM/Rc/RcRc 2 =(1+ z) -1 )
RX J1856-3754: nearby (d~120 pc) isolated neutron star Radius: L =F d2 =4 R2 T4 Deviations from Blackbody spectra: atmosphere: sensitive to local gravity (GM/dt)R2) Potentially can yield both M and R Pons et al. Astrophys. J. 564: 981-1006, 2002 Walter & Lattimer, Astrophys. J.576:L145-L148,2002 Constraints and Trends: Exotic Stars: Soft EoS Quasi-Periodic Oscillations: indicate a last stable orbit
Gravitational Red-shift: observation of spectral lines (Cottam, Paerels, Mendez, Nature 420: 51 (2002). Phases of Dense Quark Matter Attractive interactions destabilize the Fermi surface formation of cooper-pairs (BCS Theory) In quark matter most attractive channel is antisymmetric in color space spin zero pairs must be anti-symmetric in flavor 2-flavor quark matter: (2SC) u d u d
u d Rapp, Schaefer, Shuryak, and Velkovsky (1998) Phys.Rev.Lett. 81, 53 Alford, Rajagopal, Wilczek Phys.Lett.B422, 247-256, (1998) 100 MeV Color-Flavor Locked Phase Alford, Rajagopal & Wilczek, Nucl. Phys. B 558, 219 (1999) BCS pairing of all 9 quarks: 100 MeV !
E gluong E quark 2 Energy SU(3) color SU(3) L SU(3) R U(1)B SU(3) color+L+R Z 2 E GB:SU (3) SU (3)SU (3) C L R
mlight ms E GB:UB (1) = 0 Excitation Spectrum Charge Neutrality in Dense Quark Matter 2 4 2 2 Normal Quark Matter requires electrons for charge
neutrality breaks iso-spin PF u d s e CFL requires ms2/dt)4 2 4 Alford, Rajagopal, Reddy
and Wilczek Phys.Rev.D64:074017, (2001) Less symmetric phases: (when three is a crowd) Neutrality favors CFL 2 2SC = 2 4 Normal 4
Large density discontinuity D A B/dt)C Heterogeneous co-existence line: (dropletsrods-slabs) Alford, Rajagopal, Reddy and Wilczek Phys.Rev.D64:074017, (2001) Quark Matter EoS & Hybrid Stars P(() = 3 2 4
(1 c) 4 3 4 3 2 2 2 2 m + 2 Beff 2 s Alford & Reddy, Phys. Rev. D67 074024 (2003) Can Quark Stars Mimic Nuclear Stars ?
P(() = 3 2 2 3 2 2 4 (1 c) m + 2 Beff 2 2 s 4 4 3 Core Collapse Supernova Fe core becomes unstable Collapse time scale ~ 100 ms Nearly Adiabatic
B.E. ~ G Mcore/dt)Rfinal ~3 X 1053 ergs Supernova Neutrinos - a (proto) neutron star is born 1500 km Core collapse tcollapse ~100 ms B. E. ~2-3 X Shock wave 53 7 10 ergs 3X10 Eshock~1051ergs km 10 km Hot & dense Protoneutron
Star: t~1-2 s 100 km Proto-Neutron Star Evolution 31053 ergs is stored in neutrinos and internal energy. t T(t ) T(t = 0 ) 1 C R2 C CV c 3 Y (t ) 6 2
t Y(t = 0 ) exp D 3 YL R2 D = 2 Y c e Proto-neutron Star Phase: late times (t > 3-4 s) Burrows & Lattimer, Astrophys. J 307, 178 (1986) Kiel & Janka, Astrnm. & Astrophys. 296, 145 (1995) Pons, Reddy, Prakash, Lattimer, Miralles,Astrophys. J. 513, 780 (1999) Neutrino diffusion dominates evolution
Time scales set by neutrino mean free path and dense matter EoS Reddy, Prakash, Lattimer, Pons Phys. Rev. C 59, 2888 (1999) simulations with normal quark matter Delayed collapse to black-holes: Generic to most high density transitions to very soft EoS. ons, Steiner, Prakash and Lattimer, Phys.Rev.Lett. 86, 5223 (2001) E Microphysics of neutrino mean free paths
E GF l (x) j (x) 2 2 l = (x) (15 ) (x) E q L= q j = (x)(cV c A 5 + iF2 target q ) (x) 2M
d 2 2 E GF Im [ L (k,k + q) (q)] V d cos dE E L = Tr [ l (k) l (k + q) ] = d4 p Tr [ j ( p)
j ( p + q) ] 4 (2) Neutrino Mean Free Path in Nuclear Matter Horowitz & Wehrberger, Phys. Lett. B 266, 236 (1991) Burrows & Sawyer, Phys. Rev. C 58, 554 (1999) Reddy, Pons, Prakash, Lattimer, Phys. Rev. C 59, 2888 (1999) Neutrino Mean Free Path in a Heterogeneous Phase Coherent Scattering: enhances cross sections n n G2F
d = ND S q Q 2W E2 (1+ cos ()) dco() 16 Reddy, Bertsch & Prakash, Phys. Lett. B475, 1 (2000) QW~200 Neutrino Propagation in Superconducting phases r P(n (q,qo ) = d 4 p Tr [ G(p) G(p + q) ] = p+q G + G
Gn p p+q p Gn Gap modifies excitation spectrum Carter & Reddy, Phys. Rev. D 62, 103002 (2000) Effective theory for Goldstone modes: dierionrelation : E H =v p Schafer Phys. Rev .D 65, 074006 (2002) Manuel & Tytgat, Phys. Lett. B 479, 190 (2000) Hong, Lee & Min, Phys. Lett. B 477, 137 (2000)
(v 1 ) 3 E = m2 + v 2 p 2 m2s EKm = + m2k + v 2 p 2 2 Neutrino-Goldstone Boson Interactions o Z n
- e- W - n n Z n n
W en Reddy, Sadszikowski & Tachibana, Nucl. Phys. A 714, 337 (2003) Goldstone modes are space-like ( < q) o + n ne GFf GFf
n e- Neutrinos can Cerenkov radiate Goldstone modes Neutrino-Goldstone Boson Interactions Reddy, Sadszikowski & Tachibana, Nucl. Phys. A 714, 337 Neutron Star Cooling Crust cools by conduction tC~1-10 yrs, R ~ 0.5-2 km Isothermal core cools by neutrino emission t < 105 yrs TS~106 K Photon emission
Standard (slow) Cooling: nnnpe-ne & npnne+ne dE/dt)dt 1022 (ne/dt)no)1/dt)3 T98 erg/dt)cm3/dt)s Rapid Cooling: (np/dt)nB > 1/dt)9) npe-ne & e-pnne dE/dt)dt 1027 (ne/dt)no)1/dt)3 T96 erg/dt)cm3/dt)s Neutron Star Cooling: Data Standard (slow) cooling: nn->npen Rate ~1022 T98 erg/dt)cm3/dt)s Exotic (fast) cooling: n -> p en d -> u e- n Rate ~1027 T96 erg/dt)cm3/dt)s Tsuruta et al. Ap. J. 571, L143 (2002) Outlook Observation of a small star (R 8 km) would favor a soft
quark EoS /dt) Observation of a heavy star ( M 2 M) would disfavor quark matter. Hadron quark transition density is poorly known Role of the strange quark mass (and neutrality) important phase structure not fully understood Neutrino diffusion time scale is sensitive to properties of matter at supra-nuclear density Supernova neutrinos - a promising probe Need neutrino rates and thermodynamics at finite T in less symmetric quark phases (Gapless CFL, 2SC, Gapless 2SC, unpaired quark matter, mixed phases etc)
The Argumentative Essay A Review What do you remember about writing an argumentative essay? How does it differ from synthesis or analysis? In class write Thursday Argumentative prompt - review previous notes over how to write an argumentative paper.
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