# Presentation: 080360

## 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)
- Gravity Waves

- Hard Physics: E ~ 400 MeV

- Soft Physics: E ~ T 10-3-50 MeV

## Neutron Star Mass

- Physics issue : EoS at high density - what is the heaviest neutron stars one can make ?

- _Neutron Star Mass_

- Courtesy: J. Lattimer

## Radius: L∞ =F d2 =4 R∞2   T∞4  

- RX J1856-3754: nearby (d~120 pc) isolated neutron star

## Radius: L∞ =F d2 =4 R∞2  T∞4

- Pons et al. Astrophys. J. 564: 981-1006, 2002
- Walter & Lattimer, Astrophys. J.576:L145-L148,2002

- Deviations from Blackbody spectra: atmosphere: sensitive to local gravity  (GM/R2)
-  Potentially can yield both M and R

## Constraints and Trends: 

- Gravitational Red-shift: observation of spectral lines (Cottam, Paerels, Mendez, Nature 420: 51 (2002).

- Quasi-Periodic Oscillations: indicate a last stable orbit

- Exotic Stars:
- Soft EoS

## Phases of Dense Quark Matter

- Attractive interactions destabilize the Fermi surface  formation of cooper-pairs (BCS Theory)
- In quark matter most attractive channel is anti-symmetric in color space                                               spin zero pairs must be anti-symmetric in flavor

- u

- d

- u

- u

- d

- d

- 2-flavor quark matter:
- (2SC)

- Rapp, Schaefer, Shuryak, and Velkovsky   Phys.Rev.Lett. **81**, 53  (1998)
- Alford, Rajagopal, Wilczek Phys.Lett.**B422**, 247-256, (1998)

- 100 MeV

## Color-Flavor Locked Phase

- BCS pairing of all 9 quarks:
-       100 MeV !

- Excitation Spectrum

- Energy

- Alford, Rajagopal & Wilczek, Nucl. Phys. B _**558**_, 219 (1999)

## Charge Neutrality in Dense Quark Matter

- u

- d

- s

-  e-

-  PF

- Normal Quark Matter   requires electrons for charge neutrality
-                 
-     breaks iso-spin

- Alford, Rajagopal, Reddy and Wilczek  Phys.Rev.D**64**:074017, (2001)

- CFL requires   ms2/4

## Less symmetric phases:(when three is a crowd)

- 2

- 4

- CFL 

- CFLKo

- CFL

- 2SC

- 2SC 

- Normal

- Bedaque , Schafer Nucl. Phys. A697:802-822, (2002)
- Kaplan, Reddy, Phys. Rev. D65: 054042, (2002)

-  Shovkovy , Huang, Phys. Lett. B 564: 205, (2003)

- Alford, Kouvaris, Rajagopal, hep-ph/0311286

- Alford & Rajagopal,       hep-ph/0204001
- Steiner, Reddy, Prakash hep-ph/0205201

- Neutrality favors CFL

## Heterogeneous Mixed Phases(phase transitions with 2 conserved charges)Glendenning, Phys. Rev. D46:1274-1287,1992 

- Heterogeneous co-existence line: (droplets-rods-slabs)

- Sharp (polarized) interface :
- Large density discontinuity

- Alford, Rajagopal, Reddy and Wilczek  Phys.Rev.D**64**:074017, (2001)

- A

- B/C

- D

## Quark Matter EoS & Hybrid Stars

- Alford & Reddy, Phys. Rev. **D67** 074024 (2003)

## Can Quark Stars Mimic Nuclear Stars ?  

## Core Collapse Supernova 

- Core Collapse Supernova

-  Fe core becomes unstable
-  Collapse time scale ~ 100 ms
-  Nearly Adiabatic
-  B.E. ~ G Mcore/Rfinal ~3 X 1053 ergs

## Supernova Neutrinos - a (proto) neutron star is born

- 3X107 km

- 1500 km

- 10 km

- B. E. ~2-3 X 1053 ergs

- 100 km

- Hot & dense
- Proto-neutron
- Star: t~1-2 s

- Core collapse tcollapse ~100 ms

- _Supernova Neutrinos - a (proto) neutron star is born_

- Shock wave
- Eshock~1051ergs

## Proto-Neutron Star Evolution

- 31053 ergs is stored in neutrinos and internal energy.

## Proto-neutron Star Phase: late times (t > 3-4 s)

- Neutrino diffusion dominates evolution
- Time scales set by neutrino mean free path and dense matter EoS

- Burrows & Lattimer, Astrophys. J _**307**_, 178 (1986)
- Kiel & Janka, Astrnm. & Astrophys. _**296**_, 145 (1995)
- Pons,  Reddy, Prakash, Lattimer, Miralles,Astrophys. J. _**513**_, 780 (1999)

- Reddy, Prakash, Lattimer, Pons
- Phys. Rev.** C 59, **2888 (1999)

## simulations with normal quark matter

- Pons, Steiner, Prakash and Lattimer, Phys.Rev.Lett. 86, 5223 (2001)

- Delayed collapse to black-holes:
- Generic to most high density transitions to very soft EoS.

## Microphysics of neutrino mean free paths

- q

- q

- target

- E

- E’

- E

## 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

- QW~200

- Reddy, Bertsch & Prakash, Phys. Lett. B475, 1 (2000)

## Neutrino Propagation in Superconducting phases 

- Gap modifies excitation spectrum

- +

-  p+q

-  p

-  p+q

-  p

- 

- 

- 

- 

- Carter & Reddy, Phys. Rev. D _**62**_, 103002 (2000)

## Effective theory for Goldstone modes:

- Schafer Phys. Rev .D _**65**_, 074006 (2002)
- Manuel & Tytgat, Phys. Lett. B _**479**_, 190 (2000)
- Hong, Lee & Min, Phys. Lett. B _**477**_, 137 (2000)
- Hong, Phys. Lett. B _**473**_, 118 (2000)
- Son & Stephanov, Phys. Rev. D_ __**61**_**,** 074012 (2000)

## Neutrino-Goldstone Boson Interactions

- o

- 

- 

- -

- 

- 

- W-

- Z

- Z

- W-

- 

- 

- 

- 

- 

-  e-

- 

-  e-

- Reddy, Sadszikowski & Tachibana, Nucl. Phys. A _**714**_, 337 (2003)
- Jaikumar, Prakash & Schafer, Phys. Rev. D _**66**_, 063003 (2002)

## Goldstone modes are space-like ( < q) 

- 

- ’

- o

- GFf

- e

-  e-

- +

- GFf

- Neutrinos can Cerenkov radiate Goldstone modes

## Neutrino-Goldstone Boson Interactions

- Reddy, Sadszikowski & Tachibana, Nucl. Phys. A _**714**_, 337 (2003)

## Neutron Star Cooling

- Crust  cools by conduction
- C~1-10 yrs, R ~ 0.5-2 km

- TS~106 K
- Photon emission

- Isothermal core cools by neutrino emission t < 105 yrs

- Rapid Cooling: (np/nB > 1/9)
- npe-e & e-pne
- dE/dt  1027 (ne/no)1/3 T96  erg/cm3/s

- Standard (slow) Cooling:
- nnnpe-e & npnne+e
- dE/dt  1022 (ne/no)1/3 T98  erg/cm3/s

## Neutron Star Cooling: Data

- “Standard” (slow) cooling: nn->npe
- Rate ~1022 T98 erg/cm3/s
- Exotic (fast) cooling: n -> p e- 
-  d -> u e- 
- Rate ~1027 T96 erg/cm3/s

- Tsuruta et al. Ap. J. **571**, L143 (2002)

**Notes:**
C is the cold star in 3C58 (PSRJ0205+6445) discovered by Chandra: 2 is the Vela Pulsar: 4 Geminga: 5 RXJ 1856-3754

## Outlook 

- Observation of a small star (R  8 km) would favor a soft quark EoS / 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)