Prakash

Document Sample
Prakash Powered By Docstoc
					               Recent Developments in
             The Physics of Neutron Stars

                         Madappa Prakash
                               &
                             PALS


             SUNY at Stony Brook, Stony Brook, NY


Subal-Fest
Dec 4 , 2004, Montreal                              1/18
PALS




       2/18
 Physics & Astrophysics of Neutron Stars
Cores of neutron stars may contain hyperons, Bose condensates, or
quarks (Exotica)
Can observations of M, R & B.E (composition & structure)
       ˙
& P, P , TS & B etc., (evolution) reveal Exotica ?
Neutron stars implicated in x-ray & γ-ray bursters, mergers with
black holes, etc.
Observational Programs :
SK, SNO, LVD’s, AMANDA ... (ν’s)
HST, CHANDRA, XMM, ASTROE ... (γ’s)
LIGO, VIRGO, GEO600, TAMA ... (Gravity Waves)
              Connections to Nuclear Physics
Theory : Many-body theory of strongly interacting systems,
Dynamical response (ν- & γ- propagation & emissivities)
Experiment : e− and ν- scattering experiments on nuclei, masses
of neutron-rich nuclei, heavy-ion reactions, etc.
                                                              3/18
Neutrino Luminosities



                   Early detectors
                   lacked sensitivity
                   to test if SN 1987A
                   ended up as a black
                   hole
                   Current & future
                   detectors can do
                   better in the case of
                   a future event




                                    4/18
Mass Radius Relationship




                           5/18
Measured Neutron Star Masses



                      Mean & weighted
                      means in M
                      X-ray binaries:
                      1.53 & 1.48
                      Double NS
                      binaries:
                      1.34 & 1.41
                      WD & NS binaries:
                      1.58 & 1.34




                                    6/18
          Moment of inertia (I) measurements

Spin precession periods:

                               2c2 aP M (1 − e2 )
                     Pp,i   =
                              GM−i (4Mi + 3M−i )

Spin-orbit coupling causes a periodic departure from the expected
time-of-arrival of pulses from pulsar A of amplitude

                   MB a            a IA P
             δtA =      δi cos i =          sin θA cos i
                   M c                   2P
                                   c MA a A
P : Orbital period a: Orbital separation e: Eccentricity
M = M1 + M2 : Total mass
i: Orbital inclination angle θA : Angle between SA and L.
IA : Moment of Inertia of A
For PSR 0707-3039, δtA (0.17 ± 0.16)IA,80 µs ;
Needs improved technology & is being pursued.
                                                                    7/18
  Limits on R from M & I measurements




10% error bands on I in M km2
Horizontal error bar for M = 1.34 M & I = 80 ± 8 M km2
                                                         8/18
Ultimate Energy Density of Cold Matter



                            Tolman VII:
                            ρ = ρc (1 − (r/R)2 )
                            ρc ∝ (M /M )2
                            Redshift bound:
                            ρc > 1.7 × 1015
                            (M /M )2 g cm−3
                            Crucial to establish
                            an upper limit to
                            Mmax




                                            9/18
Inferred Surface Temperatures




                                10/18
                       New Cold Objects
Several cases fall below the “Minimal Cooling” paradigm & point to
enhanced cooling, if these objects correspond to neutron stars.


                        Light elements
                           envelopes



             Heavy elements
                envelopes




                                                                     11/18
The Binary Merger Experience
                    M1 ≤ M 2
                    radial separation: a(t)
                    M1 - N S or SQM
                    M2 - BH, NS, . . .
                    GW emission ⇒

                             1 G ... ...
                    LGW    =       I jk I jk
                                   – –
                             5 c 5

                             32 G4 M 3 µ2
                           =
                              5 c5 a 6
                    orbit shrinks
                    Mass transfer
                    To merge or not to
                    merge?
                                        12/18
Roche Lobe Overflow

    Energy Loss

                 1 ... ...    32 4 2 6
      LGW      =   I jk I jk = a µ ω
                   – –
                 5             5
    Angular Momentum Loss

                 2         ..   ...    32 4 2 5
    J˙GW       =     ijk   I– I km
                             jm –     = aµω
           i     5                      5
    a(t) and VRoche shrink!

    R1 = rRoche
    ⇒ Mass transfer begins!

                                              13/18
                                 Equation of State: α(M )
         25
                                                                            0.5
         20
                                                                                                   SQM2
                                                                                                  SQM1




                                                     α = d(ln M)/d(ln R)
R [km]




         15              GS          SQM2
                                                                              0
                                         APR
         10
                              SQM1                                                                       APR

          5
                                                                           -0.5

          0
           0   0.5   1    1.5        2         2.5
                     M/MSun

                                                                             -1
               αN S ≤ 0                                                                             GS



               αSQM ≥ 0                                                    -1.5
                                                                               0   0.5     1      1.5              2
                                                                                         M/MSun
               (≈ 1/3)
                                                                                                               14/18
                                    Evolution: Normal Star (AP R)
                                                                        -6
                                                 MSun = 1.5 km = 5x10        s
              200
              150
                                                                                 M = 4M , qini = 1/3
   a/MSun




                                                 pseudo-GR
              100
                                                                                 GR speeds up evolution
               50                                 Newton
                0                                                                a(t) increases after
         0.03                                                                    “touchdown”
ω MSun




         0.02             pseudo-GR     Newton
         0.01
                                                                                 ω(t) stabilizes at long
                0                                                                times
                                                                                 Little variation among
   rh+/MSun




                1
                         pseudo-GR      Newton
              0.5                                                                EOS’s of normal stars.
                0                                                                M1 approaches the NS
              0.4                                                                minimum mass; subse-
                                                                                 quent plunge (timescale
    q




                        pseudo-GR       Newton
              0.2

                0
                                                                                 ∼ a few minutes) yields
                    0           2e+05      4e+05
                                           t/MSun
                                                           6e+05         8e+05
                                                                                 a second spike in the
                                      4 2 2                                      GW signal!
                           h+       =   ω a µ cos(2ωt)
                                      r
                                                                                                    15/18
                                  Evolution: SQM Star
                                                             -6
                                      MSun = 1.5 km = 5x10        s
              200
              150
   a/MSun




              100
                                             APR   SQM1               M = 4M , qini = 1/3
               50
                0
                                                                      a(t) : “hovers” after
         0.03                                                         “touchdown”
ω MSun




         0.02                                                         ω(t) : relaxes to
         0.01
                                                                      >> ωinitial
                0
                                                                      h+/× (t) & q(t) :
   rh+/MSun




                1

              0.5
                                                                      exponential decay
                                                                      unlike for a N S
                0
                                                                                    SQM
              0.4                                                     M1,f inal → Mnugget un-
    q




              0.2                                                     like for a normal star;
                0
                                                                      time to tiny M1,f inal is
                    1e+4   3e+4    5e+4
                                  t/MSun
                                            7e+4      9e+4
                                                                      very long!
                             4 2 2
                      h+   =   ω a µ cos(2ωt)
                             r
                                                                                           16/18
                       Main Results

Incorporating GR into orbital dynamics leads to an evolution that is
faster than the Newtonian evolution.

Large differences exist between mergers of “normal” and
“self-bound (SQM)” stars.
 • SQM stars penetrate to smaller orbital radii; stable mass
   transfer is more difficult than for normal stars.
 • For stable mass transfer, q = M1 /M2 and M = M1 + M2
   limits on SQM stars are more restrictive than for normal stars.
 • The SQM case has exponentially decaying signal and mass,
   while normal star evolution is slower.




                                                                17/18
18/18

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:11/30/2011
language:English
pages:18