Diapositiva 1

1
Enlightening differences in AMSPs behaviour XTE
J1751-305 vs XTE J1814-338
Alessandro Papitto
Luciano Burderi (Univ.Cagliari) Tiziana Di Salvo
(Univ.Palermo) Alessandro Riggio (Univ.Cagliari)
Maria Teresa Menna (INAF OAR)
A Decade of AccretingMillisecond X-ray
Pulsars Amsterdam, 14 - 18 April 2008
2
Plan

• Use of timing techniques to XTE J1751-305 and
  XTE J1814-338
• Different rotational behaviour, spin up spin
  down
• Different phase stability
• Phase oscillation can be often understood in
  terms of geometry

3
XTE J1751-305

• ? 435.318 Hz Porb42.4 min
  (Markwardt et al. 02)
• Exponental decaying LC t 7.2 d
• Lpeak 2.7 x 1037 d8.52 erg / s
  (Gierlinski Poutanen 05)

4
XTE J1751-305

• ? 435.31799357(4) Hz
• ?f - 200 µs - 0.1
• SPIN UP
• lt?dotgt(3.71.0)x10-13Hz/s
• the probability of a frequency
  evolution given
  purely by chance is less
  than 10-7

Papitto et al., 2008, MNRAS
5
XTE J1751-305 spin up modelling

• torque evolution ?dot(t)
  gMdot(t),Rin(t) at least
• Hp. Rin(t) Mdot(t)-a FX(t)
  Mdot(t)
• The evolution of d?/dt depends on
• the peak value of Mdot,
• the initial location of Rin
• the LC shape
• A measure of d?/dt (t0) gives a (model
  dependent) dynamical estimate of
  the accretion rate
• ?dot (t0) ( 5.6 1.2 ) x 10-13 Hz/s
• Statistics not enough to discriminate between
  constant and variable ?dot
• Mdot(t0) gt ( 2.9 0.6 ) x 10-9 Msun/yr 0.2
  Mdot(EDD)

6
XTE J1751-305 distance magnetic field

• Comparing the dynamical Mdot with the X-ray flux
  
• d 9 kpc
• Slightly larger than max possible (8.5kpc), but
• in line with the lower limits derived from GW
  driven evolution (dgt7kpc Markwardt 02
  Galloway 05)
• The X-ray flux may be an underestimate of the
  Mdot

• Loose Magnetic Field constraints
• 5 x 107 m1.4-1/2 R6-3/4 G lt BS lt 2 x 109 m1.41/3
  R6-5/2 G
• The brightness and the short flux excursion
  dont allow any useful
  constraint

• Upper limit on quiescent flux suggest BS lt 3-7
  x 108 G (Wijnands et al. 05)

7
XTE J1814-338

• ? 314.356 Hz Porb4.27 hr
  (Markwardt et al. 03)
• 50 d outburst flux almost constant for the
  first 30d
• L 7 x 1036 d82 erg / s
  (Galloway et al. 04)
• Two harmonics
• A1 0.14-0.17
• A2 0.04
• Watts et al. 04

8
XTE J1814-338 Timing

• ? 314.35610879(1) Hz
• ?f 1900 µs 0.6
• SPIN DOWN
• lt?dotgt(-6.70.7)x10-14Hz/s
• but ?2 1618/97
• 5s oscillation around the
  mean trend in both
  the harmonics

Papitto et al., 2007, MNRAS
9
XTE J1814-338 spin down

• An accreting NS may spin down because of
  interaction between the a fast rotating
  magnetosphere and the accretion disc
  (Ghosh Lamb 1979)
• 2p I ?dot Mdot ( GMRC)1/2 - ? µ2/(9RC3)
  (Rappaport al. 2004)
• BS 8 x 108 ?1/2 G
• 3D MHD sims also showed that a NS may accrete
  and spin down in a propeller state (i.e. Rin
  gt RC) (Romanova et al. 2004)
• Matter is not ejected because the magnetosphere
  does not rotate rigidly
• The spin down torque is expected to increase
  with Mdot
• Not enough statistics to check the relation ?dot
  - Mdot

10
XTE J1814-338 phase oscillations

• Phases oscillate with ampl. 0.05 on tosc12d
• Possible interpretations
• Torque swings ? But ??dot
  5x10-12 Hz/s
• Wrong orbital solution ? Porb ltlt
  tosc
• Position uncertainties ? tosc ltlt 1
  yr
• Correlation with flux
• Superorbital period? qlt0.2
  Porb lt 1d (Ogilvie Dubus 2001)
• Hot spot motion or shape
  variations but ??40

11
A geometrical model for phase oscillations in AMSP

• A pulse profile is built from the contribution of
  two signals at the same period
• Classical framework
• Two exactly antipodal spot result in a total
  phase is the one of the spot whose amplitude is
  the largest
• If we allow for the two signal not being in
  antiphase O f1-f2 ? p
• A variation of the relative amplitudes yields a
  phase variation

Spot 1
Spot 2
12
A geometrical model for phase oscillations in AMSP

• Special and General Relativity Effects
• SR Doppler Boost angles aberration skew the
  profile even if it is sinusoidal in nature
  (produce at least an harmonic more than the
  fundamental)
• GR Light bending modifies visibility classes

• Beloborodov 2002, Poutanen Beloborodov 2006
  derived approximate analitical expressions for
  pulse profiles
• the coefficients of the Fourier
  expansions depend on
• geometry ( ? , i )
• NS parameters ( M,R,? )
• anisotropy of emission ( h )
• To have signals not in antiphase
  it is not necessary to postulate
  an offsetted
  magnetic dipole

Beloborodov (2002) Poutanen Beloborodov (2006)
13
A geometrical model for phase oscillations in AMSP
We argue that phase oscillations are related to
variations in the fraction of the mass accreted
by the two spots C2/C1 Fluctuations in C2/C1 can
be triggered by Mdot
variations as matter is brought
to funnel flows by pressure gradients
(Romanova et al. 2004)
O0.9
We also checked that amplitudes (0.15,0.05)
with their variations (0.03) can be reproduced
setting i60 and ?15 (nevertheless there
is degeneracy with h)
14
Conclusions

• AMSPs can have a bimodal behaviour for what
  concerns
• Spin frequency derivatives some (3-4 out
  of 6) spinning up at 10-12-10-13 Hz/s
• some (2 out of 6) spinning down at few x 10-14
  Hz/s

• Magnetic fields indications of B(spin up)
  few x 108G, B(spin down) 109G but there is
  degeneracy with the Mdot need for more
  outburst, please
• Phase stability
• According to our model
• Stability is related to one only spot visible (
  i lt 45)
• Phase oscillations appear when there are two
  visible spot and the accretion rate changes the
  fraction of mass accreted instantaneously by
  each of them