Title: New Results From Pulse Shape Models for the ms Pulsar SAX J1808.4-3658
1New Results From Pulse Shape Models for the ms
Pulsar SAX J1808.4-3658
- Denis Leahy
- University of Calgary
- Collaborator
- Sharon Morsink
- University of Alberta
2Overview
- SAX J1808 system
- Motivation for mass and radius measurements for
neutron stars - How pulse shape modeling constrains Mass and
Radius - Why millisecond X-ray pulsars are good candidates
- New results for SAX J1808
- Implications for neutron star (or quark star) EOS
3SAX J1808.4-3658
- First known accretion-powered millisecond pulsar
(AMP Wijnands van der Klis 1998) - missing link old pulsars are spun up to
millisecond periods by accretion in X-ray binary - OF INTEREST FOR
- the nature of magnetically channelled accretion
flow, - torques on neutron stars in low-mass X-ray
binaries (LMXBs), - orbital evolution
- Spin period 401 Hz orbital period 2.01 hr
- companion 0.05Msun brown dwarf
4SAX J1808.4-3658
- Optical spectroscopy of companion star
(Cornelisse et al 2009) f(Mc)gt0.10 Msun and
.051ltqlt.072, 0.2ltMxlt1.6 Msun - Optical photometry (Deloye et al 2008) 36ltilt67,
Mxgt2.2 Msun - Elebert et al 2009 optical spectroscopy
f(Mc)0.04 Msun 32ltilt74 no good constraint on Mx - Heinke et al 2008 quiescent x-ray flux between
outburstslt2x1031 erg/s ? enhanced cooling from
the interior ? direct URCA from protons, hyperons
or deconfined quarks
5Nuclear Equations of State(EOS)
One major goal of studying NS is to constrain the
EOS of dense matter
James Lattimer
Different NS are not on the same radius scale
6Accreting Neutron Stars rotating hot spot
Ghosh and Lamb, 1978, ApJ
Blackbody emission from surface of star
Electron plasma in hot-spot Compton scatters
seed blackbody photons
7Gravitational Deflection of Light Rays
M1.4 Msun
- Shadow zone
- Magnification
8Animation of rotating star
- View from equator
- Annular hot spot at latitude 15
9Accreting ms pulsars
- For small B and high dM/dt, we expect equilibrium
spin periods of a few ms - ms radio pulsars were subsequently discovered
after the appropriate observing hardware was
built - Search for coherent X-ray pulsations for over 20
years without success - Detected QPOs in early 1980s beat frequency
model of Lamb et al. - kHz QPOs detected later
- SAX J1808.4-3658 first detection (2002) of ms
pulsations in an accreting source
Discovery of ms burst oscillations in SAXJ1808
10What is so different for ms pulsars?
ms period means speeds at surface are not small
compared to c (v47000km/s for P2ms,
R15km) ?special-relativity light-aberration
effects are important Time delays (R/c) are
significant compared to the time for the star to
rotate Rotating star is oblate ?Pulse shape is
asymmetric for even a perfectly symmetric
emission region
11Doppler effects, time delays and oblateness
- The calculation of pulse shapes is done by ray
tracing (geodesic equations). - We use the numerical general relativity (GR)
metrics for rotating neutron stars. - Expansion of the geodesic equations in the metric
for a rotating neutron star yields redshift and
Doppler factors (Cadeau, Morsink Leahy
Campbell, 2006 (CCLC))
12Doppler effects, time delays and oblateness
(contd)
- Cadeau, Leahy, Morsink 2005 showed time-delays
are important and difference between Schwarzchild
and Kerr are not important - CCLC show that omitting oblateness produces large
errors in pulse shapes (fgt300Hz) - Morsink, Leahy, Cadeau, Braga 2007 present an
approximation method to the GR method as a
practical method calculating pulse shapes - Called the oblate-Schwarzschild approximation
13Hot spot
Drawing from Ghosh and Lamb, 1978, ApJ
Anisotropic emission (anti-beaming)
Electron plasma above spot Compton scatters
seed blackbody photons
Isotropic emission
Blackbody emission from surface of star
14Stellar Oblateness
Stellar surface has different visibility to
observer than for spherical star Spherical star
regions II,III,IV Oblate star regions I,II,III
IV
IV
15Spot at 15o from North Pole Observer at
100o from North Pole
16Data from 1998 outburst (20 days
averaged) Model M vs. R calculated by RNS code
for 401Hz rotation frequency 2 and 3 sigma
limits for sphere and no time delays agree with
results of Poutanen and Gierlinski 2003 (PG03)
?False small radius caused by mixing pulse
profiles of different shape
17Time varia-bility of SAX J1808(Hartman et al,
2008)
18Multi-epoch pulse shape modeling,(data from Jake
Hartman)
- Without scattered X-rays
- A. masses from different epochs are very
different (0.3 to 2.0 Msun), the fits are
sometimes unacceptable. - B. cannot get acceptable joint fits with 2
different data sets. - Introduce scattered x-rays from external material
(no doppler or GR effects) . - The resulting fits for single epoch data give
compatible masses (1.2Msun). - Fits for 2-epoch data give acceptable fits and
reasonable masses. - The resulting amplitude of scattered X-rays is
lt1 relative to hot spot. - For multi-epoch fitting use 2-day/2-energy band
data - Assume constant M, R, and inclination
- Allow variable hot spot location and emissivity
19(No Transcript)
20Results from 1998b4/2002b3 joint fits, with
inclinationlt90
21Results from 1998b4/2002b3 joint fits, with
inclinationlt70
22Summary
- 3-sigma error region from joint fit of
1998b4/2002b3 Mlt1.7 Msun and Rlt12.5 km - NGC6440B (Freire et al 2008) M2.1-3.3 Msun
- Possible solutions?
- 0. both are consistent with APR or ABPR1 at 3
sigma level - 1. error in assumptions
- 2. NGC6440B could be NS and SAXJ1808 a quark star
3
2
23Future work
- Simultaneous fitting of 7 epoch X 2 energy-band
pulse shapes from 1998, 2002 and 2005 outbursts
should give tighter restrictions on M and R. - Include data from 2008 outburst
- Analyze other ms X-ray pulsar profiles