New Results From Pulse Shape Models for the ms Pulsar SAX J1808.4-3658 - PowerPoint PPT Presentation

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New Results From Pulse Shape Models for the ms Pulsar SAX J1808.4-3658

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How pulse shape modeling constrains Mass and Radius. Why millisecond X-ray pulsars are good candidates. New results for SAX J1808 ... – PowerPoint PPT presentation

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Title: New Results From Pulse Shape Models for the ms Pulsar SAX J1808.4-3658


1
New Results From Pulse Shape Models for the ms
Pulsar SAX J1808.4-3658
  • Denis Leahy
  • University of Calgary
  • Collaborator
  • Sharon Morsink
  • University of Alberta

2
Overview
  • 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

3
SAX 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

4
SAX 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

5
Nuclear 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
6
Accreting 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
7
Gravitational Deflection of Light Rays
M1.4 Msun
  • Shadow zone
  • Magnification

8
Animation of rotating star
  • View from equator
  • Annular hot spot at latitude 15

9
Accreting 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
10
What 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
11
Doppler 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))

12
Doppler 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

13
Hot 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
14
Stellar 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
15
Spot at 15o from North Pole Observer at
100o from North Pole
16
Data 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
17
Time varia-bility of SAX J1808(Hartman et al,
2008)
18
Multi-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
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20
Results from 1998b4/2002b3 joint fits, with
inclinationlt90
21
Results from 1998b4/2002b3 joint fits, with
inclinationlt70
22
Summary
  • 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
23
Future 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
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