Determining the Equation of State of Ultradense Matter with the Advanced X-ray Timing Array (AXTAR)

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Determining the Equation of State of Ultradense
Matterwith the Advanced X-ray Timing Array
(AXTAR)

• Deepto Chakrabarty (MIT)
• Paul S. Ray (NRL)
• Tod Strohmayer (NASA/GSFC)
• for the AXTAR Collaboration

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Probing Fundamental Physics and Astrophysics
withX-Ray Timing of Neutron Stars and Black Holes

• Deepto Chakrabarty (MIT)
• Paul S. Ray (NRL)
• Tod Strohmayer (NASA/GSFC)
• for the AXTAR Collaboration

• Astrophysical compact objects extreme
  laboratories for physics and astrophysics
• Physical information encoded in rapid,
  structured X-ray variability on dynamical
  timescales (milliseconds) at the surface/event
  horizon
• Neutron star mass and radius (dense matter
  equation of state, exotic matter)
• Black hole mass and spin (strong-field general
  relativity)
• Neutron star spin distribution (origin of spin
  limit gravitational radiation?)
• Uncover with high-speed X-ray spectrophotometry
  of bright Galactic X-ray binaries
• Variability phenomena discovered by the Rossi
  X-Ray Timing Explorer (1996-date)
• How can we exploit these discoveries?

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Fundamental physics question What happens to
matter when it squeezed (beyond nuclear
density)? (or equivalently What is the equation
of state of ultradense matter?)
This question explores a unique region of the QCD
phase diagram and is inaccessible to laboratory
experiment. Astrophysical measurements of
neutron stars required.
Neutron star mass-radius relations
Constraints on allowed region General relativity
(Schwarzschild radius), causality (sound speed),
pulsar rotation limit (716 Hz)
Neutron star EOS is known for the outer star, but
not in the high-density inner core. (Large phase
space) This arises from an inability to
extrapolate from normal nuclei (50 protons) to
NS (0 protons). Thus, EOS models depend upon
assumptions about matter phase of inner core
(hadronic matter, pion/kaon condensates, quark
matter...). Each new phase increases
compressibility, affecting M-R relation. Radius
is key. 10 measurement strongly constraining.
5 measurement definitive. (Lattimer Prakash
2001) X-ray observations offer essentially the
only way to go after radius measurements.
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X-ray Techniques for Neutron Star Radius
Measurement

• Spectroscopy
• Solid angle measurements ( ) from
  flux and effective temperature
• Cooling curves (constrain internal structure)
• Redshifted photospheric lines (M/R, potentially
  M/R2 and/or ?R sin i)
• Timing
• X-ray burst oscillations (amplitude, harmonic
  content, pulse phase spectroscopy)
• Kilohertz quasi-periodic oscillations
• Accretion-powered pulsars

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X-Ray Binaries

• Neutron star (or black hole) accreting matter
  from a normal stellar binary companion.
  Angular momentum conservation often requires an
  accretion disk flow.
• Matter falling into the deep gravitational
  potential well of compact star emits X-rays.
• Time variability of X-ray emission from inner
  accretion flow (nearest compact star) encodes
  information about stellar properties.

• Many bright X-ray binaries known in the Galaxy.
  Over 100 known neutron stars accreting from a
  low-mass stellar companion.
• Due to messy fluid physics, accretion flow is
  not always smooth and continuous. In some
  systems, accretion is irregularly transient and
  episodic. Observationally, some sort of
  monitor/alert capability required to catch
  sources in an active state. (X-ray sky very
  variable.)

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Nuclear-Powered Millisecond X-Ray Pulsars (X-Ray
Burst Oscillations)
SAX J1808.4-3658 (Chakrabarty et al. 2003)

• Thermonuclear X-ray bursts due to unstable
  nuclear burning on NS surface, lasting tens of
  seconds, recurring every few hours to days.
• Millisecond oscillations discovered during some
  X-ray bursts by RXTE (Strohmayer et al. 1996).
  Spreading hot spot on rotating NS surface yields
  nuclear-powered pulsations.

thermonuclear burst
4U 1702-43 (Strohmayer Markwardt 1999)
contours of oscillation power as function of time
and frequency
quiescent emission due to accretion

• Burst oscillations reveal spin, but not possible
  to measure orbital parameters or spin evolution,
  since bursts only last a few tens of seconds.
• Common phenomenon gt100 examples in over a dozen
  sources.

X-ray burst count rate
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Timing and Spectral Evidence for Rotational
Modulation
Strohmayer et al. (1997)
Surface Area
GM/Rc20.284
Strohmayer (2004)
Spreading hot spot.

• Oscillations caused by hot spot on rotating
  neutron star
• Modulation amplitude drops as spot grows.
• Spectra track increasing size of X-ray emitting
  area on star.

(slide from Tod Strohmayer)
ensity
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NS Mass-Radius Constraints from X-ray Burst
Oscillations

• Pulse shape of burst oscillations encode
  information about neutron star mass and radius,
  owing to gravitational light-bending effects at
  the neutron star surface.
• Modulation amplitude sensitive to compactness
  of star, M/R.
• Pulse sharpness (Fourier harmonic content)
  sensitive to rotational velocity. For known spin
  rate, this is equivalent to radius-dependence.
• If phase-resolved spectroscopy of the burst
  emission is possible, then rotational Doppler
  shift of hot spot emission also sensitive to
  radius (for known spin rate). This measurement
  is NOT possible with RXTE due to insufficient
  sensitivity.

RXTE measurements have been able to provide
modest constraints on neutron star mass and
radius (see colored regions at left).
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Exploiting these phenomena From Discovery to
Measurement

• RXTE capable of detection, but not sufficient
  for extracting physical parameters from these
  oscillations. Detailed workshop discussion of
  what is required to proceed at X-Ray Timing 2003
  Rossi and Beyond in Cambridge, Massachusetts in
  November 2003.
• Primary requirement ability to resolve
  millisecond oscillations from bright X-ray
  sources on coherence timescales of order 0.1
  second, in the 2-30 keV range. Requires detector
  area of 10 m2 (order of magnitude larger than
  RXTE), and ability to handle the very high count
  rates from bright sources. Current and planned
  X-ray missions are principally optimized for
  faint sources.
• Additional requirements sky monitoring ability
  in order to trigger transient outbursts and
  spectral state changes. Moderately fast
  (hours) spacecraft slew capability in order to
  respond to triggers. Flexible scheduling to
  allow timely (hours) response to new transient
  triggers. These quick response requirements are
  difficult for currently planned X-ray missions.
• Will require solving formidable technical
  problems to develop appropriate detectors that
  are affordable in terms of cost, weight, and
  power. In 2003, technology path was still
  unclear.

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Choice of Detector Technology

• Proportional counters
• Workhorse technology for previous X-ray timing
  applications
• Large mass and volume per unit area, massive gas
  containment vessel required
• Potential for gas leaks, gain drifts, and high
  voltage breakdowns
• Poor spectral energy resolution
• Significant deadtime effects for bright sources
• Silicon pixel detectors
• Thin and light
• Solid state reliable and robust
• Better spectral energy resolution
• Minimal deadtime possible, even for extremely
  bright sources
• Can leverage investment by semiconductor
  industry and high-energy physics detectors
• Enables order of magnitude increase in area over
  RXTE at a reasonable cost
• Challenges low noise, low power, large area
• Current technical readiness of Si pixel
  detectors
• NRL has suitable Si pixel detectors ready (based
  on work for DHS, DTRA, DARPA)
• Brookhaven National Laboratory has readout ASICs
  that meet all requirements except low power (but
  within a factor of two)
• Development of new ASIC with lower power
  consumption currently underway

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Mission concept The Advanced X-ray Timing Array
(AXTAR)
(under development by MIT, NRL, and NASA/GSFC)

• Large Area Timing Array (LATA)
• 8 square meters, 2-50 keV range
• 1.2M pixels, 1mm thick Si
• 1 microsecond time resolution
• Sky Monitor (SM)
• 32 cameras
• Each camera covers 40x40 deg
• 2-20 keV, arcmin positioning
• All sky, 60-100 duty cycle

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Effective area comparison of AXTAR and other
current/planned missions
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Neutron star mass-radius constraints with
AXTAR Simulation of an X-ray burst oscillation
AXTAR will routinely make 5 measurements of
neutron star radii in X-ray bursters, thus
conclusively discriminating between candidate
equations of state for dense matter.
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Using existing data, constraints using the
various techniques already identify a
consistent allowed region on the
M-R diagram. With AXTAR, it should be possible
to actually associate a particular point on this
diagram for each object studied, allowing us to
map out the allowed M-R curve.
Lattimer Prakash (2004)
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Summary

• X-ray timing of neutron stars and black holes
  can address fundmental physics and astrophysics
  questions by providing precise measurements of
  mass, radius, and spin.
• A new, large (10 square meter) area timing
  mission can exploit the variability phenomena
  discovered by RXTE for such measurements.
  Pixelated thick silicon detectors offer the most
  attractive and achievable technical path to
  building such a mission. The AXTAR mission
  concept.
• Our proposed AXTAR mission concept would meet
  two primary science objectives in fundamental
  physics
• A 5 measurement of multiple neutron star radii
  from studies of X-ray burst oscillation light
  curves. Measurements of this precision would
  definitely discriminate between candidate
  equations of state for ultradense matter.
• Studies of high frequency oscillations from
  black hole accretion flows, reaching a
  sensitivity to 0.05 rms amplitude. Measurements
  of this sensitivity would probe for the presence
  of additional oscillation modes, allowing a test
  of the general relativistic resonance model for
  the oscillations in which the oscillation
  frequencies trace the mass and spin of black
  holes.
• A wide range of studies in high-energy
  astrophysics would also be enabled, as enumerated
  in the 2003 X-ray timing workshop (physics of
  nuclear burning, accretion physics, matter and
  radiation in ultrastrong magnetic fields,
  astrophysical jets, asteroseismology of neutron
  star oscillation, ...)

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Black Hole Oscillations Getting at Mass and Spin

• Stationary, high-frequency oscillations
  discovered in 8 systems (40-450 Hz).
  Intermittent, but frequency repeatable in each
  source.
• In each of 4 systems, oscillation pairs with 32
  frequency commensurability
• Frequencies observed to scale inversely with
  (dynamically measured) black hole mass (as
  expected in general relativity)
• Resonance phenomenon involving oscillations
  governed by general relativity? Dependence on
  mass and spin.
• Detections at the edge of RXTE sensitivity.
  Need to resolve waveforms at coherence timescale
  (less than a second)

McClintock Remillard (2005)
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Neutron Star Oscillations Getting at Mass and
Radius

• Quasi-periodic oscillation pairs (100-1330 Hz)
  detected in over 20 X-ray binaries.
• Separation frequency set by spin rate.
  Oscillation frequencies vary with accretion rate,
  suggesting inner disk orbit origin.
• Oscillation amplitudes decrease as frequencies
  rise.
• If orbital origin, then geometry of orbits in
  general relativity constrains allowed mass and
  radius of neutron star. Fastest oscillation sets
  strongest constraint. (Current max1330 Hz)
• Detection at frequencies above 1500 Hz would
  discriminate between relevant equations of state.

1330 Hz
M. C. Miller (2004)
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Neutron Star Spin Distribution A Cosmic Speed
Trap?

• Pulsar spin distribution cuts off sharply above
  730 Hz. Same effect observed with X-ray
  pulsars and radio pulsars. Not caused by
  observational selection.
• Unknown mechanism balances accretion spin-up
  torques.
• Possibly caused by angular momentum losses from
  gravitational radiation. This would cause
  detectable persistent signals in Advanced LIGO
  unanticipated tie-in with gravitational-wave
  astrophysics.
• Detailed shape of spin distribution needed to
  determine mechanism responsible.

No pulsars detected gt 730 Hz
Chakrabarty (2005)
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NASA Rossi X-Ray Timing Explorer (RXTE)

• Built by NASA/GSFC, MIT, and UC San Diego
• Launched Dec. 1995, will operate until at least
  2009
• Main instrument 6000 cm2 proportional counter
  array (PCA), 2-60 keV, µs time resolution
• All-sky monitor (ASM) for activity alerts on
  transients
• Rapid repointing possible (X-ray transients)
• Other major X-ray missions (e.g., Chandra,
  XMM-Newton) incapable of msec timing of bright
  X-ray binaries