Transcript The Spin Periods of Millisecond X

Determining the Equation of State of Ultradense Matter
with the Advanced X-ray Timing Array (AXTAR)
Deepto Chakrabarty (MIT)
Paul S. Ray (NRL)
Tod Strohmayer (NASA/GSFC)
for the AXTAR Collaboration
Probing Fundamental Physics and Astrophysics with
X-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?
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.
X-ray Techniques for Neutron Star Radius Measurement
• Spectroscopy:
2 /d 2
 Solid angle measurements ( R
) from flux and effective temperature
 Cooling curves (constrain internal structure)
 Redshifted photospheric lines (M/R, potentially M/R2 and/or ΩR sin i)

• Timing:
 X-ray burst oscillations (amplitude, harmonic content, pulse phase spectroscopy)
 Kilohertz quasi-periodic oscillations
 Accretion-powered pulsars
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.)
Nuclear-Powered Millisecond X-Ray Pulsars (X-Ray Burst Oscillations)
SAX J1808.4-3658 (Chakrabarty et al. 2003)
thermonuclear
burst
• 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”.
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: >100 examples in
over a dozen sources.
X-ray burst
count rate
Surface Area
Timing and Spectral Evidence for Rotational
Modulation
Strohmayer et al. (1997)
Spreading
hot spot.
GM/Rc2=0.284
Strohmayer (2004)
• 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
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).
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.
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
 NASA (APRA) funding has been requested to build a demonstration module
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
Effective area comparison of AXTAR and other current/planned missions
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.
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)
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, ...)
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 3:2
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.
McClintock & Remillard (2005)
• Detections at the edge of RXTE sensitivity. Need
to resolve waveforms at coherence timescale (less
than a second)
Neutron Star Oscillations: Getting at Mass and Radius
• Quasi-periodic oscillation pairs (100-1330 Hz)
detected in over 20 X-ray binaries.
1330 Hz
• 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 max=1330 Hz)
M. C. Miller (2004)
• Detection at frequencies above 1500 Hz would
discriminate between relevant equations of state.
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.
No pulsars detected > 730 Hz
Chakrabarty (2005)
• Unknown mechanism balances accretion spinup 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.
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