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

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?

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

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.

Constraints on allowed region: General relativity (Schwarzschild radius), causality (sound speed), pulsar rotation limit (716 Hz)

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 ΩR 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.)

• 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”.

• 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.

Nuclear-Powered Millisecond X-Ray Pulsars (X-Ray Burst Oscillations)

thermonuclearburst

quiescent emission due to accretion

contours of oscillation power asfunction of time and frequency

X-ray burstcount rate

SAX J1808.4-3658 (Chakrabarty et al. 2003)

4U 1702-43 (Strohmayer & Markwardt 1999)

Timing and Spectral Evidence for Rotational Modulation

• 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.

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Spreading hot spot.

Strohmayer et al. (1997)

Strohmayer (2004)

GM/Rc2=0.284

(slide from Tod Strohmayer)

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)

• 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

(under development by MIT, NRL, and NASA/GSFC)

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.

Lattimer & Prakash (2004)

Using existing data, constraintsusing the various techniques already identify a consistentallowed region on the M-Rdiagram.

With AXTAR, it should bepossible to actually associatea particular point on this diagramfor each object studied, allowingus to map out the allowed M-Rcurve.

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, ...)

McClintock & Remillard (2005)

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.

• Detections at the edge of RXTE sensitivity. Need to resolve waveforms at coherence timescale (less than a second)

1330 Hz

M. C. Miller (2004)

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 max=1330 Hz)

• Detection at frequencies above 1500 Hz would discriminate between relevant equations of state.

Chakrabarty (2005)

Neutron Star Spin Distribution: A Cosmic Speed Trap?

No pulsars detected > 730 Hz

• 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.

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