Probing the Neutron Star Equation of State and Synergy with Advanced LIGO and Virgo

Cole Miller

University of Maryland

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Outline

• What we know about dense matter now

• Methods of constraining M and R from X-ray observations, and benefits of new observatories

• The promise of gravitational wavesMain point: larger area with good timing and energycoverage is important to test models and reducesystematics, as well as to reduce statistical uncertainties.

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Dense Matter

• Matter in NS core is several times nucl. density Only nucleons? Quark matter? Strange matter? Condensates?

• NS mass vs. radius, maximum mass would provide clues

Theoretical curves: NS massvs. radius

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A 1.97 Msun Neutron Star!• PSR J1614-2230• NS-WD system, almost exactly

edge-on• Allows precise measurement

of both massesNo classical contributions!

• M=1.97+-0.04 Msun

Hard EOS, minimal exotica?But modelers can adjust

• More to come, due to improved timing for pulsar array GW detection Demorest et al. 2010

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Radius: The Final Frontier

• Unlike mass, which has effects at a distance, radius is much tougher to measure

• All proposed methods suffer from large and often unknown systematics, and lack of enough data to resolve themKey: larger area esp. with good timingIXO, LOFT, GRAVITAS, AXTAR, NICER

• We now discuss example methods

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X-ray Burst AnalysisIf we assume full surface radiates uniformly in tail, and that we know Eddington lum, composition, and spectrum, get mass and radius (van Paradijs 1979)

Analysis assuming no systematics gets tightconstraints.

But evidence is mountingfor non-uniform emission and problems with spectrum.For example, standardassumptions give no solutionfor M and R unless observables are pushed to improbable extremes (Steiner et al. 2010)

Guver et al. 2010; 4U 1820-30

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Note on bursts: we are currently analyzingRXTE PCA data from the 4U 1820-30 superburst using detailed spectral models.We have prospects of constraining both thesurface gravity and redshift, which would inturn constrain M and R. Stay tuned!

Work with Fred Lamb and Ka Ho Lo (Illinois),Stratos Boutloukos and Valery Suleimanov(Tuebingen), and Juri Poutanen (Oulu)

Ray Tracing and Light Curves• Rapidly rotating star

300-600 Hz vsurf~0.1c SR+GR effects

• Light curve informative about M, R

Miller & Lamb 1998 Bogdanov+ 2007,8 Many others...

• Key: need multiple harmonics, more area (e.g., NICER, LOFT) Weinberg, Miller, and Lamb 2001

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Cooling NS Observations• Transient accretion, cooling• Predictions:

Minimum level of emissionSpectrum should be thermalNot variable; slow, steady decay

• Oops!• All the predictions fail

L below minimum Large power law component Significant variability, even in thermal component

• Some possible explanations (e.g., residual accretion), but troubling

• We also need more counts to ensure that our continuum models are correct, hence that our temperatures are right

Jonker 2007

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Information from Gravitational WavesInspiral of NS into NS, or into BH; aLIGO/aVirgo tens/yearTo lowest order, inspiral described by (Peters 1964):

Here M is the total mass and is the symmetric massratio m1m2/M2. reaches max of 0.25 for m1=m2.

Chirp mass Mch5/3=M5/3 will be measured to high precision.

But a (much tougher) measurement of is needed to getboth masses independently. Maybe for strongest sources.

What about radius?

Radius Measurements from GW?• BH-BH: point masses• With NS, have tidal effects• Can look for disruption, or for

deviations from inspiral• BH-NS not as promising

unless BH are very low mass (NS swallowed nearly whole; Miller 2005)

• New theory needed of tidal deformation near merger; with this, strongest events would significantly constrain radius (Hinderer et al. 2010)

BH-BH: Baker

NS-NS: Faber

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Conclusions• NS masses ~2 Ms are established

• Radii still very much up in the air: all current methods suffer from systematics

• Larger area instruments are keyImprove statistics; more importantly, will allow systematics to be tested

• In ~5 years, GW obs very important

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Original fig:Dany Page

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Information from Gravitational Waves

• Next gen of GW detectors could see many NS-NS, NS-BH

• Can get info on masses and possibly radii

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The Symmetric Mass Ratio• To break degeneracy,

must learn as well as the chirp mass

• But over reasonable NS-NS mass ratios, varies little

• Also, only higher-order effects in GW allow determination of

• Precisions will be lower

BH-NS: The Problem of Spin

• Mass ratio more extreme, so sensitivity not as great

• But BH can spin rapidly, unlike NS in high-mass binary

• Introduces precession: complicates waveforms

Etienne et al. 2009

Tidal Measurement in Practice

• For AdLIGO, even strong sources will not give phase signals to 450 Hz that allow EOS to be distinguished

• But much theoretical development remains

• At higher freq, tidal effects are much stronger

• Work is underway!

Figs from Hinderer et al. 2010

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Caveats and Status of Ray Tracing

• One might think spot shape matters, but for small spots shape is irrelevant Broad view of surface, plus light deflection

• Beaming pattern does matter some; choose electron scattering or isotropic emission

• Current constraints are not restrictive, but future large-area instruments might get radius to 5% or better But always beware of systematic uncertainties in detector response and model!

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Emission from Cooling NS

• Old, transiently accreting NS• e capture releases energy deep in crust• If know average accretion rate, emission

provides probe of cooling (neutrinos especially)

• Predictions of simple model: Minimum level of emission Spectrum should be blackbody No variability: steady, slow decay

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Radii from qLMXB in Globular?Just statistical errors.Assumes perfect distanceknowledge.Fixes mass of star at 1.4 Ms

Fixes spectral model(pure hydrogen, no magfield)For best source (#1), 49%of emission in power law;what causes this?

Continuum spectra notgreat for constraints!

Data assembled from Guillot, Rutledge et al. 2008

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Alternate Gravity Theories?

• Keep in mind: strong gravity not tested well• Therefore, really testing joint hypothesis of

EOS and gravity• Just cautionary, though, and LIGO grav

waves should test strong GR

DeDeo & Psaltis2003

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Relevance: the High kT Problem

Balance of grav, rad accel gives maximum surfaceflux (indep of distance, luminosity of source). Fora NS mass M, maximizing BB temp at infinity overredshift gives (see also Marshall 1982)

for pure He or heavy element (1.71 keV for pure H).However, best fit BB temps often kT~3.0 keV (knownfor 30 years). Assumed that color factor will reducethis to kTeff<2.0 keV. But such large spectraldistortions should leave their imprint. What do data say?

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A Long Shot: Quasi-Periodic Oscillations

• X-ray intensity from NS LMXBs varies quasi-periodically

• Best model: upper peak close to orbital frequency at some special radius

• Some evidence for ISCO M~2Ms?

Sco X-1 (van der Klis et al. 1996)

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A Long Shot: Quasi-Periodic Oscillations

• X-ray intensity from NS LMXBs varies quasi-periodically

• Best model: upper peak close to orbital frequency at some special radius

• Some evidence for ISCO M~2Ms?

M-R constraints: Miller et al. 1998

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The Innermost Stable Circular Orbit

• GR “pit in the potential”: gravity is stronger than Newtonian

• Minimum in L Unstable for r<6M

• Matter falls in rapidly• Lower limit to disk radius• If QPO at ISCO, know mass!• How to identify ISCO?

Specific angular momentumvs. radius, for Schwarzschild

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Predicted Behavior at ISCO

Barret, Olive, Miller 2005. Expect, and see, sharpdrop in quality factor at same freq indep of count rate

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Complementary Constraints• In principle, measurement of speed would

add greatly to information• Modulo minor frame-dragging effects:

f~(GM/r3)1/2 v~(GM/r)1/2

• Would combine to give independent constraints on mass, orbital (not stellar) radius With frame-dragging, constrain a/M

• How can speed be measured?

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Broad Iron Lines• Iron fluorescence lines are seen

from many BH• Profile affected by Doppler, grav.

redshifts, and inclination• Recently seen from several NS

sources• Constrains spin and speed• Do not yet have single source with

simultaneous QPOs, good line data

Cackett et al. 2007

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Radius Measurements in Practice• Challenge 1: action at high freq (but accessible)

• Challenge 2: need to know mass to get radius

• But might get R~1 km for strongest sources

Read et al. 2009, d=100 Mpc, 1.35-1.35 Ms

AdLIGOBroadband

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