tjonnie g. f. li tgfl[email protected] · 2015-06-18 · 18 june 2015. equation of state inspiral...
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EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
INFERRING THE NUCLEAR EQUATION OF STATE FROMBINARY NEUTRON STAR MERGERS
Tjonnie G. F. [email protected]
Gravitational Wave Physics and Astronomy WorkshopOsaka, Japan
18 June 2015
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
NUCLEAR EQUATION OF STATE
I Behaviour of ultra-densematter highly uncertain
I Complex interplay amongall forces of Nature
I Manifest as relationshipamong pressure, densityand temperature, i.e.equation of state (EOS)
I Observations of neutronstars (NSs) provide a way tostudy the EOS
I Infer by measuring the massand radius (simultaneously) Fig. 1: Özel [1]
Tjonnie Li (Caltech) GWPAW 2015, Osaka 1
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
CURRENT KNOWLEDGE
I Binary millisecond radio pulsarsystems
I Demorest et al. [2]: EOS mustfacilitate mass up to 2 M
I x-ray binariesI Özel et al. [3]: R = 9− 12 km at
m = 1.4MI Steiner et al. [4]:
R = 10− 13 km at m = 1.4MI Guillot et al. [5]: R = 7− 11 km
assuming R constant Fig. 2: Özel et al. [3]
Model-dependent uncertainties in emission and absorptionmechanisms
Tjonnie Li (Caltech) GWPAW 2015, Osaka 2
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EFFECT OF EOS ON GW SIGNALS
I Gravitational waves (GWs) mainly sensitive to density profileI Different model-dependent uncertainties
I Binary NS excellent candidate to study EOS
I Inspiral regime: objects are tidally deformedI EOS-dependent tidal deformability λ(m) = 2/3 k2(m) R5(m)I Modifies the GW phase evolution
I Merger/post-merger: objects are tidally disruptedI Merger remnant GW emission depends on EOS
Tjonnie Li (Caltech) GWPAW 2015, Osaka 3
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EFFECT OF EOS ON GW SIGNALS
1.0
0.5
0.0
0.5
1.0
2MΩ
Mω22
|Rh22/(Mν)|R[Rh22/(Mν)]
2000 1000 0 1000 2000(t−tmrg)/M
-30 0 30x
-30
0
30
y
-20 0 20x
-20
0
20
y
-20 0 20x
-20
0
20
y
9
7
5
3log10(ρ)
Fig. 3: Bernuzzi et al. [6]
Tjonnie Li (Caltech) GWPAW 2015, Osaka 4
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EARLY STUDIES
I Early studies indicated that asingle loud event is required
I Hinderer et al. [7]: Earlyinspiral (f < 450Hz),signal-to-noise ratio (SNR)ρ > 30
I Damour et al. [8]: Fullinspiral, ρ > 16
I Read et al. [9]: Late inspiral +merger, ρ > 40
0.0 0.5 1.0 1.5 2.0 2.5 3.00
2
4
6
8
10
12
Mass HM
L
ΛH1
036g
cm2s2
L
npeΜ matter only
Adv
. LIG
O
Eins
tein
Tele
scop
e
AP1 AP3
FPSSLy
MPA1
MS1
MS2
Fig. 4: Hinderer et al. [7]
Such loud events are unlikely in Advanced detector era
Tjonnie Li (Caltech) GWPAW 2015, Osaka 5
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
COMBINING MULTIPLE WEAK EVENTS
Can we learn something from weak events?
I Combine multiple weak eventsI Bayesian study to facilitate combination of eventsI Expand EOS-dependent tidal deformability function λ(m)
λ(m) ≈ c0 + c1
(m−m0
M
)(1)
I Measure λ around cannonical mass of m0 = 1.4M
Tjonnie Li (Caltech) GWPAW 2015, Osaka 6
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
COMBINING MULTIPLE WEAK EVENTS
0 50 100 150 2000
1
2
3
4
5
c 0[1
0−23s5
]
χ=0Uniform mass distributionUniform mass prior
Injected value SQM3
Injected value H4
Injected value MS1
95% CI SQM3
95% CI H4
95% CI MS1
Fig. 5: Del Pozzo et al. [10] and Agathos et al. [11]Tjonnie Li (Caltech) GWPAW 2015, Osaka 7
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
INCLUDING SPIN
0 50 100 150 2000
1
2
3
4
5
c 0[1
0−23s5
]
σχ=0.02
Gaussian mass distributionGaussian mass prior
Injected value SQM3
Injected value H4
Injected value MS1
95% CI SQM3
95% CI H4
95% CI MS1
Fig. 6: Agathos et al. [11]Tjonnie Li (Caltech) GWPAW 2015, Osaka 8
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EFFECT OF PRIORS
0 50 100 150 2000
1
2
3
4
5
c 0[1
0−23s5
]
σχ=0.02
Gaussian mass distributionUniform mass prior
Injected value SQM3
Injected value H4
Injected value MS1
95% CI SQM3
95% CI H4
95% CI MS1
Fig. 7: Agathos et al. [11]Tjonnie Li (Caltech) GWPAW 2015, Osaka 9
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EFFECT OF EOS ON GW SIGNALS
1.0
0.5
0.0
0.5
1.0
2MΩ
Mω22
|Rh22/(Mν)|R[Rh22/(Mν)]
2000 1000 0 1000 2000(t−tmrg)/M
-30 0 30x
-30
0
30
y
-20 0 20x
-20
0
20
y
-20 0 20x
-20
0
20
y
9
7
5
3log10(ρ)
Fig. 3: Bernuzzi et al. [6]
Tjonnie Li (Caltech) GWPAW 2015, Osaka 10
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
EOS FROM POST-MERGER SIGNAL
I Stergioulas et al. [12], andBauswein and Janka [13]:Possible to study the EOSthrough the characteristicsof the post-mergerspectrum.
I Relationship among thepeak frequency(associated to m = 2mode) and the radius ofthe NS
I Clark et al. [14] finds thatuseful constraints can beplaced provided the sourceis at 4− 12Mpc
0 1 2 3 4 510
−23
10−22
10−21
f [kHz]
ha
v(2
0 M
pc) 0 5 10 15 20
−1
0
1x 10
−21
h+ a
t 2
0 M
pc
t [ms]
fpeak
10 12 141.5
2
2.5
3
3.5
4
R1.35
[km]
f pe
ak [kH
z]
0.04 0.06 0.08 0.1
(Mtot
/(Rmax
)3)1/2
Fig. 8: Bauswein and Janka [13]
Tjonnie Li (Caltech) GWPAW 2015, Osaka 11
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
LINKING INSPIRAL TO POST MERGER
1 2 3 4 5f [kHz]
100
101
√5/
(16π
)R|h
22(f
)|/M
MS1b-150100ALF2-140110H4-135135SLy-140120SLy-135135
2.5
3.0
3.5
4.0
4.5
5.0
Mf 2
[×10
2]
Binary Mass M2.4502.5002.5502.6002.650
2.7002.7502.8002.8502.900
EOSMS1bSLyENG2HH4APR4
MS1ALF2MPA1GNH3Γ2
100 200 300 400κT2
2.5
3.0
3.5
4.0
4.5
5.0
Mf 2
[×10
2]
Mass-ratio q1.0001.0771.0801.1541.160
1.1671.2311.2501.2731.500
100 200 300 400κT2
Γth1.6001.750
1.8002.000
Fig. 9: Bernuzzi et al. [6]
I Bernuzzi et al. [6] findsphenomenological relationshipbetween f2 and κT
2 , where
κT2 = 2
(q4
(1 + q)5kA
2
C5A
+q
(1 + q)5kB
2
C5B
)
I But κT2 can be related to λ, where
λ(m) = 2/3 k2(m) R5(m)
I Links EOS information betweeninspiral and post merger
Tjonnie Li (Caltech) GWPAW 2015, Osaka 12
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
SIMPLE TOY MODEL
102 103
f (Hz)
10−26
10−25
10−24
10−23
10−22|h
(f)|
waveform
f2
Fig. 10: Li et al., in prep.Tjonnie Li (Caltech) GWPAW 2015, Osaka 13
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
IMPROVEMENTS FROM INCLUDING POST MERGER
0 20 40 60 80 100Sources
10−1
100
101
∆c 0[ 10−
23s5]
Inspiral only
With post merger
Fig. 11: Li et al., in prep.Tjonnie Li (Caltech) GWPAW 2015, Osaka 14
EQUATION OF STATE INSPIRAL POST MERGER CONCLUSIONS
CONCLUDING REMARKS
I Strong EOS constraints possible in Advanced detector eraI Single high-SNR sourceI O(50) low-SNR sources
I Need accurate waveform to mitigate systematic errorsI Effective-One-Body waveforms with spin and tidal effects?
I Possible systematic effects from unknown mass distributionI Improve constraints by including post-merger information
I Need accurate (phenomenological) models of post-merger signal
Tjonnie Li (Caltech) GWPAW 2015, Osaka 15
Appendix References Abstract Acronyms
Thank you
Tjonnie Li (Caltech) GWPAW 2015, Osaka 16
Appendix References Abstract Acronyms
PARAMETERISATION CHOICE
I Lackey and Wade [15]performed similar study withmore physical parameterisation
I Use piecewise polytropes
p(ρ) = KiρΓi (2)
I Assume 4 parameter modelI θ = log p1,Γ1,Γ2,Γ3
I Allows for inclusion of physicalpriors (e.g. thermodynamicalstability)
9
10
11
12
13
14
15
16
R (
km)
1.2M
¯
1.6M
¯
1.93M
¯
0.0 0.5 1.0 1.5 2.0 2.5 3.0M(M¯)
0
1
2
3
4
5
6
7
8
9
λ (
10
36 g
cm
2 s
2)
Loudest 20, 3σ
Loudest 20, 2σ
Loudest 20, 1σ
Fit to MPA1
Fig. 12: Lackey and Wade [15]Tjonnie Li (Caltech) GWPAW 2015, Osaka 17
Appendix References Abstract Acronyms
SYSTEMATIC ERRORS FROM WAVEFORM UNCERTAINTY
0 200 400 600 800 1000Λ
0.000
0.002
0.004
0.006
0.008
0.010
0.012P
rob
abili
tyd
ensi
tym1 = 1.35 M, m2 = 1.35 M
F2 Injection
T1 Injection
T2 Injection
T3 Injection
T4 Injection
Fig. 13: Wade et al. [16]Tjonnie Li (Caltech) GWPAW 2015, Osaka 18
Appendix References Abstract Acronyms
TOWARDS A FAITHFUL WAVEFORM
−1.0
−0.5
0.0
0.5
1.0 SLy135, κT2 ≈ 73.55
<(Rh22)/ν, NR
100 400 800 1200 1600 2000(t− r∗)/M
−2.5
−1.5
−0.5
0.5
∆φEOBNR22
∆AEOBNR22
∆φTT4NR22
NR phase error
2200 2300 2400
Γ2164, κT2 ≈ 75.07
<(Rh22)/ν, TEOBResum
100 400 800 1200 1600(t− r∗)/M
NR merger
TEOBResum merger
TEOBResum LSO
1700 1800
0.06 0.08 0.10 0.12 0.14Mω
20
40
60
80
100
120
140
Qω
MωLSO-TEOBResum
SLy135, κT2 ≈ 73.55 BBH
TT4
TEOBNNLO
TEOBResum
NR
Fig. 14: Bernuzzi et al. [17]
Tjonnie Li (Caltech) GWPAW 2015, Osaka 19
Appendix References Abstract Acronyms
MODEL SELECTION
250 200 150 100 50 0 50 100 150
lnOEOSMS1
0.0
0.2
0.4
0.6
0.8
1.0cu
mula
tive d
istr
ibuti
on
100 sources/catalogue17 catalogues
SQM3
PP
H4
Fig. 15: Agathos et al. [11]Tjonnie Li (Caltech) GWPAW 2015, Osaka 20
Appendix References Abstract Acronyms
REFERENCES I
[1] F. Özel. “Soft equations of state for neutron-star matter ruled out by EXO 0748 -676”. Nature 441 (June 2006), pp. 1115–1117. eprint:arXiv:astro-ph/0605106.
[2] P. B. Demorest et al. “A two-solar-mass neutron star measured using Shapirodelay”. Nature 467 (Oct. 2010), pp. 1081–1083. arXiv: 1010.5788[astro-ph.HE].
[3] F. Özel et al. “Astrophysical measurement of the equation of state of neutronstar matter”. Phys. Rev. D 82.10, 101301 (Nov. 2010), p. 101301. arXiv:1002.3153 [astro-ph.HE].
[4] A. W. Steiner et al. “The Equation of State from Observed Masses and Radii ofNeutron Stars”. ApJ 722 (Oct. 2010), pp. 33–54. arXiv: 1005.0811[astro-ph.HE].
[5] S. Guillot et al. “Measurement of the Radius of Neutron Stars with HighSignal-to-noise Quiescent Low-mass X-Ray Binaries in Globular Clusters”. ApJ772, 7 (July 2013), p. 7. arXiv: 1302.0023 [astro-ph.HE].
[6] S. Bernuzzi et al. “Towards a description of the complete gravitational wavespectrum of neutron star mergers”. ArXiv e-prints (Apr. 2015). arXiv:1504.01764 [gr-qc].
Tjonnie Li (Caltech) GWPAW 2015, Osaka 21
Appendix References Abstract Acronyms
REFERENCES II[7] T. Hinderer et al. “Tidal deformability of neutron stars with realistic equations
of state and their gravitational wave signatures in binary inspiral”. Phys. Rev. D81.12, 123016 (June 2010), p. 123016. arXiv: 0911.3535 [astro-ph.HE].
[8] T. Damour et al. “Measurability of the tidal polarizability of neutron stars inlate-inspiral gravitational-wave signals”. Phys. Rev. D 85.12, 123007 (June 2012),p. 123007. arXiv: 1203.4352 [gr-qc].
[9] J. S. Read et al. “Measuring the neutron star equation of state with gravitationalwave observations”. Phys. Rev. D 79.12, 124033 (June 2009), p. 124033. arXiv:0901.3258 [gr-qc].
[10] W. Del Pozzo et al. “Demonstrating the Feasibility of Probing the Neutron-StarEquation of State with Second-Generation Gravitational-Wave Detectors”.Physical Review Letters 111.7, 071101 (Aug. 2013), p. 071101. arXiv: 1307.8338[gr-qc].
[11] M. Agathos et al. “Constraining the neutron star equation of state withgravitational wave signals from coalescing binary neutron stars”. ArXiv e-prints(Mar. 2015). arXiv: 1503.05405 [gr-qc].
[12] N. Stergioulas et al. “Gravitational waves and non-axisymmetric oscillationmodes in mergers of compact object binaries”. MNRAS 418 (Nov. 2011),pp. 427–436. arXiv: 1105.0368 [gr-qc].
Tjonnie Li (Caltech) GWPAW 2015, Osaka 22
Appendix References Abstract Acronyms
REFERENCES III
[13] A. Bauswein and H.-T. Janka. “Measuring Neutron-Star Properties viaGravitational Waves from Neutron-Star Mergers”. Physical Review Letters 108.1,011101 (Jan. 2012), p. 011101. arXiv: 1106.1616 [astro-ph.SR].
[14] J. Clark et al. “Prospects for high frequency burst searches following binaryneutron star coalescence with advanced gravitational wave detectors”.Phys. Rev. D 90.6, 062004 (Sept. 2014), p. 062004. arXiv: 1406.5444[astro-ph.HE].
[15] B. D. Lackey and L. Wade. “Reconstructing the neutron-star equation of statewith gravitational-wave detectors from a realistic population of inspirallingbinary neutron stars”. Phys. Rev. D 91.4, 043002 (Feb. 2015), p. 043002. arXiv:1410.8866 [gr-qc].
[16] L. Wade et al. “Systematic and statistical errors in a Bayesian approach to theestimation of the neutron-star equation of state using advanced gravitationalwave detectors”. Phys. Rev. D 89.10, 103012 (May 2014), p. 103012. arXiv:1402.5156 [gr-qc].
[17] S. Bernuzzi et al. “Modeling the Dynamics of Tidally Interacting Binary NeutronStars up to the Merger”. Phys. Rev. Lett. 114 (16 2015), p. 161103.
Tjonnie Li (Caltech) GWPAW 2015, Osaka 23
Appendix References Abstract Acronyms
ABSTRACT
Gravitational waves emitted by binary neutron star mergersencode information about the nuclear equation of state. We
present the prospects of Advanced LIGO/Virgo to extract thisinformation. In particular, results from simulations indicatethat one can already distinguish between extreme nuclear
equation of state models within the era of AdvancedLIGO/Virgo. Moreover, we will discuss how these results canbe further improved by including additional information such
as the post-merger behaviour.
Tjonnie Li (Caltech) GWPAW 2015, Osaka 24
Appendix References Abstract Acronyms
ACRONYMS I
EOS Equation Of State
GW Gravitational Wave
NS Neutron Star
SNR Signal-to-noise Ratio
Tjonnie Li (Caltech) GWPAW 2015, Osaka 25