Lower Bound on the Tidal Deformability of Neutron Stars
Sophia Han University of Tennessee, Knoxville In collaboration with Andrew Steiner, UTK/ORNL
Topical Program: FRIB and the GW170817 kilonova Wednesday Jul. 18th, 2018 @East Lansing QCD Phase Diagram
T Limits on computations for cold dense matter heavy ion collider • lattice QCD gives good result at finite temperature, QGP but is stymied currently at finite density non−CFL hadronic • perturbative QCD: only valid at asymptotically high densities gas liq CFL • can’t calculate properties of cold dense matter, must nuclear neutron star µ observe! superfluid Alford et al. Rev. Mod. Phys. 80 (2008) 1455 Compact Stars
Unique laboratory for extreme physics
• formed from the collapse of a massive star in a supernova explosion • static structure determined by Equation of State (pressure vs. density)
credit: D. Page
Demorest et al. (2010) Compact Stars
Unique laboratory for extreme physics
• formed from the collapse of a massive star in a supernova explosion
• static structure determined by Equation of State (pressure vs. density)
NICER mission Dense matter in neutron stars
Properties Observables equations of mass, radius, tidal state deformation, MoI…
thermal & ©NASA cooling, spin-down, transport glitches, neutrinos, properties, GW… vortex pinning
Best constraints from observation so far
-Massive pulsars observed ~2 solar masses -Pre-merger GW signals detected limit tidal deformability Low-energy Theory/Experiment
-Nuclear symmetry parameter constraints Fattoyev, Piekarewicz & Horowitz, arXiv:1711.06615 -Neutron-skin thickness of neutron-rich nuclei 208 120 R (fm) NL3 skin STOS, TM1 .16 .22 .25 .28 .30 .33 Excluded 1400 100 NL⇢ PREX TMA ut =1/2 NL⇢ 1200 80 LS220 KVOR
] FSUgold DBHF TKHS 1000 60 DD2, MeV
[ 3
KVR DD, D C, DD F ★ 1.4
L
IUFSU Λ SFHo 90% upper bound 800 40 GCR 800 HS r=0.98;α=5.28 LB (S0 ,L0) MKVOR ut =1 SFHx 20 600 Allowed
0 24 26 28 30 32 34 36 38 40 400 S [MeV] 12 12.5 13 13.5 14 14.5 15 0 1.4 Tews, Lattimer, Ohnish & Kolomeitsev, arXiv:1611.07133 R★ (km) Three Scenarios of NS
Normal hadronic stars Nuclear matter EoS -continuous and smooth density -stiffness (symmetry energy) profile
Self-bound strange Strange matter EoS (assumed quark stars as true ground state of QCD) -“bare” surface with a finite -bag constant; quark density discontinuity interaction; pairing
Hybrid stars with quark EoS with phase core & nuclear mantle transition at critical -abrupt density change inside the pressure star at phase boundary -phase transition parameters Normal hadronic EoSs
-Tidal Love numbers 0.05~0.15 -Speed of sound monotonically increasing with pressure from zero
Postnikov, Prakash & Lattimer, arXiv:1004.5098 EoSs with discontinuity
-Technical problem: matching boundary conditions properly -First studied in the incompressible limit: energy density is constant everywhere inside the star, but
0.8 ℓ =2 jump to zero at the surface ℓ =3 0.7 ℓ =4
0.6
0.5
ℓ 0.4 k
0.3
0.2
0.1
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -> c delta-function singular term proportional to 3/R Damour & Nagar, arXiv:0906.0096 -Applicable to any sharp interface with abrupt density change Generalize to PTs in hybrid stars
-Model-independent parametrization of high-density matter
Quark y
t Matter i
s -2
n ε0,QM Slope = cQM e
D Δε
y
g ε
r trans e n E
Nuclear Matter
ptrans Pressure Zdunik & Haensel, arXiv:1211.1231 Alford, SH & Prakash, arXiv:1302.4732 Tidal Parameters with PT
-Model-independent parametrization of high-density matter -Sizable decrease in both k2 and R above PT: deviated trajectories Tidal Parameters with PT
-Model-independent parametrization of high-density matter -Sizable decrease in both k2 and R above PT: deviated trajectories Smoothing to a crossover
-No singularity (good for simulations!), but rapidly changing behavior
Alford, Harris & Sachdeva, arXiv:1705.09880
1
3 0.5 0.3 ) ) ) 4 4 4 2 - 2 - - c2
fm c fm fm s 0.1 ( ( ( ε ε ε 1 0.05 0.03
0.01 0 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 p (fm-4) p (fm-4) Smoothing to a crossover
- values slightly lower compared to sharp 1st-order transition -Agrees with the discontinuous limit as e.g Mimic quark models with PT
ξ = -1.29
1
6 0.8 ξ= -1.29 ξ= 0 0.6 2
ξ= 3.62 c 0.4 4 )
-4 0.2
0 P (fm ξ = -1.29, disconnected branch 2 2×108 5×108 109 2×109 5×109 p (MeV4)
1.9 0
0 2 4 6 8 10 ) -4 ๏ 1.8 M
ε (fm ) ( M
1.7
Dexheimer, Negreiros & Schramm, 2 cQM=1, Δε/εtrans=0.73 1.6 arXiv:1411.4623 8 10 12 14 R(km) Constraints on PT-like EoSs
Better knowledge of nuclear matter helps M
M
(D) R (B) M R
Mtrans
(C) Rtrans R
-Massive pulsars observed ~2 solar masses -Pre-merger GW signals detected limit tidal deformability Combined tidal deformability
-Strikingly insensitive to the mass ratio for nuclear matter -Chirp mass measured to high accuracy -> estimate range of Combined tidal deformability
Raithel, Özel & Psaltis, arXiv:1803.07687
500
450
400
350 ˜ Λ 300
250
200
150
1.4 1.5 1.6 1.7 1.8
m1 (M⊙)
-Allows for direct probe of NS radius for purely-hadronic models -Chirp mass measured to high accuracy -> estimate range of Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation -> lowest Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF completely ruled out?
Phys. Rev. Lett. 119, 161101 Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF completely ruled out? Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF completely ruled out?
Not necessarily Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF completely ruled out?
Not necessarily Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF ruled out?
-Could we identify phase transition through future detections? Theoretical lower bound
Soft nuclear matter + strong phase transition immediately above saturation
-NSs obey the same EoS (!) Is stiffer EoS like DBHF ruled out?
-Could we identify phase transition through future detections?
-Is it possible to distinguish NS-NS, HS-HS and NS-HS mergers? Summary
• Dense matter EoSs categorized in terms of a) monotonically increasing and smooth b) abrupt discontinuity
c) smooth but varies rapidly in short range of pressures (novel feature to emerge in simulations?) • Theoretical lowest value of NS tidal deformability is determined by phase transition from soft NM to stiffest QM • Better constraints to expect a) narrow down uncertainties in NM: theory & experiment b) multiple detections to map • Future work role of PTs in properties other than (zero-T) EoS e.g. First simulation with quarks
Most et al., Yquark arXiv:1807.03684 6 5 4 3 2 1 0 60
14 14 50 crossover transition
40 12 12
30 10 [ms] [MeV] 10 t T
20 8 8 n /n 10 max sat st Tmax 1 order 6 6 phase transition 0 1.0 2.0 3.0 4.0 5.0 10.0 nb/nsat
-Evolution of temperature and density of the remnant -Different post-merger GW signal e.g. First simulation with quarks
Most et al., arXiv:1807.03684
22 10 4 ⇥ 12 M =2.8 M hadronic M =2.9 M 10 2 with quarks 8 0 [kHz] 22 6 1.5 10 aligned ringdown at 100 Mpc 2 ⇥ GW
f
22 + 4
h 0.0 4 2 1.5 0.00 0.25 0.50 0.75 1.00 6 0 3.0
[rad] 1.5
0.0 10 5 0 5 10 15 20 5 0 5 10 15 20 t t [ms] t t [ms] mer mer
-Evolution of temperature and density of the remnant -Different post-merger GW signal THANK YOU!
Q & A BACKUP
SLIDES Updated LIGO Analysis
3000 PhenomPNRT PhenomDNRT SEOBNRT <0.89 2500 TaylorF2 <0.05
1.0 2000 0.9 MS1
MS1b 2 1500 0.8 ⇤
Less Compact 0.7 H4 q 1000 More Compact 0.6 MPA1 0.5 500 SLy APR4 WFF1 0.4
0 0.3 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 1200 1400 1600 ˜ ⇤1 ⇤ LVC Collaboration, arXiv:1805.11579 Tolman-Oppenheimer-Volkoff Equation
For the interior of a spherical, static, relativistic star,
−1 p dp GM (r) ⎡ p(r)⎤⎡ 4πr 3 p(r)⎤ 2GM (r) central (r) 1 1 ⎡1 ⎤ = −ε 2 ⎢ + ⎥⎢ + ⎥ − dr r ⎣ ε(r) ⎦ M (r) ⎣⎢ r ⎦⎥ ⎣ ⎦ ε(p) where the included mass is defined as r M (r) ≡ 4π ε(r)r2dr ∫0 For a given equation of state (EoS), TOV can be solved simultaneously for the radial distribution of pressure and that of energy density.
p(r = 0) = pcentral R(pcentral ) -star surface at zero pressure p(r = R) = 0 M (R) M (pcentral ) -gravitational mass of the star M ≡ M (r = R) Third-family NSs
Soft NM (HLPS) + QM -with CSS parametrization
ntrans/n0
2.0 3.0 4.0 5.0 ncausal 6.0 1.2 Absent A 1 DisconnectedD 1 - λ
0.8 trans = s Both n B a r 0.6 t ε / Connected ∆ε ε ε C Δ 0.4
0.2
0 0 0.1 0.2 0.3 0.4 0.5
ptrans/εtrans ptrans εtrans -Below the red line in regions B -In regions B and D, there is a and C, there is a connected disconnected hybrid star branch hybrid star branch Alford, SH & Prakash, arXiv:1302.4702 Quark y t Matter i
s -2 n ε0,QM Slope = cQM e CSS Phase Diagram
D Δε y g ε
r trans e n E
Nuclear Matter
ptrans Pressure
preliminary