1/21 XQCD2019 Tokyo, June 24, 2019 Neutron star equations of state and quark-hadron continuity T oru Kojo QCD ( C entral C hina N ormal U niv.) collaborators condensed Astro G. Baym, K. Fukushima, S. Furusawa, T. Hatsuda, matter P. Powell, Y. Song, H. Togashi, T. Takatsuka D. Hou, J. Okafor, D. Suenaga (-> poster) Refs) 1) Baym et al., Rept. Prog. Phys. 81 (2018) no.5, 056902 , a review; EoS tables QHC18&19 in CompStar website 2) A talk (plenary) in Lattice2019, Wuhan, June 24 (available online) 3) Three lectures in summer school, JINR, Dubna, 20-30 August 2019 (available online)
2/21 Overall picture based on QCD � many-quark exchange � few meson exchange � Baryons overlap � structural change � Quark Fermi sea � nucleons only � hyperons, ⊿ , ... (pQCD) ( 3-body ) [Freedman-McLerran 1976 Kurkela et al 2009] ab-initio nuclear cal. most difficult strongly correlated see e.g.) ChEFT, variational (d.o.f : quasi-particles??) (d.o.f ??) Gorda's talk not explored well Hints from NSs steady progress n B ~ 5n 0 ~ 100n 0 ~ 2n 0 (p F � 400 MeV)
3/21 Contents P QCD ( μ B ) 1, M-R Hints for "soft-stiff" EoS " given " 2, P QCD ( μ B ) H EFT Attempts to get insights 3, Summary & Prospects
4/21 EoS & M-R relation Einstein eq. : QCD EoS M max M ~2M sun (observed) 1-to-1 correspondence Lindblom (1992) R n B /n 0 M TOV & R( M TOV ) 1) non-rotating, spherical NS : TOV equation max max 2) uniformly rotating NS : e.g. Hartle-Thorne M uni ~ 1.2 M TOV (stable if rotation is slow enough) max 3) differentially rotating NS : Numerical GR max M diff ~ 1.5 M TOV (short-live; dissipation and magnetic braking → collapse)
5/21 Terminology (in this talk) M TOV stiffer 1) Stiff EoS : P is large at given ε pressure gravity ( not necessarily large c s 2 = dP/d ε ) R 2) Stiffness may strongly depend on density; define, e.g., Soft - Stiff EoS : Soft at n B < 2 n 0 & Stiff at n B > 5 n 0 more specifically, R 1.4 < ~ 13 km M > ~ 2 M sun We also use terminology such as stiff-stiff EoS, etc.
6/21 Soft-Stiff vs Stiff-Stiff EoS M TOV /M sun Ref) Lattimer & Prakash (2001) ~ 5-10n 0 Observation of Pulsars (NS) quark (?) 2.17 � 0.10 M sun [Cromartie+ (2019)] (NEW) [Antoniadis+ (2013)] 2.01 � 0.04 M sun 2.0 1.93 � 0.01 M sun [Demorest+ (2010)] hadron ~ 2-5n 0 to 1.5 quark (?) crust → loosely bound by gravity ~ 2n 0 1.0 P=0 ~10 -9 n 0 ~10 -9 n 0 ~ n 0 0.5 ~ 0.1n 0 nuclear R [km] 0 13 – 15 km 11 – 13 km ~20 km
7/21 Soft-Stiff vs Stiff-Stiff EoS M TOV /M sun Ref) Lattimer & Prakash (2001) ~ 5-10n 0 Observation of Pulsars (NS) 2.17 � 0.10 M sun [Cromartie+ (2019)] (NEW) [Antoniadis+ (2013)] 2.01 � 0.04 M sun 2.0 1.93 � 0.01 M sun [Demorest+ (2010)] ~ 2-5n 0 1.5 ~ 2n 0 very stiff ~ 2n 0 1.0 nuclear EoS 0.5 nuclear R [km] 0 13 – 15 km 11 – 13 km ~20 km
7/21 Soft-Stiff vs Stiff-Stiff EoS M TOV /M sun Ref) Lattimer & Prakash (2001) ~ 5-10n 0 Observation of Pulsars (NS) 2.17 � 0.10 M sun [Cromartie+ (2019)] (NEW) [Antoniadis+ (2013)] 2.01 � 0.04 M sun 2.0 1.93 � 0.01 M sun [Demorest+ (2010)] ~ 2-5n 0 1 st order P.T. (from very stiff to stiff phases) 1.5 ~ 2n 0 very stiff ~ 2n 0 1.0 nuclear EoS 0.5 nuclear R [km] 0 13 – 15 km 11 – 13 km ~20 km
8/21 Constraints ( before GW170817) M TOV /M sun � Thermal X-ray spectra from NS [Steiner+2015, Ozel+2015, ...] 2.0 modeling of thermo bursts systematics ? 1.5 � HIC constraints ( n B ~ 2-5 n 0 , T ? ) [Danielewicz+2002, Ko, Fuchs, Bao-An Li,...] transport models with "EoS" -> flow & particle production 1.0 systematics ? � Nuclear constraints ( n B ~ n 0 ) Theory: nuclear cal. & Lab. exp. 0.5 [e.g. Lattimer-Lim 2013 for summary] nuclear R [km] 0 13 – 15 km 11 – 13 km ~20 km
9/21 NS-NS mergers [detectability 0.1~100 /year , aLIGO/Virgo] GWs time Tidally deformed BH Early inspiral Merger M/M TOVmax > ~ 1.5 < 1 kHz 1 - 4 kHz too massive HMNS GWs GWs lifetime < 100 ms GWs 1.2 < M/M TOVmax < 1.5 < ~ 100 km ~ 1000 km short life BH EM (red) jets EM (blue) M/ M TOVmax < 1.2 SMNS Finite size effect point particles EM (red) long life (tidal deformation) � oscillation freq. (GW) ~ 1 – 3 kHz R 1,2 Λ obs M 1 & M 2 M eject , R � EM signals (sGRB & kilonova) spins (?) R 1 & R 2 � life-time of merger M TOV max
10/21 Constraints ( after GW170817 - GRB170817A - AT2017gfo) M TOV /M sun Too stiff → Too long life time for post merger [ Metziger+, Shibata+, Bauswein+, Rezzola+...] ~ 2.25 No evidence of 2.0 prompt collapse Too compact Too much tidal deformation 1.5 → too little ejecta tidal: Λ obs (1.4) < 800 (90%CL) ( spin? ) [aLIGO2018, De+2018,..] [ EM signals, Radice+2018 ] R 1.4 = 11.9 � 1.4 km [Abbott+ PRL2018, updated] 1.0 10 – 11 km A single event !! More (~100) will come next 10 years 0.5 Hints for soft - stiff EoS !! nuclear R [km] 0 13 – 15 km 11 – 13 km ~20 km
11/21 stiff-soft vs stiff-stiff vs soft-stiff [More sophisticated analyses, Han-Alford-Prakash 2013, Bedaque-Steiner 2015] P c s 2 = dP/d ε (sound speed) 2 soft c 2 causality 1/3 stiff 1 st order P.T. ε ε (very strong)
11/21 stiff-soft vs stiff-stiff vs soft-stiff [More sophisticated analyses, Han-Alford-Prakash 2013, Bedaque-Steiner 2015] P c s 2 = dP/d ε (sound speed) 2 stiff c 2 causality M > 2 M sun 1/3 stiff 1 st order P.T. ε ε (strong)
11/21 stiff-soft vs stiff-stiff vs soft-stiff [More sophisticated analyses, Han-Alford-Prakash 2013, Bedaque-Steiner 2015] P c s 2 = dP/d ε (sound speed) 2 stiff c 2 tension!! causality M > 2 M sun 1/3 2 < c 2 c s R < 13 km 2 > c 2 c s ε ε soft or weak 1 st order for 2-5n 0 soft - stiff EoS → crossover " Hadron - quark continuity " ( a new baseline ? ) [Schafer-Wilczek 1998, Hatsuda+ 2006, ...; cf) quarkyonic; McLerran-Pisarski 2007]
12/21 Speed of sound : finite T vs low T crossover Their characters are different : 1/3 1 Tew+2018 dip � speed of sound QGP � thermal vs quantum P .T. 1/3 HRG � the nature of gluons ~3-5n 0 Microphysics interpretation McLerran & Reddy, PRL(2019) ? c s 2 = 0 Baym+ 2019 ?
13/21 " given " 2, P QCD ( μ B ) H EFT Attempts to get insights
14/21 3-window modeling [Masuda+2012, TK+2014, ....] P pQCD n B ~ 5 n 0 Extrapolated EoS quark model ( 1+1+1-flavor ) n B = 2 n 0 nuclear μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
14/21 3-window modeling [Masuda+2012, TK+2014, ....] P pQCD n B ~ 5 n 0 Extrapolated EoS quark model potentially ( 1+1+1-flavor ) misleading n B = 2 n 0 ? nuclear μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
15/21 3-window modeling [Masuda+2012, TK+2014, ....] P pQCD n B ~ 5 n 0 quark model boundary conditions ( 1+1+1-flavor ) n B = 2 n 0 nuclear μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
15/21 3-window modeling [Masuda+2012, TK+2014, ....] P pQCD n B ~ 5 n 0 quark model boundary conditions ( 1+1+1-flavor ) n B = 2 n 0 interpolation � baseline: smooth curve (6 th order polynomials) nuclear � option: put a small kink μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
15/21 3-window modeling [Masuda+2012, TK+2014, ....] P typically, M > 2 M sun allowed band ~ 10-20 % of total (for a given nuclear EoS) c s 2 < 1 (everywhere) n B = 2 n 0 interpolation � baseline: smooth curve (6 th order polynomials) nuclear � option: put a small kink μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
15/21 3-window modeling [Masuda+2012, TK+2014, ....] P typically, M > 2 M sun allowed band ~ 10-20 % of total (for a given nuclear EoS) Non-pert. insights to be c s 2 < 1 (everywhere) mapped out n B = 2 n 0 interpolation � baseline: smooth curve (6 th order polynomials) nuclear � option: put a small kink μ B [Akmal+1998, T ogashi+2017, Hebeler+2017, Gandolfi+, ...]
16/21 A quark model for n B > ~ 5 n 0 A guide : Hadron-Quark continuity : eff. Hamiltonian continuously evolves from hadron physics " adiabatic continuity " (Anderson) " 3-window " [Manohar-Georgi 1983, Weinberg 2010,...] Q < ~0.2 GeV ~2 GeV < Q 0.2 GeV < Q < 1-2 GeV short range very long-range (> 1fm) constituent quarks + OGE (quasi-particles) chiral SB & color- mag . int. confinement pQCD & baryon-baryon . int. A template) chiral color-mag. nB-nB int. solve within MF + color- & charge- neutrality + β -equilibrium (to be derived from color-mag. int. : attempts -> Song+2019) [Masuda+2015, TK+2014, Blaschke+....]
17/21 Color-magnetic int. is a key player Δ (1232) cf) 1) Coupling ∝ velocity ~ p/E 3M q + ... more important in relativistic regime & high density N (938) 2) Pairing : strongly channel dependent s B u R hadron mass ordering: N- Δ , etc. [ DeRujula+ (1975), Isgur-Karl (1978), ...] color-super-conductivity [Alford, Wilczek, Rajagopal, Schafer,... 1998-] lighter quark mass 3) Baryon-Baryon int. : short-range correlation [Oka-Yazaki (1980),...] ( Pauli + color-mag . ) channel dep. → non-universal hard core (some are attractive!) mass dep. → stronger hard core in relativistic quarks → consistent with the lattice QCD [HAL-collaboration]
Recommend
More recommend
