hyperon suppression in hadron- quark mixed phase t. maruyama (jaea), s. chiba (jaea), h.-j. schhulze...
TRANSCRIPT
![Page 1: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/1.jpg)
Hyperon Suppression in Hadron-Quark Mixed Phase
T. Maruyama (JAEA) , S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.)
1
• Property of nuclear matter in neutron stars.• Non uniform “Pasta” structures at first-order phase transitions and the EOS of mixed phase.• Structure and mass of neutron stars.• Particle fraction in mixed phase -- hyperon suppression.
![Page 2: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/2.jpg)
2
Hulse-Taylor
Observed Neutron Star MassesMost of them lie around 1.4 Msol
Radius ~ 10 kmCentral density ~ several r0—10 r0
Mass ~ 1.4 Msol
![Page 3: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/3.jpg)
3
At 2-3 r0,hyperons are expected to emerge in nuclear matter. Large softening of the EOS Maximum mass of neutron star becomes less than 1.4 solar mass. Contradicts obs. >1.4 Msol
Schulze et al, PRC73 (2006) 058801
With YWithout Y
![Page 4: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/4.jpg)
4
• But the existence of mixed phase may soften the EOS again! --- Bulk Gibbs calculation yields wide range of mixed phase and large softening [Glendenning, PRD46,1274].
• Phase transition to quark matter may solve this problem. [Maieron et al, PRD70 (2004) 043010 etc].
Maxwell construction
EOS of mixed phase is important !
![Page 5: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/5.jpg)
5
In the mixed phase with charged particles, non-uniform ``Pasta’’ structures are expected [Ravenhall et al, PRL 50 (1983) 2066].
Depending on the density,geometrical structure of mixed phase changes from droplet, rod, slab, tube and to bubble configuration.
Quite differentdifferent from a bulk picturebulk picture of mixed phase.We have to take into account the effect of the structure when we calculate EOS.
Surface tension & Coulomb
![Page 6: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/6.jpg)
6
Hadron-Quark mixed-phase structure and EOS (T=0)Hadron-Quark mixed-phase structure and EOS (T=0)• Assume regularity in structure: divide whole space into equivalent and neutral cells with a geometrical symmetry (3D: sphere, 2D : cylinder, 1D: plate). Wigner-Seitz cell approx.
• Divide a cell into hadron phase and quark phases.• Give a geometry (Unif/Dropl/Rod/...) and a baryon density rB. • Solve the field equations numerically. Optimize the cell size and H-Q boundary position (choose the energy-minimum).• Choose an energy-minimum geometry among 7 cases (Unif H, droplet, rod, slab, tube, bubble, Unif Q).
WS-cell
![Page 7: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/7.jpg)
(given) )(3
1)(
3
1)(
3
1)()()()(
1
charge) (total0)()(3
1)(
3
1)(
3
2)()(
volumecell
areaboundary H-Q
densitybaryon average
)(1
/
4/)(3)(
bag) MIT :phase(quark )(
BHF) :phase(hadron )()(
8/)()()()(
),,,,,,,()(
)(
,2,
3
3
surf
3
23/42
22C
BV sdunp
V esdup
B
VB
ee
Q
HB
eB
ii
enepdunsdeu
rdV
rd
V
SSrdV
AE
eV
enpsdui
rrrrrrr
rrrrrr
r
rr
r
rr
rrrr
r
r
7
Coupled equationsCoupled equations to get density profile, energy, pressure, etc of the system
Chemical equilibrium fully consistent with all the density distributions and potentials.
![Page 8: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/8.jpg)
8
Hadron EOS vs quark EOS --- Choice of parametersHadron EOS vs quark EOS --- Choice of parameters
For quark phase, we choose aS =0 and B=100 MeV/fm3.Quark threshold is abovethe hyperon threshold in uniform matter.
For hadron phase, there is no adjustable parameter in the BHF model.
Hyperon threshold 0.34 fm-3
Critical density
![Page 9: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/9.jpg)
9
Density profile in a cellDensity profile in a cell
Quark phase is negatively charged. u quarks are attracted and d,s quarks repelled. Same thing happens to p in the hadron phase.
ri(r) consistent with Ui(r)
![Page 10: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/10.jpg)
10
EOS of matterEOS of matter
Full calculation (with pasta) is close to the Maxwell construction (local charge neutral). Far from the bulk Gibbs calculation (neglects the surface and Coulomb).
![Page 11: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/11.jpg)
11
0,
4
211
41
2
0
13
2
RRRmM
dsssrmm
r
PP
r
GmP
m
Pr
r
Gm
dr
dP
r
Density at r
Mass inside rTotal mass and Radius
Pressure ( input of TOV eq.)
Solve TOV eq.
Structure of compact starsStructure of compact stars
Bulk Gibbs Full calc tsurf=40 MeV/fm2 Maxwell const.
Density profile of a compact star (M=1.4 solar mass)
![Page 12: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/12.jpg)
12
Mass-Radius relation of compact stars
Full calc yields the neutron star mass very close to that of the Maxwell constr.
The maximum mass are not very different for three cases. tsurf=40
![Page 13: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/13.jpg)
ru ~ rs 2SC?
13
Important Side-effectof Pasta StructureImportant Side-effectof Pasta Structure
Although the EOS of matter and NS mass by the full calc is close to the Maxwell constr., the particle fraction is much different.Hyperon does not appear.
Particle fraction
Full calculation
![Page 14: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/14.jpg)
Neutral hadron matter
(positively) Charged hadron matter
14
Pasta Local charge.
Without charge-neutrality condition, hyperons appear at higher density.
Neutral hadron th=0.34 fm
Hyperon mixture is favoured to reduce electron and neutron Fermi energy. Charged hadron th=1.15 fm
Heavy hyperons are not favoured.
Hyperon suppression
Mixed phase consists of negative Q and positive H phases.Hyperon suppression
part
icle
fra
ctio
npa
rtic
le f
ract
ion
![Page 15: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/15.jpg)
15
SummarySummary
• We have studied ``Pasta’’ structures of hadron-quark mixed phase. • Coulomb screening and stronger surface tension makes the EOS of mixed phase close to that of Maxwell construction instead of a bulk Gibbs calc.• The mass-radius relation of a compact star is also close to the Maxwell construction case.• But the particle fraction and the inner structure is quite different. Non uniform structure causes local charge and consequently the suppression of hyperons. All the strangeness in NS is in the quark phase.• If the mixture of hyperons is suppressed in neutron stars influence on thermal property and n opacity (cooling process).
![Page 16: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/16.jpg)
16
![Page 17: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/17.jpg)
17
R and s dependence of E/A.
Strong tsurflarge R
Weak Coulomblarge R
![Page 18: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/18.jpg)
18
• Maxwell construction:Assumes local charge neutrality (violates the Gibbs cond.)Neglects surface tension.
• Bulk Gibbs calculation:Respects the balances of mi between 2 phases but neglects surface tension and the Coulomb interaction.• Full calculation: includes everything.Strong tsurf Large R, charge-screening effectively
local charge neutral. close to the Maxwell constrctn.Weak tsurf Small R Coulomb ineffective
close to the bulk Gibbs calc.
![Page 19: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/19.jpg)
NSC89UIXAV18 :
)()(;Re2
);()(
;)()(
;
rizer)antisymmet :()()(;2
1
25
3
2
,
,
2
v
kkkekeGkkm
kkeke
wGkekew
kkQkkvvwG
kkkekeGkkm
k
F
ba
F
kk
kk ba
baba
kkk
F
A
AA
19
Energy density of Hadron phaseEnergy density of Hadron phase
YN scatt data, -nuclear levels, and nuclear saturation are fitted.
MeV200K
Brueckner Hartree Fock model
![Page 20: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/20.jpg)
2)(
2443
Fock
242
kin
Fockkin
1,/
log2
3
8
log128
3
constant) bag :(
ffffFf
ffffffS
f
fffffff
fff
xmpx
xxxm
xxxm
BB
20
Energy density of Quark phaseEnergy density of Quark phase
Electron fraction is very small in quark matter.
MIT bag model
![Page 21: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/21.jpg)
21
Phase transitions in nuclear matter
Liquid-gas, neutron drip, meson condensation, hyperon, hadron-quark, color super-conductivity etc.
EOS of mixed phase in first order phase transition
• Single component (e.g. water) Maxwell const. satisfies Gibbs cond. TI=TII, PI=PII, mI=mII.
• Many components (e.g. water+ethanol)Gibbs cond. TI=TII, Pi
I=PiII, mi
I=miII.
No Maxwell const !
• Many charged componentsGibbs cond. TI=TII, mi
I=miII.
No Maxwell const !No constant P !
rUr
rU
dr
dP iii
on of dependence
explicit an is thereif;
![Page 22: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/22.jpg)
22
![Page 23: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/23.jpg)
23
Pure Hadron (Hyperon)Nicotra et alastro-ph/0506066
Hadron+QuarkMaxwell constr.astro-h/0608021
sunmax 5.1)0( MTM
![Page 24: Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cb75503460f9497c883/html5/thumbnails/24.jpg)
24