Signals from Strange Stars Massimo Mannarelli INFN-LNGS - - PowerPoint PPT Presentation
Signals from Strange Stars Massimo Mannarelli INFN-LNGS massimo@lngs.infn.it MM, G. Pagliaroli, A. Parisi, L.Pilo Phys. Rev. D89, 103014 (2014) SEWM 2018 MM, G. Pagliaroli, A. Parisi, L.Pilo, F. Tonelli Astrophys.J. 815, 81 (2015) BCN,
INFN-LNGS massimo@lngs.infn.it
SEWM 2018 BCN, June 25, 2018 MM, G. Pagliaroli, A. Parisi, L.Pilo Phys. Rev. D89, 103014 (2014) MM, G. Pagliaroli, A. Parisi, L.Pilo, F. Tonelli Astrophys.J. 815, 81 (2015) MM and F. Tonelli Phys. Rev. D97, 123010 (2018)
u,d,s
+ + + + + + + + + + + + + + + + + + + + +2 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 RadiusKm MM
black hole photonsphere Buchdahl's limitSLy4 SS2 SS1 BBB2 MS1
3
Neutron star
n,p,e,µ
Δ, Σ, Λ ...
4
R ∼ 10 km M = 1 − 2 M
Neutron star
n,p,e,µ
Δ, Σ, Λ ...
4
R ∼ 10 km M = 1 − 2 M
Hybrid star
n,p,e,µ
u,d,s
R ∼ 10 km M = 1 − 2 M
Neutron star
n,p,e,µ
Δ, Σ, Λ ...
4
R ∼ 10 km M = 1 − 2 M
Hybrid star
n,p,e,µ
u,d,s
R ∼ 10 km M = 1 − 2 M
Strange star
u,d,s
R ∼ 0 − 10 km M < 3 M
Strange matter hypothesis: uds quark matter more stable than standard hadrons
A.Bodmer Phys. Rev. D4, 1601 (1971) E.Witten Phys. Rev. D30, 272 (1984)
nuclei “collapsed” nuclei
2 4 6 8 10 12 rfm
V If true, stars almost entirely made of quark matter exist
Very high density liquid of quarks in a bag. It can have any size.
} . 1fm
MM, G. Pagliaroli, A. Parisi, L.Pilo Phys. Rev. D89, 103014 (2014) MM, G. Pagliaroli, A. Parisi, L.Pilo, F. Tonelli Astrophys.J. 815, 81 (2015)
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
X Y Z X Y Z
CX 2cube45z
Rajagopal and Sharma Phys.Rev. D74 (2006) 094019
Def: color superconducting phase with a crystalline structure BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 3) The structure is extremely rigid
u d
0.47 MeV/fm3 < νCQM < 24 MeV/fm3
MM, K. Rajagopal and R. Sharma Phys.Rev. D76 (2007) 074026
Pairing regions on the Fermi spheres
R.Anglani+ Rev.Mod.Phys. 86 (2014) 509-561
8
positive charged star surface negative charged “electrosphere” + standard nuclei
+ + + + + + + + + + + + + + + + + + + + +
+ +
CFL CCSC Rc
8
10 20
z [fm]
1e+04 2e+04 3e+04 4e+04
/e [MeV
3]
Model A Ms=150 MeV Model A Ms=250 MeV Model B Ms=150 MeV Model B Ms=250 MeV
ρ/e ∼ ez/dquark ρ/e ∼ 1 (1 + z/delectron)3 delectron ∼ 102 − 103 fm dquark ∼ 1 − 10 fm
Debye length scales
positive charged star surface negative charged “electrosphere” + standard nuclei
+ + + + + + + + + + + + + + + + + + + + +
+ +
CFL CCSC Rc
The electric field at the surface is very large and directed outward
E ∼ 1017 − 1018 V/cm
8
10 20
z [fm]
1e+04 2e+04 3e+04 4e+04
/e [MeV
3]
Model A Ms=150 MeV Model A Ms=250 MeV Model B Ms=150 MeV Model B Ms=250 MeV
ρ/e ∼ ez/dquark ρ/e ∼ 1 (1 + z/delectron)3 delectron ∼ 102 − 103 fm dquark ∼ 1 − 10 fm
Debye length scales
positive charged star surface negative charged “electrosphere” + standard nuclei
+ + + + + + + + + + + + + + + + + + + + +
+ +
CFL CCSC Rc
r · u = 0 and ur = 0
Crystals can sustain various type of oscillations. We restrict to torsional oscillations Properties: no volume variation, no radial displacement, the wave is transverse
9
ω2
nlWnl = c2 t
− 1 r2 d dr ✓ r2 dWnl dr ◆ + l(l + 1) r2 Wnl
t = ν/ρ
Wave equation transverse (shear) velocity: amplitude of the n,l mode:
Wnl
L
F
ω ∼ ct D
Ex: slab oscillations
about 10 kHz for a 1 km thick CCSC crust about 1 GHz for a 1 cm thick CCSC crust Frequency of oscillations Estimated emitted power (assuming a giant Vela-like glitch as the trigger)
10
ω11 ∝ ct R − Rc P(a) ' 6.4 ⇥ 1041erg/s
We model the system by an oscillating magnetic dipole
about 10 kHz for a 1 km thick CCSC crust about 1 GHz for a 1 cm thick CCSC crust Frequency of oscillations Estimated emitted power (assuming a giant Vela-like glitch as the trigger)
10
ω11 ∝ ct R − Rc P(a) ' 6.4 ⇥ 1041erg/s
Many photons will be absorbed by the electrosphere. The Thomson suppression factor is
η Thomson & 0.1
Estimated electrosphere suppression We model the system by an oscillating magnetic dipole
MM and F. Tonelli Phys. Rev. D97, 123010 (2018)
Recent claim, J. Abedi and N. Afshordi, (2018), arXiv:1803.10454 [gr-qc], of a GW echo signal in the LIGO GW170817 post-merger data at a frequency
fecho ≈ 72 Hz
with a significance of 4.2 σ Interpretation: Planck-scale structure near the black hole horizon. If confirmed this may indicate quantum effects in GR.
Recent claim, J. Abedi and N. Afshordi, (2018), arXiv:1803.10454 [gr-qc], of a GW echo signal in the LIGO GW170817 post-merger data at a frequency
fecho ≈ 72 Hz
with a significance of 4.2 σ Interpretation: Planck-scale structure near the black hole horizon. If confirmed this may indicate quantum effects in GR.
A signal of an ultracompact stellar object, very close to the Buchdahl’s limit compactness
In arXiv:1805.02278 [gr-qc] we tried to figure out whether a strange star can be ultracompact and emit GW echoes
Alternative explanation:
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon
BH
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon
BH photon sphere
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon Surface of a compact star
BH photon sphere
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon Surface of a ultracompact star (UCS) Surface of a compact star
BH photon sphere
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon Surface of a ultracompact star (UCS) Surface of a compact star
photon sphere
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon Surface of a ultracompact star (UCS) Surface of a compact star
photon sphere
UCS
1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5
r/M Vphoton
Def. Ultracompact stars are stars that have a photon-sphere, that is 9/4 M < R < 3M Buchdahl’s limit R=9/4 M BH horizon Surface of a ultracompact star (UCS) Surface of a compact star
τecho =
Z
3M
dr r e2Φ(r) ⇣ 1 − 2m(r)
r
⌘
Large for configuration close to R=2M Typical echo time for UCS
photon sphere
UCS
2 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 RadiusKm MM
black hole photonsphere B u c h d a h l ' s l i m i t
SLy4 S S 2 SS1 BBB2 MS1
p = c2
s(✏ − 4B)
cs = 1 and B1 = (145 MeV)4 , B2 = (185 MeV)4
2 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 RadiusKm MM
black hole photonsphere B u c h d a h l ' s l i m i t
SLy4 S S 2 SS1 BBB2 MS1
p = c2
s(✏ − 4B)
cs = 1 and B1 = (145 MeV)4 , B2 = (185 MeV)4
“Maximally compact” configurations M/R ≃2.82
Koranda+Astrophys.J. 488 (1997) 799
2 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 RadiusKm MM
black hole photonsphere B u c h d a h l ' s l i m i t
SLy4 S S 2 SS1 BBB2 MS1
p = c2
s(✏ − 4B)
cs = 1 and B1 = (145 MeV)4 , B2 = (185 MeV)4
Strange stars can have a photon-sphere but they hardly approach the Buchdahl’s limit, thus
ω = π/τecho = 10 − 17 kHz
“Maximally compact” configurations M/R ≃2.82
Koranda+Astrophys.J. 488 (1997) 799
15
merged object is hot and rotates at high frequency
15
merged object is hot and rotates at high frequency
collapsing in a time of milliseconds or even seconds Radice+ arXiv:1803.10865. Thus one should solve the time dependent TOV’s equations.
15
merged object is hot and rotates at high frequency
collapsing in a time of milliseconds or even seconds Radice+ arXiv:1803.10865. Thus one should solve the time dependent TOV’s equations.
ultracompact object before collapsing to a black
associated to this process.
exotic stars
about 10 kHz frequencies or larger.
frequencies or larger.
GW echoes
QCD perturbative calculations and lattice QCD simulations are not feasible. Since the system is cold and there is attractive interaction, we expect that it becomes a color superconductor: system with condensation of diquarks.
18
QCD perturbative calculations and lattice QCD simulations are not feasible. Since the system is cold and there is attractive interaction, we expect that it becomes a color superconductor: system with condensation of diquarks.
18
Strange stars may actually be “color superconducting stars” Two of the candidate phases: 1) The color flavor locked (CFL) phase at large density 2) The crystalline color superconducting (CCSC) phase at smaller densities.
R
electrosphere core
R
CCSC CFL
Alford, Rajagopal, Wilczek hep-ph/9804403
Suppose that the strange quark mass is “small”. All quarks should be treated on an equal footing. Pairing of quarks of all flavors and colors h αiC5 βji / ∆CFL
3
X
I=1
"αβI✏ijI
19
Alford, Rajagopal, Wilczek hep-ph/9804403
Suppose that the strange quark mass is “small”. All quarks should be treated on an equal footing. Pairing of quarks of all flavors and colors All quarks, contribute coherently to pairing. Very robust. It is expected to be the ground state of quark matter at very large densities h αiC5 βji / ∆CFL
3
X
I=1
"αβI✏ijI
19
Alford, Rajagopal, Wilczek hep-ph/9804403
Suppose that the strange quark mass is “small”. All quarks should be treated on an equal footing. Pairing of quarks of all flavors and colors All quarks, contribute coherently to pairing. Very robust. It is expected to be the ground state of quark matter at very large densities h αiC5 βji / ∆CFL
3
X
I=1
"αβI✏ijI
19
SU(3)c × SU(3)L × SU(3)R × U(1)B → SU(3)c+L+R × Z2
⊃ U(1)Q ⊃ U(1) ˜
Q
Breaking pattern
extreme 10 g cm-3
Density
H He
.....
Fe
neutron drip
neutrons and protons Cooper pairs of quarks NGBs
Degrees of freedom
light nuclei heavy nuclei quarks and gluons Cooper pairs of quarks? .....
10 11 g cm-3 ......
weak coupling
confining
strong coupling
αs ≡ αs(µ) very large
quark drip quark soup
neutron proton soup
ρ
20
10 14 g cm-3 CSO part atmosphere
inner crust core
21
Quarks and gluons are the building blocks of hadrons The theory describing quarks and gluons is Quantum Chromodynamics (QCD): a nonabelian SU(3) gauge theory. Quarks form a triplet in the fundamental representation Gluons are the vector gauge bosons associated to the octet adjoint representation neutron proton u d u d d u .... BARYONS MESONS .... u d pions Mn ⇠ 1GeV mu,d Mπ ⇠ 135 MeV mu,d
Q quark flavor (mass in MeV) +2/3 u (3) c (1300) t (170000) −1/3 d (5) s (130) b (4000)