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, June 25, 2018 MM and F. Tonelli Phys. Rev. D97, 123010 (2018)

Outline • Background u,d,s + � � � � + + + � � + � • EM signals � + + � � + + � � + + � + � + � + + � + � + � + � + � + + � + + � + � � � • GW echo signals 3.5 Buchdahl's limit 3.0 2.5 black hole 2.0 M � M � photon � sphere 1.5 1.0 MS1 SS1 0.5 SS2 SLy4 BBB2 0.0 2 4 6 8 10 12 14 16 Radius � Km � • Conclusions

BACKGROUND 3

Taxonomy of compact stars Neutron star n,p,e,µ Δ , Σ , Λ ... R ∼ 10 km M = 1 − 2 M � 4

Taxonomy of compact stars Hybrid star Neutron star n,p,e,µ n,p,e,µ u,d,s Δ , Σ , Λ ... R ∼ 10 km M = 1 − 2 M � R ∼ 10 km M = 1 − 2 M � 4

Taxonomy of compact stars Hybrid star Neutron star n,p,e,µ n,p,e,µ u,d,s Δ , Σ , Λ ... R ∼ 10 km M = 1 − 2 M � R ∼ 10 km M = 1 − 2 M � Strange star u,d,s R ∼ 0 − 10 km M < 3 M � 4

Strange stars � V � Strange matter hypothesis: uds quark matter more stable than standard hadrons 12 r � fm � A.Bodmer Phys. Rev. D4, 1601 (1971) 2 4 6 8 10 E.Witten Phys. Rev. D30, 272 (1984) nuclei “collapsed” nuclei If true, stars almost entirely made of quark matter exist C. Alcock, E. Farhi and A. Olinto, Astrophys.J. 310, 261 (1986) } . 1fm Very high density liquid of quarks in a bag. It can have any size.

EM SIGNALS FROM STRANGE STARS 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)

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 u d Pairing regions on the Fermi spheres

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 u d Pairing regions on the Fermi spheres

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 u d Pairing regions on the Fermi spheres

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 u d Pairing regions on the Fermi spheres

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 u d Pairing regions on the Fermi spheres

Crystalline Color Superconducting (CCSC) phase Def: color superconducting phase with a crystalline structure R.Anglani+ Rev.Mod.Phys. 86 ( 2014 ) 509 - 561 BASIC FACTS 1) Cooper pairs have nonzero momentum 2) The crystal reciprocal lattice is given by the direction of these momenta 0 . 47 MeV / fm 3 < ν CQM < 24 MeV / fm 3 3) The structure is extremely rigid MM, K. Rajagopal and R. Sharma Phys.Rev. D76 ( 2007 ) 074026 CX 2cube45z Z Z u Y Y X d X Pairing regions on the Fermi spheres Rajagopal and Sharma Phys.Rev. D74 (2006) 094019

A star with two crusts negative charged “electrosphere” + standard nuclei � � � + + + � � CCSC + + � � + + � + � + R c � + � + � + � + CFL + � + � + � + � + � + � + + � + + � + � � � positive charged star surface 8

A star with two crusts 4e+04 negative charged “electrosphere” Model A M s =150 MeV Model A M s =250 MeV + standard nuclei 3e+04 Model B M s =150 MeV Model B M s =250 MeV 3 ] � / e [MeV 2e+04 � � � + + + � � CCSC + + � � + 1e+04 + � + � + R c � + � + 0 � + � + -20 -10 0 10 20 CFL z [fm] + � + � 1 + � + � ρ /e ∼ ρ /e ∼ e z/d quark (1 + z/d electron ) 3 + � + � + + � + + � + � � Debye length scales � d electron ∼ 10 2 − 10 3 fm positive charged star surface d quark ∼ 1 − 10 fm 8

A star with two crusts 4e+04 negative charged “electrosphere” Model A M s =150 MeV Model A M s =250 MeV + standard nuclei 3e+04 Model B M s =150 MeV Model B M s =250 MeV 3 ] � / e [MeV 2e+04 � � � + + + � � CCSC + + � � + 1e+04 + � + � + R c � + � + 0 � + � + -20 -10 0 10 20 CFL z [fm] + � + � 1 + � + � ρ /e ∼ ρ /e ∼ e z/d quark (1 + z/d electron ) 3 + � + � + + � + + � + � � Debye length scales � d electron ∼ 10 2 − 10 3 fm positive charged star surface d quark ∼ 1 − 10 fm E ∼ 10 17 − 10 18 V/cm The electric field at the surface is very large and directed outward 8

Torsional oscillations Crystals can sustain various type of oscillations. We restrict to torsional oscillations r · u = 0 and u r = 0 Properties: no volume variation, no radial displacement, the wave is transverse D Ex: slab oscillations ω ∼ c t F L �� � D � F  ✓ ◆ � − 1 + l ( l + 1) d r 2 dW nl Wave equation ω 2 nl W nl = c 2 W nl t r 2 r 2 dr dr transverse (shear) velocity: amplitude of the n,l mode: c 2 t = ν / ρ W nl 9

EM emission We model the system by an oscillating magnetic dipole Frequency of oscillations about 10 kHz for a 1 km thick CCSC crust c t about 1 GHz for a 1 cm thick CCSC crust ω 11 ∝ R − R c Estimated emitted power (assuming a giant Vela-like glitch as the trigger) P ( a ) ' 6 . 4 ⇥ 10 41 erg/s 10

EM emission We model the system by an oscillating magnetic dipole Frequency of oscillations about 10 kHz for a 1 km thick CCSC crust c t about 1 GHz for a 1 cm thick CCSC crust ω 11 ∝ R − R c Estimated emitted power (assuming a giant Vela-like glitch as the trigger) P ( a ) ' 6 . 4 ⇥ 10 41 erg/s Estimated electrosphere suppression Many photons will be absorbed by the electrosphere. The Thomson suppression factor is η Thomson & 0 . 1 10

GW ECHOES FROM STRANGE STARS MM and F. Tonelli Phys. Rev. D97, 123010 (2018)

GW echoes 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 f echo ≈ 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.

GW echoes 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 f echo ≈ 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. Alternative explanation: A signal of an ultracompact stellar object, very close to the Buchdahl’s limit compactness P. Pani and V. Ferrari, (2018), arXiv:1804.01444 [gr-qc]. In arXiv:1805.02278 [gr-qc] we tried to figure out whether a strange star can be ultracompact and emit GW echoes

GW echoes and ultracompact stars BH horizon 0.5 Def. 0.4 Ultracompact stars are stars that have a photon-sphere, that is 0.3 V photon 9/4 M < R < 3M 0.2 0.1 0.0 - 0.1 0 1 2 3 4 5 6 r / M Buchdahl’s limit R=9/4 M

GW echoes and ultracompact stars BH horizon 0.5 Def. 0.4 Ultracompact stars are stars that have a photon-sphere, that is 0.3 V photon 9/4 M < R < 3M 0.2 0.1 0.0 - 0.1 BH 0 1 2 3 4 5 6 r / M Buchdahl’s limit R=9/4 M

GW echoes and ultracompact stars BH horizon 0.5 Def. 0.4 Ultracompact stars are stars that have a photon-sphere, that is 0.3 V photon 9/4 M < R < 3M 0.2 photon 0.1 sphere 0.0 - 0.1 BH 0 1 2 3 4 5 6 r / M Buchdahl’s limit R=9/4 M