Neutron stars in a perturbative f(R) gravity model with strong magnetic fields and contributions of quark matter … Myung-Ki Cheoun Soongsil University, Seoul, Korea http://ssanp.ssu.ac.kr Neutron Star Matter (NSMAT) Sendai, Japan Nov. 22, 2016 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 1
Collaborators Eunja Ha, Y. S. Kwon, Ki-Seok Choi, M. Kusakabe, Ying Zhang, Gil-Seok Yang (Soongsil University)… C. Ryu (Hanyang Univ.), K. S. Kim (Korea Aviation Univ.) W. So (Kangwon Univ.), C. Hyun (Daegu Univ.)… K. Tsushima (Adelaide Univ.), T. Miyatsu, K. Saito (TSU) G. Mathews (Notre Dam), Baha Ballantekin (Wisconsin), Alex Brown (MSU) T. Kajino, Ko Nakamura (NAOJ and Tokyo Univ.) T. Maruyama (Nihon Univ.), T. Hayakawa, S. Chiba (JAEA)… C. Deliduman… (Turkey)… A. Faessler, F. Simkovic (Tuebingen Univ.)… 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 2
Contents 0. Introduction : Exotic matter, Symmetry Energy, EoS… 1. Roles of hyperons in RMF+QMC models for Dense Matter 1-1. Hartree- Fock Approximation in SU(3) scheme 1-2. With Quark Matter T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013), ApJ 777,04 (2013), ApJ 813,135(2015)… 2. Modified Gravity and Magnetic field in Neutron Stars 2-1. Modified TOV 2-2. Magnetic field MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013)… 3. Other properties in Neutron Stars PRD 86 ( 2012) 123003 ; PRD83 (2011) 081303; PRC (2014)… 4. Summary and Conclusions G potential is 6 orders larger than solar system !! Curvature is 13 orders larger than solar system !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 3
Eq. of State RMF with CQMC in H-F scheme by SU(3) +q Dyson equation 2016-12-01 4
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Eq. of State RMF with CQMC in H-F scheme by SU(3) + q In CQMC, coupling constants depend on the density !! In HF scheme, self energy has momentum dependence !! 2016-12-01 6
Eq. of State RMF with CQMC in H-F scheme by SU(3) + q T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013) In SU(3) scheme, we need only 4 parameters !! Properties of symmetric matter were not changed !!
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Eq. of State RMF with CQMC in H-F scheme by SU(3) + q
Eq. of State RMF with CQMC in H-F scheme by SU(3) + q We employed a density dependent Big Bag for quark matter with Gibbs conditions for mixed phase !!
Eq. of State Hyperon Potentials 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 11
Profile Function Results by RMF with CQMC in H-F In HF, tensor couplings and quark interactions may make Y-EoS stiffer !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 12
Profile Function RMF with CQMC in H-F scheme by SU(3) In the SU(3) scheme, strange mesons shift the appearance hyperons (hyperon threshold energy) to a bit higher density , i.e., makes the EoS stiffer !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 13
Generation of hyperons are sensitive to the coupling constant, g_sigma_Y !! Sigma^* also dpends on the model, ESC08 or SU(3)Y model !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 14
Profile Function RMF with CQMC in H-F scheme by SU(3) 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 15
Profile Function RMF with CQMC in H-F scheme by SU(3) 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 16
Profile Function RMF with CQMC in H-F scheme by SU(3) In the SU(3) scheme, strange mesons shift the appearance hyperons (hyperon threshold energy) to a bit higher density , i.e., makes the EoS stiffer !! This feature shows up in all models !!
Profile Function RMF with CQMC in H-F scheme by SU(3)+q Quark production makes the EoS softer and suppresses the hyperons in high density region !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 18 With the increase of the beta, EoS becomes softer !!
EoS & Mass-R RMF with CQMC in H-F scheme by SU(3) T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013) RMF + CQMC SU(3) extension may lead to massive NS about 2.0 Solar Mass, even with hyperons !! ?? 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 19
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EoS & Mass-R RMF with CQMC in H-F scheme by SU(3) 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 21
EoS & Mass-R RMF with CQMC in H-F scheme by SU(3)+q 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 22
Contents 0. Introduction : Exotic matter, Symmetry Energy, EoS… 1. Roles of hyperons in RMF+QMC models for Dense Matter 1-1. Hartree- Fock Approximation 1-2. With Quark Matter T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013), ApJ 777,04 (2013), ApJ 813,135(2015)… 2. Modified Gravity and Magnetic field in Neutron Stars 2-1. Modified TOV 2-2. Magnetic field MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013)… 3. Other properties in Neutron Stars PRD 86 ( 2012) 123003 ; PRD83 (2011) 081303; PRC (2014)… 4. Summary and Conclusions G potential is 6 orders larger than solar system !! Curvature is 13 orders larger than solar system !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 23
Motivation 2: Modified Gravity How will be the modified gravity effect in the stellar scale ??? 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 24
Motivation 2-1 : Yukawa correction to Newtonian Potential 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 25
Theoretical Frameworks 1 : Standard TOV Standard TOV If 1/c 2 terms go to 0, Newtonian Gravity Solution of the Einstein eq. for a given time independent and spherical symmetric metric With a boundary exp[ ν ( r )] = 1 − 2 GM ( r )/ rc 2 conditions on a boundary and continuous metric 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 26
Theoretical Frameworks 2: Modified TOV by M. Gravity Modified Action Modified E. Equation If alpha dep. terms go to 0, Modified TOV Standard Gravity 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 27
Eq. of State Results by the MTOV from Modified Gravity Modified TOV For alpha = -1(+1) , more In np phase steeper (softer) EOS and more massive (light) Masses !! Hyperonic NS may go to 2.0 solar mass by the modified gravity with reasonable magnetic field without any modification in RMF !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 28
Eq. of State Modified Gravity and Magnetic fields MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013) 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 29
Eq. of State Results by MTOV and Magnetic fields MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013) In np and nph phase with stronger magnetic field -a a For stronger m. field, we obtain more stiffer EOS and more massive Masses !! May c ompensate modified gravity (alpha >0). 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 30
Eq. of State Results by DDRMF Gamma factors from experiments may be exploited in RMF and predict EoS and MR relations of Neutrons Stars !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 31
Eq. of State Results by DDRMF with mag. field C-Y. Ryu and MKC, JKPS (2013) Gamma_i = 0.69 Mass-radius relation of neutron stars may depend heavily on the gamma factor in the Symmetry energy !!! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 32
Summary and Conclusion 1. Quark production the EoS softer and suppresses the hyperons in high density region. Hybrid star can explain the 2.0 solar massive neuron star. 2. SU(3) extension of RMF models may give rise to roles of sigma* and phi* meson, which suppress the appearance of hyperons in profile functions on the neutrons star. EoS becomes stiffer even with hyperons. 3. Modified f(R) gravity is developed to consider the dark energy (or cosmological constant) and extended to modified TOV equation for neutrons stars. 4. Magnetic fields are also included to the Modified gravity and applied to the EOS of neutron star. 5. Negative alpha can make NS, in particular, supersoft EOS, stiffer. Positive alpha may compensate the stiffness by strong magnetic fields. 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 33
Thanks for your Attention !! 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 34
Why not ¥alpha*S_1(¥rho) ? because of Isospin Symmetry of N-N force. But if we include the ISBreaking including Coulomb interaction, we may consider the term. Why not the 1 st derivative term of density in E_{SNM} ? because the derivative should be zero at rho = rho_0 in SNM. Why the 1 st term of density in the symmetry energy, which is just the symmetry pressure ? because the derivative does not need to be zero at rho = rho_0 in Asymmetric NM. Is it really true ???? 1) E_{PNM} – E_{SNM} = S_(¥rho) = S_1(¥rho) + S_2(¥rho) + S_3(¥rho) + S_4(¥rho) … ~ S_2(¥rho) for alpha = 1 = a*S_1(¥rho) + a^2*S_2(¥rho) + a^3*S_3(¥rho) … for alpha .ne. 1 2) Therefore, L term in the S_{¥rho) includes terms neglected in the standard definition. And for asymmetric matter we have to also the asymmetry coefficients. 3) How is the relation of the saturation density(¥rho_0) and asymmetry (¥alpha) ? 2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 35
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