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Neutron stars in a perturbative f(R) gravity model with strong - - PowerPoint PPT Presentation

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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,

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Myung-Ki Cheoun Soongsil University, Seoul, Korea http://ssanp.ssu.ac.kr

1 NSMAT, Nov. 21-23, 2016, Sendai

Neutron Star Matter (NSMAT) Sendai, Japan

  • Nov. 22, 2016

2016-12-01

Neutron stars in a perturbative f(R) gravity model with strong magnetic fields and contributions of quark matter …

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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.)…

NSMAT, Nov. 21-23, 2016, Sendai 2 2016-12-01

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Contents

NSMAT, Nov. 21-23, 2016, Sendai

  • 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

  • 2. Modified Gravity and Magnetic field in Neutron Stars

2-1. Modified TOV 2-2. Magnetic field

  • 3. Other properties in Neutron Stars
  • 4. Summary and Conclusions

3

  • T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013), ApJ 777,04 (2013), ApJ 813,135(2015)…

MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013)… PRD 86 (2012) 123003 ; PRD83 (2011) 081303; PRC (2014)…

2016-12-01

G potential is 6 orders larger than solar system !! Curvature is 13 orders larger than solar system !!

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4

  • Eq. of State

RMF with CQMC in H-F scheme by SU(3) +q

Dyson equation

2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai 5 2016-12-01

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6

  • Eq. of State

RMF with CQMC in H-F scheme by SU(3) + q

2016-12-01

In CQMC, coupling constants depend on the density !! In HF scheme, self energy has momentum dependence !!

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  • 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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NSMAT, Nov. 21-23, 2016, Sendai 8 2016-12-01

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  • Eq. of State

RMF with CQMC in H-F scheme by SU(3) + q

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  • 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 !!

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NSMAT, Nov. 21-23, 2016, Sendai 11

  • Eq. of State

Hyperon Potentials

2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai 12

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

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NSMAT, Nov. 21-23, 2016, Sendai 13

Profile Function RMF with CQMC in H-F scheme by SU(3)

2016-12-01

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 !!

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2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 14

Generation of hyperons are sensitive to the coupling constant, g_sigma_Y !! Sigma^* also dpends on the model, ESC08 or SU(3)Y model !!

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NSMAT, Nov. 21-23, 2016, Sendai 15 2016-12-01

Profile Function RMF with CQMC in H-F scheme by SU(3)

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NSMAT, Nov. 21-23, 2016, Sendai 16 2016-12-01

Profile Function RMF with CQMC in H-F scheme by SU(3)

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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 !!

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2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 18

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 !! With the increase of the beta, EoS becomes softer !!

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NSMAT, Nov. 21-23, 2016, Sendai

SU(3) extension may lead to massive NS about 2.0 Solar Mass, even with hyperons !! ?? RMF + CQMC

  • T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013)

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EoS & Mass-R RMF with CQMC in H-F scheme by SU(3)

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NSMAT, Nov. 21-23, 2016, Sendai 20 2016-12-01

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2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 21

EoS & Mass-R RMF with CQMC in H-F scheme by SU(3)

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2016-12-01 NSMAT, Nov. 21-23, 2016, Sendai 22

EoS & Mass-R RMF with CQMC in H-F scheme by SU(3)+q

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Contents

NSMAT, Nov. 21-23, 2016, Sendai

  • 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

  • 2. Modified Gravity and Magnetic field in Neutron Stars

2-1. Modified TOV 2-2. Magnetic field

  • 3. Other properties in Neutron Stars
  • 4. Summary and Conclusions

23

  • T. Miyatsu, MKC, K. Saito, PRC 88, 015802 (2013), ApJ 777,04 (2013), ApJ 813,135(2015)…

MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013)… PRD 86 (2012) 123003 ; PRD83 (2011) 081303; PRC (2014)…

2016-12-01

G potential is 6 orders larger than solar system !! Curvature is 13 orders larger than solar system !!

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Motivation 2: Modified Gravity

NSMAT, Nov. 21-23, 2016, Sendai

How will be the modified gravity effect in the stellar scale ???

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Motivation 2-1 : Yukawa correction to Newtonian Potential

NSMAT, Nov. 21-23, 2016, Sendai 25 2016-12-01

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Solution of the Einstein eq. for a given time independent and spherical symmetric metric exp[ν(r)] = 1 − 2GM(r)/rc2 With a boundary conditions on a boundary and continuous metric Standard TOV

Theoretical Frameworks 1 : Standard TOV

NSMAT, Nov. 21-23, 2016, Sendai

If 1/c2 terms go to 0, Newtonian Gravity

26 2016-12-01

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Modified E. Equation Modified TOV

Theoretical Frameworks 2: Modified TOV by M. Gravity

NSMAT, Nov. 21-23, 2016, Sendai

If alpha dep. terms go to 0, Standard Gravity Modified Action

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In np phase

NSMAT, Nov. 21-23, 2016, Sendai

For alpha = -1(+1), more steeper (softer) EOS and more massive (light) Masses !!

  • Eq. of State

Results by the MTOV from Modified Gravity

Modified TOV Hyperonic NS may go to 2.0 solar mass by the modified gravity with reasonable magnetic field without any modification in RMF !!

28 2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai 29

  • 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

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NSMAT, Nov. 21-23, 2016, Sendai

In np and nph phase with stronger magnetic field For stronger m. field, we obtain more stiffer EOS and more massive Masses !! May compensate modified gravity (alpha >0).

  • Eq. of State

Results by MTOV and Magnetic fields

MKC et.al, PRC 82, 025804, (2010); PRC 83, 018802 (2011); JCAP 10, 21 (2013)

30

  • a

a

2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai

  • Eq. of State

Results by DDRMF

Gamma factors from experiments may be exploited in RMF and predict EoS and MR relations of Neutrons Stars !!

31 2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai

  • Eq. of State

Results by DDRMF with mag. field

Mass-radius relation

  • f

neutron stars may depend heavily on the gamma factor in the Symmetry energy !!! Gamma_i = 0.69

C-Y. Ryu and MKC, JKPS (2013)

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NSMAT, Nov. 21-23, 2016, Sendai

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
  • f 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.

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Thanks for your Attention !!

34 NSMAT, Nov. 21-23, 2016, Sendai 2016-12-01

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NSMAT, Nov. 21-23, 2016, Sendai

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 1st derivative term of density in E_{SNM} ? because the derivative should be zero at rho = rho_0 in SNM. Why the 1st 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) ?

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