Estimating the EOS from the measurement of NS radii with 5% accuracy - - PowerPoint PPT Presentation

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Estimating the EOS from the measurement of NS radii with 5% accuracy Magdalena Sieniawska 1 , Micha Bejger 1 , Brynmor Haskell 1 1 Nicolaus Copernicus Astronomical Center Polish Academy of Sciences arXiv:1803.08813 28 March 2018 Magdalena

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Estimating the EOS from the measurement of NS radii with 5% accuracy

Magdalena Sieniawska1, Michał Bejger1, Brynmor Haskell 1

1Nicolaus Copernicus Astronomical Center

Polish Academy of Sciences

arXiv:1803.08813

28 March 2018

Magdalena Sieniawska (CAMK) EOS from the measurements

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Why do we need measurements of the global parameters of NSs?

There is a strong connection between mass-radius relation and properties of the interiors of the compact objects: cold matter equation of state (EOS) might be reconstructed from measured masses and radii.

Magdalena Sieniawska (CAMK) EOS from the measurements

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Measurements of masses

Özel & Freire 2016 Magdalena Sieniawska (CAMK) EOS from the measurements

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Theory - a plethora of EOSs

Özel & Freire 2016 Magdalena Sieniawska (CAMK) EOS from the measurements

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Challenges in modern NSs measurements

We need better estimations of NSs global parameters. → Advanced Telescope for High ENergy Astrophysics (ATHENA) & Neutron star Interior Composition ExploreR (NICER) → Predicted accuracy of M and R measurements: few % by using pulse profile modelling

Psaltis, Özel & Chakrabarty (2014); Psaltis & Özel (2014); Lo, Miller, Bhattacharyya & Lamb (2013); Miller & Lamb (2016)

Magdalena Sieniawska (CAMK) EOS from the measurements

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Challenges in modern NSs measurements

Pulse profile modelling limitations

Watts et al. 2016

Magdalena Sieniawska (CAMK) EOS from the measurements

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Idea of the study

Reference model: SLy4 model: crust + liquid core with npeν composition (Douchin & Haensel 2001) par. Model1 Model2 γ1 3.20 2.50 γ2 2.83 3.22 γ3 2.50 3.00 nb,12 0.21 0.24 nb,23 0.70 0.50 mb,1 1.017982 1.016573 mb,2 1.014858 1.021916 mb,3 0.977851 1.015670 κ1 0.006646 0.006646 κ2 0.008745 0.003538 κ3 0.016621 0.005042

5% accuracy in R measurements P = κinγi, ρ =

P γi−1 + nmbic2

Magdalena Sieniawska (CAMK) EOS from the measurements

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Idea of the study

Central parameters and GW170817 (Abbott et al. 2017).

Magdalena Sieniawska (CAMK) EOS from the measurements

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Let’s turn on rotation!

Multi-domain spectral methods library LORENE (Gourgoulhon et al. 2016) nrotstar code (Bonazzola et al. 1993) PSR J1748-2446ad: ν = 716 Hz Hessels et al. (2006) XTE J1739-285: ν = 1122 Hz Kaaret et al. (2007) not confirmed With rotation one can distinguish between EOSs!

http://www.lorene.obspm.fr

Magdalena Sieniawska (CAMK) EOS from the measurements

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NS masquerade

Spin is crucial

e.g. NS in a binary system for which bursts are observed, but which is not observed as a pulsar Accuracy in central parameters estimation: ∼40%

Magdalena Sieniawska (CAMK) EOS from the measurements

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Global parameters

Oblateness and surface area

Keplerian frequency = mass-shedding limit. PSR J1748-2446ad example - unknown mass. ∆R = ±5%: 1 M⊙: ±8% accuracy in O and to ±10% accuracy in S 2 M⊙: ±1 − 11% accuracy in O, ±10% accuracy in S

Magdalena Sieniawska (CAMK) EOS from the measurements

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Central parameters

Pressure and density

Known M: 1 M⊙ for all EOSs and f: Pc± negligible errors, ρc ± 10% and nc ± 15% 2 M⊙: fast decrease with f, Pc ± 40%, ρc ± 35%, nc ± 35% Unknown M: cut-off ∼ 1.9M⊙ known f: 10 − 50% unknown f: 30 − 85%

Magdalena Sieniawska (CAMK) EOS from the measurements

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I − Q relation

Universal (independent on the EOS) relation between the quadrupole moment Q and the moment of inertia I.

(Yagi & Yunes 2013)

¯ I = I/M3 ¯ Q = Q/(M3χ2) χ = J/M2

Can be used to distinguish between strange and ’normal’ NSs, description of binary NS inspiral waveforms.

Magdalena Sieniawska (CAMK) EOS from the measurements

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Tidal deformability

GW170817 example

λ - reaction of the NS on the external tidal field (e.g. tight binary system).

λ = 2R5k2/3 Λ = Gλ

GM/c2−5 k2 - quadrupole Love

number (Love 1911) R is the non-rotating star radius chirp mass M =

(M1M2)3/5 (M1+M2)1/5 = 1.188+0.004 −0.002 M⊙

component masses (low-spin priors): M1 = 1.36 − 1.60 M⊙ M2 = 1.17 − 1.36 M⊙

Magdalena Sieniawska (CAMK) EOS from the measurements

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Conclusions

∆R = ±5% accuracy reflects as: ∼ 10% accuracy in oblateness and surface area estimations very small errors in central parameters estimations if M ≈ 1M⊙ ∼ 40% errors in central parameters estimations if M ≈ 2M⊙ 10 − 50% errors in central parameters estimations if mass is unknown up to 85% errors in central parameters estimations if mass and spin are unknown

arXiv:1803.08813

Magdalena Sieniawska (CAMK) EOS from the measurements