Classical and general relativistic post-Keplerian effects in binary pulsars hosting fast rotating main sequence stars
We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M , spin angular momentum S , dimensionless mass quadrupole moment J 2 , equatorial and polar radii R e , R p , flattening ν ≐ ( R e - R p ) / R e , and ellipticity ε ≐ 1 - R p...
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| Published in: | The European physical journal. C, Particles and fields Vol. 79; no. 8; pp. 1 - 12 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2019
Springer Springer Nature B.V Springer Verlag (Germany) SpringerOpen |
| Subjects: | |
| ISSN: | 1434-6044, 1434-6052 |
| Online Access: | Get full text |
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| Abstract | We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass
M
, spin angular momentum
S
, dimensionless mass quadrupole moment
J
2
, equatorial and polar radii
R
e
,
R
p
, flattening
ν
≐
(
R
e
-
R
p
)
/
R
e
, and ellipticity
ε
≐
1
-
R
p
2
/
R
e
2
as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations
Δ
δ
τ
of the Rømer-like, orbital component of the pulsar’s time delay
δ
τ
induced over 10 years by the pN gravitoelectric mass monopole
Schwarzschild
,
G
M
c
-
2
, quadrupole
G
M
R
e
2
J
2
c
-
2
, gravitomagnetic spin dipole
Lense
-
Thirring
,
G
S
c
-
2
and octupole
G
S
R
e
2
ε
2
c
-
2
accelerations along with the Newtonian quadrupolar
G
M
R
e
2
J
2
one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with
M
=
15
M
⊙
,
R
e
=
5.96
R
⊙
,
ν
=
0.203
,
S
=
3.41
×
10
45
J
s
,
J
2
=
1.92
×
10
-
3
orbited by a pulsar with an orbital period
P
b
≃
40–70 days, the classical oblateness-driven effects are at the
≲
4
-
150
s
level, while the pN shifts are of the order of
≲
1.5
-
20
s
G
M
c
-
2
,
≲
10
-
40
ms
G
M
R
e
2
J
2
c
-
2
,
≲
0.5
-
6
ms
G
S
c
-
2
,
≲
5
-
20
μ
s
G
S
R
e
2
ε
2
c
-
2
, depending on their orbital configuration. The root-mean-square (rms) timing residuals
σ
τ
of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are
≲
ms
. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian (
G
M
c
-
2
,
G
M
J
2
c
-
2
, and, perhaps,
G
S
c
-
2
as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. |
|---|---|
| AbstractList | We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum \[\mathbf S \], dimensionless mass quadrupole moment \[J_2\], equatorial and polar radii \[R_\text {e},~R_\text {p}\], flattening \[\nu \doteq (R_\text {e}-R_\text {p})/R_\text {e}\], and ellipticity \[\varepsilon \doteq \sqrt{1-R_\text {p}^2/R_\text {e}^2}\] as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations \[\Delta \left( \delta \tau \right) \] of the Rømer-like, orbital component of the pulsar’s time delay \[\delta \tau \] induced over 10 years by the pN gravitoelectric mass monopole \[\left( \text {Schwarzschild}, GMc^{-2}\right) \], quadrupole \[\left( GMR^2_\text {e}J_2 c^{-2}\right) \], gravitomagnetic spin dipole \[\left( \text {Lense}{-}\text {Thirring},~GSc^{-2}\right) \] and octupole \[\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) \] accelerations along with the Newtonian quadrupolar \[\left( GMR^2_\text {e}J_2\right) \] one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with \[M = 15~\text {M}_\odot ,~R_\text {e} = 5.96~\text {R}_\odot ,~\nu = 0.203,~S = 3.41\times \]\[10^{45}~\text {J}~\text {s},\,J_2 = 1.92\times 10^{-3}\] orbited by a pulsar with an orbital period \[P_\mathrm{b}\simeq \] 40–70 days, the classical oblateness-driven effects are at the \[\lesssim 4-150~\text {s}\] level, while the pN shifts are of the order of \[ \lesssim 1.5-20~\text {s}~\left( GMc^{-2}\right) ,~ \lesssim 10-40~\text {ms}~\left( GMR^2_\text {e} J_2 c^{-2}\right) ,\]\[~ \lesssim 0.5-6~\text {ms}~\left( GSc^{-2}\right) ,~ \lesssim 5-20~\upmu \text {s}~\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) \], depending on their orbital configuration. The root-mean-square (rms) timing residuals \[\upsigma _{\tau }\] of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are \[\lesssim \text {ms}\]. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian (\[GMc^{-2},\,GMJ_2c^{-2}\], and, perhaps, \[GSc^{-2}\] as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum [Formula omitted], dimensionless mass quadrupole moment [Formula omitted], equatorial and polar radii [Formula omitted], flattening [Formula omitted], and ellipticity [Formula omitted] as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations [Formula omitted] of the Rømer-like, orbital component of the pulsar's time delay [Formula omitted] induced over 10 years by the pN gravitoelectric mass monopole [Formula omitted], quadrupole [Formula omitted], gravitomagnetic spin dipole [Formula omitted] and octupole [Formula omitted] accelerations along with the Newtonian quadrupolar [Formula omitted] one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with [Formula omitted] [Formula omitted] orbited by a pulsar with an orbital period [Formula omitted] 40-70 days, the classical oblateness-driven effects are at the [Formula omitted] level, while the pN shifts are of the order of [Formula omitted] [Formula omitted], depending on their orbital configuration. The root-mean-square (rms) timing residuals [Formula omitted] of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are [Formula omitted]. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ( [Formula omitted], and, perhaps, [Formula omitted] as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M , spin angular momentum S , dimensionless mass quadrupole moment J 2 , equatorial and polar radii R e , R p , flattening ν ≐ ( R e - R p ) / R e , and ellipticity ε ≐ 1 - R p 2 / R e 2 as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations Δ δ τ of the Rømer-like, orbital component of the pulsar’s time delay δ τ induced over 10 years by the pN gravitoelectric mass monopole Schwarzschild , G M c - 2 , quadrupole G M R e 2 J 2 c - 2 , gravitomagnetic spin dipole Lense - Thirring , G S c - 2 and octupole G S R e 2 ε 2 c - 2 accelerations along with the Newtonian quadrupolar G M R e 2 J 2 one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with M = 15 M ⊙ , R e = 5.96 R ⊙ , ν = 0.203 , S = 3.41 × 10 45 J s , J 2 = 1.92 × 10 - 3 orbited by a pulsar with an orbital period P b ≃ 40–70 days, the classical oblateness-driven effects are at the ≲ 4 - 150 s level, while the pN shifts are of the order of ≲ 1.5 - 20 s G M c - 2 , ≲ 10 - 40 ms G M R e 2 J 2 c - 2 , ≲ 0.5 - 6 ms G S c - 2 , ≲ 5 - 20 μ s G S R e 2 ε 2 c - 2 , depending on their orbital configuration. The root-mean-square (rms) timing residuals σ τ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are ≲ ms . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ( G M c - 2 , G M J 2 c - 2 , and, perhaps, G S c - 2 as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum $\mathbf S $ , dimensionless mass quadrupole moment $J_2$ , equatorial and polar radii $R_\text {e},~R_\text {p}$ , flattening $\nu \doteq (R_\text {e}-R_\text {p})/R_\text {e}$ , and ellipticity $\varepsilon \doteq \sqrt{1-R_\text {p}^2/R_\text {e}^2}$ as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations $\Delta \left( \delta \tau \right) $ of the Rømer-like, orbital component of the pulsar’s time delay $\delta \tau $ induced over 10 years by the pN gravitoelectric mass monopole $\left( \text {Schwarzschild}, GMc^{-2}\right) $ , quadrupole $\left( GMR^2_\text {e}J_2 c^{-2}\right) $ , gravitomagnetic spin dipole $\left( \text {Lense}{-}\text {Thirring},~GSc^{-2}\right) $ and octupole $\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $ accelerations along with the Newtonian quadrupolar $\left( GMR^2_\text {e}J_2\right) $ one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with $M = 15~\text {M}_\odot ,~R_\text {e} = 5.96~\text {R}_\odot ,~\nu = 0.203,~S = 3.41\times $ $10^{45}~\text {J}~\text {s},\,J_2 = 1.92\times 10^{-3}$ orbited by a pulsar with an orbital period $P_\mathrm{b}\simeq $ 40–70 days, the classical oblateness-driven effects are at the $\lesssim 4-150~\text {s}$ level, while the pN shifts are of the order of $ \lesssim 1.5-20~\text {s}~\left( GMc^{-2}\right) ,~ \lesssim 10-40~\text {ms}~\left( GMR^2_\text {e} J_2 c^{-2}\right) ,$ $~ \lesssim 0.5-6~\text {ms}~\left( GSc^{-2}\right) ,~ \lesssim 5-20~\upmu \text {s}~\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $ , depending on their orbital configuration. The root-mean-square (rms) timing residuals $\upsigma _{\tau }$ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $\lesssim \text {ms}$ . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ( $GMc^{-2},\,GMJ_2c^{-2}$ , and, perhaps, $GSc^{-2}$ as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. Abstract We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum $$\mathbf S $$ S , dimensionless mass quadrupole moment $$J_2$$ J2 , equatorial and polar radii $$R_\text {e},~R_\text {p}$$ Re,Rp , flattening $$\nu \doteq (R_\text {e}-R_\text {p})/R_\text {e}$$ ν≐(Re-Rp)/Re , and ellipticity $$\varepsilon \doteq \sqrt{1-R_\text {p}^2/R_\text {e}^2}$$ ε≐1-Rp2/Re2 as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations $$\Delta \left( \delta \tau \right) $$ Δδτ of the Rømer-like, orbital component of the pulsar’s time delay $$\delta \tau $$ δτ induced over 10 years by the pN gravitoelectric mass monopole $$\left( \text {Schwarzschild}, GMc^{-2}\right) $$ Schwarzschild,GMc-2 , quadrupole $$\left( GMR^2_\text {e}J_2 c^{-2}\right) $$ GMRe2J2c-2 , gravitomagnetic spin dipole $$\left( \text {Lense}{-}\text {Thirring},~GSc^{-2}\right) $$ Lense-Thirring,GSc-2 and octupole $$\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $$ GSRe2ε2c-2 accelerations along with the Newtonian quadrupolar $$\left( GMR^2_\text {e}J_2\right) $$ GMRe2J2 one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with $$M = 15~\text {M}_\odot ,~R_\text {e} = 5.96~\text {R}_\odot ,~\nu = 0.203,~S = 3.41\times $$ M=15M⊙,Re=5.96R⊙,ν=0.203,S=3.41× $$10^{45}~\text {J}~\text {s},\,J_2 = 1.92\times 10^{-3}$$ 1045Js,J2=1.92×10-3 orbited by a pulsar with an orbital period $$P_\mathrm{b}\simeq $$ Pb≃ 40–70 days, the classical oblateness-driven effects are at the $$\lesssim 4-150~\text {s}$$ ≲4-150s level, while the pN shifts are of the order of $$ \lesssim 1.5-20~\text {s}~\left( GMc^{-2}\right) ,~ \lesssim 10-40~\text {ms}~\left( GMR^2_\text {e} J_2 c^{-2}\right) ,$$ ≲1.5-20sGMc-2,≲10-40msGMRe2J2c-2, $$~ \lesssim 0.5-6~\text {ms}~\left( GSc^{-2}\right) ,~ \lesssim 5-20~\upmu \text {s}~\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $$ ≲0.5-6msGSc-2,≲5-20μsGSRe2ε2c-2 , depending on their orbital configuration. The root-mean-square (rms) timing residuals $$\upsigma _{\tau }$$ στ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $$\lesssim \text {ms}$$ ≲ms . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ($$GMc^{-2},\,GMJ_2c^{-2}$$ GMc-2,GMJ2c-2 , and, perhaps, $$GSc^{-2}$$ GSc-2 as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. |
| ArticleNumber | 690 |
| Audience | Academic |
| Author | Rieutord, Michel de Souza, Armando Domiciano Iorio, Lorenzo Rozelot, Jean-Pierre |
| Author_xml | – sequence: 1 givenname: Lorenzo surname: Iorio fullname: Iorio, Lorenzo email: lorenzo.iorio@libero.it organization: Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione – sequence: 2 givenname: Michel surname: Rieutord fullname: Rieutord, Michel organization: IRAP, Université de Toulouse, CNRS, UPS, CNES – sequence: 3 givenname: Jean-Pierre surname: Rozelot fullname: Rozelot, Jean-Pierre organization: Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS – sequence: 4 givenname: Armando Domiciano surname: de Souza fullname: de Souza, Armando Domiciano organization: Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, UMR7293 Lagrange |
| BackLink | https://hal.science/hal-02147941$$DView record in HAL |
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| CitedBy_id | crossref_primary_10_1016_j_dark_2024_101770 crossref_primary_10_1140_epjc_s10052_024_13298_0 |
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| PublicationSubtitle | Particles and Fields |
| PublicationTitle | The European physical journal. C, Particles and fields |
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| Publisher | Springer Berlin Heidelberg Springer Springer Nature B.V Springer Verlag (Germany) SpringerOpen |
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| Snippet | We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass
M
, spin angular momentum
S
,... We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum [Formula... We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum \[\mathbf S... We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum $\mathbf S... Abstract We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum... |
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| SubjectTerms | Analysis Angular momentum Astronomy Astrophysics Astrophysics and Cosmology Binary stars Dipoles Electric waves Electromagnetic radiation Electromagnetic waves Elementary Particles Ellipticity General Relativity and Quantum Cosmology Gravitational fields Gravity Hadrons Heavy Ions Main sequence stars Measurement Science and Instrumentation Millisecond pulsars Nuclear Energy Nuclear Physics Orbits Physics Physics and Astronomy Quadrupoles Quantum Field Theories Quantum Field Theory Regular Article - Theoretical Physics Stellar rotation String Theory Time lag Wave propagation |
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| Title | Classical and general relativistic post-Keplerian effects in binary pulsars hosting fast rotating main sequence stars |
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