On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B

On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B

One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>k&...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Lorenzo Iorio
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
Materias:
gravitation
general relativity
relativistic mechanics
neutron stars
Elementary particle physics
QC793-793.5
Acceso en línea:https://doaj.org/article/be58365fbbb74401b2fcda58f53ab5d0
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
id oai:doaj.org-article:be58365fbbb74401b2fcda58f53ab5d0
record_format dspace
institution DOAJ
collection DOAJ
language EN
topic gravitation
general relativity
relativistic mechanics
neutron stars
Elementary particle physics
QC793-793.5
spellingShingle gravitation
general relativity
relativistic mechanics
neutron stars
Elementary particle physics
QC793-793.5
Lorenzo Iorio
On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
description One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>k</mi><mi>PK</mi></msup></semantics></math></inline-formula>. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>PK</mi></msup></semantics></math></inline-formula>. It was recently remarked that the periastron <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> of PSR J0737–3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense–Thirring precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mi>LT</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="normal">A</mi></mrow></msup><mo>≃</mo><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00060</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> from the experimentally determined periastron rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>obs</mi></msub></semantics></math></inline-formula> provided that the other post-Newtonian (PN) contributions to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>exp</mi></msub></semantics></math></inline-formula> can be accurately modeled. Among them, the 2PN seems to be of the same order of magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mi>LT</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="normal">A</mi></mrow></msup></semantics></math></inline-formula>. An analytical expression of the total 2PN periastron precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided, thereby elucidating the subtleties implied in correctly calculating it from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>k</mi><mrow><mn>1</mn><mi>PN</mi></mrow></msup><mo>+</mo><msup><mi>k</mi><mrow><mn>2</mn><mi>PN</mi></mrow></msup></mrow></semantics></math></inline-formula> and correcting some past errors by the present author. The formula for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> is demonstrated to be equivalent to that obtainable from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>k</mi><mrow><mn>1</mn><mi>PN</mi></mrow></msup><mo>+</mo><msup><mi>k</mi><mrow><mn>2</mn><mi>PN</mi></mrow></msup></mrow></semantics></math></inline-formula> by Damour and Schäfer expressed in the Damour–Deruelle (DD) parameterization. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> actually depends on the initial orbital phase, hidden in the DD picture, so that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00080</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>≤</mo><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup><mo>≤</mo><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00045</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. A recently released prediction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> for PSR J0737–3039A/B is discussed.
format article
author Lorenzo Iorio
author_facet Lorenzo Iorio
author_sort Lorenzo Iorio
title On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
title_short On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
title_full On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
title_fullStr On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
title_full_unstemmed On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B
title_sort on the 2pn periastron precession of the double pulsar psr j0737–3039a/b
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/be58365fbbb74401b2fcda58f53ab5d0
work_keys_str_mv AT lorenzoiorio onthe2pnperiastronprecessionofthedoublepulsarpsrj07373039ab
_version_ 1718410239507693568
spelling oai:doaj.org-article:be58365fbbb74401b2fcda58f53ab5d02021-11-25T19:09:50ZOn the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B10.3390/universe71104432218-1997https://doaj.org/article/be58365fbbb74401b2fcda58f53ab5d02021-11-01T00:00:00Zhttps://www.mdpi.com/2218-1997/7/11/443https://doaj.org/toc/2218-1997One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>k</mi><mi>PK</mi></msup></semantics></math></inline-formula>. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>PK</mi></msup></semantics></math></inline-formula>. It was recently remarked that the periastron <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> of PSR J0737–3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense–Thirring precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mi>LT</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="normal">A</mi></mrow></msup><mo>≃</mo><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00060</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> from the experimentally determined periastron rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>obs</mi></msub></semantics></math></inline-formula> provided that the other post-Newtonian (PN) contributions to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mi>exp</mi></msub></semantics></math></inline-formula> can be accurately modeled. Among them, the 2PN seems to be of the same order of magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mi>LT</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="normal">A</mi></mrow></msup></semantics></math></inline-formula>. An analytical expression of the total 2PN periastron precession <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided, thereby elucidating the subtleties implied in correctly calculating it from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>k</mi><mrow><mn>1</mn><mi>PN</mi></mrow></msup><mo>+</mo><msup><mi>k</mi><mrow><mn>2</mn><mi>PN</mi></mrow></msup></mrow></semantics></math></inline-formula> and correcting some past errors by the present author. The formula for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> is demonstrated to be equivalent to that obtainable from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>k</mi><mrow><mn>1</mn><mi>PN</mi></mrow></msup><mo>+</mo><msup><mi>k</mi><mrow><mn>2</mn><mi>PN</mi></mrow></msup></mrow></semantics></math></inline-formula> by Damour and Schäfer expressed in the Damour–Deruelle (DD) parameterization. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> actually depends on the initial orbital phase, hidden in the DD picture, so that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00080</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>≤</mo><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup><mo>≤</mo><mo>−</mo><mn>0</mn><mo>.</mo><msup><mn>00045</mn><mo>∘</mo></msup><mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. A recently released prediction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>ω</mi><mo>˙</mo></mover><mrow><mn>2</mn><mi>PN</mi></mrow></msup></semantics></math></inline-formula> for PSR J0737–3039A/B is discussed.Lorenzo IorioMDPI AGarticlegravitationgeneral relativityrelativistic mechanicsneutron starsElementary particle physicsQC793-793.5ENUniverse, Vol 7, Iss 443, p 443 (2021)

Ejemplares similares