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&...
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| Formato: | article |
| Lenguaje: | EN |
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MDPI AG
2021
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| Acceso en línea: | https://doaj.org/article/be58365fbbb74401b2fcda58f53ab5d0 |
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| Sumario: | 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. |
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