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Temporal Data Analysis A.A. 2011/2012 Figure 6.18: Delays of the TOA in Her X–1 due to its orbital motion and theoretical sine curve for the 35 day orbital period. The residuals refer to different orbital parameters solutions. From Staubert et al. 2009 106 M.Orlandini
A.A. 2011/2012 Temporal Data Analysis 6.10.1 Determination of Neutron Star Masses X–ray binary pulsars are an important laboratory for measurements of astrophysical quantities. One of the most important is the determination of the mass of the neutron star orbiting its companion. From the orbital parameters determined in the previous section, the mass function can be expressed as f (M) = 4π2 (a x sini ) 3 G P 2 orb = 1.1 × 10 −3 ( ax sini 1 lt-s ) 3 ( ) −2 Porb M ⊙ (6.51) 1 d where G is the gravitational constant. The ratio of the neutron star mass M x to that of the companion star M c is obtained as q ≡ M x = K c P orb 1 − e 2 M c 2πa x sini = 4.6 × 10 −2√ ( 1 − e 2 K c )( Porb 1 Km s −1 1 d )( ax sini 1 lt-s where K c is the semi-amplitude of the Doppler velocity curve of the companion star as measured from optical observations. Because in the Doppler fitting we are able to determine only the product a x sini, we need an independent estimate of the inclination angle i. This can be obtained if the source shows X–ray eclipses. Indeed, the average radius of the companion star R c is related to the eclipse half-angle Θ c as R c = a ( cos 2 i + sin 2 i sin 2 Θ c ) 1/2 (6.52) where a = a x + a c is the separation of the centers of mass of the two stars in the binary system. Putting the things together, we can estimate the inclination angle in terms of the critical Roche-lobe radius R L as sini = ) −1 [ ( ) 2 ]1/2 1 − β 2 RL a (6.53) cosΘ c where β ≡ R c /R L . With all this in<strong>format</strong>ion it is possible to resolve the binary system and derive an estimate of the mass of the neutron star. All measured masses are consistent at 4σ with a maximum mass of 1.5–1.65 M ⊙ . M.Orlandini 107
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Temporal Data Analysis: Theory and
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Course Outline Table of Contents Li
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A.A. 2011/2012 Temporal Data Analys
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List of Figures 1.1 Classification
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List of Definitions 2.1 Even and od
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List of Theorems 2.1 Convolution th
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Part I Theory 1
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