Basically, pulsar timing provides the following Keplerian orbital parameters of the binary system: the
binary orbital period as measured from periodic Doppler variations of the pulsar spin, the projected
semimajor axis
as measured from the semi-amplitude of the pulsar radial velocity curve (
is
the binary inclination angle defined such that
for face-on systems), the orbital eccentricity
as
measured from the shape of the pulsar radial velocity curve, and the longitude of periastron
at a
particular epoch
. The first two parameters allow one to construct the mass function of the secondary
companion,
Long-term pulsar timing allows measurements of several relativistic phenomena: the advance of
periastron , the redshift parameter
, the Shapiro delay within the binary system qualified through
post-Keplerian parameters
,
, and the binary orbit decay
. From the post-Keplerian parameters
the individual masses
,
and the binary inclination angle
can be calculated [46].
Of the post-Keplerian parameters of binary pulsars, the periastron advance rate is usually measured most readily. Assuming it to be entirely due to general relativity, the total mass of the system can be evaluated:
High values of the derived total mass of the system ( If the individual masses, binary period, and eccentricity of a compact binary system are
known, it is easy to calculate the time it takes for the binary companions to coalesce due to GW
emission using the quadrupole formula for GW emission [309] (see Section 3.1.4 for more detail):
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Ref. |
[ms] | [d] | [lt-s] | [deg yr–1] | [× 10–12] | |||
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J0737–3039A | 22.70 | 0.102 | 1.42 | 0.088 | 16.88 | –1.24 | [49![]() |
J0737–3039B | 2773 | — | — | — | — | — | [241] |
J1518+4904 | 40.93 | 8.634 | 20.04 | 0.249 | 0.011 | ? | [290] |
B1534+12 | 37.90 | 0.421 | 3.73 | 0.274 | 1.756 | –0.138 | [455, 388] |
J1756–2251 | 28.46 | 0.320 | 2.75 | 0.181 | 2.585 | ? | [98] |
J1811–1736 | 104.18 | 18.779 | 34.78 | 0.828 | 0.009 | < 30 | [242] |
J1906+0746 | 144.07 | 0.116 | 1.42 | 0.085 | 7.57 | ? | [239] |
B1913+16 | 59.03 | 0.323 | 2.34 | 0.617 | 4.227 | –2.428 | [155] |
B2127+11C | 30.53 | 0.335 | 2.52 | 0.681 | 4.457 | –3.937 | [7, 333] |
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[Myr] | [Myr] | |
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J0737–3039A | 0.29 | 2.58 | 210 | 87 |
J0737–3039B | — | — | 50 | — |
J1518+4904 | 0.12 | 2.62 | 9.6 × 106 | |
B1534+12 | 0.31 | 2.75 | 248 | 2690 |
J1756–2251 | 0.22 | 2.57 | 444 | 1690 |
J1811–1736 | 0.13 | 2.6 | 1.7 × 106 | |
J1906+0746 | 0.11 | 2.61 | 0.112 | 300 |
B1913+16 | 0.13 | 2.83 | 108 | 310 |
B2127+11C | 0.15 | 2.71 | 969 | 220 |
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http://www.livingreviews.org/lrr-2006-6 |
© Max Planck Society and the author(s)
Problems/comments to |