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Table 7.1 Data of the binary pulsar system PSR1913+16

7 Gravitational Waves and the Binary Pulsars

Right ascension

19 h 13 m 12.4 s

Declination

+1601 08

Distance

21,000 light years

Mass of detected pulsar

1.441 × MSun

Mass of companion

1.387 × MSun

Rotational period of detected pulsar

59.02 ms

Diameter of each neutron star

20 km

Orbital period

7.752 h

Eccentricity

0.62

Semilatus rectum

1.95 × 106 km

7.4.3 The Fate of the Binary System

Defining

 

 

 

α ≡ u(G, c) · g1, μ2) · f(e)

(7.4.46)

whose numerical value is:

 

 

 

α = −0.625128 × 104

5

(7.4.47)

s 3

The revolution period obeys the following differential equation

 

dT

5

 

 

 

 

+ αT 3 = 0

 

(7.4.48)

 

dt

 

which is immediately integrated. Considering as initial the present instant of time and fixing the boundary condition at T (0) = T0 = 7.751 h we obtain:

83/8

T (t) = T08/3 + (7.4.49)

3

hence the period constantly decreases while the orbit radius shrinks and eventually T will reduce to zero when the two stars come so close as to coalesce. From (7.4.49) we can get a rough estimate of the time needed to reach coalescence. Such an estimate is determined by solving T (tf ) = 0 for tf . We obtain:

tf =

3T08/3

= 4.2983 × 1015 s = 1.382 × 108 years

(7.4.50)

8α

In other words the two neutron stars will fall one on top of the other in about 140 millions of years. Clearly the quadrupole approximation will loose its validity when approaching coalescence. At short distances the non-linear nature of Einstein equations will play an essential role and the only known methods to calculate gravitational radiation in such situations are numerical.

7.4 Quadruple Radiation from the Binary Pulsar System

307

Fig. 7.16 The double pulsar system PSR J0737-3039A/B, in the representation of an artist

7.4.4 The Double Pulsar

December 12th 2003, on journals and on the Internet appeared the official announcement of a new exciting discovery. An international team of radio-astronomers, including a strong and driving group of Italians,7 found the the Double Pulsar system officially named PSR J0737-3039A/B (see Fig. 7.16). This system is quite similar to the system PSR1913+16 but it has some additional features that make it an extraordinary precise laboratory to test General Relativity and Neutron Star Physics under extreme strong field conditions. The relevant data are displayed in Table 7.2. The first feature, in contrast with the case of PSR1913+16 is that both members of PSR J0737-3039A/B are pulsars and therefore they are both directly detectable. The second notable feature of the system is its extreme narrowness which emphasizes all General Relativity effects. The orbit has low eccentricity but the semilatus rectum is less than a million of Kilometers which results in a revolution period of just 2.4 hours. The periastron advance is accordingly very high and its measured value perfectly fits the predictions of General Relativity. Similarly the shortness of the revolution period allowed a rapid measure of its shrinking with very high statistics and the indirect evidence of the emission of gravitational waves was tested once again in excellent agreement with General Relativity. Using the measured parameters we

7The Italian Team participating to the discovery is constituted by members of INAF, the Istituto Nazionale di Astrofisica, belonging to the Cagliari Pulsar Group and to the Universities of Cagliari and Bologna, including Marta Burgay, Andrea Possenti and Nichi d’Amico. The main international partners of the collaboration were the Jodrell Bank pulsar group in Manchester, the ATNF pulsar group in Sydney (Australia) and the Swinburne pulsar group also in Australia (Melbourne). Finally also the European Pulsar Timing Array collaboration was involved. The radio-telescope used for the discovery is the Parkes radio telescope in Australia (see Fig. 7.17). Further observations were carried on at the Northern Cross radio-telescope near Bologna in Italy and in other European radio observatories.

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