Gravitational Radiation Induced Spiral-in Offsets the Pulsar Pairfrom its Final Lock-in Position- a New Metric for Relativistic PulsarBinaries

Abstract

Author has extensively studied Earth-Moon system, Phobos-Mars system, Deimos-Mars System, Charon-Pluto system and Iapetus-Saturn system and developed Kinematic Model (KM) of tidally interacting binary systems. KM predicts two Geo-synchronous orbits aG1 and aG2 in case of Earth-Moon system and two Clarke’s orbits aG1 and aG2 in case of Phobos-Mars system, Deimos-Mars System, Charon-Pluto system and Iapetus-Saturn system. The secondary of the tidally interacting is always born at aG1 but aG1 is total energy maxima hence the secondary is in an unstable equilibrium state and any perturbing force nudges the secondary either short of aG1 or long of aG1. If the secondary falls short of aG1 the secondary is launched on a gravitational runaway collapsing sub-synchronous spiral path destined to make a glancing collision with the primary if the secondary does not get pulverized after entering the Roche’s limit of the primary as is the case with Phobos with respect to Mars. If the secondary falls long of aG1 as is the case with Earth-Moon system or Pluto-Charon system, the secondary experiences a powerful gravitational sling shot impulsive torque and secondary gets launched on an expanding spiral path with a radial recessive velocity. Eventually secondary gets tidally locked in a triple synchrony state [ Tspin_primary = Tspin_secondary = Tb (orbital period)] with zero radial velocity of recession. This is the case with Pluto-Charon. While describing these tidally interacting binaries there are three relevant parameters: ‘q’ = ratio of secondary to primary mass, time constant of evolution τ where Vmax = the maximum velocity experienced by the secondary at a semi-major axis a1 the point of maximm impulsive torque during ‘gravitational sling shot’ and evolution factor where ‘a’ is the current semi major axis of the secondary. KM states that if ‘q’ is less than 0.0001 that is the mass ratio is infinitesimal as is the case with artificial geo-synchronous satellites, the man-made geo-synchronous satellite is trapped in 36,000 Km synchronous orbit above the equator of Earth with geo- tationary position with resect to Earth’s surface. When ‘q’ is less than 0.0001, then time constant of evolutions is infinite, evolution factor is zero and the second art is stay put in aG1 orbit. When 0.001 <q <0.2 then secondary has a finite time constant of evolution from Gy to Ky in inverse proportion to some power of ‘q’ and evolution factor is 0 to Unity. When 0.2 <q <1 evolution factor approaches UNITY and secondary settles in aG2 orbit in years, months and days. Pluto Charon, Brown Dwarf pairs and star pairs up to White Dwarfs state are examples of this. But as we go to Neutron Star pairs or Neutron Star and Black Hole pairs or Black Hole pairs, we enter high gravitational field regime and Gravitational Radiation is induced which results in Gravitational Radiation induced spiral-in and hence offseted from the final lockin position at aG2. The strength of relativity is decided by the APSIDAL MOTION or the rate of periastron advance. Higher is the apsidal motion of relativistic pair, higher is ‘the offset’ from final locking position. This is precisely the finding of this paper. 6 Double Neutron Star Binaries (DNSBs) namely PSR J1811-1736, PSR J1518+4904, PSR B1534+12, PSR B1913+16(Hulse-Taylor Pair), PSR 2127+11C and PSR J0737-3039 are tested for KM prediction of Unity Evolution Factor. This off-set with respect to final lock-in is in proportion to the relativistic strength of the DNSB measured
by apsidal motion or rate of periastron advance. In this paper Keplerian Binaries such as Main Sequence Star Binary RW Lacerate, M Dwarf-White Dwarf pre-cataclysmic NN Serpentis are also studied as examples of non-relativistic binaries. Main Sequence Star Binary RW Lacerate and M Dwarf-White Dwarf pre-cataclysmic NN Serpentis are found to be in outer Clarke’s Configuration with triple synchrony state achieved as predicted.