Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..507k&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Astronomy and Astrophysics
Astronomy
Scientific paper
ABSTRACT Observation of pulsars is a powerful source of information for studying the dynamics and internal structure of neutron stars. Known about quasi-periodical fluctuations of the time-of-arrival of radiation(TOA) for some pulsars, which we explain as Chandler wobble, Free core nutation, Free inner core nutation and Inner core wobble in case three layer model. Using hamilton approximation to theory rotation of multilayer celestial bodies we estimate dynamical flattening for different layers for PSR B1828-11. It is known that an innate feature of pulsar radiation is high stability of the time-of-arrival (TOA) of pulses, and therefore the analysis of TOA fluctuations can reflect subtle effects of neutron stars dynamics. TOA variations of pulsars can be interpreted by three reasons: gravitational perturbation of pulsar by planetary bodies, peculiarities of a pulsar interior like Tkachenko oscillations and free precession motion, when axis of rotation do not coincide with vectors of the angular moment of solid crust, liquid outer core and crystal core. The radial velocity of a star is obtained by measuring the magnitude of the Doppler effect in its spectrum. Stars showing a small amplitude variation of the radial velocity can be interpreted as systems having planetary companions. Assuming that the pulsar PSR B1257+12 has a mass of 1:35M¯, the Keplerian orbital radii are 0.9, 1.4 and 2.1 AU and with masses are 3:1M©=sin(i), 10:2M©=sin(i), 4:6M©=sin(i), where i is the orbital inclination [7]. In 2000, Stairs, Lyne and Shemar reported about their discovery of long-term, highly-periodic and correlated variations of pulse shape and the rate of slow-down of the pulsar PSR B182811 with period variations approximately 1000, 500, 250 and 167 days, which may be a result of the spin axis caused by an asymmetry in the shape of the pulsar. The long-periodic precession phenomenon was also detected for a few pulsars: PSR 2217+47, PSR 0531+21, PSR B083345, PSR B182811, PSR B164203 [2,3,6,]. The rotation of the terrestrial planets having rigid mantle, outer liquid and inner solid cores is characterized by Chandler wobble, Inner core wobble, Free Core Nutation, Free Inner Core Nutation. Like the Earth, a neutron star can undergo a free precession [4]. The period of precession is defined by deformation of a pulsar and tension in crust and mantle. If the crust and the core of pulsar have differential rotation then axis of a pulsar rotation will be precess, because axis of deformation will not coincide with axis of rotation. The three-layer model is more complicated than the previous case therefore classical methods fail. Escapa, Getino and Ferrandiz [1] developed a canonical formulation for an three-layer Earth model. We research model of pulsar, which includes three layers (fig. 1): an axis symmetrical rigid mantle, a fluid outer core (FOC) and a solid inner core (SIC). Flattened of the pulsar, it's FOC and SIC are Here A;C;Af ;Cf ;As;Cs;Ac;Cc are moments of inertia of the pulsar, FOC, SIC and total core accordingly; e, ef , ec are the flattening of total pulsar, FOC, core and SIC accordingly. In case rotation of a three-layer neutron star we have variations of next types: the Chandler Wobble (CW) is a motion of the pulsar rotation axis around its dynamical figure due to the bulges of the pulsar (it is the only global rotational mode for completely solid pulsar); the Free Core Nutation (FCN) is a differential rotation of the liquid core relatively the crust rotation; This mode does exist only if the core is liquid; the Free Inner Core Nutation (FICN) is a mode related to the differential rotation of the inner core with respect to the other layers of the pulsar. The mode exists only if the pulsar has two-layer core contains outer liquid and inner solid components; the Inner Core Wobble (ICW) is a differential rotation of the figure axis of the pulsar core with respect to the rotation axis of the pulsar and is due to the flattened of the inner core, having an excess of density with respect to the liquid core. This mode does exist only if there is an ellipsoidal solid inner core inside a liquid core in the pulsar. We propose the explanation for four harmonics of TOA pulses variations as precession of a neutron star owing to differential rotation of crust, outer liquid core and inner crystal core of the pulsar PSR B1828-11. In the frame of the three-layer model we investigate the free rotation of dynamically-symmetrical PSR B1828-11 by Hamilton methods proposed Getino [1]. The model explains generation of four modes in the rotation of the pulsar: two modes of Chandler wobbles (CW, ICW) and two modes connecting with free core nutation (FCN, FICN). The neutron star has rigid the crust, the fluid outer core and the solid inner core. We consider four models of an internal structure of pulsars (tabl. 1) in the frame of three-layer approximation. We are used three models of pulsar (tabl. 1, M1 - M3) for modeling of inner, outer cores flattening and total pulsar. The periods of variations can be described in next way where ± is a small parameter has the analytical expression [6] here Cb f and Ab f are the principal inertia moments corresponding to a spherical layer in the FOC with radius equal to the major semiaxia of the SIC which encloses the solid inner core [1]. The observation of PSR B1828-11 has revealed the existence of four periodic variations TOA pulses. In the frame of the three-layer model we proposed the explanation for all pulse fluctuations by differential rotation crust, outer core and inner core of the neutron star. We received estimations of dynamical flattening of the inner and outer cores for pulsar. We have offered the realistic model of the dynamical pulsar structure and two explanations of the feature of flattened of the crust, the outer core and the inner core of the pulsar. (Kitiashvili and Gusev, 2008) References [1] Escapa, A. et al. (2001), J.Geoph.Res., 106, B6, 11387. [2] Kitiashvili, I. (2004) PhD thesis, Moscow University. [3] Kitiashvili, I.N. and Gusev, A.V. (2008) Astronomy Reports, 52(1), 61. [4] Pines, D. and Shaham J. (1974), Nature, 248, 483. [5] Stairs, I.H. et al. (2000), Nature, 406, 484. [6] Suleymanova, S.A. and Shitov, Y.P. (1994), ApJ.Lett., 422, 17. [7] Wolszczan A. (1997), Celest. & Dyn. Astr., 68, 13.
Gusev Alexander A.
Kitiashvili Irina
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