Orbital Decay of the PSR J0045-7319/B Star Binary System: Age of Radio Pulsar and Initial Spin of Neutron Star

Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of |\Porb/\dot\Porb|=0.5 Myr, shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi et al.~1996a). We study mechanisms for the orbital decay. The standard weak friction theory based on static tide requires far too short a viscous time to explain the observed \dot\Porb. We show that dynamical tidal excitation of g-modes in the B star can be responsible for the orbital decay. However, to explain the observed short decay timescale, the B star must have some significant retrograde rotation with respect to the orbit --- The retrograde rotation brings lower-order g-modes, which couple much more strongly to the tidal potential, into closer ``resonances'' with the orbital motion, thus significantly enhancing the dynamical tide. A much less likely possibility is that the g-mode damping time is much shorter than the ordinary radiative damping time. The observed orbital decay timescale combined with a generic orbital evolution model based on dynamical tide can be used as a ``timer'', giving an upper limit of $1.4$ Myr for the age of the binary system since the neutron star formation. Thus the characteristic age of the pulsar is not a good age indicator. Assuming standard magnetic dipole braking for the pulsar and no significant magnetic field decay on a timescale \lo 1 Myr, the upper limit for the age implies that the initial spin of the neutron star at birth was close to its current value.Comment: AASTeX, 9 pages, 3 ps figures. ApJ Letters, in pres

Dipolar modes in luminous red giants

Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Helioseismology and the solar age

The problem of measuring the solar age by means of helioseismology hasbeen recently revisited by Guenther & Demarque (1997) and by Weiss & Schlattl (1998). Different best values for $t_{\rm seis}$ and different assessment of the uncertainty resulted from these two works. We show that depending on the way seismic data are used, one may obtain the value $t_{\rm seis}\approx 4.6$ Gy, close to the age of the oldest meteorites, $t_{\rm met}=4.57$ Gy, like in the first paper, or above 5 Gy like in the second paper. The discrepancy in the seismic estimates of the solar age may be eliminated by assuming higher than the standard metal abundance and/or an upward revision of the opacities in the solar radiative interior.We argue that the most accurate and robust seismic measure of the solar age are the small frequency separations, $D_{\ell,n}=\nu_{l,n}-\nu_{\ell+1,n-1}$, for spherical harmonic degrees $\ell=0,2$ and radial orders $n\gg\ell$.The seismic age inferred by minimization of the sum of squared differences between the model and the solar small separations is $t_{\rm seis}=4.66\pm0.11$, a number consistent with meteoritic data.Our analysis supports earlier suggestions of using small frequency separations as stellar age indicators.Comment: 8 pages + 4 ps figures included, LaTeX file with l-aa.sty, submitted to Astronomy and Astrophysic