Over the last several years , we have embarked on a long term effort to exploit the strong potential that hot B subdwarf ( sdB ) pulsators have to offer in terms of asteroseismology .
This effort is multifaceted as it involves , on the observational front , the acquisition of high sensitivity photometric data supplemented by accurate spectroscopic measurements , and , on the theoretical and modeling fronts , the development of appropriate numerical tools dedicated to the asteroseismological interpretation of the seismic observations .
In this paper , we report on the observations and thorough analysis of the rapidly pulsating sdB star ( or EC14026 star ) PG~1219+534 .
Our model atmosphere analysis of the time averaged optical spectrum of PG~1219+534 obtained at the new Multiple Mirror Telescope ( MMT ) leads to estimates of T _ { { eff } } = 33,600 \pm 370 K and \log g = 5.810 \pm 0.046 ( with \log N ( { He } ) / N ( { H } ) = -1.49 \pm 0.08 ) , in good agreement with previous spectroscopic measurements of its atmospheric parameters .
This places PG~1219+534 right in the middle of the EC14026 instability region in the \log g - T _ { { eff } } plane .
A standard Fourier analysis of our high signal-to-noise ratio Canada-France-Hawaii Telescope ( CFHT ) light curves reveals the presence of nine distinct harmonic oscillations with periods in the range 122 - 172 s , a significant improvement over the original detection of only four periods by .
On this basis , we have carried out a detailed asteroseismic analysis of PG~1219+534 using the well-known forward method and assuming that the observed modes have \ell \leq 3 .
Our analysis leads objectively to the identification of the ( k , \ell ) indices of the nine periods observed in the star PG~1219+534 , and to the determination of its structural parameters .
The periods all correspond to low-order acoustic modes with adjacent values of k and with \ell = 0 , 1 , 2 , and 3 .
They define a band of unstable modes , in close agreement with nonadiabatic pulsation theory .
Furthermore , the average dispersion between the nine observed periods and the periods of the corresponding nine theoretical modes of the optimal model is only \sim 0.6 % , comparable to the results of a similar analysis carried out by on the rapid sdB pulsator PG 0014+067 .
On the basis of our combined spectroscopic and asteroseismic analysis , the inferred global structural parameters of PG~1219+534 are T _ { { eff } } = 33,600 \pm 370 K , \log g = 5.8071 \pm 0.0057 , \log M _ { { env } } / M _ { * } = -4.254 \pm 0.147 , M _ { * } = 0.457 \pm 0.012 M _ { \odot } , R / R _ { \odot } = 0.1397 \pm 0.0028 , and L / L _ { \odot } = 22.01 \pm 1.85 .
Combined with detailed model atmosphere calculations , we estimate , in addition , that this star has an absolute visual magnitude M _ { V } = 4.62 \pm 0.06 and is located at a distance d = 531 \pm 23 pc ( using V = 13.24 \pm 0.20 ) .
Finally , if we interpret the absence of fine structure ( frequency multiplets ) as indicative of a slow rotation rate of that star , we further find that PG~1219+534 rotates with a period longer than 3.4 days , and has a maximum rotational broadening velocity of V \sin i \lesssim 2.1 km.s ^ { -1 } .