To maximize the number of planet detections, current microlensing follow-up observations are focusing on high-magnification events which have a higher chance of being perturbed by central caustics. In this paper, we investigate the properties of central caustics and the perturbations induced by them. We derive analytic expressions of the location, size, and shape of the central caustic as a function of the star-planet separation, $s$, and the planet/star mass ratio, $q$, under the planetary perturbative approximation and compare the results with those based on numerical computations. While it has been known that the size of the planetary caustic is \propto \sqrt{q}, we find from this work that the dependence of the size of the central caustic on $q$ is linear, i.e., \propto q, implying that the central caustic shrinks much more rapidly with the decrease of $q$ compared to the planetary caustic. The central-caustic size depends also on the star-planet separation. If the size of the caustic is defined as the separation between the two cusps on the star-planet axis (horizontal width), we find that the dependence of the central-caustic size on the separation is \propto (s+1/s). While the size of the central caustic depends both on $s$ and q, its shape defined as the vertical/horizontal width ratio, R_c, is solely dependent on the planetary separation and we derive an analytic relation between R_c and s. Due to the smaller size of the central caustic combined with much more rapid decrease of its size with the decrease of q, the effect of finite source size on the perturbation induced by the central caustic is much more severe than the effect on the perturbation induced by the planetary caustic. Abridged.Comment: 5 pages, 4 figures, ApJ accepte

Three-filter observations of the hot, detached close binary CW Cephei are used as the basis for light curves dating to the mid-1980s. The ephemeris of apsidal rotation is improved as a result of a lengthier time base. The light-curve synthesis converges to essentially the same orbital and stellar parameters that have been accepted for almost 40 years. For the first time, emphasis is given to a new type of complication confusing the apsidal rotation behavior, and it is shown that this complication is photometric and not dynamical. In addition, we find that the light curve is itself beset by substantial complications, which may be associated with the rather feeble stellar winds.

In this paper, we measure the ellipticities of 30 LSB dI galaxies and compare the ellipticity distribution with that of 80 dEs (Ryden & Terndrup 1994;Ryden et al. 1998) and 62 BCDs (Sung et al. 1998). We find that the ellipticity distribution of LSB dIs is very similar to that of BCDs, and marginally different from that of dEs. We then determine the distribution of intrinsic shapes of dI galaxies and compare to those of other type dwarf galaxies under various assumptions. First, we assume that LSB dIs are either all oblate or all prolate, and use non-parametric analysis to find the best-fitting distribution of intrinsic shapes. With this assumption, we find that the scarcity of nearly circular LSB dIs implies, at the 99% confidence level, that they cannot be a population of randomly oriented oblate or prolate objects. Next, we assume that dIs are triaxial, and use parametric analysis to find permissible distributions of intrinsic shapes. We find that if the intrinsic axis ratios, β and γ, are distributed according to a Gaussian with means β 0 and γ 0 and a common standard deviation of σ, the best-fitting set of parameters for LSB dIs is (β 0 , γ 0 , σ) = (0.66, 0.50, 0.15), and the best fit for BCDs is (β 0 , γ 0 , σ) = (0.66, 0.55, 0.16), while the best fit for dEs is (β 0 , γ 0 , σ) = (0.78, 0.69, 0.24). The dIs and BCDs thus have a very similar shape distribution, given this triaxial hypothesis, while the dEs peak at a somewhat more spherical shape. Our results are consistent with an evolutionary scenario in which the three types of dwarf galaxy have a close relation with each other.

High-resolution optical wavelength spectroscopic data were secured in the optical wavelengths, 3700È 10050 for the planetary nebula IC 5217 with the Hamilton Echelle Spectrograph at Lick Observatory. A , These optical spectra have been analyzed along with the near-UV and UV archive data. Diagnostic analyses indicate a nebular physical condition with electron temperature of about 10,700 K (from the [O III] lines) and the density of cm~1. Ionic concentrations have been derived with the repre-N v \ 5000 sentative diagnostics, and with the aid of a photoionization model construction, we derived the elemental abundances. Contrary to the previous studies found in the literature, He and C appear to be depleted compared to the average planetary nebula and to the Sun (and S marginally so), while the remaining elements appear to be close to the average value. IC 5217 may have evolved from an O-rich progenitor, and the central star temperature of IC 5217 is likely to be 92,000 K.

We present the full VRI light curves and the times of minima of TY UMa to provide a complete photometric solution and a long‐term trend of period variation. The light curves show a high degree of asymmetry (the O'Connell effect). The maxima at 0.25 phase (Max I) are 0.021, 0.015, and 0.020 mag fainter than those at 0.75 phase (Max II) in V, R, and I, respectively. The period of TY UMa has varied in a sinusoidal way, superimposed on the long‐term upward parabolic variation. The secularly increasing rate of the period is deduced as 1.83 s per century (P˙/P=5.788×10‐10 d d‐1). The period of sinusoidal variation is about 57.4 yr. The spot model has been applied to fit the asymmetric light curves of TY UMa, to explain light variations. By changing only the spot parameters, the model light curves can fit the observed light curves for three epochs. This indicates that the variation of the spot location and size is the main reason for changing the shape of light curves, including two different maxima and the interchanging depths of occultation and transit minima.