Photometric investigation and orbital period analyses of the W UMa binaries FP Lyn, FV CVn and V354 UMa

New light curves and photometric solutions of FP Lyn,FV CVn and V354 UMa are presented.We found that these three systems are W-subtype shallow contact binaries.In addition,it is obvious that the light curves of FP Lyn and V354 UMa are asymmetric.Therefore,a hot spot was added on the primary star of FP Lyn and a dark spot was added on the secondary star of V354 UMa.At the same time,we added a third light to the photometric solution of FP Lyn for the final result.The obtained mass ratios and fill-out factors are q = 1.153 and f = 13.4% for FP Lyn,q = 1.075 and f = 4.6% for FV CVn,and q = 3.623 and f = 10.7% for V354 UMa respectively.The investigations of orbital period for these three systems indicate that the periods are variable.FP Lyn and V354 UMa were discovered to have secularly increasing components with rates of dp/dt = 4.19 ×10^-7 dyr^-1 and dp/dt = 7.70 ×10^-7 dyr^-1 respectively,which are feasibly caused by conservative mass transfer from the less massive component to the more massive component.In addition,some variable components were discovered for FV CVn,including a rate of dp/dt =-1.13 ×10^-6 dyr^-1 accompanied by a cyclic oscillation with amplitude and period of 0.0069 d and 10.65 yr respectively.The most likely explanation for the long-term decrease is angular momentum loss.The existence of an additional star is the most plausible explanation for the periodic variation.

Photometric and Spectroscopic Studies for Two Magnetic-activity Contact Binaries:V724 And and QR Com

We presented new CCD photometry for two contact binaries,V724 And and QR Com,which were observed during the 2020–2022 observing seasons.By using the Wilson–Devinney method,the photometric solutions were deduced from new observed data and TESS ones.Their asymmetric light curves were modeled by a dark spot on the more massive component.Results indicate that the starspot may immigrate or disappear on the surface of the active component.From the TESS observations of QR Com,it is discovered that the difference between light maxima exhibits a 29.5 day oscillation,which implies the continuous evolution of spot feathers on the timescale of several weeks.Their mass ratio and fill-out factor are q=2.308 and f=11.55% for V724 And,and q=0.624 and f=12.77% for QR Com,respectively.From the(O-C)curve,the orbital period secularly decrease at a rate of d P/dt=-1.66×10^(-7)day yr^(-1)for V724 And and d P/dt=-3.98×10^(-7)day yr^(-1)for QR Com,which was interpreted by mass transfer from the more massive component to the less massive one.With period decreasing,this kind of shallow-contact binaries,V724 And and QR Com,will evolve into the deep-contact configurations.

Gravitational Lensing by Spherical Lenses

In this work we introduced a new proposal to study the gravitational lensing theory by spherical lenses, starting from its surface mass density ∑(x) written in terms of a decreasing function f of a dimensionless coordinate x on the lens plane. The main result is the use of the function f(x) to find directly the lens properties, at the same time that the lens problem is described by a first order differential equation which encodes all information about the lens. SIS and NIS profiles are used as examples to find their functions f(x). Using the Poisson equation we find that the deflection angle is directly proportional to f(x), and therefore the lens equation can be written in terms of the function and the parameters of the lens. The critical and caustic curves, as well as image formation and magnification generated by the lens are analyzed. As an example of this method, the properties of a lens modeled by a NFW profile are determined. Although the puntual mass is spherically symmetric, its mass density is not continuous so that its f(x) function is discussed in Appendix 1.