The benefits of the orthogonal LSM models

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The most popular method of data treatment remains for many decades Linear Regression (LR) based on the principles of Least Squares Method (LSM) or linearized LSM. Unfortunately, we have to state that the method of linear regression is not as a rule used accordingly namely in the evaluation of uncertainties of the LR parameters and estimates of the uncertainty of the LR predictions. We present the matrix version of basic relations of LR and the true estimate of the uncertainty of the LR predictions. We define properties of the orthogonal LR models and show how to transform general LR models into orthogonal ones. We give relations for orthogonal models for common polynomial series.Comment: 5 pages, 2 figures, submitted to Odessa Astronomical Publications, vol. 20, 200

Visual and ultraviolet flux variability of the bright CP star θ\theta Aur

Chemically peculiar stars of the upper part of the main sequence show periodical variability in line intensities and continua, modulated by the stellar rotation, which is attributed to the existence of chemical spots on the surface of these stars. The flux variability is caused by the changing redistribution rate of the radiative flux predominantly from the short-wavelength part of the spectra to the long-wavelength part, which is a result of abundance anomalies. We study the nature of the multi-spectral variability of one of the brightest chemically peculiar stars, $\theta$ Aur. We predict the flux variability of $\theta$ Aur from the emerging intensities calculated for individual surface elements of the star taking into account horizontal variation of chemical composition derived from Doppler abundance maps. The simulated optical variability in the Str\"omgren photometric system and the ultraviolet flux variability agree well with observations. The IUE flux distribution is reproduced in great detail by our models. The resonance lines of magnesium and possibly also some lines of silicon are relatively weak in the ultraviolet domain, which indicates non-negligible vertical abundance gradients in the atmosphere. We also derive a new period of the star, $P=3.618\,664(10)$ d, from all available photometric and magnetic measurements and show that the observed rotational period is constant over decades. The ultraviolet and visual variability of $\theta$ Aur is mostly caused by silicon bound-free absorption and chromium and iron line absorption. These elements redistribute the flux mainly from the far-ultraviolet region to the near-ultraviolet and optical regions in the surface abundance spots. The light variability is modulated by the stellar rotation. The ultraviolet domain is key for understanding the properties of chemically peculiar stars. (abridged)Comment: 12 pages, accepted for publication in Astronomy & Astrophysic

Study of Eclipsing Binary and Multiple Systems in OB Associations: I. Ori OB1a - IM Mon

All available photometric and spectroscopic observations were collected and used as the basis of a detailed analysis of the close binary IM Mon. The orbital period of the binary was refined to 1.19024249(0.00000014) days. The Roche equipotentials, fractional luminosities (in (B, V) and H_p bands) and fractional radii for the component stars in addition to mass ratio q, inclination i of the orbit and the effective temperature T_eff of the secondary cooler less massive component were obtained by the analysis of light curves. IM Mon is classified to be a detached binary system in contrast to the contact configuration estimations in the literature. The absolute parameters of IM Mon were derived by the simultaneous solutions of light and radial velocity curves as M_1,2=5.50(0.24)M_o and 3.32(0.16)M_o, R1,2=3.15(0.04)R_o and 2.36(0.03)R_o, T_eff1,2=17500(350) K and 14500(550) K implying spectral types of B4 and B6.5 ZAMS stars for the primary and secondary components respectively. The modelling of the high resolution spectrum revealed the rotational velocities of the component stars as V_rot1=147(15) km/s and V_rot2=90(25) km/s. The photometric distance of 353(59) pc was found more precise and reliable than Hipparcos distance of 341(85) pc. An evolutionary age of 11.5(1.5) Myr was obtained for IM Mon. Kinematical and dynamical analysis support the membership of the young thin-disk population system IM Mon to the Ori OB1a association dynamically. Finally, we derived the distance, age and metallicity information of Ori OB1a sub-group using the information of IM Mon parameters.Comment: 26 pages, 5 figures and 6 tables, accepted for publication in Publication of the Astronomical Society of Japa

Transient jets in the symbiotic prototype Z Andromedae

We present development of the collimated bipolar jets from the symbiotic prototype Z And that appeared and disappeared during its 2006 outburst. In 2006 July Z And reached its historical maximum at U ~ 8.0. During this period, rapid photometric variations with Dm ~ 0.06 mag on the timescale of hours developed. Simultaneously, high-velocity satellite components appeared on both sides of the H-alpha and H-beta emission line profiles. They were launched asymmetrically with the red/blue velocity ratio of 1.2 - 1.3. From about mid-August they became symmetric. Their spectral properties indicated ejection of bipolar jets collimated within an average opening angle of 6.1 degrees. We estimated average outflow rate via jets to dM(jet)/dt ~ 2xE10-6(R(jet)/1AU)**(1/2) M(Sun)/year, during their August - September maximum, which corresponds to the emitting mass in jets, M(jet, emitting) ~ 6xE-10(Rjet)/1AU)^{3/2} M(Sun). During their lifetime, the jets released the total mass of M(jet, total) approx 7.4x1E-7 M(Sun). Evolution in the rapid photometric variability and asymmetric ejection of jets around the optical maximum can be explained by a disruption of the inner parts of the disk caused by radiation-induced warping of the disk.Comment: 31 pages, 9 figures, 2 tables, accepted for Ap

Study of Eclipsing Binary and Multiple Systems in OB Associations II. The Cygnus OB Region: V443 Cyg, V456 Cyg and V2107 Cyg

Three presumably young eclipsing binary systems in the direction of the Cygnus OB1, OB3 and OB9 associations are studied. Component spectra are reconstructed and their orbits are determined using light curves and spectra disentangling techniques. V443 Cyg and V456 Cyg have circular orbits, while the light curve of V2107\,Cyg imposes a slightly eccentric orbit ($e=0.045\pm0.03)$. V443 Cyg harbours F-type stars, and not young early-A stars as previously suggested in the literature based on photometry solely. It appears to be situated in the foreground (distance $0.6\pm0.2$ kpc) of the young stellar populations in Cygnus. V456 Cyg, at a distance of $0.50\pm0.03$ kpc consists of a slightly metal-weak A--type and an early--F star. The age of both systems, on or very near to the main sequence, remains uncertain by an order of magnitude. V2107 Cyg is a more massive system ($8.9\pm2$ and $4.5\pm1.2 M_\odot$) at $1.5\pm0.5$ kpc and, also kinematically, a strong candidate-member of Cyg OB1. The more massive component is slightly evolved and appears to undergo non-radial $\beta Cep$-type pulsations. The Doppler signal of the secondary is barely detectable. A more extensive study is important to fix masses more precisely, and an asteroseismological study would then become appropriate. Nevertheless, the position of the primary in the HR-diagram confines the age already reasonably well to $20\pm5$ Myr, indicating for Cyg OB1 a similar extent of star formation history as established for Cyg OB2.Comment: 27 pages, including 9 figures and 6 tables, accepted for publication in Astronomical Journa

Revisiting the Rigidly Rotating Magnetosphere model for σ\sigma Ori E - II. Magnetic Doppler imaging, arbitrary field RRM, and light variability

The initial success of the Rigidly Rotating Magnetosphere (RRM) model application to the B2Vp star sigma OriE by Townsend, Owocki & Groote (2005) triggered a renewed era of observational monitoring of this archetypal object. We utilize high-resolution spectropolarimetry and the magnetic Doppler imaging (MDI) technique to simultaneously determine the magnetic configuration, which is predominately dipolar, with a polar strength Bd = 7.3-7.8 kG and a smaller non-axisymmetric quadrupolar contribution, as well as the surface distribution of abundance of He, Fe, C, and Si. We describe a revised RRM model that now accepts an arbitrary surface magnetic field configuration, with the field topology from the MDI models used as input. The resulting synthetic Ha emission and broadband photometric observations generally agree with observations, however, several features are poorly fit. To explore the possibility of a photospheric contribution to the observed photometric variability, the MDI abundance maps were used to compute a synthetic photospheric light curve to determine the effect of the surface inhomogeneities. Including the computed photospheric brightness modulation fails to improve the agreement between the observed and computed photometry. We conclude that the discrepancies cannot be explained as an effect of inhomogeneous surface abundance. Analysis of the UV light variability shows good agreement between observed variability and computed light curves, supporting the accuracy of the photospheric light variation calculation. We thus conclude that significant additional physics is necessary for the RRM model to acceptably reproduce observations of not only sigma Ori E, but also other similar stars with significant stellar wind-magnetic field interactions.Comment: 16 pages, 17 figures, accepted for publication in MNRA

Understanding the rotational variability of K2 targets. HgMn star KIC 250152017 and blue horizontal branch star KIC 249660366

Ultraprecise space photometry enables us to reveal light variability even in stars that were previously deemed constant. A large group of such stars show variations that may be rotationally modulated. This type of light variability is of special interest because it provides precise estimates of rotational rates. We aim to understand the origin of the light variability of K2 targets that show signatures of rotational modulation. We used phase-resolved medium-resolution XSHOOTER spectroscopy to understand the light variability of the stars KIC~250152017 and KIC~249660366, which are possibly rotationally modulated. We determined the atmospheric parameters at individual phases and tested the presence of the rotational modulation in the spectra. KIC 250152017 is a HgMn star, whose light variability is caused by the inhomogeneous surface distribution of manganese and iron. It is only the second HgMn star whose light variability is well understood. KIC 249660366 is a He-weak, high-velocity horizontal branch star with overabundances of silicon and argon. The light variability of this star is likely caused by a reflection effect in this post-common envelope binary.Comment: 8 pages, accepted for publication in Astronomy & Astrophysic