An improved solution to geometric distortion using an orthogonal method

The geometric distortion of a CCD field of view has a direct influence on the positional measurements of CCD observations. In order to obtain high precision astrometric results, the geometric distortion should be derived and corrected precisely. As presented in our previous work, a convenient solution has been carried out and has also been applied to observations of Phoebe. In order to fur- ther improve the solution, an orthogonal method based on Zernike polynomials is used in this work. Four nights of CCD observations including Himalia, the sixth satellite of Jupiter, and open clusters （NGC 1664 or NGC 2324） on each night have been processed as an application. The observations were obtained from the 2.4 m telescope administered by Yunnan Observatories. The catalog UCAC4 was used to match reference stars in all of the CCD frames. The ephemeris of Himalia is retrieved from the Institut de M6canique C61este et de Calcul des Ephemerides （IMCCE）. Our results show that the means of observed minus calculated （O - C） positional residuals are -0.034 and -0.026 arcsec in right ascension and declination, respectively. The corresponding standard deviations are 0.031＂ and 0.028＂. The measurement dispersion is significantly improved compared to that by using our previous solution.

Timing in the Time Domain: Cygnus X-1

Quantities characterizing temporal property, e.g., power density, coherence, and time lag, can be defined and calculated directly in the time domain without using the Fourier transformation. Spectral hardness, variability duration, and correlation between different characteristic quamtities on different time scale can be studied in the time domain as well. The temporal analysis technique in the time domain is a powerful tool, particularly in studying rapid variability on short time scales (or in high frequencies). Results of studying variabilities of X-rays from Cyg X-1 with the analysis technique in the time domain and RXTE data reveal valuable clues to understanding production and propagation processes of X-rays and structure of accretion disk in the black hole system.

A Periodicity Analysis of the Light Curve of 3C 454.3

We analyzed the radio light curves of 3C 454.3 at frequencies 22 and 37 GHz taken from the database of Metsaeovi Radio Observatory, and found evidence of quasi-periodic activity. The light curves show great activity with very complicated non-sinusoidal variations. Two possible periods, a very weak one of 1.57 ± 0.12 yr and a very strong one of 6.15 ±0.50 yr were consistently identified by two methods, the Jurkevich method and power specmun estimation. The period of 6.15 ± 0.50 yr is consistent with results previously reported by Ciaramella et al. and Webb et al. Applying the binary black hole model to the central structure we found black hole masses of 1.53 × 10^9M⊙ and 1.86 × 10^8M⊙, and predicted that the next radio outburst is to take place in 2006 March and April.

Radio Phase-Resolved Spectra of the Conal-Double Pulsar B1133+16

Based on dividing the profile into a number of absolute phase intervals, the phaseresolved spectra （PHRS） are derived from published time-aligned average profiles at radio frequencies over two decades for the classic conal-double pulsar B1133＋16. The relative spectral index, defined as the difference between the spectral indices of a reference and the given arbitrary phase interval, is obtained by power-law fit at each phase interval. The derived phase-resolved spectra show an ＂M-like＂ shape, of which the leading part and trailing part are approximately symmetrical. The basic feature of the PHRS is that the spectrum first flattens then steepens as the pulse phase sweeps from the profile center to the profile edges. The PHRS provide a coherent explanation of the major features of profile evolution of B 1133＋ 16, namely, the pulse width shrinkage with increasing frequency and the frequency evolution of the relative intensity between the leading and trailing conal components, and the bridge emission. The PHRS may be an indicator for emission spectral variation across the pulsar magnetosphere. Possible mapping from PHRS to emission-location-dependent spectral variation is presented, and some intrinsic mechanisms are discussed.

Preliminary results of CCD observations targeting Himalia acquired at Yunnan Observatories in 2015

In order to study the potential associated with high precision CCD astrometry of irregular satel- lites, we have acquired experimental observations of Himalia, the sixth and irregular satellite of Jupiter. A total of 185 CCD observations were obtained by using the 2.4m and 1 m telescopes administered by Yunnan Observatories over ten nights. Preliminary analysis of the observations were made, including geo- metric distortion, atmospheric refraction, and also the phase effect. All positions of Himalia are measured relative to the reference stars from the catalog UCAC4 in each CCD field of view. The theoretical positions of Himalia were retrieved from the Institute de M6chanique C61este et de Calcul des t^ph6m6rides, while the positions of Jupiter were obtained based on the planetary ephemeris INPOP13c. The results show that the means of observed minus computed （O - C） residuals are -0.004＂ and -0.002＂ in right ascension and declination, respectively. The standard deviations of （O - C） residuals are estimated to be about 0.04＂ in each direction.

Z Draconis with two companions in a 2:1 mean-motion resonance

All available mid-eclipse times of the eclipsing binary Z Draconis are analyzed, and three sets of cyclic variations with periods of 20.1, 29.96 and 59.88 yr are found. The low-amplitude variations with a period of 20.1 yr may be attributed to the unavoidable slight imperfection in the double-Keplerian model, which gives periods of 29.96 and 59.88 yr. Interestingly, the Z Draconis system is close to a 2：1 mean- motion resonance, or a 6：3：2 mean-motion resonance if the 20.1 yr period really exists. We also find that the best solutions tend to give the minimum eccentricities. Based on Kepler＇s third law, the outermost companion has a minimum mass of - 0.77 Mo, whereas the middle companion is an M dwarf star with a mass of - 0.40 MG, suggesting that Z Draconis is a general N-body system.

Confirming the 115.5-day periodicity in the X-ray light curve of ULX NGC 5408 X-1

The Swift/XRT light curve of the ultraluminous X-ray source NGC 5408 X-1 was re-analyzed with two new numerical approaches, the Weighted Wavelet Ztransform and CLEANest, and the results are different from previous studies. Both techniques detected a prominent periodicity with a time scale of 115.5 ± 1.5 days, in excellent agreement with the detection of the same periodicity first reported by Strohmayer . Monte Carlo simulations were employed to test the statisitical confidence of the 115.5-day periodicity, yielding a statistical significance of 〉 99.98% （or 〉 3.8σ）. The robust detection of the 115.5-day quasi-periodic oscillations, if they are due to the orbital motion of the binary, would infer a mass of a few thousand M⊙ for the central black hole, implying there is an intermediate-mass black hole in NGC 5408 X-1.

The silicate and carbon-rich models of CoRoT-7b,Kepler-9d and Kepler-10b

Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are deduced using a suitable equation of state for the materials. The degeneracy problems of their compo- sitions can be partly overcome, based on the fact that all three planets are extremely close to their host stars. By analyzing the numerical results, we conclude： 1） the iron core of CoRoT-7b is not more than 27% of its total mass within lc~ mass-radius error bars, so an Earth-like composition is less likely, but its carbon rich model can be com- patible with an Earth-like core/mantle mass fraction; 2） Kepler-10b is more likely to have a Mercury-like composition, with its old age implying that its high iron content may be a result of strong solar wind or giant impact; 3） the transiting-only super-Earth Kepler-9d is also discussed. Combining its possible composition with the formation theory, we can place some constraints on its mass and bulk composition.

Measuring the Distance of VX Sagittarii with SiO Maser Proper Motions

We report on 43 GHz v=1, J=1-0 SiO maser proper motions in the circumstellar envelope of the M-type semi-regular variable star VX Sgr, observed by Very Long Baseline Array （VLBA） at 3 epochs during 1999 April-May. Applying the statistical parallax analysis to these proper motions, we estimated a distance of VX Sgr of 1.57±0.27kpc, which is consistent with that based on the proper motions of H20 masers, or on the assumption that VX Sgr belongs to the Sgr OB1 association. At this distance, VX Sgr can be classified as a red supergiant. Comparing the statistical parallax method with those of model fitting and annual parallax, we think that the statistical parallax method may be a good way of estimating SiO maser distances at present.

Autoregressive Spectral Estimation for Quasi-Periodic Oscillations

Modern methods of spectral estimation based on parametric time-series models are useful tools in power spectral analysis. We apply the autoregressive （AR） model to study quasi-periodic oscillations （QPOs）. An empirical formula to estimate the expectation and standard deviation of the noise AR power densities is derived, which can be used to estimate the statistical significance of an apparent QPO peak in an AR spectrum. An iterative adding-noise algorithm in AR spectral analysis is proposed and applied to studying QPOs in the X-ray binary Cir X-1.

R-band host galaxy contamination of TeV γ-ray blazar Mrk 501： effects of aperture size and seeing

We simulated the R-band contribution of the host galaxy of TeV γ-ray BL Lac object Mrk 501 in different aperture sizes and seeing conditions. An intensive set of observations was acquired with the 1.02m optical telescope, managed by Yunnan Observatories, from 2010 May 15 to 18. Based on the host subtraction data usually used in the literature, the subtraction of host galaxy contamination results in significant seeing-brightness correlations. These correlations would lead to illusive large amplitude variations at short timescales, which will mask the intrinsic microvariability, thus giving rise to difficulty in detecting the intrinsic microvariability. Both aperture size and seeing condition influence the flux measurements, but the aperture size impacts the result more significantly. Based on the parameters of an elliptical galaxy provided in the literature, we simulated the host contributions of Mrk 501 in different aperture sizes and seeing conditions. Our simulation data of the host galaxy obviously weaken these significant seeing-brightness correlations for the host-subtracted brightness of Mrk 501, and can help us discover the intrinsic short timescale microvariability. The pure nuclear flux is -8.0 mJy in the R band, i.e., the AGN has a magnitude of R - 13.96 mag.

Individual and combination approaches to forecasting hierarchical time series with correlated data:an empirical study

Hierarchical time series arise in manufacturing and service industries when the products or services have the hierarchical structure,and top-down and bottomup methods are commonly used to forecast the hierarchical time series.One of the critical factors that affect the performance of the two methods is the correlation between the data series.This study attempts to resolve the problem and shows that the top-down method performs better when data have high positive correlation compared to high negative correlation and combination of forecasting methods may be the best solution when there is no evidence of the correlationship.We conduct the computational experiments using 240 monthly data series from the‘Industrial’category of the M3-Competition and test twelve combination methods for the hierarchical data series.The results show that the regression-based,VAR-COV and the Rank-based methods perform better compared to the other methods.