Gnomon shadow lengths recorded in the Zhoubi Suanjing： the earliest meridian observations in China？

The Zhoubi Suanjing, one of the most important ancient Chinese books on mathematical astronomy, was compiled about 100 BC in the Western Han dynasty （BC 206 - AD 23）. We study the gnomon shadow lengths for the 24 solar terms as recorded in the book. Special attention is paid to the so-called law of ‘cun qian li’, which says the shadow length of a gnomon of 8 chi （about 1.96 m） high will increase （or decrease） 1 cun （1/10chi） for every 10001i （roughly 400kin） the gnomon moves northward （or south- ward）. From these data, one can derive the time and location of the observations. The resuits, however, do not fit historical facts. We suggest that compilers of the Zhoubi Suanjing must have modified the original data according to the law of ‘cun qian li’. Through reversing the situation, we recovered the original data, our analysis of which reveals the best possible observation time as 564 BC and the location of observation as 35.78° N latitude. We conclude that this must be the earliest records of solar meridian observations in China. In the meantime, we give the errors of solar altitudes for the 24 solar terms. The average deviation is 5.22°, and the mean absolute deviation is 5.52°, signifying the accuracy of astronomical calculations from that time.     

A 96-antenna radioheliograph

Here we briefly present some design approaches for a multifrequency 96-antenna radioheliograph. The configuration of the array antenna, transmission lines and digital receivers is the main focus of this work. The radioheliograph is a T-shaped centrally condensed radiointerferometer operating in the frequency range 4–8 GHz.The justification for the choice of such a configuration is discussed. The signals from antennas are transmitted to a workroom by analog optical links. The dynamic range and phase errors of the microwave-over-optical signal are considered. The signals after downconverting are processed by digital receivers for delay tracking and fringe stopping. The required step of delay tracking and data rates are considered. Two 3-bit data streams(I and Q) are transmitted to a correlator with the transceivers embedded in Field Programmed Gate Array chips and with PCI Express cables.     

Analysis of interval constants in calendars affiliated with the Shoushili

We study interval constants that are related to motions of the Sun and Moon,i.e., the Qi, Intercalation, Revolution and Crossing interval, in calendars affiliated with the Shoushi calendar(Shoushili), such as Datongli and Chiljeongsannaepyeon. It is known that these interval constants were newly introduced in the Shoushili calendar and revised afterward, except for the Qi interval constant, and the revised values were adopted in later calendars affiliated with the Shoushili. We first investigate the accuracy of these interval constants and then the accuracy of calendars affiliated with the Shoushili in terms of these constants by comparing times for the new moon and the maximum solar eclipse calculated by each calendar with modern methods of calculation. During our study, we found that the Qi and Intercalation interval constants used in the early Shoushili were well determined, whereas the Revolution and Crossing interval constants were relatively poorly measured. We also found that the interval constants used by the early Shoushili were better than those of the later one, and hence better than those of Datongli and Chiljeongsannaepyeon. On the other hand, we found that the early Shoushili is, in general, a worse calendar than Datongli for use in China but a better one than Chiljeongsannaepyeon for use in Korea in terms of times for the new moon and when a solar eclipse occurs, at least for the period 1281 – 1644.Finally, we verified that the times for sunrise and sunset in the Shoushili-Li-Cheng and Mingshi are those at Beijing and Nanjing, respectively.     

A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis ＊

A new calibration model of a radio telescope that includes pointing error is presented, which considers nonlinear errors in the azimuth axis. For a large radio telescope, in particular for a telescope with a turntable, it is difficult to correct pointing errors using a traditional linear calibration model, because errors produced by the wheel-on-rail or center bearing structures are generally nonlinear. Fourier expansion is made for the oblique error and parameters describing the inclination direction along the azimuth axis based on the linear calibration model, and a new calibration model for pointing is derived. The new pointing model is applied to the 40 m radio telescope administered by Yunnan Observatories, which is a telescope that uses a turntable. The results show that this model can significantly reduce the residual systematic errors due to nonlinearity in the azimuth axis compared with the linear model.     

New upper limit on the cosmological constant from solar system dynamics

The cosmological constantΛis the simplest model for explaining the dark energy which supposedly drives the observed accelerated expansion rate of the Universe.Together with the concept of cold dark matter,it satisfactorily accommodates a wealth of observations related to cosmology.Due to its assumed constancy throughout the Universe,Λmight also affect the dynamics of the planets in the solar system,although with extremely small effects.However,modern high-precision ephemerides provide a promising tool for constraining it.Using the supplementary advances in the perihelia provided by current INPOP10a and EPM2011 ephemerides,we obtain a new upper limit onΛin the solar system when the Lense-Thirring effect due to the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment are properly taken into account.These two factors were mostly absent in previous works dealing withΛ.We find that INPOP10a yields an upper limit ofΛ=(0.26±1.45)×10-43m-2and EPM2011 givesΛ=(-0.44±8.93)×10-43m-2.Such bounds are about 10 times less than previously estimated results.     

New upper limits on deviation from the inverse-square law of gravity in the solar system： a Yukawa parameterization

New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and A is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun＇s quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α =- 3.1× 10-11 and λ= 0.15 au, and EPM2011 gives α = 5.2 × 10-11 and λ=- 0.21 au. In both of them, α is at least 10 times less than the previous results.     

Relativistic transformation between y and TCG for Mars missions under IAU Resolutions

Considering the fact that the general theory of relativity has become an in- extricable part of deep space missions, we investigate the relativistic transformation between the proper time of an onboard clock τ and the Geocentric Coordinate Time （TCG） for Mars missions. By connecting τ with this local timescale associated with the Earth, we extend previous works which focus on the transformation between τ and the Barycentric Coordinate Time （TCB）. （TCB is the global coordinate time for the whole solar system.） For practical convenience, the relation between τ and TCG is recast to directly depend on quantities which can be read from ephemerides. We find that the difference between τ and TCG can reach the level of about 0.2 seconds in a year. To distinguish various sources in the transformation, we numerically calculate the contributions caused by the Sun, eight planets, three large asteroids and the space- craft. It is found that if the threshold of 1 microsecond is adopted, this transformation must include effects due to the Sun, Venus, the Moon, Mars, Jupiter, Saturn and the velocities of the spacecraft and Earth.     

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

The attitude dynamics of a rigid artificial satellite subject to a gravity gradient and Lorentz torques in a circular orbit are considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite's surface. We assume that the satellite is moving in a Low Earth Orbit in the geomagnetic field, which is considered to be a dipole. Our model of torque due to the Lorentz force is developed for an artificial satellite with a general shape, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and conditions for their existence are obtained.The numerical results show that the charge q and radius ρ0of the center of charge for the satellite provide a certain type of semi-passive control for the attitude of the satellite. The technique for this kind of control would be to increase or decrease the electrostatic screening on the satellite. The results obtained confirm that the change in charge can affect the magnitude of the Lorentz torque, which can also affect control of the satellite. Moreover, the relationship between magnitude of the Lorentz torque and inclination of the orbit is investigated.     

Electromagnetic effects on the orbital motion of a charged spacecraft

This paper deals with the effects of electromagnetic forces on the orbital motion of a spacecraft.The electrostatic charge which a spacecraft generates on its surface in the Earth’s magnetic field will be subject to a perturbative Lorentz force.A model incorporating all Lorentz forces as a function of orbital elements has been developed on the basis of magnetic and electric fields.This Lorentz force can be used to modify or perturb the spacecraft’s orbits.Lagrange’s planetary equations in the Gauss variational form are derived using the Lorentz force as a perturbation to a Keplerian orbit.Our approach incorporates orbital inclination and the true anomaly.The numerical results of Lagrange’s planetary equations for some operational satellites show that the perturbation in the orbital elements of the spacecraft is a second order perturbation for a certain value of charge.The effect of the Lorentz force due to its magnetic component is three times that of the Lorentz force due to its electric component.In addition,the numerical results confirm that the strong effects are due to the Lorentz force in a polar orbit,which is consistent with realistic physical phenomena that occur in polar orbits.The results confirm that the magnitude of the Lorentz force depends on the amount of charge.This means that we can use artificial charging to create a force to control the attitude and orbital motion of a spacecraft.     

Ionization state of cosmic hydrogen by early stars and quasars

Cosmic hydrogen is reionized and maintained in its highly ionized state by the ultraviolet emission attributed to an early generation of stars and quasars. The Lyα opacity observed in absorption spectra of high-redshift quasars permits more stringent constraints on the ionization state of cosmic hydrogen. Based on density perturbation and structure formation theory, we develop an analytic model to trace the evolution of the ionization state in the post-overlap epoch of reionization, in which the bias factor is taken into account. For quasars, we represent an improved luminosity function by utilizing a hybrid approach for the halo formation rate that is in reasonable agreement with the published measurements at 2 ≤ z ≤ 6. Comparison with the classic Press-Schechter mass function of dark matter halos, we demonstrate that the biased mass distribution indeed enhances star formation efficiency in the overdense environment by more than 25 per cent following the overlap of ionized bubbles. In addition, an alternative way is introduced to derive robust estimates of the mean free path for ionizing photons. In our model, star-forming galaxies are likely to dominate the ionizing background radiation beyond z = 3, and quasars contribute equally above a redshift of z ～ 2.5. From 5 ≤ z ≤ 6, the lack of evolution in photoionization rate can thus be explained by the relatively flat evolution in star formation efficiency, although the mean free path of ionizing photons increases rapidly. Moreover, in the redshift interval z ～ 2 - 6, the expected mean free path and Gunn-Peterson optical depth obviously evolve by a factor of ～ 500 and ～50 respectively. We find that the relative values of critical overdensities for hydrogen ionization and collapse could be 430% at z ≈2 and 2% at z ≈6, suggesting a rapid overlap process in the overdense regions around instant quasars following reionization. We further illustrate that the absolute estimates of the fraction of neutral hydrogen computed from theoretical models may n     

Relations between stellar mass and electron temperature-based metallicity for star-forming galaxies in a wide mass range

We select 947 star-forming galaxies from SDSS-DR7 with [O III]λ4363emission lines detected at a signal-to-noise ratio larger than 5σ. Their electron temperatures and direct oxygen abundances are then determined. We compare the results from different methods. t2, the electron temperature in the low ionization region, estimated from t3, that in the high ionization region, is compared using three analysis relations between t2- t3. These show obvious differences, which result in some different ionic oxygen abundances. The results of t3, t2, O++/H+and O+/H+derived by using methods from IRAF and literature are also compared. The ionic abundances O++/H+are higher than O+/H+for most cases. The different oxygen abundances derived from Teand the strong-line ratios show a clear discrepancy, which is more obvious following increasing stellar mass and strong-line ratio R23. The sample of galaxies from SDSS with detected [O III]λ4363 have lower metallicites and higher star formation rates, so they may not be typical representatives of the whole population of galaxies. Adopting data objects from Andrews Martini, Liang et al. and Lee et al. data, we derive new relations of stellar mass and metallicity for star-forming galaxies in a much wider stellar mass range: from 106 M to 1011 M.     

The dynamical architecture and habitable zones of the quintuplet planetary system 55 Cancri

We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.     

Astrometric calibration of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anti-center （XSTPS-GAC）

We present astrometric calibration of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anti-center(XSTPS-GAC). XSTPS-GAC is the photometric part of the Digital Sky Survey of the Galactic Anti-center(DSS-GAC),which is a photometric and spectroscopic sky survey, in combination with LAMOST.In order to select an astrometric reference catalog, we made comparisons between the four widely used astrometric catalogs, GSC2.3, USNO-B1.0, UCAC3 and PPMXL.PPMXL shows relatively small systematic errors in positions and more homogeneous proper motion distributions toward the Galactic Anti-center(GAC), and was selected as the reference catalog. Based on the high quality and bright reference stars that were picked out from PPMXL, we performed a 4th-order polynomial fitting in image units,to construct the transformation relation between coordinates used by XSTPS-GAC and standard coordinates, and to simultaneously correct the image distortions in the CCD. Then we applied the derived relation to all sources to obtain their mean celestial coordinates based on the International Celestial Reference System. For bright point sources with r 17.0 mag, the accuracy of astrometric calibration could reach about80 mas for each of the g, r, i bands, with systematic errors being less than 10 mas. But for the faint sources at the brightness limit of the survey, which was r ～ 19.0 mag, the accuracy can still reach 200 mas. After combining all observations, the final weighted average coordinates could reach an accuracy of less than 70 mas for bright stars. For faint stars, the rms residuals of weighted coordinates decrease to ～ 110 mas. The final combined XSTPS-GAC coordinates show a good consistency with the Sloan Digital Sky Survey.     

Evolution of isolated G-band bright points： size,intensity and velocity

We study the evolution pattern of isolated G-band bright points(GBPs)in terms of their size, intensity and velocity. Using a high resolution image sequence taken with the Hinode/Solar Optical Telescope(SOT), we detect GBPs in each image by the Laplacian and Morphological Dilation algorithm, and track their evolutions by a 26-adjacent method in a three-dimensional space-time cube. For quantifying the evolution, we propose a quantification method based on lifetime normalization which aligns the different lifetimes to common stages. The quantification results show that, on average, the diameter of isolated GBPs changes from 166 to 173 km, then down to 165 km; the maximum intensity contrast changes from 1.012 to 1.027, then down to 1.011; however, the velocity changes from 1.709 to 1.593 km s-1, then up to 1.703 km s-1. The results indicate that the evolution follows a pattern such that the GBP is small, faint and fast-moving at the birth stage, becomes big, bright and slow-moving at the middle stage, then gets small, faint and fast-moving at the decay stage until disappearance. Although the differences are very small, a two-sample t-test is used to demonstrate there are significant differences in means between the distributions of the different stages. Furthermore, we quantify the relationship between the lifetimes of GBPs and their properties. It is found that there are positive correlations between the lifetimes and their sizes and intensities with correlation coefficients of0.83 and 0.65, respectively; however, there is a negative correlation between the lifetimes and velocities with a correlation coefficient of –0.49. In summary, the longer the GBP persists, the bigger, brighter and slower it will be.     

What does the Sun tell and hint now？

Some historical records, which have held since the beginning of modern solar activity cycles, are being broken by the present Sun： cycle 23 records the longest cycle length and fall time; latitudes of high-latitude sunspots belonging to a new cycle around the minimum time of the cycle are statistically the lowest at present, compared with those of other cycles; there are only one or no sunspots in a month appearing at high latitudes for 58 months, which is the first time that such a long duration has been observed. The solar dynamo is believed to be slowing down due to： （1） the minimum smoothed monthly mean sunspot number is the smallest since cycle 16 onwards, and even probably among all modern solar cycles; and （2） once the time interval between the first observations of two neighboring sunspot groups is larger than 14 d, it should be approximately regarded as an observation of no sunspots on the visible solar disk, called a spotless event. Spotless events occur with the highest frequency around the minimum time of cycle 24, and the longest spotless event also appears around the minimum time for observations of the Sun since cycle 16. Cycle 24 is expected to have the lowest level of sunspot activity from cycle 16 onwards and even probably for all of the modern solar cycles.     

Noise reduction methods in the analysis of near infrared lunar occultation light curves for high angular resolution measurements

A lunar occultation （LO） technique in the near-infrared （NIR） provides angular resolution down to milliarcseconds for an occulted source, even with ground- based 1 m class telescopes. LO observations are limited to brighter objects because they require a high signal-to-noise ratio （S/N ~40） for proper extraction of angular diameter values. Hence, methods to improve the S/N ratio by reducing noise using Fourier and wavelet transforms have been explored in this study. A sample of 54 NIR LO light curves observed with the IR camera at Mt Abu Observatory has been used. It is seen that both Fourier and wavelet methods have shown an improvement in S/N compared to the original data. However, the application of wavelet transforms causes a slight smoothing of the fringes and results in a higher value for angular diameter. Fourier transforms which reduce discrete noise frequencies do not distort the fringe. The Fourier transform method seems to be effective in improving the S/N, as well as improving the model fit, particularly in the fainter regime of our sample. These methods also provide a better model fit for brighter sources in some cases, though there may not be a significant imorovement in S/N.     

Redshift drift reconstruction for some cosmological models from observations

Redshift drift is a tool to directly probe the expansion history of the uni- verse. Based on the Friedmann-Robertson-Walker framework, we reconstruct the ve- locity drift and deceleration factor for several cosmological models using observa- tional H（z） data from the differential ages of galaxies and baryon acoustic oscillation peaks, luminosity distance of Type Ia supernovae, cosmic microwave background shift parameter, and baryon acoustic oscillation distance parameter. They can, for the first time, provide an objective and quantifiable measure of the redshift drift. We find that reconstructed velocity drift with different peak values and corresponding redshifts can potentially provide a method to distinguish the quality of competing dark energy mod- els at low redshifts. Better fitting between models and observational data indicate that current data are insufficient to distinguish the quality of these models. However, by comparing with the simulated velocity drift from Liske et al, we find that the Dvali- Gabadadze-Porrati model is inconsistent with the data at high redshift, which origi- nally piqued the interest of researchers in the topic of redshift drift. Considering the deceleration factor, we are able to give a stable instantaneous estimation of a transition redshift of zt ~ 0.7 from joint constraints, which incorporates a more complete set of values than the previous study that used a single data set.     

Automated estimation of stellar fundamental parameters from low resolution spectra： the PLS method

PLS （Partial Least Squares regression） is introduced into an automatic estimation of fundamental stellar spectral parameters. It extracts the most correlative spectral component to the parameters （Teff, log g and [Fe/H]）, and sets up a linear regression function from spectra to the corresponding parameters. Considering the properties of stellar spectra and the PLS algorithm, we present a piecewise PLS regression method for estimation of stellar parameters, which is composed of one PLS model for Teff, and seven PLS models for log g and [Fe/H] estimation. Its performance is investigated by large experiments on flux calibrated spectra and continuum normalized spectra at different signal-to-noise ratios （SNRs） and resolutions. The results show that the piecewise PLS method is robust for spectra at the medium resolution of 0.23 nm. For low resolution 0.5 nm and 1 nm spectra, it achieves competitive results at higher SNR. Experiments using ELODIE spectra of 0.23 nm resolution illustrate that our piecewise PLS models trained with MILES spectra are efficient for O ～ G stars： for flux calibrated spectra, the systematic offsets are 3.8%, 0.14 dex, and -0.09 dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.44 dex and 0.38 dex, respectively; for continuum normalized spectra, the systematic offsets are 3.8%, 0.12dex, and -0.13 dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.49 dex and 0.41 dex, respectively. The PLS method is rapid, easy to use and does not rely as strongly on the tightness of a parameter grid of templates to reach high precision as Artificial Neural Networks or minimum distance methods do.     

Mass flow in a circumbinary disk with a gap around supermassive binary black holes

We study the interaction between supermassive binary black holes in an elliptical orbit and their surrounding disk with a gap. The gap in the disk is a low density region formed due to the tidal effects of the less massive black hole. The binary we have investigated has a sub-parsec separation and is coplanar with the disk. We find that the maximum variation of the surface density in the gap reaches 50% during an orbital period. However, in other regions of the disk, the density variation is much less than 1%. Furthermore, we calculate the corresponding variation of spectral energy distribution within a period, but little variation is found. The reason for these results is that the viscosity timescale of the disk at the binary radius is much longer than the orbital period of the binary.