Table of contents

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) is the most sensitive ground-based, single-dish radio telescope on Earth. However, the original H i spectra produced by FAST are affected by standing waves. To maximize the power of FAST for high-sensitivity observations, we proposed an algorithm that combines fast Fourier transforms and extreme envelope curves to automatically correct the baselines of FAST H i spectra and remove standing waves from the baselines. This algorithm can reduce the amplified noise level caused by standing waves to a near-ideal level without losing signals or introducing false signals. The root mean square of the average baseline reaches ∼8 mK, approaching the theoretical sensitivity of an H i spectrum produced by FAST for an integration time of 335 minutes, i.e., ∼6 mK.

Flux densities are basic observation parameters to describe pulsars. In the most updated pulsar catalog, 24% of the listed radio pulsars have no flux density measurement at any frequency. Here, we report the first flux density measurements, spectral indices, pulse profiles, and correlations of the spectral index with pulsar parameters for 19 pulsars employing the Ultra-Wideband Low receiver system installed on the Parkes radio telescope. The results for spectral indices of 17 pulsars are in the range between −0.6 and −3.10. The polarization profiles of thirteen pulsars are shown. There is a moderate correlation between the spectral index and spin frequency. For most pulsars detected, the signal-to-noise ratio of pulse profile is not high, so DM, Faraday rotation measure, and polarization cannot be determined precisely. Twenty-nine pulsars were not detected in our observations. We discuss the possible explanations for why these pulsars were not detected.

In this work, the γ-ray photon flux, photon spectral index (α_ph), variability index ($\mathrm{log}\,V.I.$), and the synchrotron peak frequency ($\mathrm{log}\,{\nu }_{{\rm{p}}}$) are compiled for 851 common blazars from the 3FGL and 4FGL catalogs and Fan et al. to investigate variability properties for Fermi blazars. Our calculations and analyses reach following results: (1) the averaged luminosity, spectral index, and variability index of FSRQs are higher than those of BL Lacs for the whole sample. (2) It is found that the spectral index variation is closely anti-correlated with the luminosity variation implying that the spectrum becomes harder when the source becomes brighter in the γ-ray band. (3) Positive correlations are found between the photon spectral index and both γ-ray luminosity and variability index ($\mathrm{log}\,V.I.$) for the whole sample, but anti-correlations are found in the two correlations for FSRQs. For BL Lac subclass, there is a marginal anti-correlation between the photon spectral index and both γ-ray luminosity, and a positive correlation between the photon spectral index and the variability index ($\mathrm{log}\,V.I.$). We think those two positive correlations found for the whole sample are apparent. (4) We adopted the SVM machine learning method to separate BL Lacs and FSRQs in the ${\alpha }_{\mathrm{ph}}\,\,\mathrm{versus}\,\,\mathrm{log}\,{L}_{\gamma }$ and ${\alpha }_{\mathrm{ph}}\,\,\mathrm{versus}\,\,\mathrm{log}\,V.I.$ plots and proposed that a BCU is an FSRQ candidate if it satisfies $\mathrm{log}\,V.I.\,\gt \,-10.119\alpha +24.855$, or ${\alpha }_{\mathrm{ph}}\gt -0.048\,\mathrm{log}\,{L}_{\gamma }+4.498$, otherwise, it is a BL Lac candidate. Our classification results are quite consistent with those by Kang et al (2019).

The existence of pulsating stars in eclipsing binaries has been known for decades. These types of objects are extremely valuable systems for astronomical studies as they exhibit both eclipse and pulsation variations. The eclipsing binaries are the only way to directly measure the mass and radius of stars with a good accuracy (≤1%), while the pulsations are a unique way to probe the stellar interior via oscillation frequencies. There are different types of pulsating stars existing in eclipsing binaries. One of them is the δ Scuti variables. Currently, the known number of δ Scuti stars in eclipsing binaries is around 90 according to the latest catalog of these variables. An increasing number of these kinds of variables is important to understand the stellar structure, evolution and the effect of binarity on the pulsations. Therefore, in this study, we focus on discovering new eclipsing binaries with δ Scuti component(s). We searched within the northern Transiting Exoplanet Survey Satellite (TESS) field with a visual inspection by following some criteria such as light curve shape, the existence of pulsation like variations in the out-of-eclipse light curve and the T_eff values of the targets. As a result of these criteria, we discovered some targets. The orbital variations were first removed from the TESS light curves and frequency analysis was performed on the residuals. The luminosity, and absolute and bolometric magnitudes of the targets were calculated as well. To find how much of these parameters represent the primary (more luminous) binary component, we also computed the flux density ratio of the systems by utilizing the area of the eclipses. In addition, the positions of the systems in the H-R diagram were examined considering the flux density ratios. As a consequence of the investigation, we defined 38 candidate δ Scuti stars and also one Maia variable in eclipsing binary systems.

We study the vertical distribution of the highly inclined galaxies from the Continuum Halos in Nearby Galaxies—an EVLA Survey (CHANG-ES). We explore the feasibility of photometrically deriving the H i disk scale heights from the moment-0 images of the relatively edge-on galaxies with inclination >80°, by quantifying the systematic broadening effects and thus deriving correction equations for direct measurements. The corrected H i disk scale heights of the relatively edge-on galaxies from the CHANG-ES sample show trends consistent with the quasi-equilibrium model of the vertical structure of gas disks. The procedure provides a convenient way to derive the scale heights and can easily be applied to statistical samples in the future.

Our analysis presents an explanation of the Sun–Earth coupling mechanism during declining phase of a solar cycle, and how the dominant 13.5 and 27 day periods play roles in the coupling mechanism which led to intense terrestrial magnetic storms during this declining phase compared to the rising phase of a solar cycle. Moreover, it is observed that while the 27 day period gets strongly modulated in the rising phase, the 13.5 day period modulation is more prominent during the declining phase. It is suggested that out of the 27 and 13.5 day periods of Sun–Earth interaction, the preferred period of modulation happens to be the one which is more dominant for the less random or quieter system participating in the coupling. It is reported for the first time that the 13.5 day period is more prominent in the Sun–Earth interaction during the declining phase of a solar cycle, as it is the most dominant period of Earth's magnetic system, which happens to be more persistent as a dynamical system and hence quieter or more receptive than the Sun.

Astronomical outliers, such as unusual, rare or unknown types of astronomical objects or phenomena, constantly lead to the discovery of genuinely unforeseen knowledge in astronomy. More unpredictable outliers will be uncovered in principle with the increment of the coverage and quality of upcoming survey data. However, it is a severe challenge to mine rare and unexpected targets from enormous data with human inspection due to a significant workload. Supervised learning is also unsuitable for this purpose because designing proper training sets for unanticipated signals is unworkable. Motivated by these challenges, we adopt unsupervised machine learning approaches to identify outliers in the data of galaxy images to explore the paths for detecting astronomical outliers. For comparison, we construct three methods, which are built upon the k-nearest neighbors (KNN), Convolutional Auto-Encoder (CAE) + KNN, and CAE + KNN + Attention Mechanism (attCAE_KNN) separately. Testing sets are created based on the Galaxy Zoo image data published online to evaluate the performance of the above methods. Results show that attCAE_KNN achieves the best recall (78%), which is 53% higher than the classical KNN method and 22% higher than CAE+KNN. The efficiency of attCAE_KNN (10 minutes) is also superior to KNN (4 h) and equal to CAE+KNN (10 minutes) for accomplishing the same task. Thus, we believe that it is feasible to detect astronomical outliers in the data of galaxy images in an unsupervised manner. Next, we will apply attCAE_KNN to available survey data sets to assess its applicability and reliability.

Diffuse interstellar bands (DIBs) have always been a mysterious existence in astronomical research. In this work, we provide more DIB samples to slightly uncover this mystery. With the LAMOST medium-resolution survey (MRS) spectra, we detected three DIBs λ6379, λ6614, and λ6660, obviously superimposed on the spectra of 11,003 stars. These spectra cover spectral types from O to K, which can provide a large number of candidates for further research on DIBs. The sample shows a clear positive correlation between the strength of DIBs and extinction, which agrees with the result in the literature. In addition, there exist two peaks in each of the velocity distribution of these three DIBs, and the velocity differences between two peaks of each pair are consistent. The reason for the two velocity components is due to the Galactic rotation.

Investigating the length scales of granules could help understand the dynamics of granules in the photosphere. In this work, we detected and identified granules in an active region near disk center observed at wavelength of TiO (7057 Å) by the 1.6 m Goode Solar Telescope (GST). By a detailed analysis of the size distribution and flatness of granules, we found a critical size that divides the granules in motions into two regimes: convection and turbulence. The length scales of granules with sizes larger than 600 km follow Gauss function and demonstrate "flat" in flatness, which reveal that these granules are dominated by convection. Those with sizes smaller than 600 km follow power-law function and behave power-law tendency in flatness, which indicate that the small granules are dominated by turbulence. Hence, for the granules in active regions, they are originally convective in large length scale, and directly become turbulent once their sizes turn to small, likely below the critical size of 600 km. Comparing with the granules in quiet regions, they evolve with the absence of the mixing motions of convection and turbulence. Such a difference is probably caused by the interaction between fluid motions and strong magnetic fields in active regions. The strong magnetic fields make high magnetic pressure which creates pressure walls and slows down the evolution of convective granules. Such walls cause convective granules extending to smaller sizes on one hand, and cause wide intergranular lanes on the other hand. The small granules isolated in such wide intergranular lanes are continually sheared, rotated by strong downflows in surroundings and hereby become turbulent.

This paper presents the analytical results of solar Mg ib₂ flash spectra, obtained by the prototype Fiber Arrayed Solar Optic Telescope in process of the 2013 Gabon total solar eclipse. The analysis reveals irregular distributions of the spectral line parameters like ratio of line source function to continuum one β, ratio of line emissivity to continuum emissivity ζ, ratio of the continuum opacity to the line opacity r₀, line center optical depth τ₀, the line width Δλ_D, and the line-of-sight velocity v_los, while the approximately spherical symmetry can be found in the maps of integrated line intensity and continuum intensity. These irregular distributions originate from those of line profile features like the maximum intensity, the line width and line center wavelength. It is also found from the recovered line center optical depth τ₀ that in the middle chromosphere, the optical depth is not small due to non-ignorable absorption and the long light path along the line-of-sight. Finally, we show that the excessive broadening of spectral lines can be due to co-existence of multiple radiative sources with different line-of-sight velocities unresolved in one detector pixel.

We attempt to model magnetic reconnection during the two-ribbon flare in a gravitationally stratified solar atmosphere with the Lundquist number of S = 10⁶ using 2D simulations. We found that the tearing mode instability leads to inhomogeneous turbulence inside the reconnecting current sheet (CS) and invokes the fast phase of reconnection. Fast reconnection brings an extra dissipation of magnetic field which enhances the reconnection rate in an apparent way. The energy spectrum in the CS shows a power law pattern and the dynamics of plasmoids govern the associated spectral index. We noticed that the energy dissipation occurs at a scale l_ko of 100–200 km, and the associated CS thickness ranges from 1500 to 2500 km, which follows the Taylor scale l_T = l_koS^1/6. The termination shock (TS) appears in the turbulent region above flare loops, which is an important contributor to heating flare loops. Substantial magnetic energy is converted into both kinetic and thermal energies via TS, and the cumulative heating rate is greater than the rate of the kinetic energy transfer. In addition, the turbulence is somehow amplified by TS, in which the amplitude is related to the local geometry of the TS.

Energetic X-ray radiations emitted from various accretion systems are widely considered to be produced by Comptonization in the hot corona. The corona and its interaction with the disk play an essential role in the evolution of the system and are potentially responsible for many observed features. However, many intrinsic properties of the corona are still poorly understood, especially for the geometrical configurations. The traditional spectral fitting method is not powerful enough to distinguish various configurations. In this paper, we intend to investigate the possible configurations by modeling the polarization properties of X-ray radiations. The geometries of the corona include the slab, sphere and cylinder. The simulations are implemented through the publicly available code, Lemon, which can deal with the polarized radiative transfer and different electron distributions readily. The results demonstrate clearly that the observed polarizations are dependent heavily on the geometry of the corona. The slab-like corona produces the highest polarization degrees (PDs), followed by the cylinder and sphere. One of the interesting things is that the PDs first increase gradually and then decrease with the increase of photon energy. For slab geometry, there exists a zero-point where the polarization vanishes and the polarization angle (PA) rotates by 90°. These results may potentially be verified by the upcoming missions for polarized X-ray observations, such as IXPE and eXTP.

A new digital receiver with excellent performances has been designed and developed for solar radio observation, which can receive the radio signal from direct current (DC) to 9 GHz in the direct acquisition way. On the digital receiver, the analog-to-digital converter (ADC) with 14-bit, two input channels and 3 Giga Samples per second (Gsps) are used to acquire observed signal, and the field-programmable-gate-array chip XCKU115 acts as the processing module. The new digital receiver can be used to directly sample the solar radio signals of frequency under 9 GHz. When receiving the solar radio signal above 9 GHz, the new digital receiver can save 1–2 stages of frequency down-conversion, and effectively improve many indexes of the solar radio observation system, i.e., the time resolution, analog front-end circuit, weight and volume of the analog circuit system. Compared with the digital receiver with sampling rate below 1 Gsps used in existing solar radio telescope, the new digital receiver reduces the frequency switching times of large bandwidth, which is beneficial to improving the frequency and time resolutions. The ADC sampling resolution of 14 bits, providing a large dynamic range, is very beneficial to observing smaller solar eruptions. This receiver, which would be used in the solar radio observation system, well meets the latest requirements with the resolutions of time (≤1 ms) and frequency (≤0.5 MHz) for fine observation of radio signals.

The present work aims to build a new statistical distance scale for planetary nebulae (PNe) based on a rigorous calibration sample. The distances of the calibration sample are derived from the trigonometric parallax method using the recent measurements of Gaia Early Data Release 3 (Gaia EDR3). The new distance scale is created by applying the well-known linear relationship between the radio surface brightness temperature and the nebular radius. The calibration sample is made up of 96 PNe of accurately computed distances with uncertainties less than 20%. Earlier ground- and space-based trigonometric parallaxes of PNe display inconsistency with those of Gaia, particularly the Hipparcos results. In addition, these measurements have appreciably lower precision than those of Gaia. When compared to the trigonometric technique, the expansion and kinematic methods exhibited more consistency than the spectroscopic, extinction, gravity, and photoionization methods. Furthermore, contrary to earlier results in the literature, the extinction and gravity methods, on average, underestimate and slightly overestimate the PN distances respectively. As a byproduct of extracting the Gaia parallaxes, we detect the radial velocity and variability for 14 and 3 PN central stars (CSs), respectively. To our knowledge, the variability of Hen 2-447 CS has been determined for the first time.

It is crucial to measure the mass of supermassive black holes (SMBHs) in understanding the co-evolution between the SMBHs and their host galaxies. Previous methods usually require spectral data which are expensive to obtain. We use the AGN catalog from the Sloan Digital Sky Survey project Data Release 7 (DR7) to investigate the correlations between SMBH mass and their host galaxy properties. We apply the machine learning algorithms, such as Lasso regression, to establish the correlation between the SMBH mass and various photometric properties of their host galaxies. We find an empirical formula that can predict the SMBH mass according to galaxy luminosity, colors, surface brightness, and concentration. The root-mean-square error is 0.5 dex, comparable to the intrinsic scatter in SMBH mass measurements. The 1σ scatter in the relation between the SMBH mass and the combined galaxy properties relation is 0.48 dex, smaller than the scatter in the SMBH mass versus galaxy stellar mass relation. This relation could be used to study the SMBH mass function and the AGN duty cycles in the future.

We have studied the spectral behavior of the II Peg binary system in the ultraviolet band by using International Ultraviolet Explorer (IUE) observations over the period 1979–1993. The ultraviolet observations reveal indication of flare activity in both chromosphere and transition region with their enhanced emission lines. Before and after the flare activity the ultraviolet emission lines show low, intermediate and high flux. The spectral behavior is compared with previous studies. We detect prominent flare activity in 1989, 1990 and 1992. Before and after this period there is a gradual clear decrease in the level of activity. The reddening of II Peg was determined from a 2200 Å absorption feature to be E(B − V) = 0.10 ± 0.02. We ascertained the average mass loss rate to be ≈1 × 10⁻⁸ M_⊙ yr⁻¹, and an average ultraviolet luminosity to be ≈6 × 10²⁹ erg s⁻¹. We attributed the spectral variations to a cyclic behavior of the underlying magnetic dynamo and the prominent activity can be interpreted by the model of a two-ribbon flare.

Although the spatial curvature has been measured with very high precision, it still suffers from the well-known cosmic curvature tension. In this paper, we use an improved method to determine the cosmic curvature, by using the simulated data of binary neutron star mergers observed by the second generation space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO). By applying the Hubble parameter observations of cosmic chronometers to the DECIGO standard sirens, we explore different possibilities of making measurements of the cosmic curvature referring to a distant past: one is to reconstruct the Hubble parameters through the Gaussian process without the influence of hypothetical models, and the other is deriving constraints on Ω_K in the framework of the non-flat Λ cold dark matter model. It is shown that in the improved method DECIGO could provide a reliable and stringent constraint on the cosmic curvature (Ω_K = −0.007 ± 0.016), while we could only expect the zero cosmic curvature to be established at the precision of ΔΩ_K = 0.11 in the second model-dependent method. Therefore, our results indicate that in the framework of methodology proposed in this paper, the increasing number of well-measured standard sirens in DECIGO could significantly reduce the bias of estimations for cosmic curvature. Such a constraint is also comparable to the precision of Planck 2018 results with the newest cosmic microwave background (CMB) observations (ΔΩ_K ≈ 0.018), based on the concordance ΛCDM model.

The distribution of ultraviolet (UV) radiation field provides critical constraints on the physical environments of molecular clouds. Within 1 kpc of our solar system and fostering protostars of different masses, the giant molecular clouds in the Gould Belt present an excellent opportunity to resolve the UV field structure in star-forming regions. We performed spectral energy distribution (SED) fitting of the archival data from the Herschel Gould Belt Survey (HGBS). Dust radiative transfer analysis with the DUSTY code was applied to 23 regions in 14 molecular complexes of the Gould Belt, resulting in the spatial distribution of the radiation field in these regions. For 10 of 15 regions with independent measurements of star formation rate, their star formation rate and UV radiation intensity largely conform to a linear correlation found in previous studies.

Currently, data-driven models of solar activity forecast are investigated extensively by using machine learning. For model training, it is highly demanded to establish a large database which may contain observations coming from different instruments with different spatio-temporal resolutions. In this paper, we employ deep learning models for super-resolution (SR) of magnetogram of Michelson Doppler Imager (MDI) in order to achieve the same spatial resolution of Helioseismic and Magnetic Imager (HMI). First, a generative adversarial network (GAN) is designed to transfer characteristics of MDI onto downscaled HMI, getting low-resolution HMI magnetogram in the same domain as MDI. Then, with the paired low-resolution and high-resolution HMI magnetograms, another GAN is trained in a supervised learning way, which consists of two streams, one is for generating high-fidelity image content, the other is explicitly optimized for generating elaborate image gradients. Thus, these two streams work together to guarantee both high-fidelity and photorealistic super-resolved images. Experimental results demonstrate that the proposed method can generate super-resolved magnetograms with perceptual-pleasant visual quality. Meanwhile, the best PSNR, LPIPS, RMSE, comparable SSIM and CC are obtained by the proposed method. The source code and data set can be accessed via https://github.com/filterbank/SPSR.

We investigate the effects of binaries on the cluster age determination for 561 open clusters in the Galactic disk via the Bayesian statistical framework. Stellar properties of these star clusters, including age, metallicity, distance modulus, color excess, binary fraction, and rotating star fraction, are derived from color–magnitude-diagrams (CMDs) via isochrone fitting to high-precision Gaia EDR3 data. Across the simple stellar population of binary and single-star, age differences can be found with the same star cluster. A Bayesian applied regression modeling software, Stan, is employed to explore how much binaries affect the age determination of open clusters. Our results present less statistically significant difference between the binary-star simple populations (bsSSPs) and the single-star simple populations (ssSSPs) for cluster age determination. For all clusters in our sample, the ages estimated using the bsSSPs models are younger than those estimated using the ssSSPs, with a mean value of ∼70 Myr. However, it is found that for 52.5% clusters in our sample, ages are relatively sensitive to the presence of binaries, at least ∼25% younger. This suggests that in studies of open cluster age determinations, the effects of binary interactions on the whole sample are not prominent, but its effects on some clusters should still be included as an essential ingredient.

Predicting the activity of solar flares is of great significance for studying its physical mechanism and the impact on human production and life. Problems such as class imbalance, high time-series sensitivity, and over-localization of important features exist in the sample data used for flare forecasting. We design a solar flare fusion method based on resampling and the CNN-GRU algorithm to try to solve the above problems. In order to verify the effectiveness of this fusion method, first, we compared the forecast performance of different resampling methods by keeping the forecast model unchanged. Then, we used the resampling algorithm with high performance to combine some single forecast models and fusion forecast models respectively. We use the 2010–2017 sunspot data set to train and test the performance of the flare model in predicting flare events in the next 48 h. Through the conclusion of the above steps, we prove that the resampling method SMOTE and its variant SMOTE-ENN are more advantageous in class imbalance problem of flare samples. In addition, after the fusion of one-dimensional convolution and recurrent network with "forget-gate" , combined with the SMOTE-ENN to achieve TSS = 61%, HSS = 61%, TP_Rate = 77% and TN_Rate = 83%. This proves that the fusion model based on resampling and the CNN-GRU algorithm is more suitable for solar flare forecasting.

We present the broadband numerical modeling of afterglows for two remarkably bright long gamma-ray bursts (GRBs), GRB 050820A and GRB 070125, with a wide range of observations from the radio band to the X-ray band. In our work, we fit light curves and constrain physical parameters using a standard forward shock model from the afterglowpy Python package, considering different jet structures and the jet lateral expansion. For GRB 050820A, the constrained jet is close to a top-hat jet with an extremely small half opening angle of about 0.015 rad, and the circumburst matter density is as small as 10⁻⁷ cm⁻³, which suggests that this peculiar long GRB might originate from metal-poor stars with low mass-loss rates. To explain the late time optical light curves of GRB 070125, the effects of the lateral expansion and the participation factor of electrons that are accelerated by the shock have to be taken into account. The constrained results for GRB 070125 show that the jet is also close to a top-hat jet with a half opening angle of about 0.1 rad, the viewing angle is about 0.05 rad, the circumburst density is about 10 cm⁻³, and the participation factor is about 0.1. The jet energy of the two bursts is required to be ∼10⁵¹–10⁵² erg, which can be produced by a millisecond magnetar or a hyper-accreting black hole.

The first photometric solution in the B, V, R_c and I_c filters of the short period V1833 Ori eclipsing binary is presented based on new ground-based CCD photometric observations. We analyzed the BVRI photometric light curves of the system, using PHOEBE 0.31a, a binary star modeling program, with the Wilson-Devinney method based on Roche geometry to achieve the best accordance with the photometric observations to determine their absolute parameters from the light curves. We updated the ephemeris of V1833 Ori using two new light curve minima derived by our new observational data from those collected in the literature and analyzed the change of the system's orbital period. The O–C analysis indicates that the variations of the orbital period of V1833 Ori with time are increasing at a rate of 3.03 × 10⁻⁷ days yr⁻¹. The distance of V1833 Ori is 173.7 ± 15.6 pc. From the solutions, we find that V1833 Ori is an A-subtype W UMa overcontact binary with q = 0.701 mass ratio and f = 1.14 fill-out factor. The HR diagram positions of the eclipsing binary system's components are discussed. The system's absolute dimensions were compared to those of similar binaries in the $\mathrm{log}{T}_{\mathrm{eff}}-\mathrm{log}L$, logM − logL, logM − logR and $\mathrm{log}M-\mathrm{log}{J}_{0}$ diagrams.

We construct a multiple-population discrete axisymmetric Jeans model for the Andromeda (M31) galaxy, considering three populations of kinematic tracers: 48 supergiants and 721 planetary nebulae (PNe) in the bulge and disk regions, 554 globular clusters extending to ∼30 kpc, and halo stars extending to ∼150 kpc of the galaxy. The three populations of tracers are organized in the same gravitational potential, while each population is allowed to have its own spatial distribution, rotation, and internal velocity anisotropy. The gravitational potential is a combination of stellar mass and a generalized NFW dark matter halo. We created two sets of models, one with a cusped dark matter halo and one with a cored dark matter halo. Both the cusped and cored model fit kinematics of all the three populations well, but the cored model is not preferred due to a too high concentration compared to that predicted from cosmological simulations. With a cusped dark matter halo, we obtained total stellar mass of 1.0 ± 0.1 × 10¹¹M_⊙, dark matter halo virial mass of M₂₀₀ = 7.0 ± 0.9 × 10¹¹M_⊙, virial radius of r₂₀₀ = 184 ± 4 kpc, and concentration of c = 20 ± 4. The mass of M31 we obtained is at the lower side of the allowed ranges in the literature and consistent with the previous results obtained from the H i rotation curve and PNe kinematics. Velocity dispersion profile of the outer stellar halo is important in constraining the total mass while it is still largely uncertain. Further proper motion of bright sources from Gaia or the Chinese Space Station Telescope might help on improving the data and lead to stronger constraints on the total mass of M31.

Based on the long-term light curves collected from the Catalina Sky Survey (CSS) (from 2005 to 2013) and the All-Sky Automated Survey for Supernovae (ASAS-SN) (from 2014 to 2018), optical quasi-periodic oscillations (QPOs) about 300 days can be well determined in the well-known blazar PKS 2155-304 through four different methods: the generalized Lomb-Scargle periodogram (GLSP) method, the weighted wavelet Z-transform technique, the epoch-folded method and the redfit method. The GLSP determined significance level for the periodicity is higher than 99.9999% based on a false alarm probability. The redfit provided confidence level for the periodicity is higher than 99% in the ASAS-SN light curve, after considering the effects of red noise. Based on continuous autoregressive process created artificial light curves, the probability of detecting fake QPOs is lower than 0.8%. The determined optical periodicity of 300 days from the CSS and ASAS-SN light curves is well consistent with the reported optical periodicity in the literature. Moreover, three possible models are discussed to explain the optical QPOs in PKS 2155-304: the relativistic frame-dragging effect, the binary black hole model and the jet precession model.