Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case

The error propagation among estimated parameters reflects the correlation among the parameters.We study the capability of machine learning of"learning"the correlation of estimated parameters.We show that machine learning can recover the relation between the uncertainties of different parameters,especially,as predicted by the error propagation formula.Gravitational lensing can be used to probe both astrophysics and cosmology.As a practical application,we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters(effective lens mass ML and Einstein radiusθ_(E))in accordance with the theoretical formula for the singular isothermal ellipse(SIE)lens model.The relation of errors of lens mass and Einstein radius,(e.g.,the ratio of standard deviations F=σ_(ML)/σ_(θ_(E)))predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model.As a proof-of-principle test,a toy model of linear relation with Gaussian noise is presented.We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise.Error propagation plays a crucial role in identifying the physical relation among parameters,rather than a coincidence relation,therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

Research on a 3.7-year Quasi-periodic Oscillation for FSRQ J0351-1153

From the Owens Valley Radio Observatory 40 m radio telescope,we have collected the light curves of the 15 GHz radio band for FSRQ J0153-1153,spanning from 2009 February to 2018 February.The Lomb-Scargle Periodogram method and the Weighted Wavelet Z-transform method are employed to search for the quasi-periodic oscillation(QPO)signal of these data,and the simulation method for the light curve is utilized to estimate the significance level of this QPO signal;thus through these techniques,the QPO signal of 3.7±0.5 yr with a significance level of 3.68σis revealed for the first time.It is most likely an explanation for the QPO signal that a binary black hole system gives rise to a Newtonian-driven the precession of jet.Based on this assumption,we find that the mass of the secondary black hole in this system may be larger than the mass of the primary black hole;and we estimate the intrinsic QPO of jet precession and the QPO of companion star orbit.

Do Minor Interactions Trigger Star Formation in Galaxy Pairs?

We analyze the galaxy pairs in a set of volume limited samples from the Sloan Digital Sky Survey to study the effects of minor interactions on the star formation rate(SFR)and color of galaxies.We carefully design control samples of isolated galaxies by matching the stellar mass and redshift of the minor pairs.The SFR distributions and color distributions in the minor pairs differ from their controls at>99%significance level.We also simultaneously match the control galaxies in stellar mass,redshift and local density to assess the role of the environment.The null hypothesis can be rejected at>99%confidence level even after matching the environment.Our analysis shows a quenching in the minor pairs where the degree of quenching decreases with the increasing pair separation and plateaus beyond 50 kpc.We also prepare a sample of minor pairs with Hαline information.We calculate the SFR of these galaxies using the Hαline and repeat our analysis.We observe a quenching in the Hαsample too.We find that the majority of the minor pairs are quiescent systems that could be quenched due to minor interactions.Combining data from the Galaxy Zoo and Galaxy Zoo 2,we find that only∼1%galaxies have a dominant bulge,4%–7%galaxies host a bar and 5%–10%of galaxies show active galactic nucleus(AGN)activity in minor pairs.This indicates that the presence of bulge,bar or AGN activity plays an insignificant role in quenching the galaxies in minor pairs.The more massive companion satisfies the criteria for mass quenching in most of the minor pairs.We propose that the stripping and starvation likely caused the quenching in the less massive companion at a later stage of evolution.

Galaxy Interactions in Filaments and Sheets:Effects of the Large-scale Structures Versus the Local Density

Major interactions are known to trigger star formation in galaxies and alter their color.We study the major interactions in filaments and sheets using SDSS data to understand the influence of large-scale environments on galaxy interactions.We identify the galaxies in filaments and sheets using the local dimension and also find the major pairs residing in these environments.The star formation rate(SFR) and color of the interacting galaxies as a function of pair separation are separately analyzed in filaments and sheets.The analysis is repeated for three volume limited samples covering different magnitude ranges.The major pairs residing in the filaments show a significantly higher SFR and bluer color than those residing in the sheets up to the projected pair separation of~50 kpc.We observe a complete reversal of this behavior for both the SFR and color of the galaxy pairs having a projected separation larger than 50 kpc.Some earlier studies report that the galaxy pairs align with the filament axis.Such alignment inside filaments indicates anisotropic accretion that may cause these differences.We do not observe these trends in the brighter galaxy samples.The pairs in filaments and sheets from the brighter galaxy samples trace relatively denser regions in these environments.The absence of these trends in the brighter samples may be explained by the dominant effect of the local density over the effects of the large-scale environment.

Correcting the Contamination of Second-order Spectra:Improving HαMeasurements in Reverberation Mapping Campaigns

Long-term spectroscopic monitoring campaigns on active galactic nuclei(AGNs)provide a wealth of information about its interior structure and kinematics.However,a number of the observations suffer from the contamination of second-order spectra(SOS)which will introduce some undesirable uncertainties at the red side of the spectra.In this paper,we test the effect of SOS and propose a method to correct it in the time domain spectroscopic data using the simultaneously observed comparison stars.Based on the reverberation mapping(RM)data of NGC 5548 in2019,one of the most intensively monitored AGNs by the Lijiang 2.4 m telescope,we find that the scientific object,comparison star,and spectrophotometric standard star can jointly introduce up to~30%SOS for Grism 14.This irregular but smooth SOS significantly affects the flux density and profile of the emission line,while having little effect on the light curve.After applying our method to each spectrum,we find that the SOS can be corrected effectively.The deviation between corrected and intrinsic spectra is~2%,and the impact of SOS on time lag is very minor.This method makes it possible to obtain the HαRM measurements from archival data provided that the spectral shape of the AGN under investigation does not have a large change.

A Statistical Analysis of Point-like Sources in the Chandra Galactic Center Survey

The Chandra Galactic Center Survey detected -800 X-ray point-like sources in the 2°× 0.8° sky region around the Galactic Center. We study the spatial and luminosity distributions of these sources according to their spectral properties. Fourteen bright sources detected are used to fit jointly an absorbed power-law model, from which the power-law photon index is determined to be -2.5. Assuming that all other sources have the same power-law form, the relation between hardness ratio and HI column density NH is used to estimate the NH values for all sources. Monte Carlo simulations show that these sources are more likely concentrated in the Galactic center region, rather than distributed throughout the Galactic disk. We also find that the luminosities of the sources are positively correlated with their HI column densities, i.e., a more luminous source has a higher HI column density. From this relation, we suggest that the X-ray luminosity comes from the interaction between an isolated old neutron star and interstellar medium （mainly dense molecular clouds）. Using the standard Bondi accretion theory and the statistical information of molecular clouds in the Galactic center, we confirm this positive correlation and calculate the luminosity range in this scenario, which is consistent with the observation （10^32 - 10^35 erg s^-1）.