In this work, we select spectra of stars with high signal-to-noise ratio from LAMOST data and map their MK classes to the spectral features. The equivalent widths of prominent spectral lines, which play a similar role...In this work, we select spectra of stars with high signal-to-noise ratio from LAMOST data and map their MK classes to the spectral features. The equivalent widths of prominent spectral lines, which play a similar role as multi-color photometry, form a clean stellar locus well ordered by MK classes. The advantage of the stellar locus in line indices is that it gives a natural and continuous classification of stars consistent with either broadly used MK classes or stellar astrophysical parameters. We also employ an SVM-based classification algorithm to assign MK classes to LAMOST stellar spectra. We find that the completenesses of the classifications are up to 90% for A and G type stars, but they are down to about 50% for OB and K type stars. About 40% of the OB and K type stars are mis-classified as A and G type stars,respectively. This is likely due to the difference in the spectral features between late B type and early A type stars or between late G and early K type stars being very weak. The relatively poor performance of the automatic MK classification with SVM suggests that the direct use of line indices to classify stars is likely a more preferable choice.展开更多
Average pulse profiles of pulsar signals are analyzed using the bispectrum technique. The result shows that there are nonlinear phase couplings between the two frequency axes of the bispectrum charts, which indicate n...Average pulse profiles of pulsar signals are analyzed using the bispectrum technique. The result shows that there are nonlinear phase couplings between the two frequency axes of the bispectrum charts, which indicate nonlinear factors in the generation and propagation of pulsar signals. Bispectra can be used as feature vectors of pulsar signals because of their being translation invariant. A one-dimension selected line spectrum algorithm for extracting pulsar signal characteristic is proposed. Compared with selected bispectra, the proposed selected line spectra have the maximum interclass separability measurements from the point of view of the whole one-dimension feature vector. Recognition experiments on several pulsar signals received at several frequency bands are carried out. The result shows that the selected line spectrum algorithm is suitable for extracting pulsar signal characteristics and has a good classification performance.展开更多
In this study,we determined the physical parameters of W UMa type contact binaries and their stability of mass transfer with different stellar mass ranges over a broad space by applying the basic dynamical evolution e...In this study,we determined the physical parameters of W UMa type contact binaries and their stability of mass transfer with different stellar mass ranges over a broad space by applying the basic dynamical evolution equations of the W UMa type contact binaries using accretor and donor masses between 0.079 and 2.79 M_(⊙).In these systems,we have studied the three subclasses of W UMa systems of A-,B-and W-type contact binaries using the initial and final mass ranges and we investigated different stellar and orbital parameters for the subclasses of W UMa systems.We examined the stability of the W UMa type contact binaries using the orbital parameters such as critical mass ratio,Roche lobe radius of the donor star and mass ratio of these systems.Thus,we computed the observed and calculated physical parameters of A-,B-and W-type W UMa systems.Moreover,we determined the combined and color temperatures to classify the three subclasses of the systems.Also,we presented the result of the internal stellar structure and evolution of W UMa type contact binaries by using the polytropic model.展开更多
GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to~1020 s and the true timescale of the central engine activity t_(burst)≥4×10^(4) s.The late X-ray light cur...GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to~1020 s and the true timescale of the central engine activity t_(burst)≥4×10^(4) s.The late X-ray light curve with a decay index ofα=7.53 is steeper than the steepest possible decay from an external shock model.We propose that this X-ray afterglow can be driven by dipolar radiation from the magnetar spindown during its early stage,while the magnetar collapsed into the black hole before its spindown,resulting in a very steep decay of the late X-ray light curve.The optical data show that the light curve is still rising after 1.1 ks,suggesting a late onset.We show that GRB 200612A’s optical afterglow light curve is fitted with the forward shock model by Gaussian structured off-axis jet.This is a special case among GRBs,as it may be an ultralong gamma-ray burst powered by a magnetar in an off-axis observation scenario.展开更多
After launching a jet,outflows of magnetar were used to account for the achromatic plateau of afterglow and the early X-ray flux plateau known as“internal plateau”.The lack of detecting magnetic dipole emission toge...After launching a jet,outflows of magnetar were used to account for the achromatic plateau of afterglow and the early X-ray flux plateau known as“internal plateau”.The lack of detecting magnetic dipole emission together with the energy injection feature in a single observation poses confusion until the long gamma-ray burst(GRB)210610B is detected.GRB 210610B is presented with an optical bump following an early X-ray plateau during the afterglow phase.The plateau followed by a steep decline flux overlays in the steadily decaying X-ray flux with indexα_(X,1)~2.06,indicating an internal origin and that can be fitted by the spin-down luminosity law with the initial plateau luminosity log_(10)L_(X)~48.29 erg s~(-1)and the characteristic spin-down timescale T~2818 s.A subsequent bump begins at~4000 s in the R band with a rising indexα_(R,1)~-0.30 and peaks at~14125 s,after which a decay indexα_(R,2)~0.87 and finally transiting to a steep decay withα_(R,3)~1.77 achieve the closure relation of the external shock for the normal decay phase as well as the magnetar spin-down energy injection phase,provided that the average value of the photon indexΓ_γ=1.80 derived from the spectral energy distributions(SEDs)between the X-ray and optical afterglow.The closure relation also works for the late X-ray flux.Akin to the traditional picture of GRB,the outflow powers the early X-ray plateau by dissipating energy internally and collides with the leading decelerating blast burst as time goes on,which could interpret the exotic feature of GRB 210610B.We carry out a Markov Chain Monte Carlo simulation and obtain a set of best parameters:■.The artificial light curve can fit the afterglow data well.After that,we estimated the average Lorentz factor and the X-ray radiation efficiency of the later ejecta are 35%and 0.13%,respectively.展开更多
Long period variable(LPV)stars are very promising distance indicators in the infrared bands.We selected asymptotic giant branch(AGB)stars in the Large and Small Magellanic Cloud(LMC and SMC)from the Gaia Data Release ...Long period variable(LPV)stars are very promising distance indicators in the infrared bands.We selected asymptotic giant branch(AGB)stars in the Large and Small Magellanic Cloud(LMC and SMC)from the Gaia Data Release 3 LPV catalog,and classified them into oxygen-rich(O-rich)and carbon-rich(C-rich)AGB stars.Using the Wide-field Infrared Survey Explorer database,we determined the W1-and W2-band period-luminosity relations(PLRs)for each pulsation-mode sequence of AGB stars.The dispersion of the PLRs of O-rich AGB stars in sequences C'and C is relatively small,around 0.14 mag.The PLRs of LMC and SMC are consistent in each sequence.In the W2 band,the PLR of large-amplitude C-rich AGB stars is steeper than that of small-amplitude C-rich AGB stars,due to their more circumstellar dust.By two methods,we find that some PLR sequences of O-rich AGB stars in the LMC are dependent on metallicity.The coefficients of the metallicity effect areβ=-0.533±0.213 mag dex~1andβ=-0.767±0.158 mag dex~1for sequence C in W1 and W2 bands,respectively.The significance of the metallicity effect in W1 band for the four sequences is 2.2-3.5σ.Both of these imply that distance measurements using O-rich Mira may need to take the metallicity effect into account.展开更多
I build a toy model in the frame of the jittering jets explosion mechanism(JJEM)of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly b...I build a toy model in the frame of the jittering jets explosion mechanism(JJEM)of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly born neutron star(NS)accretes and the constant angular momentum component,and show that the JJEM can account for the≃2.5–5M⊙mass gap between NSs and black holes(BHs).The random component of the angular momentum results from pre-collapse core convection fluctuations that are amplified by post-collapse instabilities.The fixed angular momentum component results from pre-collapse core rotation.For slowly rotating pre-collapse cores the stochastic angular momentum fluctuations form intermittent accretion disks(or belts)around the NS with varying angular momentum axes in all directions.The intermittent accretion disk/belt launches jets in all directions that expel the core material in all directions early on,hence leaving an NS remnant.Rapidly rotating pre-collapse cores form an accretion disk with angular momentum axis that is about the same as the pre-collapse core rotation.The NS launches jets along this axis and hence the jets avoid the equatorial plane region.Inflowing core material continues to feed the central object from the equatorial plane increasing the NS mass to form a BH.The narrow transition from slow to rapid pre-collapse core rotation,i.e.,from an efficient to inefficient jet feedback mechanism,accounts for the sparsely populated mass gap.展开更多
This work presents the charge-coupled device(CCD)photometric survey of the old open cluster NGC 188.Timeseries V-band photometric observations were conducted for ten nights in 2017 January using the Nanshan Onemeter W...This work presents the charge-coupled device(CCD)photometric survey of the old open cluster NGC 188.Timeseries V-band photometric observations were conducted for ten nights in 2017 January using the Nanshan Onemeter Wide-field Telescope to search for variable stars in the field of the cluster.A total of 25 variable stars,including one new variable star,were detected in the target field.Among the detected variables,16 are cluster member stars,and the others are identified as field stars.The periods,radial velocities,effective temperatures,and classifications of the detected variables are discussed in this work.Most of the stars’effective temperatures are between 4200 and 6600 K,indicating their spectral types are G or K.The newly discovered variable is probably a W UMa system.In this study,a known cluster variable star(V21=V0769 Cep)is classified as an EA-type variable star based on the presence of an 0.5 mag eclipse in its light curve.展开更多
Theories of modified gravity suggest that the propagation speed of gravitational waves(GW)v_gmay deviate from the speed of light c.A constraint can be placed on the difference between c and v_gwith a simple method tha...Theories of modified gravity suggest that the propagation speed of gravitational waves(GW)v_gmay deviate from the speed of light c.A constraint can be placed on the difference between c and v_gwith a simple method that uses the arrival time delay between GW and electromagnetic wave simultaneously emitted from a burst event.We simulated the joint observation of GW and short gamma-ray burst signals from binary neutron star merger events in different observation campaigns,involving advanced LIGO(aLIGO)in design sensitivity and Einstein Telescope(ET)joint-detected with Fermi/GBM.As a result,the relative precision of constraint on v_gcan reach~10~(-17)(aLIGO)and~10^(-18)(ET),which are one and two orders of magnitude better than that from GW170817,respectively.We continue to obtain the bound of graviton mass m_g≤7.1(3.2)×10~(-20)eV with aLIGO(ET).Applying the Standard-Model Extension test framework,the constraint on v_gallows us to study the Lorentz violation in the nondispersive,nonbirefringent limit of the gravitational sector.We obtain the constraints of the dimensionless isotropic coefficients S_(00)^(4)at mass dimension d=4,which are-1×10^(-15)<S_(00)^(4)<9×10^(-17)for aLIGO and-4×10^(-16)<s_(00)^(4<8<10^(-18))for ET.展开更多
I estimate the frequencies of gravitational waves from jittering jets that explode core collapse supernovae(CCSNe)to crudely be 5–30 Hz,and with strains that might allow detection of Galactic CCSNe.The jittering jets...I estimate the frequencies of gravitational waves from jittering jets that explode core collapse supernovae(CCSNe)to crudely be 5–30 Hz,and with strains that might allow detection of Galactic CCSNe.The jittering jets explosion mechanism(JJEM)asserts that most CCSNe are exploded by jittering jets that the newly born neutron star(NS)launches within a few seconds.According to the JJEM,instabilities in the accreted gas lead to the formation of intermittent accretion disks that launch the jittering jets.Earlier studies that did not include jets calculated the gravitational frequencies that instabilities around the NS emit to have a peak in the crude frequency range of 100–2000Hz.Based on a recent study,I take the source of the gravitational waves of jittering jets to be the turbulent bubbles(cocoons)that the jets inflate as they interact with the outer layers of the core of the star at thousands of kilometers from the NS.The lower frequencies and larger strains than those of gravitational waves from instabilities in CCSNe allow future,and maybe present,detectors to identify the gravitational wave signals of jittering jets.Detection of gravitational waves from local CCSNe might distinguish between the neutrino-driven explosion mechanism and the JJEM.展开更多
The extremely accurate estimates of stellar variability and radial velocity in the Gaia Data Release 3(Gaia DR3)have enabled us to examine the close binarity and radial velocity(RV)of central stars(CSs)of planetary ne...The extremely accurate estimates of stellar variability and radial velocity in the Gaia Data Release 3(Gaia DR3)have enabled us to examine the close binarity and radial velocity(RV)of central stars(CSs)of planetary nebulae(PNe).This study is twofold:(1)searching for new close binary CS candidates to better understand how binarity affects the formation and evolution of PNe;and(2)extending the sample size of known RVs of PNe in order to understand their kinematics and the dynamics of the Milky Way.As a target sample,we used all true,possible,and likely PNe available in the literature.Then,we looked for their matched Gaia DR3 sources that provide measurements of variability and RV.As a result,we detected the first large collection of trustworthy photometric variability of 26 symbiotic stars and 82 CSs.In this CS group,there are 24 sources already classified as true close binary CSs in the literature.Hence,we discovered 58 new close binary CS candidates.This close binary(CB)sample represents more than half of what is currently available in the literature.In addition,we identified the radial velocities for 51 PNe.To our knowledge,24 of these were measured for the first time.The RV measurements predicted by Gaia,based on the Doppler shift of the CS absorption lines,and those derived from nebular emission lines,show satisfactory agreement except for a few extremely high-velocity PNe.展开更多
Open clusters(OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each meth...Open clusters(OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each method has its limitations and therefore, different approaches to discovering OCs hold significant values. We develop a comprehensive approach method to automatically explore the data space and identify potential OC candidates with relatively reliable membership determination. This approach combines the techniques of Hierarchical Density-Based Spatial Clustering of Applications with Noise, Gaussian mixture model, and a novel cluster member identification technique, color excess constraint. The new method exhibits efficiency in detecting OCs while ensuring precise determination of cluster memberships. Because the main feature of this technique is to add an extra constraint(EC) for the members of cluster candidates using the homogeneity of color excess,compared to typical blind search codes, it is called Blind Search-Extra Constraint(BSEC) method. It is successfully applied to the Gaia Data Release 3, and 83 new OCs are found, whose color–magnitude diagrams(CMDs) are fitted well to the isochrones. In addition, this study reports 621 new OC candidates with discernible main sequence or red giant branch. It is shown that BSEC technique can discard some false negatives of previous works, which takes about three percentage of known clusters. It shows that as an EC, the color excess(or twocolor) constraint is useful for removing fake cluster member stars from the clusters that are identified from the positions and proper motions of stars, and getting more precise CMDs, when differential reddening of member stars of a cluster is not large(e.g., ΔE(G_(BP)-G_(RP)) < 0.5 mag). It makes the CMDs of 15% clusters clearer(in particular for the region near turnoff) and therefore is helpful for CMD and stellar population studies. Our result suggests that the color excess constraint is more appropriate for clusters with展开更多
The braking indices of pulsars may contain important information about the internal physics of neutron stars(NSs),such as neutron superfluidity and internal magnetic fields.As a subsequent paper of Cheng et al.,we per...The braking indices of pulsars may contain important information about the internal physics of neutron stars(NSs),such as neutron superfluidity and internal magnetic fields.As a subsequent paper of Cheng et al.,we perform the same analysis as that done in the previous paper to other young pulsars with a steady braking index,n.Combining the timing data of these pulsars with the theory of magnetic field decay,and using their measured magnetic tilt angles,we can set constraints on the number of precession cycles,ξ,which represents the interactions between superfluid neutrons and other particles in the NS interior.For the pulsars considered in this paper,the results show thatξis within the range of a few×10~3 to a few×10~6.Interestingly,for the Crab and Vela pulsars,the constraints onξobtained with our method are generally consistent with that derived from modeling of the glitch rise behaviors of the two pulsars.Furthermore,we find that the internal magnetic fields of pulsar with n<3 may be dominated by the toroidal components.Our results may not only help to understand the interactions between the superfluid neutrons and other particles in the interior of NSs but also be important for the study of continuous gravitational waves from pulsars.展开更多
In this paper,we study five luminous supernovae(LSNe)Ibc(SN 2009ca,ASASSN-15mj,SN 2019omd,SN 2002ued,and SN 2021bmf)whose peak absolute magnitudes M_(peakare)≈-19.5 to-21 mag by fitting their multi-band light curves(...In this paper,we study five luminous supernovae(LSNe)Ibc(SN 2009ca,ASASSN-15mj,SN 2019omd,SN 2002ued,and SN 2021bmf)whose peak absolute magnitudes M_(peakare)≈-19.5 to-21 mag by fitting their multi-band light curves(LCs)with different energy source models.We find that SN 2009ca might be powered by the^(56)Ni model since the required^(56)Ni mass(0.56 M_(⊙))is comparable to those of energetic SNe Ic,while the rest four SNe cannot be accounted for the^(56)Ni model since their derived^(56)Ni masses are(?)1 M_(⊙)or the ratios of the^(56)Ni mass to the ejecta mass are larger than 0.2.This indicates that some LSNe might be powered by^(56)Ni decay,while most of them need additional energy sources.We then use the magnetar plus^(56)Ni model and the fallback plus^(56)Ni model to fit the LCs of the four LSNe that cannot be explained by the^(56)Ni model,finding that the two models can account for the four SNe,and the derived parameters are comparable to those of LSNe or superluminous SNe in the literature,if they were(mainly)powered by magnetars or fallback.We suggest that the magnetar plus^(56)Ni model is more reasonable than the fallback plus^(56)Ni model,since the validity of the fallback plus^(56)Ni model depends on the value of accretion efficiency(η)and favors a largeηvalue,and the magnetar plus^(56)Ni model yields smallerχ^(2)/dof values.It should be pointed out that,however,the fallback plus^(56)Ni model is still a promising model that can account for the four SNe in our sample as well as other LSNe.展开更多
Fast Radio Bursts （FRBs） are intense radio flashes from the sky that are characterized by mil- lisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs that have been discove...Fast Radio Bursts （FRBs） are intense radio flashes from the sky that are characterized by mil- lisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs that have been discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be ~ 660 pc cm-3, supporting their being from a cosmological origin. Their energy released in the radio band spans about two orders of magnitude, with a mean value of ~ 10-39 erg. More interestingly, although the study of FRBs is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by the Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as dN/dFobs = （4.1± 1.3） × 103 F-obs1.1±0.2 sky-1 d-l, where Fobs is the observed radio obs fluence in units of Jy ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope （FAST） is predicted to be able to detect about five FRBs for every 1000 h of observation time.展开更多
We present a sample of about 120 000 red clump candidates selected from the LAMOST DR2 catalog based on the empirical distribution model in the effective temperature vs. surface gravity plane. Although, in general, re...We present a sample of about 120 000 red clump candidates selected from the LAMOST DR2 catalog based on the empirical distribution model in the effective temperature vs. surface gravity plane. Although, in general, red clump stars are considered as standard candles, they do not exactly stay in a narrow range of absolute magnitude, but may have a range of more than one magnitude depending on their initial mass. Consequently, conventional oversimplified distance estimations with the assumption of a fixed luminosity may lead to systematic bias related to the initial mass or age, which can potentially affect the study of the evolution of the Galaxy with red clump stars. We therefore employ an isochrone-based method to estimate the absolute magnitude of red clump stars from their observed surface gravities, effective temperatures and metallicities. We verify that the estimation removes the systematics well and provides initial mass/age estimates that are independent of distance with accuracy better than 10%.展开更多
Up to 2022 November,267 pulsars had been discovered in 36 globular clusters(GCs).In this paper,we present our studies on the distribution of GC pulsar parameters and the detection efficiency.The power law relation bet...Up to 2022 November,267 pulsars had been discovered in 36 globular clusters(GCs).In this paper,we present our studies on the distribution of GC pulsar parameters and the detection efficiency.The power law relation between average dispersion measure(■)and dispersion measure difference(ΔDM)of known pulsars in GCs is lgΔDM∝1.52lg■.The sensitivity could be the key to finding more pulsars.As a result,several years after the construction of a large radio telescope facility,the number of known GC pulsars will likely be increased accordingly.We suggest that currently GCs in the southern hemisphere could have higher possibilities for finding new pulsars.展开更多
The increasing radio frequency interference(RFI)is a well-recognized problem in radio astronomy research.Pulsars and Fast Radio Bursts(FRBs)are high-priority science targets of the ongoing Commercial Radio Astronomy F...The increasing radio frequency interference(RFI)is a well-recognized problem in radio astronomy research.Pulsars and Fast Radio Bursts(FRBs)are high-priority science targets of the ongoing Commercial Radio Astronomy FAST Survey(CRAFTS).To improve the quality of RFI removal in searches of pulsars and FRBs based on CRAFTS multi-beam data,we here propose an intuitive but powerful RFI mitigation pipeline(CCF-ST).The“CCF-ST”is a spatial filter constructed by signal cross-correlation function(CCF)and Sum-Threshold(ST)algorithm.The RFI marking result is saved in a“mask”file,a binary format for RFI masks in PRESTO.Three known pulsars,PSR B0525-21,PSR B0621-04,and PSR J0943+2252 from CRAFTS L-band 19 beams data are used for evaluation of the performance of CCF-ST in comparison with other methods,such as PRESTO’s“rfifind”,ArPLS-ST and ArPLS-SF.The result shows that CCF-ST can reduce effective data loss rate and improves the detected signal-to-noise ratio of the pulsations by~26%and~18%respectively compared with PRESTO’s“rfifind”and ArPLS-ST.The CCF-ST also has the advantage of low computational cost,e.g.,reducing the time consumption by~40%and memory consumption by~90%compared with ArPLS-SF.We expect that the new RFI mitigation and analysis toolkit(CCF-ST)demonstrated in this paper can be applied to CRAFTS and other multi-beam telescope observations to improve the data quality and efficiency of pulsar and FRB searches.展开更多
We present a method by using the phase characteristics of radio observation data for pulsar search and candidate identification.The phase characteristics are relations between the pulsar signal and the phase correctio...We present a method by using the phase characteristics of radio observation data for pulsar search and candidate identification.The phase characteristics are relations between the pulsar signal and the phase correction in the frequency-domain,and we regard it as a new search diagnostic characteristic.Based on the phase characteristics,a search method is presented:calculating dispersion measure(DM)—frequency data to select candidate frequencies,and then confirming of candidates by using the broadband characteristics of pulsar signals.Based on this method,we performed a search test on short observation data of M15 and M71,which were observed by Five-hundredmeter Aperture Spherical radio Telescope,and some of the Galactic Plane Pulsar Snapshot survey data.Results show that it can get similar search results to PRESTO(Pulsa R Exploration and Search TOolkit)while having a faster processing speed.展开更多
Pulsars are believed to be one of the most interesting objects in the universe.The emission mechanism of pulsars is still a conundrum to physicists,as there is no completely acceptable theory that can establish a cons...Pulsars are believed to be one of the most interesting objects in the universe.The emission mechanism of pulsars is still a conundrum to physicists,as there is no completely acceptable theory that can establish a consensus between theory and observation.Pulsars possess a gigantic magnetic field,to the order of 10^(12)Gauss,and generate a very powerful radio beam from the magnetic pole.However,the powerful radio beam is generated by some complicated coherent plasma processes and acceleration in the pulsar magnetosphere.The location of the origin of the radio waves has been predicted to come out exclusively from the polar cap zone,whose boundary is defined by the footprint of the last open field line.However,in this paper,we mainly try to generate the shape of the polar cap structure from an analytical solution and discuss how it gets distorted for different geometrical parameters due to the presence of perturbation such as polar cap current flow.Also,apart from that,we try to emphasize understanding the variation of radio emission height and polarization angle with respect to different geometryrelated parameters as well as with frequency.展开更多
基金supported by the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (Grant No. XDB09000000)the National Key Basic Research Program of China (2014CB845700)CL acknowledges the National Natural Science Foundation of China (NSFC, Grant Nos. 11373032, 11333003 and U1231119)
文摘In this work, we select spectra of stars with high signal-to-noise ratio from LAMOST data and map their MK classes to the spectral features. The equivalent widths of prominent spectral lines, which play a similar role as multi-color photometry, form a clean stellar locus well ordered by MK classes. The advantage of the stellar locus in line indices is that it gives a natural and continuous classification of stars consistent with either broadly used MK classes or stellar astrophysical parameters. We also employ an SVM-based classification algorithm to assign MK classes to LAMOST stellar spectra. We find that the completenesses of the classifications are up to 90% for A and G type stars, but they are down to about 50% for OB and K type stars. About 40% of the OB and K type stars are mis-classified as A and G type stars,respectively. This is likely due to the difference in the spectral features between late B type and early A type stars or between late G and early K type stars being very weak. The relatively poor performance of the automatic MK classification with SVM suggests that the direct use of line indices to classify stars is likely a more preferable choice.
基金the National Natural Science Foundation of China.
文摘Average pulse profiles of pulsar signals are analyzed using the bispectrum technique. The result shows that there are nonlinear phase couplings between the two frequency axes of the bispectrum charts, which indicate nonlinear factors in the generation and propagation of pulsar signals. Bispectra can be used as feature vectors of pulsar signals because of their being translation invariant. A one-dimension selected line spectrum algorithm for extracting pulsar signal characteristic is proposed. Compared with selected bispectra, the proposed selected line spectra have the maximum interclass separability measurements from the point of view of the whole one-dimension feature vector. Recognition experiments on several pulsar signals received at several frequency bands are carried out. The result shows that the selected line spectrum algorithm is suitable for extracting pulsar signal characteristics and has a good classification performance.
基金the Space Science and Geospatial Institute (SSGI) -Entoto Observatory and Research Center (EORC)Astronomy and Astrophysics Department for supporting this research。
文摘In this study,we determined the physical parameters of W UMa type contact binaries and their stability of mass transfer with different stellar mass ranges over a broad space by applying the basic dynamical evolution equations of the W UMa type contact binaries using accretor and donor masses between 0.079 and 2.79 M_(⊙).In these systems,we have studied the three subclasses of W UMa systems of A-,B-and W-type contact binaries using the initial and final mass ranges and we investigated different stellar and orbital parameters for the subclasses of W UMa systems.We examined the stability of the W UMa type contact binaries using the orbital parameters such as critical mass ratio,Roche lobe radius of the donor star and mass ratio of these systems.Thus,we computed the observed and calculated physical parameters of A-,B-and W-type W UMa systems.Moreover,we determined the combined and color temperatures to classify the three subclasses of the systems.Also,we presented the result of the internal stellar structure and evolution of W UMa type contact binaries by using the polytropic model.
基金supported by the National Natural Science Foundation of China(Nos.U1938201 and 12373042)。
文摘GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to~1020 s and the true timescale of the central engine activity t_(burst)≥4×10^(4) s.The late X-ray light curve with a decay index ofα=7.53 is steeper than the steepest possible decay from an external shock model.We propose that this X-ray afterglow can be driven by dipolar radiation from the magnetar spindown during its early stage,while the magnetar collapsed into the black hole before its spindown,resulting in a very steep decay of the late X-ray light curve.The optical data show that the light curve is still rising after 1.1 ks,suggesting a late onset.We show that GRB 200612A’s optical afterglow light curve is fitted with the forward shock model by Gaussian structured off-axis jet.This is a special case among GRBs,as it may be an ultralong gamma-ray burst powered by a magnetar in an off-axis observation scenario.
基金funded by the National Natural Science Foundation of China(Nos.12373042,U1938201,12273005 and 12133003)the Programme of Bagui Scholars Programme(WXG)support of the China Space Station Telescope(CSST)。
文摘After launching a jet,outflows of magnetar were used to account for the achromatic plateau of afterglow and the early X-ray flux plateau known as“internal plateau”.The lack of detecting magnetic dipole emission together with the energy injection feature in a single observation poses confusion until the long gamma-ray burst(GRB)210610B is detected.GRB 210610B is presented with an optical bump following an early X-ray plateau during the afterglow phase.The plateau followed by a steep decline flux overlays in the steadily decaying X-ray flux with indexα_(X,1)~2.06,indicating an internal origin and that can be fitted by the spin-down luminosity law with the initial plateau luminosity log_(10)L_(X)~48.29 erg s~(-1)and the characteristic spin-down timescale T~2818 s.A subsequent bump begins at~4000 s in the R band with a rising indexα_(R,1)~-0.30 and peaks at~14125 s,after which a decay indexα_(R,2)~0.87 and finally transiting to a steep decay withα_(R,3)~1.77 achieve the closure relation of the external shock for the normal decay phase as well as the magnetar spin-down energy injection phase,provided that the average value of the photon indexΓ_γ=1.80 derived from the spectral energy distributions(SEDs)between the X-ray and optical afterglow.The closure relation also works for the late X-ray flux.Akin to the traditional picture of GRB,the outflow powers the early X-ray plateau by dissipating energy internally and collides with the leading decelerating blast burst as time goes on,which could interpret the exotic feature of GRB 210610B.We carry out a Markov Chain Monte Carlo simulation and obtain a set of best parameters:■.The artificial light curve can fit the afterglow data well.After that,we estimated the average Lorentz factor and the X-ray radiation efficiency of the later ejecta are 35%and 0.13%,respectively.
基金supported by the National Natural Science Foundation of China(NSFC,Grant Nos.12173047,12322306,12003046,12233009,and 12133002)support from the Youth Innovation Promotion Association of the Chinese Academy of Sciences(no.2022055 and 2023065)support from the National Key Research and Development Program of China,grants 2022YFF0503404 and 2019YFA0405504。
文摘Long period variable(LPV)stars are very promising distance indicators in the infrared bands.We selected asymptotic giant branch(AGB)stars in the Large and Small Magellanic Cloud(LMC and SMC)from the Gaia Data Release 3 LPV catalog,and classified them into oxygen-rich(O-rich)and carbon-rich(C-rich)AGB stars.Using the Wide-field Infrared Survey Explorer database,we determined the W1-and W2-band period-luminosity relations(PLRs)for each pulsation-mode sequence of AGB stars.The dispersion of the PLRs of O-rich AGB stars in sequences C'and C is relatively small,around 0.14 mag.The PLRs of LMC and SMC are consistent in each sequence.In the W2 band,the PLR of large-amplitude C-rich AGB stars is steeper than that of small-amplitude C-rich AGB stars,due to their more circumstellar dust.By two methods,we find that some PLR sequences of O-rich AGB stars in the LMC are dependent on metallicity.The coefficients of the metallicity effect areβ=-0.533±0.213 mag dex~1andβ=-0.767±0.158 mag dex~1for sequence C in W1 and W2 bands,respectively.The significance of the metallicity effect in W1 band for the four sequences is 2.2-3.5σ.Both of these imply that distance measurements using O-rich Mira may need to take the metallicity effect into account.
基金a grant from the Israel Science Foundation(769/20).
文摘I build a toy model in the frame of the jittering jets explosion mechanism(JJEM)of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly born neutron star(NS)accretes and the constant angular momentum component,and show that the JJEM can account for the≃2.5–5M⊙mass gap between NSs and black holes(BHs).The random component of the angular momentum results from pre-collapse core convection fluctuations that are amplified by post-collapse instabilities.The fixed angular momentum component results from pre-collapse core rotation.For slowly rotating pre-collapse cores the stochastic angular momentum fluctuations form intermittent accretion disks(or belts)around the NS with varying angular momentum axes in all directions.The intermittent accretion disk/belt launches jets in all directions that expel the core material in all directions early on,hence leaving an NS remnant.Rapidly rotating pre-collapse cores form an accretion disk with angular momentum axis that is about the same as the pre-collapse core rotation.The NS launches jets along this axis and hence the jets avoid the equatorial plane region.Inflowing core material continues to feed the central object from the equatorial plane increasing the NS mass to form a BH.The narrow transition from slow to rapid pre-collapse core rotation,i.e.,from an efficient to inefficient jet feedback mechanism,accounts for the sparsely populated mass gap.
基金the Resource sharing platform construction project of Xinjiang Uygur Autonomous Region(No.PT2306)the Chinese Academy of Sciences(CAS)“Light of West China”Program(No.2020-XBQNXZ-016,2022-XBQNXZ-016)。
文摘This work presents the charge-coupled device(CCD)photometric survey of the old open cluster NGC 188.Timeseries V-band photometric observations were conducted for ten nights in 2017 January using the Nanshan Onemeter Wide-field Telescope to search for variable stars in the field of the cluster.A total of 25 variable stars,including one new variable star,were detected in the target field.Among the detected variables,16 are cluster member stars,and the others are identified as field stars.The periods,radial velocities,effective temperatures,and classifications of the detected variables are discussed in this work.Most of the stars’effective temperatures are between 4200 and 6600 K,indicating their spectral types are G or K.The newly discovered variable is probably a W UMa system.In this study,a known cluster variable star(V21=V0769 Cep)is classified as an EA-type variable star based on the presence of an 0.5 mag eclipse in its light curve.
基金supported by the National Natural Science Foundation of China under grant 12065017Jiangxi Provincial Natural Science Foundation under grant 20224ACB211001support from the Chinese Academy of Sciences(grant Nos.E329A3M1,E32983U8,and E3545KU2)。
文摘Theories of modified gravity suggest that the propagation speed of gravitational waves(GW)v_gmay deviate from the speed of light c.A constraint can be placed on the difference between c and v_gwith a simple method that uses the arrival time delay between GW and electromagnetic wave simultaneously emitted from a burst event.We simulated the joint observation of GW and short gamma-ray burst signals from binary neutron star merger events in different observation campaigns,involving advanced LIGO(aLIGO)in design sensitivity and Einstein Telescope(ET)joint-detected with Fermi/GBM.As a result,the relative precision of constraint on v_gcan reach~10~(-17)(aLIGO)and~10^(-18)(ET),which are one and two orders of magnitude better than that from GW170817,respectively.We continue to obtain the bound of graviton mass m_g≤7.1(3.2)×10~(-20)eV with aLIGO(ET).Applying the Standard-Model Extension test framework,the constraint on v_gallows us to study the Lorentz violation in the nondispersive,nonbirefringent limit of the gravitational sector.We obtain the constraints of the dimensionless isotropic coefficients S_(00)^(4)at mass dimension d=4,which are-1×10^(-15)<S_(00)^(4)<9×10^(-17)for aLIGO and-4×10^(-16)<s_(00)^(4<8<10^(-18))for ET.
基金supported by a grant from the Israel Science Foundation(769/20)。
文摘I estimate the frequencies of gravitational waves from jittering jets that explode core collapse supernovae(CCSNe)to crudely be 5–30 Hz,and with strains that might allow detection of Galactic CCSNe.The jittering jets explosion mechanism(JJEM)asserts that most CCSNe are exploded by jittering jets that the newly born neutron star(NS)launches within a few seconds.According to the JJEM,instabilities in the accreted gas lead to the formation of intermittent accretion disks that launch the jittering jets.Earlier studies that did not include jets calculated the gravitational frequencies that instabilities around the NS emit to have a peak in the crude frequency range of 100–2000Hz.Based on a recent study,I take the source of the gravitational waves of jittering jets to be the turbulent bubbles(cocoons)that the jets inflate as they interact with the outer layers of the core of the star at thousands of kilometers from the NS.The lower frequencies and larger strains than those of gravitational waves from instabilities in CCSNe allow future,and maybe present,detectors to identify the gravitational wave signals of jittering jets.Detection of gravitational waves from local CCSNe might distinguish between the neutrino-driven explosion mechanism and the JJEM.
文摘The extremely accurate estimates of stellar variability and radial velocity in the Gaia Data Release 3(Gaia DR3)have enabled us to examine the close binarity and radial velocity(RV)of central stars(CSs)of planetary nebulae(PNe).This study is twofold:(1)searching for new close binary CS candidates to better understand how binarity affects the formation and evolution of PNe;and(2)extending the sample size of known RVs of PNe in order to understand their kinematics and the dynamics of the Milky Way.As a target sample,we used all true,possible,and likely PNe available in the literature.Then,we looked for their matched Gaia DR3 sources that provide measurements of variability and RV.As a result,we detected the first large collection of trustworthy photometric variability of 26 symbiotic stars and 82 CSs.In this CS group,there are 24 sources already classified as true close binary CSs in the literature.Hence,we discovered 58 new close binary CS candidates.This close binary(CB)sample represents more than half of what is currently available in the literature.In addition,we identified the radial velocities for 51 PNe.To our knowledge,24 of these were measured for the first time.The RV measurements predicted by Gaia,based on the Doppler shift of the CS absorption lines,and those derived from nebular emission lines,show satisfactory agreement except for a few extremely high-velocity PNe.
基金supported by Yunnan Academician Workstation of Wang Jingxiu(202005AF150025)China Manned Space Project(NO.CMS-CSST-2021-A08)Guanghe project(ghfund202302019167)。
文摘Open clusters(OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each method has its limitations and therefore, different approaches to discovering OCs hold significant values. We develop a comprehensive approach method to automatically explore the data space and identify potential OC candidates with relatively reliable membership determination. This approach combines the techniques of Hierarchical Density-Based Spatial Clustering of Applications with Noise, Gaussian mixture model, and a novel cluster member identification technique, color excess constraint. The new method exhibits efficiency in detecting OCs while ensuring precise determination of cluster memberships. Because the main feature of this technique is to add an extra constraint(EC) for the members of cluster candidates using the homogeneity of color excess,compared to typical blind search codes, it is called Blind Search-Extra Constraint(BSEC) method. It is successfully applied to the Gaia Data Release 3, and 83 new OCs are found, whose color–magnitude diagrams(CMDs) are fitted well to the isochrones. In addition, this study reports 621 new OC candidates with discernible main sequence or red giant branch. It is shown that BSEC technique can discard some false negatives of previous works, which takes about three percentage of known clusters. It shows that as an EC, the color excess(or twocolor) constraint is useful for removing fake cluster member stars from the clusters that are identified from the positions and proper motions of stars, and getting more precise CMDs, when differential reddening of member stars of a cluster is not large(e.g., ΔE(G_(BP)-G_(RP)) < 0.5 mag). It makes the CMDs of 15% clusters clearer(in particular for the region near turnoff) and therefore is helpful for CMD and stellar population studies. Our result suggests that the color excess constraint is more appropriate for clusters with
基金supported by the National Natural Science Foundation of China(Grant Nos.12003009,and 12033001)CAS“Light of West China”Program(Grant No.2019-XBQNXZ-B-016)the National SKA program of China(Grant No.2020SKA0120300)。
文摘The braking indices of pulsars may contain important information about the internal physics of neutron stars(NSs),such as neutron superfluidity and internal magnetic fields.As a subsequent paper of Cheng et al.,we perform the same analysis as that done in the previous paper to other young pulsars with a steady braking index,n.Combining the timing data of these pulsars with the theory of magnetic field decay,and using their measured magnetic tilt angles,we can set constraints on the number of precession cycles,ξ,which represents the interactions between superfluid neutrons and other particles in the NS interior.For the pulsars considered in this paper,the results show thatξis within the range of a few×10~3 to a few×10~6.Interestingly,for the Crab and Vela pulsars,the constraints onξobtained with our method are generally consistent with that derived from modeling of the glitch rise behaviors of the two pulsars.Furthermore,we find that the internal magnetic fields of pulsar with n<3 may be dominated by the toroidal components.Our results may not only help to understand the interactions between the superfluid neutrons and other particles in the interior of NSs but also be important for the study of continuous gravitational waves from pulsars.
基金supported by the National Natural Science Foundation of China(grant Nos.11963001,12133003,11833003,11973020(C0035736),U1938201)。
文摘In this paper,we study five luminous supernovae(LSNe)Ibc(SN 2009ca,ASASSN-15mj,SN 2019omd,SN 2002ued,and SN 2021bmf)whose peak absolute magnitudes M_(peakare)≈-19.5 to-21 mag by fitting their multi-band light curves(LCs)with different energy source models.We find that SN 2009ca might be powered by the^(56)Ni model since the required^(56)Ni mass(0.56 M_(⊙))is comparable to those of energetic SNe Ic,while the rest four SNe cannot be accounted for the^(56)Ni model since their derived^(56)Ni masses are(?)1 M_(⊙)or the ratios of the^(56)Ni mass to the ejecta mass are larger than 0.2.This indicates that some LSNe might be powered by^(56)Ni decay,while most of them need additional energy sources.We then use the magnetar plus^(56)Ni model and the fallback plus^(56)Ni model to fit the LCs of the four LSNe that cannot be explained by the^(56)Ni model,finding that the two models can account for the four SNe,and the derived parameters are comparable to those of LSNe or superluminous SNe in the literature,if they were(mainly)powered by magnetars or fallback.We suggest that the magnetar plus^(56)Ni model is more reasonable than the fallback plus^(56)Ni model,since the validity of the fallback plus^(56)Ni model depends on the value of accretion efficiency(η)and favors a largeηvalue,and the magnetar plus^(56)Ni model yields smallerχ^(2)/dof values.It should be pointed out that,however,the fallback plus^(56)Ni model is still a promising model that can account for the four SNe in our sample as well as other LSNe.
基金supported by the National Basic Research Program of China(973 program,Grant Nos.2014CB845800 and 2012CB821802)the National Natural Science Foundation of China(Grant Nos.11473012,U1431126 and 11263002)+1 种基金the Strategic Priority Research Program(Grant Nos.XDB09010302 and XDB23000000)the support from the CAS Interdisciplinary Innovation Team and the CAS Key International Collaboration Program
文摘Fast Radio Bursts （FRBs） are intense radio flashes from the sky that are characterized by mil- lisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs that have been discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be ~ 660 pc cm-3, supporting their being from a cosmological origin. Their energy released in the radio band spans about two orders of magnitude, with a mean value of ~ 10-39 erg. More interestingly, although the study of FRBs is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by the Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as dN/dFobs = （4.1± 1.3） × 103 F-obs1.1±0.2 sky-1 d-l, where Fobs is the observed radio obs fluence in units of Jy ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope （FAST） is predicted to be able to detect about five FRBs for every 1000 h of observation time.
基金supported by the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (Grant No. XDB09000000)the National Key Basic Research Program of China (2014CB845700)CL acknowledges the National Natural Science Foundation of China (NSFC, Grant Nos. 11373032, 11333003 and U1231119)
文摘We present a sample of about 120 000 red clump candidates selected from the LAMOST DR2 catalog based on the empirical distribution model in the effective temperature vs. surface gravity plane. Although, in general, red clump stars are considered as standard candles, they do not exactly stay in a narrow range of absolute magnitude, but may have a range of more than one magnitude depending on their initial mass. Consequently, conventional oversimplified distance estimations with the assumption of a fixed luminosity may lead to systematic bias related to the initial mass or age, which can potentially affect the study of the evolution of the Galaxy with red clump stars. We therefore employ an isochrone-based method to estimate the absolute magnitude of red clump stars from their observed surface gravities, effective temperatures and metallicities. We verify that the estimation removes the systematics well and provides initial mass/age estimates that are independent of distance with accuracy better than 10%.
基金supported by the National SKA Program of China No.2020SKA0120100the National Natural Science Foundation of China(NSFC,Grant Nos.11963002,11703047,11773041,U2031119,12173052,12003047 and 12173053)+7 种基金the fostering project of Guizhou University with No.201911Cultivation Project for FAST Scientific Payoff and Research Achievement of CAMS-CASsupported by the Specialized Research Fund for State Key Laboratoriessupported by the CAS“Light of West China”Programthe Youth Innovation Promotion Association of CAS(id 2023064)supported by the Youth Innovation Promotion Association of CAS(id.2018075 and Y2022027)supported by Guizhou Provincial Basic Research Program(Natural Science)(ZK[2023]039)Key Technology R&D Program([2023]352)。
文摘Up to 2022 November,267 pulsars had been discovered in 36 globular clusters(GCs).In this paper,we present our studies on the distribution of GC pulsar parameters and the detection efficiency.The power law relation between average dispersion measure(■)and dispersion measure difference(ΔDM)of known pulsars in GCs is lgΔDM∝1.52lg■.The sensitivity could be the key to finding more pulsars.As a result,several years after the construction of a large radio telescope facility,the number of known GC pulsars will likely be increased accordingly.We suggest that currently GCs in the southern hemisphere could have higher possibilities for finding new pulsars.
基金supported by National Natural Science Foundation of China(NSFC)under Nos.11988101,U183110134,11703047,11773041,and U1831131support by the Youth Innovation Promotion Association CAS(id.2021055)cultivation project for FAST scientific payoff and research achievement of CAMS-CAS。
文摘The increasing radio frequency interference(RFI)is a well-recognized problem in radio astronomy research.Pulsars and Fast Radio Bursts(FRBs)are high-priority science targets of the ongoing Commercial Radio Astronomy FAST Survey(CRAFTS).To improve the quality of RFI removal in searches of pulsars and FRBs based on CRAFTS multi-beam data,we here propose an intuitive but powerful RFI mitigation pipeline(CCF-ST).The“CCF-ST”is a spatial filter constructed by signal cross-correlation function(CCF)and Sum-Threshold(ST)algorithm.The RFI marking result is saved in a“mask”file,a binary format for RFI masks in PRESTO.Three known pulsars,PSR B0525-21,PSR B0621-04,and PSR J0943+2252 from CRAFTS L-band 19 beams data are used for evaluation of the performance of CCF-ST in comparison with other methods,such as PRESTO’s“rfifind”,ArPLS-ST and ArPLS-SF.The result shows that CCF-ST can reduce effective data loss rate and improves the detected signal-to-noise ratio of the pulsations by~26%and~18%respectively compared with PRESTO’s“rfifind”and ArPLS-ST.The CCF-ST also has the advantage of low computational cost,e.g.,reducing the time consumption by~40%and memory consumption by~90%compared with ArPLS-SF.We expect that the new RFI mitigation and analysis toolkit(CCF-ST)demonstrated in this paper can be applied to CRAFTS and other multi-beam telescope observations to improve the data quality and efficiency of pulsar and FRB searches.
基金supported by the National Natural Science Foundation of China(Nos.12203039 and 11873083)the National Natural Science Foundation of China(Nos.12173053 and 12041303)+4 种基金supported by the National SKA Program of China(No.2020SKA0120100)the Youth Innovation Promotion Association of CAS(id.2018075)the CAS“Light of West China”Programthe Specialized Research Fund for State Key Laboratoriesthe Science and Technology Program of Guizhou Province([2021]4001)。
文摘We present a method by using the phase characteristics of radio observation data for pulsar search and candidate identification.The phase characteristics are relations between the pulsar signal and the phase correction in the frequency-domain,and we regard it as a new search diagnostic characteristic.Based on the phase characteristics,a search method is presented:calculating dispersion measure(DM)—frequency data to select candidate frequencies,and then confirming of candidates by using the broadband characteristics of pulsar signals.Based on this method,we performed a search test on short observation data of M15 and M71,which were observed by Five-hundredmeter Aperture Spherical radio Telescope,and some of the Galactic Plane Pulsar Snapshot survey data.Results show that it can get similar search results to PRESTO(Pulsa R Exploration and Search TOolkit)while having a faster processing speed.
基金Department of Science and Technology,Govt.of India for providing financial assistance to carry out research。
文摘Pulsars are believed to be one of the most interesting objects in the universe.The emission mechanism of pulsars is still a conundrum to physicists,as there is no completely acceptable theory that can establish a consensus between theory and observation.Pulsars possess a gigantic magnetic field,to the order of 10^(12)Gauss,and generate a very powerful radio beam from the magnetic pole.However,the powerful radio beam is generated by some complicated coherent plasma processes and acceleration in the pulsar magnetosphere.The location of the origin of the radio waves has been predicted to come out exclusively from the polar cap zone,whose boundary is defined by the footprint of the last open field line.However,in this paper,we mainly try to generate the shape of the polar cap structure from an analytical solution and discuss how it gets distorted for different geometrical parameters due to the presence of perturbation such as polar cap current flow.Also,apart from that,we try to emphasize understanding the variation of radio emission height and polarization angle with respect to different geometryrelated parameters as well as with frequency.
