Using a semi-analytic approach,we estimate halo spins for a large sample of H I-rich galaxies from the Arecibo Legacy Fast ALFA Survey and examine the correlation between H I mass fractions and halo spins.Our analysis...Using a semi-analytic approach,we estimate halo spins for a large sample of H I-rich galaxies from the Arecibo Legacy Fast ALFA Survey and examine the correlation between H I mass fractions and halo spins.Our analysis reveals a strong correlation between halo spin and the H I-to-stellar mass ratio in both low-mass and massive galaxy samples.This finding suggests a universal formation scenario:higher halo spin reduces angular momentum loss and gas condensation,leading to lower star formation rates and weaker feedback,which in turn help retain gas within dark matter halos.展开更多
We present the morphological study of 18,572 massive quiescent galaxies at z~1.2, selected by i-y colors in the Hyper Suprime-Cam(HSC) Deep and UltraDeep fields. The majority of our sample(94.3%) fall in the quiescent...We present the morphological study of 18,572 massive quiescent galaxies at z~1.2, selected by i-y colors in the Hyper Suprime-Cam(HSC) Deep and UltraDeep fields. The majority of our sample(94.3%) fall in the quiescent region in the rest-frame UVJ diagram. Comparing the five HSC bands and the subsample with HST F160W images, consistent with the decreasing effective radius re, Sérsic index n shows an increasing trend indicating a more bulge-dominant morphology towards the infrared. Even for our massive, quiescent galaxies,which are dominated by typical elliptical galaxies with bulges, the reand n values still vary with the wavelengths.For instance, there is a systematic drop in n of ~0.4 going from y band to F160W, making 20% of the HSC “disklike” galaxies appear “bulge-like” in the HST images. We suggest to use caution when comparing galaxy morphological types based on images at different resolutions or at different wavelengths, and whenever possible,to apply a reor n correction. More massive quiescent galaxies are systematically larger than the less massive ones,though no mass dependence is found for n measurements. The size–mass relation based on our sample and lowerz control samples show a monotonic increase of rewith M*, with a power-law of 0.61 ± 0.01, lower than previously found in similar samples of smaller sizes. Future high-resolution space-based surveys like NGRST will help confirm the possible n evolution, and if the flattening at the low-mass end is a genuine physical trend or limited by the image resolutions.展开更多
This paper presents a statistical study of the division of the[CⅡ]158μm line into ionized and neutral components,using a new carbon-to-nitrogen abundance ratio,log(C/N)=0.75,for a sample of 108 local galaxies.We inv...This paper presents a statistical study of the division of the[CⅡ]158μm line into ionized and neutral components,using a new carbon-to-nitrogen abundance ratio,log(C/N)=0.75,for a sample of 108 local galaxies.We investigate the correlation between the ionized-to-total[CⅡ]ratio([CⅡ]_(ionized)/[CⅡ]_(total))and the farinfrared color f60/f100,finding a moderate negative correlation.Additionally,we explore the dependence of[CⅡ]_(ionized)/[CⅡ]_(total)on various physical properties.We find that[CⅡ]_(ionized)/[CⅡ]_(total)exhibits a weak negative correlation with the offset from the main sequence and a moderate negative correlation with the[OⅢ]88μm/[NⅡ]122μm.Furthermore,no significant correlation with molecular gas mass is found.It shows a positive correlation with metallicity.Our results suggest that[CⅡ]_(ionized)/[CⅡ]_(total)is influenced by the ionization parameter,star formation efficiency and metallicity.展开更多
Leveraging the semi-analytic method,we compute halo spins for a substantial sample of H I-bearing galaxies observed in the Arecibo Legacy Fast ALFA Survey.Our statistical analysis reveals a correlation between halo sp...Leveraging the semi-analytic method,we compute halo spins for a substantial sample of H I-bearing galaxies observed in the Arecibo Legacy Fast ALFA Survey.Our statistical analysis reveals a correlation between halo spin and environment,although the trend is subtle.On average,galaxies exhibit a decreasing halo spin tendency in denser environments.This observation contrasts with previous results from N-body simulations in the Lambda Cold Dark Matter framework.The discrepancy may be attributed to environmental gas stripping,leading to an underestimation of halo spins in galaxies in denser environments,or to baryonic processes that significantly alter the original dark matter halo spins,deviating from previous N-body simulation findings.展开更多
We investigate the small-scale clustering of star-forming galaxies(SFGs) in the local universe, using both observational samples from the final data release of the Sloan Digital Sky Survey and IllustrisTNG300, one of ...We investigate the small-scale clustering of star-forming galaxies(SFGs) in the local universe, using both observational samples from the final data release of the Sloan Digital Sky Survey and IllustrisTNG300, one of the state-of-the-art hydrodynamic simulations of galaxy formation. We measure the projected two-point crosscorrelation function, wp(rp), for subsamples of SFGs with different specific star formation rates(sSFRs) and stellar masses(M*), with respect to reference samples of galaxies with early-type or late-type morphology. On scales smaller than ~100 kpc and at fixed M*, SFGs with higher sSFR are more strongly clustered, reflecting the interaction-induced central star formation found in previous studies. More importantly, the small-scale clusteringsSFR correlation is stronger when the reference sample is limited to late-type galaxies only. This confirms the previous finding that the enhancement of star formation in close pairs depends on the morphology of companion galaxies. These observational trends are broadly reproduced by IllustrisTNG300, indicating that current hydrodynamic simulations are capable of capturing the main recipes governing star formation in interacting/merging galaxies, although further work is needed to identify the exact physical processes involved.展开更多
The discovery of massive galaxies at high redshifts,especially the passive ones,poses a big challenge for the current standard galaxy formation models.Here we use the semi-analytic galaxy formation model developed by ...The discovery of massive galaxies at high redshifts,especially the passive ones,poses a big challenge for the current standard galaxy formation models.Here we use the semi-analytic galaxy formation model developed by Henriques et al.to explore the formation and evolution of massive galaxies(MGs,stellar-mass M*>1011 M⊙).Different from previous works,we focus on the ones just formed(e.g.just reach?1011 M⊙).We find that most of the MGs are formed around z=0.6,with the earliest formation at z>4.Interestingly,although most of the MGs in the local Universe are passive,we find that only 13%of the MGs are quenched at the formation time.Most of the quenched MGs at formation already host a very massive supermassive black hole(SMBH)which could power the very effective AGN feedback.For the star-forming MGs,the ones with more massive SMBH prefer to quench in shorter timescales;in particular,those with MSMBH>107.5 M⊙have a quenching timescale of~0.5 Gyr and the characteristic MSMBH depends on the chosen stellar mass threshold in the definition of MGs as a result of their co-evolution.We also find that the"in-situ"star formation dominates the stellar mass growth of MGs until they are formed.Over the whole redshift range,we find the quiescent MGs prefer to stay in more massive dark matter halos,and have more massive SMBH and less cold gas masses.Our results provide a new angle on the whole life of the growth of MGs in the Universe.展开更多
Using a sample of 13 early-type spiral galaxies hosting nuclear rings,we report remarkable correlations between the properties of the nuclear rings and the central intensity ratio(CIR) of their host galaxies.The CIR,a...Using a sample of 13 early-type spiral galaxies hosting nuclear rings,we report remarkable correlations between the properties of the nuclear rings and the central intensity ratio(CIR) of their host galaxies.The CIR,a function of intensity of light within the central 1.5 and 3 arcsec region,is found to be a vital parameter in galaxy evolution,as it shares strong correlations with many structural and dynamical properties of early-type galaxies,including mass of the central supermassive black hole(SMBH).We use archival HST images for aperture photometry at the centre of the galaxy image to compute the CIR.We observe that the relative sizes of nuclear rings and ring cluster surface densities strongly correlate with the CIR.These correlations suggest reduced star formation in the centres of galaxies hosting small and dense nuclear rings.This scenario appears to be a consequence of strong bars as advocated by the significant connection observed between the CIR and bar strengths.In addition,we observe that the CIR is closely related with the integrated properties of the stellar population in the nuclear rings,associating the rings hosting older and less massive star clusters with low values of CIR.Thus,the CIR can serve as a crucial parameter in unfolding the coupled evolution of bars and rings as it is intimately connected with both their properties.展开更多
The coevolution between supermassive black holes(SMBHs) and their host galaxies has been proposed for more than a decade,albeit with little direct evidence about black hole accretion activities regulating galaxy star ...The coevolution between supermassive black holes(SMBHs) and their host galaxies has been proposed for more than a decade,albeit with little direct evidence about black hole accretion activities regulating galaxy star formation at z> 1.In this paper,we study the lifetimes of X-ray active galactic nuclei(AGNs) in UV-selected red sequence(RS),blue cloud(BC) and green valley(GV) galaxies,finding that AGN accretion activities are most prominent in GV galaxies at z ~1.5-2,compared with RS and BC galaxies.We also compare AGN accretion timescales with typical color transition timescales of UV-selected galaxies.We find that the lifetime of GV galaxies at z~1.5-2 is very close to the typical timescale when the AGNs residing in them stay in the high-accretion-rate mode at these redshifts;for BC galaxies,the consistency between the color transition timescale and the black hole strong accretion lifetime is more likely to happen at lower redshifts(z <1).Our results support the scenario where AGN accretion activities govern UV color transitions of host galaxies,making galaxies and their central SMBHs coevolve with each other.展开更多
We present galactic spectroscopic data from a pencil beam of 10.75×7.5 centered on the X-ray cluster RXJ0054.0–2823 at z=0.29.We study the spectral evolution of galaxies from z=1 down to the cluster redshift in ...We present galactic spectroscopic data from a pencil beam of 10.75×7.5 centered on the X-ray cluster RXJ0054.0–2823 at z=0.29.We study the spectral evolution of galaxies from z=1 down to the cluster redshift in a magnitude-limited sample at R≤23,for which the statistical properties of the sample are well understood.We divide emission-line galaxies into star-forming galaxies,Low Ionization Nuclear Emission line Regions（LINERs） ,and Seyferts by using emission-line ratios of[OII],Hβ,and[OIII],and derive stellar fractions from population synthesis models. We focus our analysis on absorption and low-ionization galaxies.For absorption-line galaxies,we recover the well-known result that these galaxies have had no detectable evolution since z～0.6-0.7,but we also find that in the range z=0.65-1,at least 50% of the stars in bright absorption systems are younger than 2.5 Gyr.Faint absorption-line galaxies in the cluster at z=0.29 also had significant star formation during the previous 2-3 Gyr,but their brighter counterparts seem to be only composed of old stars.At z～0.8,our dynamically young cluster had a truncated red-sequence.This result seems to be consistent with a scenario where the final assembly of E/S0 took place at z1.In the volume-limited range 0.35≤z≤0.65,we find that 23% of the early-type galaxies have LINER-like spectra with Hβin absorption and have a significant component of A stars.The vast majority of LINERs in our sample have significant populations of young and intermediate-aged stars and are thus not related to AGNs,but to the population of‘retired galaxies’recently identified by Cid Fernandes et al.in the Sloan Digital Sky Survey（SDSS） .Early-type LINERs with various fractions of A stars and E＋A galaxies appear to play an important role in the formation of the red sequence.展开更多
Galaxy formation and evolution is one of the most active research areas in astrophysics,so many people have studied this area.But since they didn’t understand thoroughly the evolution law from satellite to planet the...Galaxy formation and evolution is one of the most active research areas in astrophysics,so many people have studied this area.But since they didn’t understand thoroughly the evolution law from satellite to planet then to star,their theories are very weak.In their theories,they proposed that large gas clouds collapsing to form a galaxy or more recently that matter started out in smaller clumps merged to form galaxy,which is incredible.Hence,the author of this paper,through studying the formation and orbit-variation of satellites,planets and stars,has put forward a new theory of galaxy formation and evolution,therefore revealing the hierarchical structure of galaxies and the formation and evolution of black holes and quasars.展开更多
We used the Sloan Digital Sky Survey （SDSS） Data Release 5 （DR5） to study the morphological properties of 1137 nearby infrared （IR） galaxies, most of which are brighter than 15.9 mag in r-band. This sample was d...We used the Sloan Digital Sky Survey （SDSS） Data Release 5 （DR5） to study the morphological properties of 1137 nearby infrared （IR） galaxies, most of which are brighter than 15.9 mag in r-band. This sample was drawn from a cross-correlation of the Infra-Red Astronomical Satellite （IRAS） point source catalog redshift survey with DR5 at z ≤ 0.08. Based on this IR galaxy sample, we constructed five volume-limited sub-samples with IR luminosity ranging from 10^9.5 L⊙ to 10^12L⊙. By deriving the IR luminosity functions （LF） for different morphological types, we found that normal spiral galaxies are the dominant population below LIR ~ 8 ~ 10^10 L⊙; while the fraction of barred spiral galaxies increases with increasing IR luminosity and becomes dominant in spiral galaxies beyond LIR ≈ 5 × 10^10L⊙. As the IR luminosity decreases, the IR galaxies become more compact and have lower stellar masses. The analysis also shows that normal spiral galaxies give the dominant contribution to the total comoving IR energy density in the nearby universe, while, in contrast, the contribution from peculiar galaxies is only 39%.展开更多
Early-type galaxies （ETGs） are very important for understanding the formation and evolution of galaxies. Recent observations suggest that ETGs are not simply old stellar spheroids as we previously thought. Widesprea...Early-type galaxies （ETGs） are very important for understanding the formation and evolution of galaxies. Recent observations suggest that ETGs are not simply old stellar spheroids as we previously thought. Widespread recent star formation, cool gas and dust have been detected in a substantial fraction of ETGs. We make use of the radial profiles of 9 - r color and the concentration index from the Sloan Digital Sky Survey database to pick out 31 peculiar ETGs with central blue cores. By analyzing the photometric and spectroscopic data, we suggest that the blue cores are caused by star formation activities rather than the central weak active galactic nucleus. From the results of stellar population synthesis, we find that the stellar population of the blue cores is relatively young, spreading from several Myr to less than one Gyr. In 14 galaxies with H I observations, we find that the average gas fraction of these galaxies is about 0.55. The bluer galaxies show a higher gas fraction, and the total star forma- tion rate （SFR） correlates very well with the H I gas mass. The star formation history of these ETGs is affected by the environment, e.g. in the denser environment the H I gas is less and the total SFR is lower. We also discuss the origin of the central star formation of these early-type galaxies.展开更多
To address the disk-halo degeneracy problem,we investigate the nearby barred spiral galaxy NGC 1097.We construct mass models using 3.6 and 4.5μm near-infrared photometric images from the S^(4)G survey,constrained by ...To address the disk-halo degeneracy problem,we investigate the nearby barred spiral galaxy NGC 1097.We construct mass models using 3.6 and 4.5μm near-infrared photometric images from the S^(4)G survey,constrained by rotation curves derived from CO(J=2–1)data from the PHANGS-ALMA survey.These models serve as inputs for a suite of hydrodynamic simulations,where we systematically test the influence of key parameters including the disk mass scaling factor(f_(M)),bar pattern speed(Ω_(b)),and gas sound speed(c_(s)).By comparing the CO(2–1)kinematic maps in the bar region with those from the simulations,we perform a standardχ^(2)analysis to identify the best-fit model.The best-fit model reproduces the observed morphological and kinematic gas features of the galaxy,indicating that NGC 1097 likely hosts a maximal disk with a slowly rotating bar.We also test the influence of a boxy/peanut-shaped(B/P)bulge by incorporating a double-peaked vertical density profile into the model.This B/P structure tends to weaken the bar’s non-axisymmetric potential and necessitate a higher bar pattern speed to reproduce the observed gas morphology.展开更多
I present the results oféchelle spectroscopy of a bright H II region in the irregular galaxy IC 4662 and their comparison with results from long-slit spectroscopy of the same region.All observations were obtained...I present the results oféchelle spectroscopy of a bright H II region in the irregular galaxy IC 4662 and their comparison with results from long-slit spectroscopy of the same region.All observations were obtained with the standard spectrographs of the Southern African Large Telescope:(1)low and medium spectral resolution spectrograph Robert Stobie Spectrograph(R≈800)and(2)échelle spectrograph HRS(R=16,000–1,7000).In both types of data the intensities of most of the emission lines were measured and abundances of oxygen and N Ne,S,Ar,Cl and Fe were determined as well as physical parameters of the H II region.The chemical abundances were obtained from both types of data with the Te-method.Abundances calculated from both types of data agree to within the cited uncertainties.The analysis of theéchelle data revealed three distinct kinematic subsystems within the studied H II region:a narrow component(NC,σ≈12 km s^(-1)),a broad component(BC,σ≈40 km s^(-1)),and a very broad component(VBC,σ≈60–110 km s^(-1),detected only in the brightest emission lines).The elementa abundances for the NC and BC subsystems were determined using the Te-method.The velocity dispersion dependence on the ionization potential of elements showed no correlation for the NC,indicating a well-mixed turbulent medium,while the BC exhibited pronounced stratification,characteristic of an expanding shell.Based on a detailed analysis of the kinematics and chemical composition,it was concluded that the BC is associated with the region surrounding a Wolf-Rayet(WR)star of spectral type WN7-8.The stellar wind from this WR star interacts with a shell ejected during an earlier evolutionary stage(either as a red supergiant or a luminous blue variable LBV),which is enriched in nitrogen.These findings highlight the importance of high spectral resolution for detecting small-scale(25 pc)chemical inhomogeneities and for understanding the feedback mechanisms of massive stars in low-metallicity environments.展开更多
The role of galaxy morphology and stellar population properties in galaxy evolution is crucial for understanding the transition from star-forming to quiescent galaxies.We present an analysis of 94 galaxies with Hδabs...The role of galaxy morphology and stellar population properties in galaxy evolution is crucial for understanding the transition from star-forming to quiescent galaxies.We present an analysis of 94 galaxies with Hδabsorption line equivalent widths greater than 2?,selected from the DEEP2 survey EGS field(0<z<1).The wealth of multi-wavelength coverage enables accurate stellar mass measurements from SED fitting,SFR measurements from UV and MIR,and galaxy population classification based on the UVJ diagram.Using HST F814W images,we performed a morphological analysis and found that most galaxies exhibit disk-like structures,with some showing bulge-dominated profiles.The size of our sample is roughly in between the star-forming and quiescent galaxies,implying a transition of galaxy population.We also examined the role of central stellar density(Σ1)in galaxy evolution and found that galaxies with higherΣ1tend to evolve into quiescent galaxies earlier,supporting the“downsizing”scenario.These findings underscore the importance of size,mass,and central density in galaxy evolution.展开更多
A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is poss...A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as energy of the universe <i>U</i>, cosmological constant <i>E</i><sub>Λ</sub>, curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λ<i>e</i></sub>, age of the universe <i>t</i><sub>Ω</sub> (part 1). That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses (part 2). Indeed, such residual, non-baryonic energy, when considered in Newton’s gravity equation, adds the term <i>F</i><sub>Λ</sub>(<i>r</i>), which can partially explain, without recourse to dark matter, the rotations of some galaxies, such as M33, UGC12591, UGC2885, NGC3198, NGC253, DDO161, UDG44, the MW and the Coma cluster. Today, in the MW, that cosmological gravity force is in the order of 10<sup>26</sup> times smaller than the conventional gravity force. The model predicts an acceleration of the mass in the universe (<i>q</i>~-0.986);the energy associated with curvature <i>E<sub>k</sub></i> is the driving force behind the expansion of the universe, rather than the energy associated with the cosmological constant <i>E</i><sub>Λ</sub>. An equation to determine expansion is obtained using the energy form of the Friedmann equation relative to Planck power <i>P<sub>P</sub></i> and cosmic time or Planck force <i>F<sub>P</sub></i> acting at the frontier of the universe moving at <i>c</i>. This constant Planck force, from unknown sources, acts everywhere to the expansion of the universe as a stretching effect on the volume. Finally, the model partly explains the value a<sub>0</sub> of the MOND theory. Indeed, <i>a</i><sub>0</sub> is not a true constant, but depends on the cosmological constant at the time the great structures were formed (~1 [Gy]), as well as an adjustment of the typical mass and dimension of those great structures, such as galaxies. The constant a<sub>0</sub> is a different expression of the cosmological gravity force <i>F</i><sub>Λ</sub> as expressed by the cosmological constant, Λ, acting through the energy-mass equivalent during the formation of the structures. It does not put in question the value of <i>G</i>.展开更多
Based on a sample of 79 local advanced merger （adv-merger） （U）LIRGs, we search for evidence of quenching processes by investigating the distributions of star formation history indicators （EW（Ha）, EW（HfiA） and...Based on a sample of 79 local advanced merger （adv-merger） （U）LIRGs, we search for evidence of quenching processes by investigating the distributions of star formation history indicators （EW（Ha）, EW（HfiA） and D,（4000）） on the NUV-r color-mass and SFR-M, diagrams. The distributions of EW（Ha） and Dn（4000） on the NUV-r color-mass diagram show clear trends that at a given stellar mass, galaxies with redder NUV-r colors have smaller EW（Ha） and larger Dn （4000）. The reddest adv-merger （U）LIRGs close to the green valley mostly have Dn（4000）〉 1.4. In addition, in the SFR-M, diagram, as the SFR decreases, the EW（Ha） decreases and the Dn （4000） increases, implying that the adv-merger （U）LIRGs on the star formation main sequence have more evolved stellar populations than those above the main sequence. These results indicate that a fraction of the adv-merger （U）LIRGs have already exhibited signs of fading from the starburst phase and that the NUV-r reddest adv-merger （U）LIRGs are likely at the initial stage of post-starbursts with an age of - 1 Gyr, which is consistent with the gas exhaustion time-scales. Therefore, our results offer additional support for the fast evolutionary track from the blue cloud to the red sequence.展开更多
We use a semi-analytic galaxy formation model to study the co-evolution of supermassive black holes(SMBHs) with their host galaxies.Although the coalescence of SMBHs is not important,the quasarmode accretion induced b...We use a semi-analytic galaxy formation model to study the co-evolution of supermassive black holes(SMBHs) with their host galaxies.Although the coalescence of SMBHs is not important,the quasarmode accretion induced by mergers plays a dominant role in the growth of SMBHs.Mergers play a more important role in the growth of SMBH host galaxies than in the SMBH growth.It is the combined contribution from quasar mode accretion and mergers to the SMBH growth and the combined contribution from starburst and mergers to their host galaxy growth that determine the observed scaling relation between the SMBH masses and their host galaxy masses.We also find that mergers are more important in the growth of SMBH host galaxies compared to normal galaxies which share the same stellar mass range as the SMBH host galaxies.展开更多
We compile a new sample of 89 open clusters with ages, distances and metallicities available. We derive a radial iron gradient of about -0.099±0.008 dex kpc^(-1) (unweighted) for the whole sample, which is somewh...We compile a new sample of 89 open clusters with ages, distances and metallicities available. We derive a radial iron gradient of about -0.099±0.008 dex kpc^(-1) (unweighted) for the whole sample, which is somewhat greater than the most recent determination of oxygen gradient from nebulae and young stars. By dividing the clusters into age groups, we show that the iron gradient was steeper in the past and has evolved slowly in time. Current data show a substantial scatter of the cluster metallicities indicating that the Galactic disk has undergone a very rapid, inhomogeneous enrichment. Also, based on a simple, but quite successful model of chemical evolution of the Milky Way disk, we make a detailed calculation of the iron abundance gradient and its time evolution. The predicted current iron gradient is about -0.072 dex kpc^(-1). The model also predicts a steady flattening of the iron gradient with time, which agrees with the result from our open cluster sample.展开更多
Based on the undisturbed, finite thickness disk gravitational potential, we carried out 3-D Monte Carlo simulations of normal pulsars. We find that their scale height evolves in a similar way for different velocity di...Based on the undisturbed, finite thickness disk gravitational potential, we carried out 3-D Monte Carlo simulations of normal pulsars. We find that their scale height evolves in a similar way for different velocity dispersions （δv）： it first increases linearly with time, reaches a peak, then gradually decreases, and finally approaches a stable asymptotic value. The initial velocity dispersion has a very large influence on the scale height. The time evolution of the scale height is studied. When the magnetic decay age is used as the time variable, the observed scale height has a similar trend as the simulated results in the linear stage, from which we derive velocity dispersions in the range 70 - 178km s^-1, which are near the statistical result of 90 - 270km s^-1 for 92 pulsars with known transverse velocities. If the characteristic age is used as the time variable, then the observed and theoretical curves roughly agree for t 〉 10^8 yr only if av 〈 25km s^-1.展开更多
基金support from the National Natural Science Foundation of China(NSFC)grant 12273037the CAS Pioneer Hundred Talents Program(Category B)+1 种基金the USTC Research Funds of the Double First-Class Initiativesupported by the China Manned Space Program with grant No.CMS-CSST-2025-A06 and CMS-CSST-2025-A08.
文摘Using a semi-analytic approach,we estimate halo spins for a large sample of H I-rich galaxies from the Arecibo Legacy Fast ALFA Survey and examine the correlation between H I mass fractions and halo spins.Our analysis reveals a strong correlation between halo spin and the H I-to-stellar mass ratio in both low-mass and massive galaxy samples.This finding suggests a universal formation scenario:higher halo spin reduces angular momentum loss and gas condensation,leading to lower star formation rates and weaker feedback,which in turn help retain gas within dark matter halos.
基金sponsored by the National Key R&D Program of China(MOST)with grant No.2022YFA1605300the National Natural Science Foundation of China(NSFC,grant Nos.12273051 and 11933003)Support for this work is also partly provided by the Chinese Academy of Sciences(CAS)through a grant to the South America Center for Astronomy(CASSACA)。
文摘We present the morphological study of 18,572 massive quiescent galaxies at z~1.2, selected by i-y colors in the Hyper Suprime-Cam(HSC) Deep and UltraDeep fields. The majority of our sample(94.3%) fall in the quiescent region in the rest-frame UVJ diagram. Comparing the five HSC bands and the subsample with HST F160W images, consistent with the decreasing effective radius re, Sérsic index n shows an increasing trend indicating a more bulge-dominant morphology towards the infrared. Even for our massive, quiescent galaxies,which are dominated by typical elliptical galaxies with bulges, the reand n values still vary with the wavelengths.For instance, there is a systematic drop in n of ~0.4 going from y band to F160W, making 20% of the HSC “disklike” galaxies appear “bulge-like” in the HST images. We suggest to use caution when comparing galaxy morphological types based on images at different resolutions or at different wavelengths, and whenever possible,to apply a reor n correction. More massive quiescent galaxies are systematically larger than the less massive ones,though no mass dependence is found for n measurements. The size–mass relation based on our sample and lowerz control samples show a monotonic increase of rewith M*, with a power-law of 0.61 ± 0.01, lower than previously found in similar samples of smaller sizes. Future high-resolution space-based surveys like NGRST will help confirm the possible n evolution, and if the flattening at the low-mass end is a genuine physical trend or limited by the image resolutions.
基金supported by the National Natural Science Foundation of China(NSFC,grant No.12173079)。
文摘This paper presents a statistical study of the division of the[CⅡ]158μm line into ionized and neutral components,using a new carbon-to-nitrogen abundance ratio,log(C/N)=0.75,for a sample of 108 local galaxies.We investigate the correlation between the ionized-to-total[CⅡ]ratio([CⅡ]_(ionized)/[CⅡ]_(total))and the farinfrared color f60/f100,finding a moderate negative correlation.Additionally,we explore the dependence of[CⅡ]_(ionized)/[CⅡ]_(total)on various physical properties.We find that[CⅡ]_(ionized)/[CⅡ]_(total)exhibits a weak negative correlation with the offset from the main sequence and a moderate negative correlation with the[OⅢ]88μm/[NⅡ]122μm.Furthermore,no significant correlation with molecular gas mass is found.It shows a positive correlation with metallicity.Our results suggest that[CⅡ]_(ionized)/[CⅡ]_(total)is influenced by the ionization parameter,star formation efficiency and metallicity.
基金supports from the CAS Pioneer Hundred Talents Program(Category B)the National Natural Science Foundation of China(NSFC,grant No.12273037)the USTC Research Funds of the Double First-Class Initiative。
文摘Leveraging the semi-analytic method,we compute halo spins for a substantial sample of H I-bearing galaxies observed in the Arecibo Legacy Fast ALFA Survey.Our statistical analysis reveals a correlation between halo spin and environment,although the trend is subtle.On average,galaxies exhibit a decreasing halo spin tendency in denser environments.This observation contrasts with previous results from N-body simulations in the Lambda Cold Dark Matter framework.The discrepancy may be attributed to environmental gas stripping,leading to an underestimation of halo spins in galaxies in denser environments,or to baryonic processes that significantly alter the original dark matter halo spins,deviating from previous N-body simulation findings.
基金supported by the National Key R&D Program of China through grant 2020YFC2201400the NSFC Key Program through grants 11733010 and 11333008.
文摘We investigate the small-scale clustering of star-forming galaxies(SFGs) in the local universe, using both observational samples from the final data release of the Sloan Digital Sky Survey and IllustrisTNG300, one of the state-of-the-art hydrodynamic simulations of galaxy formation. We measure the projected two-point crosscorrelation function, wp(rp), for subsamples of SFGs with different specific star formation rates(sSFRs) and stellar masses(M*), with respect to reference samples of galaxies with early-type or late-type morphology. On scales smaller than ~100 kpc and at fixed M*, SFGs with higher sSFR are more strongly clustered, reflecting the interaction-induced central star formation found in previous studies. More importantly, the small-scale clusteringsSFR correlation is stronger when the reference sample is limited to late-type galaxies only. This confirms the previous finding that the enhancement of star formation in close pairs depends on the morphology of companion galaxies. These observational trends are broadly reproduced by IllustrisTNG300, indicating that current hydrodynamic simulations are capable of capturing the main recipes governing star formation in interacting/merging galaxies, although further work is needed to identify the exact physical processes involved.
基金supports from National Key R&D Program of China(Grant Nos.2018YFA0404503,2018YFE0202902)the National Key Program for Science and Technology Research and Development of China(2017YFB0203300,2015CB857005)+2 种基金the National Natural Science Foundation of China(NSFC,Nos.11988101,11425312,11503032,11773032,11390372,11873051,118513,11573033,11622325,12033008,and 11622325)funding supports from FONDECYT Postdoctoral Fellowship Project(No.3190354)NSFC(No.11703037)。
文摘The discovery of massive galaxies at high redshifts,especially the passive ones,poses a big challenge for the current standard galaxy formation models.Here we use the semi-analytic galaxy formation model developed by Henriques et al.to explore the formation and evolution of massive galaxies(MGs,stellar-mass M*>1011 M⊙).Different from previous works,we focus on the ones just formed(e.g.just reach?1011 M⊙).We find that most of the MGs are formed around z=0.6,with the earliest formation at z>4.Interestingly,although most of the MGs in the local Universe are passive,we find that only 13%of the MGs are quenched at the formation time.Most of the quenched MGs at formation already host a very massive supermassive black hole(SMBH)which could power the very effective AGN feedback.For the star-forming MGs,the ones with more massive SMBH prefer to quench in shorter timescales;in particular,those with MSMBH>107.5 M⊙have a quenching timescale of~0.5 Gyr and the characteristic MSMBH depends on the chosen stellar mass threshold in the definition of MGs as a result of their co-evolution.We also find that the"in-situ"star formation dominates the stellar mass growth of MGs until they are formed.Over the whole redshift range,we find the quiescent MGs prefer to stay in more massive dark matter halos,and have more massive SMBH and less cold gas masses.Our results provide a new angle on the whole life of the growth of MGs in the Universe.
基金the financial support from Kerala State Council for Science,Technology and Environment(KSCSTE)
文摘Using a sample of 13 early-type spiral galaxies hosting nuclear rings,we report remarkable correlations between the properties of the nuclear rings and the central intensity ratio(CIR) of their host galaxies.The CIR,a function of intensity of light within the central 1.5 and 3 arcsec region,is found to be a vital parameter in galaxy evolution,as it shares strong correlations with many structural and dynamical properties of early-type galaxies,including mass of the central supermassive black hole(SMBH).We use archival HST images for aperture photometry at the centre of the galaxy image to compute the CIR.We observe that the relative sizes of nuclear rings and ring cluster surface densities strongly correlate with the CIR.These correlations suggest reduced star formation in the centres of galaxies hosting small and dense nuclear rings.This scenario appears to be a consequence of strong bars as advocated by the significant connection observed between the CIR and bar strengths.In addition,we observe that the CIR is closely related with the integrated properties of the stellar population in the nuclear rings,associating the rings hosting older and less massive star clusters with low values of CIR.Thus,the CIR can serve as a crucial parameter in unfolding the coupled evolution of bars and rings as it is intimately connected with both their properties.
基金support from the National Natural Science Foundation of China (grant Nos. 12025303, 11890693,11421303 and 12003031)the CAS Frontier Science Key Research Program (QYZDJ-SSW-SLH006)+2 种基金the K.C. Wong Education Foundationthe science research grants from the China Manned Space Project with No. CMS-CSST-2021-A06support from the Chinese Academy of Sciences President’s International Fellowship Initiative (grant No. 2019PM0020)。
文摘The coevolution between supermassive black holes(SMBHs) and their host galaxies has been proposed for more than a decade,albeit with little direct evidence about black hole accretion activities regulating galaxy star formation at z> 1.In this paper,we study the lifetimes of X-ray active galactic nuclei(AGNs) in UV-selected red sequence(RS),blue cloud(BC) and green valley(GV) galaxies,finding that AGN accretion activities are most prominent in GV galaxies at z ~1.5-2,compared with RS and BC galaxies.We also compare AGN accretion timescales with typical color transition timescales of UV-selected galaxies.We find that the lifetime of GV galaxies at z~1.5-2 is very close to the typical timescale when the AGNs residing in them stay in the high-accretion-rate mode at these redshifts;for BC galaxies,the consistency between the color transition timescale and the black hole strong accretion lifetime is more likely to happen at lower redshifts(z <1).Our results support the scenario where AGN accretion activities govern UV color transitions of host galaxies,making galaxies and their central SMBHs coevolve with each other.
基金Supported by the National Natural Science Foundation of China(Grant Nos.10878010,10221001 and 10633040)the National Basic Research Program(973 program,No.2007CB815405)
文摘We present galactic spectroscopic data from a pencil beam of 10.75×7.5 centered on the X-ray cluster RXJ0054.0–2823 at z=0.29.We study the spectral evolution of galaxies from z=1 down to the cluster redshift in a magnitude-limited sample at R≤23,for which the statistical properties of the sample are well understood.We divide emission-line galaxies into star-forming galaxies,Low Ionization Nuclear Emission line Regions（LINERs） ,and Seyferts by using emission-line ratios of[OII],Hβ,and[OIII],and derive stellar fractions from population synthesis models. We focus our analysis on absorption and low-ionization galaxies.For absorption-line galaxies,we recover the well-known result that these galaxies have had no detectable evolution since z～0.6-0.7,but we also find that in the range z=0.65-1,at least 50% of the stars in bright absorption systems are younger than 2.5 Gyr.Faint absorption-line galaxies in the cluster at z=0.29 also had significant star formation during the previous 2-3 Gyr,but their brighter counterparts seem to be only composed of old stars.At z～0.8,our dynamically young cluster had a truncated red-sequence.This result seems to be consistent with a scenario where the final assembly of E/S0 took place at z1.In the volume-limited range 0.35≤z≤0.65,we find that 23% of the early-type galaxies have LINER-like spectra with Hβin absorption and have a significant component of A stars.The vast majority of LINERs in our sample have significant populations of young and intermediate-aged stars and are thus not related to AGNs,but to the population of‘retired galaxies’recently identified by Cid Fernandes et al.in the Sloan Digital Sky Survey（SDSS） .Early-type LINERs with various fractions of A stars and E＋A galaxies appear to play an important role in the formation of the red sequence.
文摘Galaxy formation and evolution is one of the most active research areas in astrophysics,so many people have studied this area.But since they didn’t understand thoroughly the evolution law from satellite to planet then to star,their theories are very weak.In their theories,they proposed that large gas clouds collapsing to form a galaxy or more recently that matter started out in smaller clumps merged to form galaxy,which is incredible.Hence,the author of this paper,through studying the formation and orbit-variation of satellites,planets and stars,has put forward a new theory of galaxy formation and evolution,therefore revealing the hierarchical structure of galaxies and the formation and evolution of black holes and quasars.
基金Supported by the National Natural Science Foundation of China grant Nos. 10333060 and 10778622.
文摘We used the Sloan Digital Sky Survey （SDSS） Data Release 5 （DR5） to study the morphological properties of 1137 nearby infrared （IR） galaxies, most of which are brighter than 15.9 mag in r-band. This sample was drawn from a cross-correlation of the Infra-Red Astronomical Satellite （IRAS） point source catalog redshift survey with DR5 at z ≤ 0.08. Based on this IR galaxy sample, we constructed five volume-limited sub-samples with IR luminosity ranging from 10^9.5 L⊙ to 10^12L⊙. By deriving the IR luminosity functions （LF） for different morphological types, we found that normal spiral galaxies are the dominant population below LIR ~ 8 ~ 10^10 L⊙; while the fraction of barred spiral galaxies increases with increasing IR luminosity and becomes dominant in spiral galaxies beyond LIR ≈ 5 × 10^10L⊙. As the IR luminosity decreases, the IR galaxies become more compact and have lower stellar masses. The analysis also shows that normal spiral galaxies give the dominant contribution to the total comoving IR energy density in the nearby universe, while, in contrast, the contribution from peculiar galaxies is only 39%.
基金supported by the Doctoral Fund of the Ministry of Education of China (20100091110009)the National Natural Science Foundation of China (Grant Nos. 10878010, 10221001 and 10633040)the National Basic Research Program (973 Program, No. 2007CB815405)
文摘Early-type galaxies （ETGs） are very important for understanding the formation and evolution of galaxies. Recent observations suggest that ETGs are not simply old stellar spheroids as we previously thought. Widespread recent star formation, cool gas and dust have been detected in a substantial fraction of ETGs. We make use of the radial profiles of 9 - r color and the concentration index from the Sloan Digital Sky Survey database to pick out 31 peculiar ETGs with central blue cores. By analyzing the photometric and spectroscopic data, we suggest that the blue cores are caused by star formation activities rather than the central weak active galactic nucleus. From the results of stellar population synthesis, we find that the stellar population of the blue cores is relatively young, spreading from several Myr to less than one Gyr. In 14 galaxies with H I observations, we find that the average gas fraction of these galaxies is about 0.55. The bluer galaxies show a higher gas fraction, and the total star forma- tion rate （SFR） correlates very well with the H I gas mass. The star formation history of these ETGs is affected by the environment, e.g. in the denser environment the H I gas is less and the total SFR is lower. We also discuss the origin of the central star formation of these early-type galaxies.
基金supported by the National Natural Science Foundation of China under grant Nos.12103032,12025302,11773052 and 11761131016(NSFC-DFG)the“111”Project of the Ministry of Education of China under grant No.B20019+1 种基金the China Manned Space Project under grant No.CMS-CSST-2025-A11support from a Newton Advanced Fellowship awarded by the Royal Society and the Newton Fund。
文摘To address the disk-halo degeneracy problem,we investigate the nearby barred spiral galaxy NGC 1097.We construct mass models using 3.6 and 4.5μm near-infrared photometric images from the S^(4)G survey,constrained by rotation curves derived from CO(J=2–1)data from the PHANGS-ALMA survey.These models serve as inputs for a suite of hydrodynamic simulations,where we systematically test the influence of key parameters including the disk mass scaling factor(f_(M)),bar pattern speed(Ω_(b)),and gas sound speed(c_(s)).By comparing the CO(2–1)kinematic maps in the bar region with those from the simulations,we perform a standardχ^(2)analysis to identify the best-fit model.The best-fit model reproduces the observed morphological and kinematic gas features of the galaxy,indicating that NGC 1097 likely hosts a maximal disk with a slowly rotating bar.We also test the influence of a boxy/peanut-shaped(B/P)bulge by incorporating a double-peaked vertical density profile into the model.This B/P structure tends to weaken the bar’s non-axisymmetric potential and necessitate a higher bar pattern speed to reproduce the observed gas morphology.
基金support from the National Research Foundation(NRF)of South Africa。
文摘I present the results oféchelle spectroscopy of a bright H II region in the irregular galaxy IC 4662 and their comparison with results from long-slit spectroscopy of the same region.All observations were obtained with the standard spectrographs of the Southern African Large Telescope:(1)low and medium spectral resolution spectrograph Robert Stobie Spectrograph(R≈800)and(2)échelle spectrograph HRS(R=16,000–1,7000).In both types of data the intensities of most of the emission lines were measured and abundances of oxygen and N Ne,S,Ar,Cl and Fe were determined as well as physical parameters of the H II region.The chemical abundances were obtained from both types of data with the Te-method.Abundances calculated from both types of data agree to within the cited uncertainties.The analysis of theéchelle data revealed three distinct kinematic subsystems within the studied H II region:a narrow component(NC,σ≈12 km s^(-1)),a broad component(BC,σ≈40 km s^(-1)),and a very broad component(VBC,σ≈60–110 km s^(-1),detected only in the brightest emission lines).The elementa abundances for the NC and BC subsystems were determined using the Te-method.The velocity dispersion dependence on the ionization potential of elements showed no correlation for the NC,indicating a well-mixed turbulent medium,while the BC exhibited pronounced stratification,characteristic of an expanding shell.Based on a detailed analysis of the kinematics and chemical composition,it was concluded that the BC is associated with the region surrounding a Wolf-Rayet(WR)star of spectral type WN7-8.The stellar wind from this WR star interacts with a shell ejected during an earlier evolutionary stage(either as a red supergiant or a luminous blue variable LBV),which is enriched in nitrogen.These findings highlight the importance of high spectral resolution for detecting small-scale(25 pc)chemical inhomogeneities and for understanding the feedback mechanisms of massive stars in low-metallicity environments.
基金sponsored by the National Key R&D Program of China for grant No.2022YFA1605300the National Natural Science Foundation of China(NSFC,Grant Nos.11933003,12173045,and 12273051)。
文摘The role of galaxy morphology and stellar population properties in galaxy evolution is crucial for understanding the transition from star-forming to quiescent galaxies.We present an analysis of 94 galaxies with Hδabsorption line equivalent widths greater than 2?,selected from the DEEP2 survey EGS field(0<z<1).The wealth of multi-wavelength coverage enables accurate stellar mass measurements from SED fitting,SFR measurements from UV and MIR,and galaxy population classification based on the UVJ diagram.Using HST F814W images,we performed a morphological analysis and found that most galaxies exhibit disk-like structures,with some showing bulge-dominated profiles.The size of our sample is roughly in between the star-forming and quiescent galaxies,implying a transition of galaxy population.We also examined the role of central stellar density(Σ1)in galaxy evolution and found that galaxies with higherΣ1tend to evolve into quiescent galaxies earlier,supporting the“downsizing”scenario.These findings underscore the importance of size,mass,and central density in galaxy evolution.
文摘A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as energy of the universe <i>U</i>, cosmological constant <i>E</i><sub>Λ</sub>, curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λ<i>e</i></sub>, age of the universe <i>t</i><sub>Ω</sub> (part 1). That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses (part 2). Indeed, such residual, non-baryonic energy, when considered in Newton’s gravity equation, adds the term <i>F</i><sub>Λ</sub>(<i>r</i>), which can partially explain, without recourse to dark matter, the rotations of some galaxies, such as M33, UGC12591, UGC2885, NGC3198, NGC253, DDO161, UDG44, the MW and the Coma cluster. Today, in the MW, that cosmological gravity force is in the order of 10<sup>26</sup> times smaller than the conventional gravity force. The model predicts an acceleration of the mass in the universe (<i>q</i>~-0.986);the energy associated with curvature <i>E<sub>k</sub></i> is the driving force behind the expansion of the universe, rather than the energy associated with the cosmological constant <i>E</i><sub>Λ</sub>. An equation to determine expansion is obtained using the energy form of the Friedmann equation relative to Planck power <i>P<sub>P</sub></i> and cosmic time or Planck force <i>F<sub>P</sub></i> acting at the frontier of the universe moving at <i>c</i>. This constant Planck force, from unknown sources, acts everywhere to the expansion of the universe as a stretching effect on the volume. Finally, the model partly explains the value a<sub>0</sub> of the MOND theory. Indeed, <i>a</i><sub>0</sub> is not a true constant, but depends on the cosmological constant at the time the great structures were formed (~1 [Gy]), as well as an adjustment of the typical mass and dimension of those great structures, such as galaxies. The constant a<sub>0</sub> is a different expression of the cosmological gravity force <i>F</i><sub>Λ</sub> as expressed by the cosmological constant, Λ, acting through the energy-mass equivalent during the formation of the structures. It does not put in question the value of <i>G</i>.
基金supported by the National Natural Science Foundation of China(Grant Nos11373027,10973011 and 11003015)sponsored by SRF for ROCS, SEM
文摘Based on a sample of 79 local advanced merger （adv-merger） （U）LIRGs, we search for evidence of quenching processes by investigating the distributions of star formation history indicators （EW（Ha）, EW（HfiA） and D,（4000）） on the NUV-r color-mass and SFR-M, diagrams. The distributions of EW（Ha） and Dn（4000） on the NUV-r color-mass diagram show clear trends that at a given stellar mass, galaxies with redder NUV-r colors have smaller EW（Ha） and larger Dn （4000）. The reddest adv-merger （U）LIRGs close to the green valley mostly have Dn（4000）〉 1.4. In addition, in the SFR-M, diagram, as the SFR decreases, the EW（Ha） decreases and the Dn （4000） increases, implying that the adv-merger （U）LIRGs on the star formation main sequence have more evolved stellar populations than those above the main sequence. These results indicate that a fraction of the adv-merger （U）LIRGs have already exhibited signs of fading from the starburst phase and that the NUV-r reddest adv-merger （U）LIRGs are likely at the initial stage of post-starbursts with an age of - 1 Gyr, which is consistent with the gas exhaustion time-scales. Therefore, our results offer additional support for the fast evolutionary track from the blue cloud to the red sequence.
基金supported by NSFC grants (Nos.11573033,11622325,11425312 and 11988101)supported by NSFC grant (No.11803045)+2 种基金the “Recruitment Program of Global Youth Experts” of China,the NAOC (Grant Y434011V01)supported by the National Key R&D Program of China (No.2017YFB0203300)the Key Program of NFSC (Grant 11733010)。
文摘We use a semi-analytic galaxy formation model to study the co-evolution of supermassive black holes(SMBHs) with their host galaxies.Although the coalescence of SMBHs is not important,the quasarmode accretion induced by mergers plays a dominant role in the growth of SMBHs.Mergers play a more important role in the growth of SMBH host galaxies than in the SMBH growth.It is the combined contribution from quasar mode accretion and mergers to the SMBH growth and the combined contribution from starburst and mergers to their host galaxy growth that determine the observed scaling relation between the SMBH masses and their host galaxy masses.We also find that mergers are more important in the growth of SMBH host galaxies compared to normal galaxies which share the same stellar mass range as the SMBH host galaxies.
基金the National Natural Science Foundation ofChina (No. 19873014) and NKBRSFG19990754, and partly by SRF for ROCS, SEM.
文摘We compile a new sample of 89 open clusters with ages, distances and metallicities available. We derive a radial iron gradient of about -0.099±0.008 dex kpc^(-1) (unweighted) for the whole sample, which is somewhat greater than the most recent determination of oxygen gradient from nebulae and young stars. By dividing the clusters into age groups, we show that the iron gradient was steeper in the past and has evolved slowly in time. Current data show a substantial scatter of the cluster metallicities indicating that the Galactic disk has undergone a very rapid, inhomogeneous enrichment. Also, based on a simple, but quite successful model of chemical evolution of the Milky Way disk, we make a detailed calculation of the iron abundance gradient and its time evolution. The predicted current iron gradient is about -0.072 dex kpc^(-1). The model also predicts a steady flattening of the iron gradient with time, which agrees with the result from our open cluster sample.
基金Supported by the National Natural Science Foundation of China.
文摘Based on the undisturbed, finite thickness disk gravitational potential, we carried out 3-D Monte Carlo simulations of normal pulsars. We find that their scale height evolves in a similar way for different velocity dispersions （δv）： it first increases linearly with time, reaches a peak, then gradually decreases, and finally approaches a stable asymptotic value. The initial velocity dispersion has a very large influence on the scale height. The time evolution of the scale height is studied. When the magnetic decay age is used as the time variable, the observed scale height has a similar trend as the simulated results in the linear stage, from which we derive velocity dispersions in the range 70 - 178km s^-1, which are near the statistical result of 90 - 270km s^-1 for 92 pulsars with known transverse velocities. If the characteristic age is used as the time variable, then the observed and theoretical curves roughly agree for t 〉 10^8 yr only if av 〈 25km s^-1.
