We estimated radiative efficiency,spin and supermassive black hole(SMBH)mass values for sample of 33 distant low luminosity active galactic nuclei(AGNs).The distribution of the estimated spin values(majority of object...We estimated radiative efficiency,spin and supermassive black hole(SMBH)mass values for sample of 33 distant low luminosity active galactic nuclei(AGNs).The distribution of the estimated spin values(majority of objects have a spin greater than 0.8)is fairly typical for many types of AGNs.The dependence of the estimated spin values on the estimated SMBH masses shows strong correlation between them,which suggests a rapid increase in spin with mass,i.e.,that the main mechanism of mass growth in this case is disk accretion.We did not find any significant qualitative differences in the spin characteristics between our objects and objects of other types considered in the paper.展开更多
We present u＇g＇R optical images taken with the MMT/Megacam and the Subaru/Suprime telescopes of the Extended Groth Strip survey. The total survey covers an area of about -1 degree2, including four sub-fields and is ...We present u＇g＇R optical images taken with the MMT/Megacam and the Subaru/Suprime telescopes of the Extended Groth Strip survey. The total survey covers an area of about -1 degree2, including four sub-fields and is optimized for the study of galaxies at z - 3. Our methods for photometric calibration in AB magnitudes, the limiting magnitude and the galaxy number count are described. A sample of 1642 photometrically selected candidate Lyman-Break Galaxies （LBGs） to an apparent RAB magnitude limit of 25.0 is presented. The average sky surface density of our LBG sample is -1.0 arcmin-2, slightly higher than the previous finding.展开更多
Based on measured broad line region sizes in the reverberation-mapping AGN sample, two new empirical relations are introduced to estimate the central black hole masses of radio-loud high-redshift （z 〉 0.5） AGNs. Fi...Based on measured broad line region sizes in the reverberation-mapping AGN sample, two new empirical relations are introduced to estimate the central black hole masses of radio-loud high-redshift （z 〉 0.5） AGNs. First, using the archival IUE/HST spectroscopy data at UV band for the reverberation-mapping objects, we obtained two new empirical relations between the BLR size and Mg Ⅱ/C Ⅳ emission line luminosity. Secondly, using the newly determined black hole masses of the reverberation-mapping sample as calibration, we found two new relationships for determining the black hole mass with the full width at half maximum and the luminosity of Mg Ⅱ/C Ⅳ line. We then apply the relations to estimate the black hole masses of the AGNs in the Large Bright Quasar Survey and a sample of radio-loud quasars. For the objects with small radio-loudness, the black hole mass estimated using the RBLR-LMg Ⅱ/C Ⅳ relation is consistent with that from the RBLR-L3000 A/1350 A relation. For radio-loud AGNs, however, the mass estimated from the RBLR-LMg Ⅱ/C Ⅳ relation is systematically lower than that from the continuum luminosity L3000 A/13S0 A Because jets could have significant contributions to the UV/optical continuum luminosity of radio-loud AGNs, we emphasize once again that for radio-loud AGNs, the emission line luminosity may be a better tracer of the ionizing luminosity than the continuum luminosity, so that the relations between the BLR size and UV emission line luminosities should be used to estimate the black hole masses of high redshift radio-loud AGNs.展开更多
The observational data of high redshift galaxies become increasingly abundant,especially since the operation of the James Webb Space Telescope,which allows us to verify and optimize the galaxy formation model at high ...The observational data of high redshift galaxies become increasingly abundant,especially since the operation of the James Webb Space Telescope,which allows us to verify and optimize the galaxy formation model at high redshifts.In this work,we investigate the merging history of massive galaxies at 3<z<6 using a well-developed semi-analytic galaxy formation catalog.We find that the major merger rate increases with redshift up to 3 and then flattens.The fraction of wet mergers,during which the sum of the cold gas mass is higher than the sum of the stellar mass in two merging galaxies,also increases from~34%at z=0 to 96%at z=3.Interestingly,almost all major mergers are wet at z>3.This can be attributed to the high fraction(>50%)of cold gas at z>3.In addition,we study some special systems of massive merging galaxies at 3<z<6,including the massive gas-rich major merging systems and extreme dense proto-clusters,and investigate the supermassive black hole-dark matter halo mass relation and dual active galactic nuclei.We find that the galaxy formation model reproduces the incidence of those observed massive galaxies,but fails to reproduce the relation between the supermassive black hole mass and the dark matter halo mass at z~6.The latter requires more careful estimates of the supermassive black hole masses observationally.Otherwise,it could suggest modifications of the modeling of the supermassive black hole growth at high redshifts.展开更多
High resolution deep imaging from space and adaptive optics techniques with large ground-based facilities have enabled studies examining faint host galaxies of high redshift quasi-stellar objects (QSOs). However, the ...High resolution deep imaging from space and adaptive optics techniques with large ground-based facilities have enabled studies examining faint host galaxies of high redshift quasi-stellar objects (QSOs). However, the related image processing techniques, especially for a precise point-spread function (PSF) reconstruction and characterization of the host galaxy light profiles, have yet to be optimized. We present here the scientific performance of a principal component analysis (PCA) based PSF subtraction of the central bright point source of high redshift QSO images, as well as further characterization of the host galaxy profile by directly fitting a Sèrsic model to the residual image using the Markov Chain Monte Carlo (MCMC) algorithm. With a set of reference PSF star images which represent interleaving exposures between the QSO imaging, we can create an orthogonal basis of eigen-images and restore the PSF of QSO images by projecting the QSO images onto the basis. In this way, we can quantify the modes in which the PSF varies with time by a basis function that characterizes the temporal variations of the reference star as well as the QSO images. To verify the algorithm, we performed a simulation and applied this method to one of the high-z QSO targets from Mechtley et al. We demonstrate that the PCA-based PSF subtraction and further modeling of the galaxy’s light profile using MCMC fitting would sufficiently remove the effects from central dominating point sources, and improve characterization ability for the host galaxies of high-z QSOs to the background noise level which is much better than previous two-component fitting procedures.展开更多
Based on a large sample of massive(M* 1010 M⊙) compact galaxies at 1.0 < z < 3.0 in five 3 D-HST/CANDELS fields, we quantify the fractional abundance and comoving number density of massive compact galaxies as a...Based on a large sample of massive(M* 1010 M⊙) compact galaxies at 1.0 < z < 3.0 in five 3 D-HST/CANDELS fields, we quantify the fractional abundance and comoving number density of massive compact galaxies as a function of redshift. The samples of compact quiescent galaxies(cQGs) and compact star-forming galaxies(cSFGs) are constructed by various selection criteria of compact galaxies in the literature, and the effect of compactness definition on abundance estimate has proven to be remarkable,particularly for the cQGs and cSFGs at high redshifts. Regardless of the compactness criteria adopted,their overall redshift evolutions of fractional abundance and number density are found to be rather similar.Large samples of the cQGs exhibit a sustained increase in number density from z ~ 3 to 2 and a plateau at 1 < z < 2. For massive cSFGs, a plateau in the number density at 2 < z < 3 can be found, as well as a continuous drop from z ~ 2 to 1. The evolutionary trends of the cQG and cSFG abundances support the scenario that the cSFGs at z≥ 2 may have been rapidly quenched into quiescent phase via violent dissipational processes, such as major merger and disk instabilities. The rarity of the cSFGs at lower redshifts(z < 1) can be interpreted by the decrease of gas reservoirs in dark matter halos and the consequent low efficiency of gas-rich dissipation.展开更多
通过利用CANDELS-EGS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey-Extended Groth Strip)场中HST WFC3(Hubble Space Telescope Wide Field Camera 3)F160W高分辨率的观测图像,研究了9个光谱红极亮红外星系的形...通过利用CANDELS-EGS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey-Extended Groth Strip)场中HST WFC3(Hubble Space Telescope Wide Field Camera 3)F160W高分辨率的观测图像,研究了9个光谱红极亮红外星系的形态结构特征.发现这些星系的形态表现出多样性(从椭圆到多个亮核或弥散的结构),如:双核,气体桥,双不对称体,不规则或椭圆结构.为了定量地研究这些极亮红外星系的形态,测量了它们在静止光学波段的形态参数(基尼系数G和矩指数M20).与近邻极亮红外星系相比,高红移极亮红外星系的G偏小而M20偏大,表明这些星系的星族分布聚集度小且不对称性大.基于对样本中极亮红外星系2维面亮度轮廓的拟合,得到这些星系的有效半径分布在2.4 kpc到5.8 kpc之间,其平均值是(3.9±1.1)kpc.相比较于近邻相似质量的恒星形成星系来说,高红移极亮红外星系的平均大小要小1到2倍.在类似红移和红外光度条件下,得出的这些结果也与其它文献中给出的结论相一致.展开更多
基于COSMOS(Cosmic Evolution Survey)天区的多波段测光数据和HST(Hubble Space Telescope)近红外高分辨率观测图像,利用质量限(恒星质量M*≥1010.5M⊙)选取了362个红移分布在1≤z≤3的星系样本,并对这些大质量星系的形态特征进行了分...基于COSMOS(Cosmic Evolution Survey)天区的多波段测光数据和HST(Hubble Space Telescope)近红外高分辨率观测图像,利用质量限(恒星质量M*≥1010.5M⊙)选取了362个红移分布在1≤z≤3的星系样本,并对这些大质量星系的形态特征进行了分类研究.来自UVJ(U-V和V-J)双色图分类系统、目视分类系统、非模型化分类系统(基尼系数G和矩指数M20)和模型化分类系统(S′ersic index,n)的分类结果彼此相一致.相比较于恒星形成星系(SFGs),通过UVJ双色图定义的宁静星系(QGs)表现出致密的椭圆结构,而且G和n值偏大,但M20和星系有效半径(re)偏小.不同星系分类系统(双色图分类系统、非模型化分类系统和模型化分类系统)定义的SFGs和QGs样本,都明显存在星系的大小随红移的演化关系,这种演化趋势QGs比SFGs更剧烈,而且不依赖于星系分类方法的选择.展开更多
基于CANDELS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey)5个深场巡天的多波段测光数据和HST WFC3(Hubble Space Telescope Wide Field Camera 3)近红外(F125W和F160W)高分辨率观测图像,利用质量限(恒星质量M_*&g...基于CANDELS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey)5个深场巡天的多波段测光数据和HST WFC3(Hubble Space Telescope Wide Field Camera 3)近红外(F125W和F160W)高分辨率观测图像,利用质量限(恒星质量M_*>10^(10)M_⊙)选取了8002个红移分布在1<z<3范围内的星系样本,并对这些大质量星系的形态和结构性质进行了定量分析研究.通过星系形态的神经网络分类方法(Conv Nets),将样本中的星系划分为4类:椭球星系(SPHeroids,SPH)、早型盘星系(Early-Type Disks,ETD)、晚型盘星系(Late-Type Disks,LTD)和不规则星系(IRRegulars,IRR).结果发现星系的形态和结构随红移发生演化,在高红移宇宙星系主要表现出不规则形态,但到低红移处椭球和盘主导的哈勃星系形态序列已经形成.在相同红移区间内,不同类型星系的物理尺寸(r_e)中值从大到小的排序是IRR、LTD、ETD和SPH,而对应的Sersic指数(n)中值大小排序却相反.另外,不同类型星系的re与红移之间存在明显的演化关系,但这样的现象在平均轴比(b/a)和Sersic指数与红移的关系中并没有被发现.展开更多
We study the growth of black holes and stellar population in spheroids at high redshift using several （sub）mm-loud QSO samples. Applying the same criteria established in an earlier work, we find that, similar to IR ...We study the growth of black holes and stellar population in spheroids at high redshift using several （sub）mm-loud QSO samples. Applying the same criteria established in an earlier work, we find that, similar to IR QSOs at low redshift, the far-infrared emission of these （sub）mm-loud QSOs mainly originates from dust heated by starbursts. By combining low-z IR QSOs and high-z （sub）mm-loud QSOs, we find a trend that the star formation rate （M＊） increases with the accretion rate （Mace）. We compare the values of M＊/Macc for submm emitting galaxies （SMGs）, far-infrared ultraluminous/hypeduminous QSOs and typical QSOs, and construct a likely evolution scenario for these objects. The （sub）mm-loud QSO transition phase has both high Macc and M＊ and hence is important for establishing the correlation between the masses of black holes and spheroids.展开更多
We have collected a sample of 70 BL Lacs （33 radio-selected BL Lacs and 37 X-ray selected BL Lacs） with multi-waveband data for investigating the classifying criteria of BL Lacertae Objects. For each source, we esti...We have collected a sample of 70 BL Lacs （33 radio-selected BL Lacs and 37 X-ray selected BL Lacs） with multi-waveband data for investigating the classifying criteria of BL Lacertae Objects. For each source, we estimate its luminosities in radio, optical and X-ray, the broad-band spectral index from radio to X-ray and the peak frequency of the synchrotron emission, and make a statistical analysis of the data obtained. Our main results are as follows： （1） The broad-band spectral index and the peak frequency have no correlation with the redshift, while they are inversely correlated with each other and they could be regarded as equivalent classifying criteria of BL Lac objects. （2） There are significant effects of the luminosity/redshift relation on the observed luminosity distribution in our sample, hence, if the radio luminosity is to be used as a classifying criterion of BL Lac objects, it should not be regarded as equivalent to the broad-band spectral index or the peak frequency. （3） Our resuits supply a specific piece of evidence for the suggestion that the use of luminosities always introduces a redshift bias to the data and show that the location of the peak frequency is not always linked to the luminosity of any wave band.展开更多
文摘We estimated radiative efficiency,spin and supermassive black hole(SMBH)mass values for sample of 33 distant low luminosity active galactic nuclei(AGNs).The distribution of the estimated spin values(majority of objects have a spin greater than 0.8)is fairly typical for many types of AGNs.The dependence of the estimated spin values on the estimated SMBH masses shows strong correlation between them,which suggests a rapid increase in spin with mass,i.e.,that the main mechanism of mass growth in this case is disk accretion.We did not find any significant qualitative differences in the spin characteristics between our objects and objects of other types considered in the paper.
基金support from the China Scholarship Council (CSC)the Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0802031C)the K.C. Wong Education Foundation, Hong Kong
文摘We present u＇g＇R optical images taken with the MMT/Megacam and the Subaru/Suprime telescopes of the Extended Groth Strip survey. The total survey covers an area of about -1 degree2, including four sub-fields and is optimized for the study of galaxies at z - 3. Our methods for photometric calibration in AB magnitudes, the limiting magnitude and the galaxy number count are described. A sample of 1642 photometrically selected candidate Lyman-Break Galaxies （LBGs） to an apparent RAB magnitude limit of 25.0 is presented. The average sky surface density of our LBG sample is -1.0 arcmin-2, slightly higher than the previous finding.
基金Supported by the National Natural Science Foundation of China.
文摘Based on measured broad line region sizes in the reverberation-mapping AGN sample, two new empirical relations are introduced to estimate the central black hole masses of radio-loud high-redshift （z 〉 0.5） AGNs. First, using the archival IUE/HST spectroscopy data at UV band for the reverberation-mapping objects, we obtained two new empirical relations between the BLR size and Mg Ⅱ/C Ⅳ emission line luminosity. Secondly, using the newly determined black hole masses of the reverberation-mapping sample as calibration, we found two new relationships for determining the black hole mass with the full width at half maximum and the luminosity of Mg Ⅱ/C Ⅳ line. We then apply the relations to estimate the black hole masses of the AGNs in the Large Bright Quasar Survey and a sample of radio-loud quasars. For the objects with small radio-loudness, the black hole mass estimated using the RBLR-LMg Ⅱ/C Ⅳ relation is consistent with that from the RBLR-L3000 A/1350 A relation. For radio-loud AGNs, however, the mass estimated from the RBLR-LMg Ⅱ/C Ⅳ relation is systematically lower than that from the continuum luminosity L3000 A/13S0 A Because jets could have significant contributions to the UV/optical continuum luminosity of radio-loud AGNs, we emphasize once again that for radio-loud AGNs, the emission line luminosity may be a better tracer of the ionizing luminosity than the continuum luminosity, so that the relations between the BLR size and UV emission line luminosities should be used to estimate the black hole masses of high redshift radio-loud AGNs.
基金supported by the National Key R&D Program of China(Nos.2018YFE0202900 and 2022YFA1602901)the NSFC grant(Nos.11988101,11873051 and 12125302)+6 种基金NSFC grant(No.12033008)CAS Project for Young Scientists in Basic Research Grant(No.YSBR-062)the K.C.Wong Education Foundationthe National Key Research and Development of China(No.2018YFA0404503)the support by the National Natural Science Foundation of China(Nos.12047569 and 12147217)the science research grants from the China Manned Space Project with Nos.CMSCSST-2021-A03 and CMS-CSST-2021-A07by the Natural Science Foundation of Jilin Province,China(No.20180101228JC)。
文摘The observational data of high redshift galaxies become increasingly abundant,especially since the operation of the James Webb Space Telescope,which allows us to verify and optimize the galaxy formation model at high redshifts.In this work,we investigate the merging history of massive galaxies at 3<z<6 using a well-developed semi-analytic galaxy formation catalog.We find that the major merger rate increases with redshift up to 3 and then flattens.The fraction of wet mergers,during which the sum of the cold gas mass is higher than the sum of the stellar mass in two merging galaxies,also increases from~34%at z=0 to 96%at z=3.Interestingly,almost all major mergers are wet at z>3.This can be attributed to the high fraction(>50%)of cold gas at z>3.In addition,we study some special systems of massive merging galaxies at 3<z<6,including the massive gas-rich major merging systems and extreme dense proto-clusters,and investigate the supermassive black hole-dark matter halo mass relation and dual active galactic nuclei.We find that the galaxy formation model reproduces the incidence of those observed massive galaxies,but fails to reproduce the relation between the supermassive black hole mass and the dark matter halo mass at z~6.The latter requires more careful estimates of the supermassive black hole masses observationally.Otherwise,it could suggest modifications of the modeling of the supermassive black hole growth at high redshifts.
基金support of a grant from the John Templeton Foundation and the National Astronomical Observatories, Chinese Academy of Sciencesthe Subaru team and the National Natural Science Foundation of China (Grant No. 11890694)+1 种基金the National Natural Science Foundation of China (Grant Nos. 10173025, 10673013, 10778709, 11073031 and 11653005)the National Basic Research Program of China (973 Program, TG 2000077602)
文摘High resolution deep imaging from space and adaptive optics techniques with large ground-based facilities have enabled studies examining faint host galaxies of high redshift quasi-stellar objects (QSOs). However, the related image processing techniques, especially for a precise point-spread function (PSF) reconstruction and characterization of the host galaxy light profiles, have yet to be optimized. We present here the scientific performance of a principal component analysis (PCA) based PSF subtraction of the central bright point source of high redshift QSO images, as well as further characterization of the host galaxy profile by directly fitting a Sèrsic model to the residual image using the Markov Chain Monte Carlo (MCMC) algorithm. With a set of reference PSF star images which represent interleaving exposures between the QSO imaging, we can create an orthogonal basis of eigen-images and restore the PSF of QSO images by projecting the QSO images onto the basis. In this way, we can quantify the modes in which the PSF varies with time by a basis function that characterizes the temporal variations of the reference star as well as the QSO images. To verify the algorithm, we performed a simulation and applied this method to one of the high-z QSO targets from Mechtley et al. We demonstrate that the PCA-based PSF subtraction and further modeling of the galaxy’s light profile using MCMC fitting would sufficiently remove the effects from central dominating point sources, and improve characterization ability for the host galaxies of high-z QSOs to the background noise level which is much better than previous two-component fitting procedures.
基金the 3D-HST Treasury Program (GO 12177 and 12328) with the NASA/ESA HSTsupported by the National Natural Science Foundation of China (Nos. 11673004, 11873032 and 11433005)by the Research Fund for the Doctoral Program of Higher Education of China (No. 20133207110006)he support from Yunnan young and middleaged academic and technical leaders reserve talent program (No. 201905C160039)
文摘Based on a large sample of massive(M* 1010 M⊙) compact galaxies at 1.0 < z < 3.0 in five 3 D-HST/CANDELS fields, we quantify the fractional abundance and comoving number density of massive compact galaxies as a function of redshift. The samples of compact quiescent galaxies(cQGs) and compact star-forming galaxies(cSFGs) are constructed by various selection criteria of compact galaxies in the literature, and the effect of compactness definition on abundance estimate has proven to be remarkable,particularly for the cQGs and cSFGs at high redshifts. Regardless of the compactness criteria adopted,their overall redshift evolutions of fractional abundance and number density are found to be rather similar.Large samples of the cQGs exhibit a sustained increase in number density from z ~ 3 to 2 and a plateau at 1 < z < 2. For massive cSFGs, a plateau in the number density at 2 < z < 3 can be found, as well as a continuous drop from z ~ 2 to 1. The evolutionary trends of the cQG and cSFG abundances support the scenario that the cSFGs at z≥ 2 may have been rapidly quenched into quiescent phase via violent dissipational processes, such as major merger and disk instabilities. The rarity of the cSFGs at lower redshifts(z < 1) can be interpreted by the decrease of gas reservoirs in dark matter halos and the consequent low efficiency of gas-rich dissipation.
文摘通过利用CANDELS-EGS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey-Extended Groth Strip)场中HST WFC3(Hubble Space Telescope Wide Field Camera 3)F160W高分辨率的观测图像,研究了9个光谱红极亮红外星系的形态结构特征.发现这些星系的形态表现出多样性(从椭圆到多个亮核或弥散的结构),如:双核,气体桥,双不对称体,不规则或椭圆结构.为了定量地研究这些极亮红外星系的形态,测量了它们在静止光学波段的形态参数(基尼系数G和矩指数M20).与近邻极亮红外星系相比,高红移极亮红外星系的G偏小而M20偏大,表明这些星系的星族分布聚集度小且不对称性大.基于对样本中极亮红外星系2维面亮度轮廓的拟合,得到这些星系的有效半径分布在2.4 kpc到5.8 kpc之间,其平均值是(3.9±1.1)kpc.相比较于近邻相似质量的恒星形成星系来说,高红移极亮红外星系的平均大小要小1到2倍.在类似红移和红外光度条件下,得出的这些结果也与其它文献中给出的结论相一致.
文摘基于CANDELS(Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey)5个深场巡天的多波段测光数据和HST WFC3(Hubble Space Telescope Wide Field Camera 3)近红外(F125W和F160W)高分辨率观测图像,利用质量限(恒星质量M_*>10^(10)M_⊙)选取了8002个红移分布在1<z<3范围内的星系样本,并对这些大质量星系的形态和结构性质进行了定量分析研究.通过星系形态的神经网络分类方法(Conv Nets),将样本中的星系划分为4类:椭球星系(SPHeroids,SPH)、早型盘星系(Early-Type Disks,ETD)、晚型盘星系(Late-Type Disks,LTD)和不规则星系(IRRegulars,IRR).结果发现星系的形态和结构随红移发生演化,在高红移宇宙星系主要表现出不规则形态,但到低红移处椭球和盘主导的哈勃星系形态序列已经形成.在相同红移区间内,不同类型星系的物理尺寸(r_e)中值从大到小的排序是IRR、LTD、ETD和SPH,而对应的Sersic指数(n)中值大小排序却相反.另外,不同类型星系的re与红移之间存在明显的演化关系,但这样的现象在平均轴比(b/a)和Sersic指数与红移的关系中并没有被发现.
基金Supported by the National Natural Science Foundation of China.
文摘We study the growth of black holes and stellar population in spheroids at high redshift using several （sub）mm-loud QSO samples. Applying the same criteria established in an earlier work, we find that, similar to IR QSOs at low redshift, the far-infrared emission of these （sub）mm-loud QSOs mainly originates from dust heated by starbursts. By combining low-z IR QSOs and high-z （sub）mm-loud QSOs, we find a trend that the star formation rate （M＊） increases with the accretion rate （Mace）. We compare the values of M＊/Macc for submm emitting galaxies （SMGs）, far-infrared ultraluminous/hypeduminous QSOs and typical QSOs, and construct a likely evolution scenario for these objects. The （sub）mm-loud QSO transition phase has both high Macc and M＊ and hence is important for establishing the correlation between the masses of black holes and spheroids.
基金the National Natural Science Foundation of China
文摘We have collected a sample of 70 BL Lacs （33 radio-selected BL Lacs and 37 X-ray selected BL Lacs） with multi-waveband data for investigating the classifying criteria of BL Lacertae Objects. For each source, we estimate its luminosities in radio, optical and X-ray, the broad-band spectral index from radio to X-ray and the peak frequency of the synchrotron emission, and make a statistical analysis of the data obtained. Our main results are as follows： （1） The broad-band spectral index and the peak frequency have no correlation with the redshift, while they are inversely correlated with each other and they could be regarded as equivalent classifying criteria of BL Lac objects. （2） There are significant effects of the luminosity/redshift relation on the observed luminosity distribution in our sample, hence, if the radio luminosity is to be used as a classifying criterion of BL Lac objects, it should not be regarded as equivalent to the broad-band spectral index or the peak frequency. （3） Our resuits supply a specific piece of evidence for the suggestion that the use of luminosities always introduces a redshift bias to the data and show that the location of the peak frequency is not always linked to the luminosity of any wave band.
