【摘要】 本文以Burbidge最近编纂的类星体表为基础,对1467个类星体作了统计分析,得到了光度演化规律:类星体的光度演化恰好补偿了随距离衰减的效应。采用弗里德曼宇宙模型,进而得出了类星体的折合星等随时间t的演化公式。并且据此论证了Burbidge指出的N-Z图中存在的三个高峰确实表示了类星体空间分布的不均匀性。更多还原

【Abstract】 During his visit to Beijing, G. R. Burbidge reaffirmed their view point: the statistical distribution of observed number of QSOs versus it’s redshift (figure of N-Z) has three peaks nearly at Z≈0.5, 1.5, 2.0 (ef. Fig. 1). Though their statistical analysis based directly on the observation is model-independence, it has no apparent physical meaning. In order to give physical meaning to the relevant quantities, it is necessary to have recourse to cosmological model. Basing on Friedman’s model, we have done the statistical analysis of 1467 QSOs collected in Burbidge’s catalog, then obtained the luminosity evolutionary law of QSOs and the statistical distribution of its number versus the luminosity distance.In Friedman’s model, the redshift is naturally related to the luminosity distance:Here H0 is Hubble ’s constant, and q0 the deacceleration parameter. Considering that it is recently discoved that the neutrino has rest mass, we only take account of two typical quantities of q0: i.e. q0= + 1 (closed universe) and q0 = 1/2 (flat universe).The vertical axis N in Fig. 1 represents the observed number of QSOs (apparent magnitude m≤21). In order to obtain the distribution of actual number (relative ratio), we must do some reasonable correction. According to the relation between apparent magnitude and luminosity distance :m = M + 5 log dL ?5. (2)we know that the more distant the QSOs are, the less the observed number of QSOs is Therefore, we ought to do number counting after removing all of QSOs at the same distant. Because there are a few of QSOs with largest redshift (Z≈3.5) in Burbidge’s catalog, the reference position is chosen at Z=3.0. The apparent magnitude of QSOs after removing them to the position corresponding to Z= 3.0 is called "reduced magnitude" m’. From Bq. (2), we haveSince there is only one of QSOs which m’ > 21 in the catalog, we choose the visual limit as 21. If m’ < 21, it is counted ; if m’ > 21, it is not counted.In addition, we must take acount of luminosity evolution. We must analyse statistically the luminosity distribution of QSOs at different intervals of Z. At first, we count the number of QSOs within the intervals Am = 0.5 and AZ = 0.05. Then, we draw the figures of normalized number counting versus apparent magnitude (cf. Fig. 2). The result reveals that all of Figs. N/Nmax--m at different Z are appeared to have the same shape (normal distribution), especially appear a common peak at m≈1819 (except for Z < 0.3). This suggests that the luminosity evolution of QSOs just compensates the decrease of it’s luminosity with distance, so that the apparent magnitude of QSOs at different distance appear the same distribution.Hence, if we take m in Eq. (3) as correspondent constant, and substitute Eq. (1) into Eq. (3), we would obtained the relation between the reduced magnitude of QSOs and redshift Z. For the QSOs at peak, this relation is more accurate, and is written as following:(i) for q0= 1,m = 5 log 3/Z + 18 (4a)(ii) for q0= 1/2, In Friedman’s model, it is easily to derive the relations between cosmological time t and redshift Z as following:(i) for q0 = 1,(ii) for q0 = 1/2,Combining the Bqs. (4a, b) and (5a, b), we ultimately obtained the evolutionary law of reduced magnitude of QSOs at peak. For the case of q0 = 1/2, we haveThe curves shown in Fig. 3 represent the theoretical formula above obtained, in which the vertical line segments represent the observed peaks of reduced magnitude of QSOs at different, Z (the interval is chosen as 0.05). The corresponding t are marked in the horizontal axis. (II0 is chosen as 100 km/see kpe.) It is apparent that the observed data is well fit. to the theoretical curves.Because the luminosity evolution of QSOs just compensates the decrease of its luminosity with distance, the observed number of QSOs is also its actual number (relative ratio). The intended correction mentioned at begining is not necessary. Therefore, it is concluded that the Fig. 1 given by Burbidge also represents the actual number distribution of QSOs versus its luminosity distance, provided that更多还原