The galaxy luminosity function from MR=−25 to MR=−9

Redshift surveys such as the Sloan Digital Sky Survey (SDSS) have given a very precise measurement of the galaxy luminosity function down to about   M_R =−17 (≈ M_B =−16)  . Fainter absolute magnitudes cannot be probed because of the flux limit required for spectroscopy. Wide-field surveys of nearby groups using mosaic CCDs on large telescopes are able to reach much fainter absolute magnitudes, about   M_R =−10  . These diffuse, spiral-rich groups are thought to be typical environments for galaxies, so their luminosity functions should be the same as the field luminosity function. The luminosity function of the groups at the bright end  ( M_R < −17)  is limited by Poisson statistics and is far less precise than that derived from redshift surveys. Here we combine the results of the SDSS and the surveys of nearby groups, and we supplement the results with studies of Local Group galaxies in order to determine the galaxy luminosity function over the entire range  −25 < M_R < −9  . The average logarithmic slope of the field luminosity function between   M_R =−19  and   M_R =−9  is  α=−1.26  , although a single power law is a poor fit to the data over the entire magnitude range. We also determine the luminosity function of galaxy clusters and demonstrate that it is different from the field luminosity function at a high level of significance; there are many more dwarf galaxies in clusters than in the field, due to a rise in the cluster luminosity function of  α∼−1.6  between   M_R =−17  and   M_R =−14  .     

The abundance of brown dwarfs

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass–luminosity relation to convert a luminosity function to a mass function, I predict the mass–luminosity relation from assumed mass functions and the luminosity functions of Jahreiss & Wielen and Gould, Bahcall & Flynn. Comparison of the resulting mass–luminosity relations with data for binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best-fitting slope lies either side of the critical slope, α =−2, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001 M_⊙, the contribution to the local density from stars lies between 0.013 and 0.10 M_⊙ pc⁻³ depending on the mass at which the mass function is normalized and the adopted value of α . Recent dynamical estimates of the local mass density rule out stellar mass densities above ∼0.05 M_⊙ pc⁻³. Hence, power laws steeper than α =−2 that extend down to 0.001 M_⊙ are allowed only if one adopts an implausible normalization of the mass function. If the mass function is generalized from a power law to a low-order polynomial in log( M ), the mass in stars with M <0.1 M_⊙ is either negligible or strongly divergent, depending on the order of the polynomial adopted.     

Virgo星系团的光度函数和质量函数

本文对Ｖｉｒｇｏ星系团中央６°天区内的成员星系作了光度函数和质量函数的研究。成员星系是以视向速度作为判据并合理地考虑了密度分布因素后确定的。研究表明，该天区全部成员星系的光度函数为Ｓｃｈｅｃｈｔｅｒ型，而各类Ｓ星系的光度函数则为Ｇａｕｓｓ型，且峰值位置按Ｓａ→Ｓｄ序列向暗端移动，宽度亦逐渐变宽；Ｖｉｒｇｏ团质量函数与恒星质量函数一样可以用指数形式来描述，文中还利用光度函数和质量函数对该团的形态和质量分层进行了讨论，并计算了该天区团的总光度。     

Derivative of Kaula's inclination function

The derivative of Kaula's inclination function is expressed as a linear combination of two inclination functions themselves.On leave from Institute of Applied Astronomy, 197042 St.-Petersburg, Russia.     

Improvement of astronomical refraction by mapping function

In this paper we used the method of generator function to gave an improved mapping function of astronomical refraction, separately for optical and radio frequencies. We included a complete consideration of the corrections introduced by the physical and geophysical factors required in astronomy and space techniques. We used sounding balloon data to assess the actual accuracy of our corrected refraction formula. The result is 5″ at elevation 2° and 1″ at elevation 5°. We believe that the main factor that limits the accuracy is departure of the model atmosphere from the real atmosphere.     

映射函数对天文大气折射的改进

本文利用大气折射积分母函数方法,分别给出在射电波段和光学波段上天文大气折射改正的映射函数,并完整地考虑了天文学和空间技术所需要的物理和地球物理因素引入的改正．本文还利用探空气球的资料分析了新天文大气折射改正公式的实际精度;计算结果证明：它在2°高度角时达到5”左右,而在5°高度角时约为1”．我们认为：限制计算精度的主要因素是真实地球大气分布与理论大气模型的区别．     

On the cosmological evolution of the quasar population

Zwei ausgewählte Felder (südöstlich der Galaxie M 82 und in SA 57) werden vollständig spektroskopisch nach Quasaren durchmustert. Die (N — m)-Relation wird um 0.4 bzw. 1.6 Größenklassen in bezug auf den von KRON und CHIU (1981) bestimmten Werte erweitert. Konsequenzen für Modelle der Entwicklung der Leuchtkraftfunktion werden diskutiert.     

The cluster galaxy luminosity function at z= 0.3: a recent origin for the faint-end upturn?

We derive deep luminosity functions (LFs) (to   M _z =−15  ) for galaxies in Abell 1835  ( z = 0.25)  and AC 114  ( z = 0.31)  , and compare these with the local z ' LF for 69 clusters. The data show that the faint-end upturn, the excess of galaxies above a single Schechter function at   M _z < −17  , does not exist in the higher redshift clusters. This suggests that the faint-end upturn galaxies have been created recently, by infall into clusters of star-forming field populations or via tidal disruption of brighter objects.     

Schmidt plate survey in the Galactic centre and anticentre direction. Luminosity and mass functions of open clusters

The proper motions and stellar magnitudes for more than 20 000 stars distributed in areas around eight open clusters in the directions of the Sagittarius-Carina and Perseus spiral arms were used to determine the cluster membership. Both spatial-kinematical and statistical criteria were used for member seletion. The luminosity functions of cluster members were constructed and used for the further data improvement. The safest portions of the luminosity function free both from evolved stars and faint field star contamination were used for mass function construction. The composite mass function was derived from the data on five young clusters with log t < 8.2. A dependence of the mass function slope on the adopted input parameters (mass-luminosity relation and distance scale) and on member selection procedure was tested. The slope was found to vary in a range from 1.36 to 1.80 for lg M/M⊙ between 0.3 and 1.2. A possible relation between the individual MF slopes and cluster ages was indicated. The results are in good agreement with published data.     

Binary stars and the fundamental initial mass function

We have carried out Monte Carlo simulations in which we generate a random pairing of objects drawn from a pre-assumed single-star power-law initial mass function (IMF), which we call the fundamental IMF. We show how the mass functions of primary stars and secondary stars and the mass function of the total mass of systems (if we could resolve them) differ from the underlying fundamental IMF for different slopes of this IMF. We also compare our results with the observed IMF, the binary frequency and the binary mass-ratio distributions for field stars and conclude that the fundamental IMF of subsolar mass stars could be steeper than is currently believed. In other words, the low-mass turn-over of the observed ('apparent') IMF could be spurious, if the main-sequence binary fraction of field stars is close to 100 per cent (perhaps owing to invisible companions).     

The Effect of the Initial Mass Function of Stars on the Burst Rate of GRBs

For the mechanism of production of γ-ray bursts (GRBs) it is rather generally recognized that the long-term γ-ray burst (LGRB) originates from the deaths of massive stars while the short-term γ-ray burst (SGRB) originates from the merging of close binaries. Therefore the speculation naturally follows that the number of LGRBs is directly proportional to the star formation rate (SFR). However, it is indicated from recent data analyses that this speculation does not fit the observations very well. It is considered that only massive stars with masses greater than a certain critical mass can produce the LGRB, so the initial mass function (IMF) of stars can significantly affect the production rate of LGRBs. In this paper it is considered that the IMF of stars can be used to explain the observed number distribution of the LGRBs with the redshift, and this has led to some good results.     

类星体的光度函数

主要讨论了光学选类星体的光度函数有其演化的达几年中的进展，目前在小红移范围已取得比较一致的结论，对ｚ〉２．２，由于类星样品的限制，对类星体光度函数的演化还存在着很大的分岐，在文中还比较了类星体光学，射电，Ｘ射线的光度函数的性质。     

The quasar population density as a result of the formation rate and the evolutionary pathes II. Adaption to the observation

The continuity equation of CAVALIERE et al. (1971) generalized to age-dependent luminosity evolution (BOLLER and LIEBSCHER 1989) is used to calculate quasar luminosity functions. For some combinations of source functions S(L, t) and evolutionary pathes M(L) we discuss the resulting N — m relations and the amount of the X-ray background and compare them with actual results of observation. We can exclude certain models, (S(L, t), M(L)). We cannot yet decide what the actual source function and the actual evolutionary path are.     

The quasar population density as a result of the formation rate and the evolutionary pathes. I. Analytical formulas and numerical simulations

Wir verallgemeinern die Kontinuitätsgleichung von CAVALIERE et al. (1971) für den Fall, daß die Leuchtkraftentwicklung nicht nur von der aktuellen Leuchtkraft abhängt. Wir zeigen, daß einfache Fälle (monomiale Entstehungsraten) integrierbar sind und vergleichen einige interessante Merkmale. Testverfahren und die Einbeziehung der Beobachtung sind in Vorbereitung.     

大气折射母函数方法、大气折射解析解和映射函数

回顾了作为实用天文学和大地测量学中基本研究课题之一的大气折射映射函数研究的进展。介绍了近几年上海天文台发展的大气折射母函数方法 ,以及由此导出的大气折射解析解。对如今广泛地应用在空间测量技术中的几种映射函数做出评述 ;分析了NMF模型的优点和不足之处。介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天文大气折射的映射函数方法。利用VLBI实验中高度截止角与基线长度重复率的关系、探空气球 (radiosonde)观测资料、PRARE资料比较了各种映射函数的结果。特别指出了映射函数方法对天文大气折射和光学波段测距精度的改进。讨论了大气折射计算中的主要误差源。