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 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.     

The galaxy luminosity function in clusters and the field

We present the results from a CCD survey of the B -band luminosity function of nine clusters of galaxies, and compare them to published photographic luminosity functions of nearby poor clusters like Virgo and Fornax, and also to the field luminosity function. We derive a composite luminosity function by taking the weighted mean of all the individual cluster luminosity functions; this composite luminosity function is steep at bright and faint magnitudes and is shallow in-between.
All clusters have luminosity functions consistent with this single composite function. This is true both for rich clusters like Coma and for poor clusters like Virgo.
This same composite function is also individually consistent with the deep field luminosity functions found by Cowie et al. and Ellis et al., and also with the faint end of the Las Campanas Redshift Survey R -band luminosity function, shifted by 1.5 mag. A comparison with the Loveday et al. field luminosity function, which is well determined at the bright end, shows that the composite function, which fits the field data well fainter than M _B=−19, drops too steeply between M _B=−19 and −22 to fit the field data there.     

The dwarf galaxy population of the Coma cluster to MR=−11: a detailed description

We present the luminosity function and measurements of the scalelengths, colours and radial distribution of dwarf galaxies in the Coma cluster down to R =24. Our survey area is 674 arcmin²; this is the deepest and most detailed survey covering such a large area.
Our measurements agree with those of most previous authors at bright and intermediate magnitudes. The new results are as follows.
(1) Galaxies in the Coma cluster have a luminosity function φ( L )∝ L ^α that is steep (α∼−1.7) for −15< M_R <−11, and is shallower brighter than this. The curvature in the luminosity function at M_R ∼−15 is statistically significant.
(2) The galaxies that contribute most strongly to the luminosity function at −14< M_R <−12 have colours and scalelengths that are consistent with those of local dwarf spheroidal galaxies placed at the distance of Coma.
(3) These galaxies with −14< M_R <−12 have a colour distribution that is very strongly peaked at B − R =1.3. This is suggestive of a substantial degree of homogeneity in their star formation histories and metallicities.
(4) These galaxies with −14< M_R <−12 also appear to be more confined to the cluster core ( r ∼200 kpc) than the brighter galaxies. Alternatively, this observation may be explained in part or whole by the presence of an anomalously high number of background galaxies behind the cluster core. Velocity measurements of these galaxies would distinguish between these two possibilities.     

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.     

The fraction of galaxies that contain active nuclei and their accretion rates

We investigate the relationship between the present-day optical luminosity function of galaxies and the X-ray luminosity function of Seyfert 1s to determine the fraction of galaxies that host Seyfert 1 nuclei and their Eddington ratios. The local type 1 active galactic nuclei (AGN) X-ray luminosity function is well reproduced if ∼1 per cent of all galaxies are type 1 Seyferts which have Eddington ratios of ∼10⁻³. However, in such a model the X-ray luminosity function is completely dominated by AGN in E and S0 galaxies, contrary to the observed mix of Seyfert host galaxies. To obtain a plausible mix of AGN host galaxy morphologies requires that the most massive black holes in E and S0 galaxies accrete with lower Eddington ratios, or have a lower incidence of Seyfert activity, than the central black holes of later-type galaxies.     

An improved method of constructing binned luminosity functions

We show that binned differential luminosity functions constructed using the 1/ V _a method have a significant systematic error for objects close to the flux limit(s) of their parent sample. This is particularly noticeable when luminosity functions are produced for a number of different redshift ranges as is common in the study of AGN or galaxy evolution. We present a simple method of constructing a binned luminosity function which overcomes this problem and has a number of other advantages over the traditional 1/ V _a method. We also describe a practical method for comparing binned and model luminosity functions, by calculating the expectation values of the binned luminosity function from the model.
Binned luminosity functions produced by the two methods are compared for simulated data and for the Large Bright QSO Survey (LBQS). It is shown that the 1/ V _a method produces a very misleading picture of evolution in the LBQS. The binned luminosity function of the LBQS is then compared with a model two-power-law luminosity function undergoing pure luminosity evolution from Boyle et al. The comparison is made using a model luminosity function averaged over each redshift shell, and using the expectation values for the binned luminosity function calculated from the model. The luminosity function averaged in each redshift shell gives a misleading impression that the model over predicts the number of QSOs at low luminosity even for 1.0< z <1.5, when model and data are consistent. The expectation values show that there are significant differences between model and data: the model overpredicts the number of low luminosity sources at both low and high redshift. The luminosity function does not appear to steepen relative to the model as redshift increases.