An interview with Anatoly Piskunov

Interview by Bo Reipurth, SFN #352 - April 2022

During the 1970s you published several papers in Russian journals on open clusters and the initial mass function. How did your interest in this topic get kindled?

I graduated from the Urals University in Sverdlovsk City, present day Yekaterinburg, where open clusters were one of the main areas of astronomical interest. My course work dealt with the application of Zwicky's morphological analysis (originally developed for fast colorimetry of galaxies) to study h & Chi Per, the famous open star cluster with plenty of blue and red supergiants. I was interested in the evolutionary aspects, and wanted to know not only how something looks now, but also how it was formed, and how it will look in the future. During my studies at the University, the theory of stellar evolution underwent a rapid development, and the first theoretical Hertzsprung-Russell diagrams (HRDs) that appeared in the journals made a big impact on me. Therefore, when in 1970 it was time for me to choose an institution for my practicum I chose the Astronomical Council of the USSR Academy of Sciences (now renamed the INASAN) - a small institution in Moscow, where stellar models were being actively developed. At that time I had been greatly impressed by papers of Dr. Olga Dluzhnevskaya on the construction of theoretical HRDs, and I was lucky to work under her guidance for 3 months of my practice stay. Subsequently Dr. Dluzhnevskaya suggested for my diploma work a subject focusing on the building of theoretical isochrones and luminosity and mass functions of open cluster stars based on, at the time, unpublished evolutionary tracks for Population I stars with masses of 0.8-15 M_ⵙ by Bohdan Paczyński.

In 1996 you returned again to a theoretical study of the initial mass function of clusters in a paper with Andrey Belikov. What were the key results?

This has a specific background. In the 1980s I was engaged in studies of kinematics, spatial structure, chemical composition, history of star formation, and luminosity/mass functions (LFs/MFs) of the populations of the local galactic disk. These studies helped me to understand the extremely important role of fine details in the mass-luminosity relation for achieving a correct interpretation of the observational mass function (for example the F/G-stars segment, the Wielen dip, the low/lowest-mass segment). Analysis of open clusters suggested that the luminosity functions of their stars possibly have a minor detail

You and your collaborators published in 2006 a highly cited paper on the galactic open cluster population in which you derived the formation rate and lifetime of clusters, among other parameters.

Again about the background. The classic studies of star clusters in the last century were based on heterogeneous observations with different characteristics of spatial coverage, magnitude depth, photometric system, the presence of kinematic data etc. The first opportunities to supersede this patchwork opened up with the construction of all-sky catalogues based on homogeneous observations (such as Hipparcos/Tycho), which radically changed this situation. Using this opportunity my wife and colleague Nina Kharchenko performed a full-sky survey of the ASCC-2.5 catalogue, an extended version of the Hipparcos/Tycho family of catalogues, and established basic parameters for 401 clusters known in the literature. In 2005, she expanded this work to 650 well-known as well as newly-detected open clusters all over the sky. As a result, a sample of clusters (referred to as COCD) with an unprecedentedly wide set of homogeneous parameters was constructed. For every cluster the COCD was providing membership probabilities, the average position in the sky, apparent size, average 2D (sometimes 3D) kinematics, the photometric reddening, distance and age. All the data were highly homogeneous, i.e. based on a single catalogue, and treated in a uniform manner by the same person. This made it very attractive for us to perform the first multilateral study of the local population of star clusters viewing it from different aspects: their spatial, kinematic and age properties. The paper you mention was the first attempt to study this cluster sample. First of all, we found that the sample is complete within 0.85 kpc, its symmetry plane is determined to be at Z₀= -22 +/- 4 pc, and the scale height of open clusters is only 56 +/- 3 pc. The total surface density is Σ = 114 kpc^-2, which leads to the total number of open clusters in the Galactic disk to be of order of 10⁵ at present. We found that the youngest cluster complex (log t < 7.9), with 19 deg inclination to the Galactic plane, is apparently a signature of Gould's Belt. The formation rate and lifetime of open clusters were found to be 0.23 +/- 0.03 kpc^-2 Myr^-1 and 322 +/- 31 Myr, respectively. This implies a total number of cluster generations in the history of the Galaxy between 30 to 40.

In a subsequent study, you analyzed the luminosity and mass functions for Galactic open clusters, aiming to derive the initial luminosity and mass functions, and to determine the percentage of field stars that have originated in open clusters. What did you learn?

Although luminosity functions of clusters are widely used in extra-galactic studies, they were only rather poorly known within the Milky Way by the time when the COCD cluster sample was created. The large and homogeneous sample of cluster parameters offered an excellent opportunity to fill in this gap. Because the survey covered the whole sky uniformly it was possible to determine the boundaries of clusters restricted by tidal interaction with the gravitational field of the Galaxy. This allowed an independent estimation of cluster mass, which, together with the measured integrated magnitudes and ages, were used to build the respective distributions of mass, luminosity and age. Knowing the age of the clusters made it possible to study these distributions from an evolutionary perspective. Simultaneously, young clusters gave us cluster initial mass functions, and showed how the cluster luminosity functions change over time, reflecting the process of "loss of flesh" owing to dynamical evolution. We found that both luminosity and mass functions for higher masses can be represented by a power law with a slope close to the slope of luminosity functions of extragalactic clusters. At the same time, the lower-mass section of the cluster mass function turned out to be consistent with the mass distribution of embedded clusters. I note that simple and obvious statistics based on the parameters of the cluster mass function indicates a significant role of open clusters in the formation of the field population of the galactic disk. According to our estimates, up to 40 percent of the disk stars in our Galaxy have been formed in an open cluster.

Recently you and your collaborators analyzed several thousand clusters and constructed an age distribution and a cluster formation history.

This was done on the basis of our latest Milky Way Star Cluster survey using PPMXL proper motions and 2MASS near-infrared photometry in 2012. This survey has significantly expanded our previous COCD sample: it includes more than 3,000 well-known and newly-identified open clusters and by a factor of more than two expands the limits of the sample completeness to about 1.8 kpc, while retaining the extensive set of cluster parameters inherent in the COCD. The more comprehensive data obtained within the Milky Way Star Cluster survey allowed us to repeat the COCD results with greater accuracy. In particular, we were able to study the history of cluster formation in the disk using approximately an order of magnitude more clusters than in the 2006 paper mentioned above. The correct interpretation of these data requires the use of a model that reproduces the history of the Milky Way disk. We have built a simple model consisting of the initial cluster mass function, a variable rate of cluster formation, and a “cluster lifetime -- initial mass relation”. Optimization of the parameters of these relations provided the best fit of the model to the observations. We find that the best fit to the observed age distribution is ensured by a two-section, moderately falling cluster initial mass function with the slope of the massive section equal to x= 0.54 +/- 0.05, which is flatter than the Salpeter slope of 1.35. Also the rate of cluster formation should strongly decline with time, and the “lifetime-initial mass” relation should follow the pattern typical for clusters underfilling their initial potential well. Note, however, that some other fit options give optimizations that are not much worse. We hope to get a more definite answer after a detailed study of the galactic cluster mass function, which is currently underway in cooperation with younger colleagues from my institute and collaborators from Ukraine and Germany. In several studies of individual clusters we use Gaia data. For example, we explore the evolutionary history of the newly detected double open cluster Cr 135+UBC 7 in the Carina star formation complex.