Astronomy Reports, Vol. 45, No. 1, 2001, pp. 1–15. Translated from Astronomicheskiœ Zhurnal, Vol. 78, No. 1, 2001, pp. 3–20. Original Russian Text Copyright © 2001 by Sakhibov, Smirnov. Star Formation in Extragalactic HII Regions. Determination of Parameters of the Initial Mass Function F. Kh. Sakhibov1 and M. A. Smirnov2 1Institute of Astrophysics, Academy of Sciences of Tajikistan, ul. Bukhoro 22, Dushanbe, 734670 Tajikistan 2Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya ul. 48, Moscow, 109017 Russia Received January 27, 1999 Abstract—A method for using the colors of star-forming complexes to derive the slope and upper mass limit of the initial mass function (IMF) and the age of the complex is proposed in the framework of synthetic evolu- tionary models of star-cluster populations. The star-formation parameters of 105 complexes in 20 spiral and irregular galaxies are determined. The IMF slopes in different star-forming complexes differ appreciably, and their dependence on the luminosities and masses of the complexes is derived. The duration of the star-formation period increases with the luminosity of the complex, and complexes with longer star-formation periods are richer in metals. The slope of the integrated IMF in a Galaxy depends on the mass spectrum of its complexes, and the upper mass limit of the IMF is lower in early-type spirals. © 2001 MAIK “Nauka/Interperiodica”. 1. INTRODUCTION in irregular galaxies. We wish to study star formation in the individual SFCs in these galaxies: the IMF slope (α), One of the main characteristics of stellar systems, in IMF upper mass limit (M ), and age t of the SFC. particular of young star clusters, is the mass spectrum max of the stellar population. The mass spectrum, or mass In many studies, star formation in spiral and irregu- function, of a stellar population reflects both the initial lar galaxies has been investigated using computed syn- conditions for star formation in the cluster and its his- thetic spectra and the observed integrated colors of tory. To distinguish the initial conditions for star forma- individual SFCs/giant HII regions [2–10]. There are tion from evolutionary effects, we must know the initial two approaches to such studies: (1) the synthetic spec- mass function (IMF) of the cluster stars. One aim of tra are computed based on stellar evolutionary tracks this paper is to derive the IMF and ages of young star- and model atmospheres—so-called evolutionary syn- forming complexes (SFCs) from the observed spectral thesis [4, 6, 11, 12]; or (2) libraries of stellar and star- energy distributions in integrated spectra. We will also cluster spectra are used—so-called population synthe- analyze the variations of star-formation parameters as a sis [13]. Both methods are useful when comparing function of the individual characteristics of SFCs and observations with the predictions of theories of stellar the morphological type and luminosity class of the par- evolution, stellar atmospheres, and star formation. The ent Galaxy. difficulty with these approaches is that they involve too Earlier [1], we proposed a program to investigate many free parameters, making the results fairly uncer- SFCs in external galaxies based on analysis of their tain. Drawing on observational characteristics at multi- integrated colors, and a technique for translating these ple wavelengths from UV to radio and comparing these colors into the parameters of the IMF. This required the with the predictions of evolutionary population-synthe- construction of a grid of theoretical models to calibrate sis models enabled Mas-Hesse and Kunth [6] to derive photometric diagrams in terms of the IMF parameters. with considerable certainty information about the IMF A method for calibrating two-color photometric dia- slope, age, and star-formation regime in 17 starburst grams in terms of IMF parameters and the ages of stel- regions in irregular and blue compact galaxies. They − lar groups was developed by Piskunov and Myakutin found that the IMF slopes of SFCs range from –1 to 3, [2]. Here, we discuss a technique for comparing the and discovered both young bursts of star formation observed colors of SFCs to theoretical colors in order to (4 Myr) and older objects (10–15 Myr) with continuous infer the parameters of the IMF and the cluster age; in star formation. other words, a technique for translating an SFC’s color In this paper, we propose our own technique for indices into information about the star formation in it. comparing the observed integrated colors of SFCs with The objects of study are young SFCs in spiral and theoretical colors in the framework of an evolutionary irregular galaxies, visible as bright clumps and also known model for a star-cluster population, considering star- as giant extragalactic HII regions. Young SFCs in spiral formation parameters varying over a wide range. The galaxies are concentrated in the spiral arms rather than in comparison of observed spectral energy distributions the interarm space, and appear as the brightest objects with theoretical spectra is an effective tool for analyz- 1063-7729/01/4501-0001 $21.00 © 2001 MAIK “Nauka/Interperiodica” 2 SAKHIBOV, SMIRNOV ing the structure of stellar populations in SFCs. Our characteristics of this model. Most importantly, we technique can be characterized as the conversion of assume that the star-formation function can be separated integrated SFC colors into parameters describing the into two parts: the IMF f(m) and the star-formation rate star formation. Once we have determined the star-forma- r(t). The IMF has a power-law form, f(m) ∝ mα with slope tion parameters in individual SFCs, we can analyze the α, and the masses of stars born lie in the interval m ∈ variations of these parameters among SFCs in other (Mmin, Mmax), where Mmin and Mmax are lower and upper galaxies. mass limits for the IMF. We consider two possibilities We now list the main arguments in favor of using for the star-formation function: individual SFCs to study star formation: (1) Simultaneous star formation, when we assume (1) SFCs/HII regions have uniform chemical com- that all the stars in the SFC were born simultaneously t δ positions (metal abundance z), which can be derived years ago at time t0 = 0, –r(t) = (t0); from observations; (2) Continuous star-formation, when we assume (2) SFCs are sufficiently compact and young for that star formation in the SFC began t years ago and has their IMFs to be uniform in space and time; continued until the present time, –r(t) = const. (3) SFCs/giant HII regions are nebulae whose ion- To compute the fluxes emitted by the stars of an ized volume is determined by radiation from the cluster SFC, Piskunov and Myakutin [2] constructed theoreti- stars; cal Hertzsprung–Russell diagrams for SFCs of speci- (4) Extinction can be taken into account more accu- fied ages and IMFs based on evolutionary tracks and rately in SFCs than in an entire Galaxy; model atmospheres. Their evolutionary tracks included (5) A simple star-formation history for a young SFC the effects of can be described either by a time-independent IMF and (1) both early and late evolutionary stages; constant star-formation rate r(t), or by a starburst, when (2) both low-mass and massive star models; all stars are assumed to have been born simultaneously t years ago; (3) differences in chemical composition (within the (6) Young SFCs/giant HII regions are common in range of abundances for Population I); galaxies of various types and luminosities, and are con- (4) specific physical effects, such as mass loss dur- venient tools for analyzing variations of the IMFs in ing stellar evolution. galaxies with different physical conditions; Since there were no published grids of evolutionary (7) Extensive observational data have been accumu- tracks that satisfied these conditions, a homogeneous lated for these objects, including the integrated colors grid was constructed based on a compilation of results for 836 extragalactic SFCs in 49 spiral and irregular from various studies [17]. Piskunov and Myakutin [2] galaxies [14]. used Schmidt-Kaler’s [17] calibrations to convert bolo- metric stellar luminosities into U, B, V, and R fluxes. Lyman continuum fluxes were computed using the cal- 2. MODEL FOR THE STELLAR POPULATION ibration of Avedisova [18], based on non-LTE model IN A SFC atmospheres. Star formation can be described by the function The theoretical stellar composition of an SFC was b(m, t), which specifies the number of stars N forming represented using four-dimensional tables of the inte- in a mass interval dm during a time interval dt: grated colors U–B, B–V, V–R, and the Lyman contin- 2 uum index LCI as functions of various star-formation d N α b(m, t) = ------------. parameters, namely, slope and upper mass limit Mmax dmdt of the IMF, age t of the SFC, and its metal abundance Z: Assuming a simple star-formation history in an individ- (α, , , ) ual young SFC, which we expect to consist of a single V–B = f 1 Mmax t Z , generation of stars, the star-formation function b(m, t) (α, , , ) B–V = f 2 Mmax t Z , can be written as the product of a function f(m) describ- (1) (α, , , ) ing the mass distribution of the stars born (i.e., the IMF) V–R = f 3 Mmax t Z , and a function r(t) describing the star-formation inten- (α, , , ) sity as a function of time t (i.e., star-formation rate): LCI = f 4 Mmax t Z , b(m, t) = f(m)r(t). ( where LCI = 2 – log IH + NII /IB) is the Lyman contin- Adopting a power-law IMF f(m) ∝ mα and α = –2.35, α uum index (the intensity of the I line emission in we obtain the well-known Salpeter initial mass func- Hα + NII –1 –2 −1 –2 –1 tion [15].