Astron. Astrophys. 354, 802-814 (2000)

7. Integral IMF in galaxies

In Sect. 6, throughout the calculations of masses of individual SFCs in galaxies NGC 2403, 2903, 4038/39, 4303, 4449 the estimations of slope , upper mass limit and normalising constant A of IMF in all observed SFCs were derived. This gives the possibility to estimate the initial number of stars at fixed mass m in an individual SFC:

where is the estimated slope of the IMF in the individual SFC, is the value of the normalising constant estimated from Eq. (19). Since the samples of SFCs in these galaxies are mostly complete, we can calculate a total initial number of stars of fixed mass m in all SFCs in a given galaxy as

where is the total number of star forming regions in the galaxy. In Fig. 8 we have plotted on a logarithmic scale the calculated total initial number of stars of mass m versus the stellar mass m (in instantaneous burst approximation) separately for each of the studied galaxies. Because the lower mass end of the IMF is not known from observations and about 80% of the luminosity of SFCs is provided by high mass stars (), the integral IMF in a given galaxy is built for the stellar mass interval from to . Star forming regions with a low upper mass limit (for example with ) do not contribute to the high mass part of the galactic integral IMF. This effect causes the sharp decreasing of the number of high mass stars in the galaxy NGC 2403 (see Fig. 8a). Since the major part of the integral IMF ( or in ) provides more than 90% of the luminosity and contains more than 97% mass of SFCs, we adopted the stellar mass value as upper mass limit of the integral IMF in the galaxy NGC 2403.

Fig. 8. a Integral stellar IMF in the NGC 2403. The sharp jump down at mass is due to the sharp decrease of the number of SFCs with upper mass limit . b The integral IMFs in the studied galaxies are close to Salpeter IMF().

Slopes of stellar mass distributions estimated by the least mean square method for five studied galaxies are indicated in Table 6. We have presented both cases: instantaneous burst (SSF model) and continuous star formation (CSF model). Both approximations constrain the slope of the integral IMFs close to Salpeter IMF, despite the broad range of variation of the slope in individual SFCs from to (see Table 6). The high mass SFCs () provide the major contribution to the integral IMF in a galaxy. Therefore the underestimation of the number of faint SFCs is not important.

Table 6. IMF, rate of star formation, SN frequency in studied galaxies.

We have estimated the star formation rate in a galaxy within the stellar mass interval from to the upper mass limit of the integral IMF from the total amount of gas transformed into stars (total stellar mass within the stellar mass interval ) in all SFCs:

where constant A is estimated from the integral IMF in a galaxy plotted in Fig. 8b. Since the parameters , in formula (26) are related to the IMF of individual SFCs, not to the present stellar mass functions, the value of the total amount of gas transformed into stars () corresponds to the onset of star formation. The total mass is computed assuming instantaneous star burst. In the case of continuous star formation the low limit of the total amount of gas transformed into stars and appropriately the low limit of the rate of star formation can be estimated (see Table 6, Column 4). The star formation rate (see Table 6) was derived from the estimated and average age of SFCs in a given galaxy:

Star formation rate (SFR) from observed FIR flux is computed using the above estimated above slope of integral IMF, and mean age of SFCs of a given galaxy:

where

and

We assumed that the observed FIR luminosity accounts for the bolometric luminosity of all stars borne in all SFCs in the parent galaxy. Comparison between estimation of SFR from integral IMF (Column 4 in Table 6) and that from observed FIR luminosity can constrain the regime of star formation into the benefit of instantaneous burst in NGC 2403, 2903, 4303.

We also estimated the SN frequency () in these galaxies as a number of formed stars with mass greater then per year (see Table 6, Column 6). In the case of continuous star formation model estimations of are the upper limit of intervals between SN events. The observed average interval between successive supernovae in NGC 4303 (Flin et al. 1979) is 19 years and the interval computed from the radio fluxes of NGC 4303 is 13 years (Smirnov & Sakhibov 1984). These two values are close to the interval estimated assuming instantaneous burst in NGC 4303. The observed average interval between SN in NGC 4038/39 is about 50 years (Flin et al. 1979). The detection of the frequent SN calculated for this starburst galaxy could be hidden by very large light absorption.

The estimated star formation rate for the three spirals (NGC2403, NGC2903, NGC4303) and the one irregular (NGC4449) galaxy are in good agreement with evolution models of galaxies (Samland & Hensler 1996) and IRAS observations (Sage 1993; Soifer et al. 1989).

Peculiar colliding galaxy NGC4038/39 shows the highest star formation rate. Apparently the burst of star formation is caused by interaction of two galaxies. The mid-infrared spectroscopic observations of the interacting galaxies NGC 4038/39 obtained with the ISO Short Wavelength Spectrometer are well described by star burst models for a recent star burst with an initial mass function extending up to 100 Solar Masses (Genzel et al. 1997). This is an observational confirmation of our estimation of a very high rate of star formation and high SN frequency.

© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000
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