IS T HE P R E S E N T S T E L L A R B I R T H R A T E R E A L L Y D E T E R -

M I N E D BY GAS D E N S I T Y ?

DAVID C. BLACK and SANFORD A. KELLMAN Theoretical Studies Branch, Space Science Division, NASA-Ames Research Center,

Moffet Field, Calf, U.S.A.

(Received 23 June, 1973)

Abstract. Observed supernovae rates in Sb and Sc galaxies, and a recent re-examination of the mean gas density in these galactic types, implies that if the 'dumpiness' of gas in the disks of Sb and Sc galaxies is similar, the gas density is not the primary factor in determining the overall present stellar birthrate.

1. Introduction

Schmidt (1959) concluded from a study of the rate of star formation in our galaxy that the birthrate of population I stars depends primarily on the gas density, ~ . Specifically, Schmidt suggested that R , oc@ Several subsequent studies on the rate of star formation (cf. Sanduleak, 1969; Einasto, 1972) have also assumed that the rate of star formation depends on @ Studies of galactic evolution (cf. Larson, 1969; Quirk and Tinsley, 1973) are predicated, in part, on Schmidt's proposed expression for the rate of star formation. Theoretical models of star formation (Field and Saslaw, 1965; Field and Hutchins, 1968), based on specific assumptions, provide ex- pressions for the rate of star formation similar to that suggested by Schmidt.

The purpose of this communication is to examine whether or not the results of recent studies of (1) supernovae rates in Sb and Sc galaxies (Tammann, 1970) and (2) mean H I space densities in the disks of these galaxies (Kellman and Black, 1973) are consistent with the assumption that the present star formation rate is determined primarily by Qg.

2. Discussion

It is generally believed that type II supernovae (SN) are related to a young stellar population (Ilovaisky and Lequeux, 1972); i.e., that the progenitor star was born ~< 108 yr before the SN event occurred. Observational studies of SN rates (number per unit time per 1010 Mo ) in various galaxies, although far from comprehensive, are sufficient to determine if a systematic variation of SN activity exists as a function of galactic type. Tammann (1970) has concluded from a study of the observations that the SN rate for Sc galaxies is ~-4 times greater than for Sb galaxies. Further, he finds that the relative number of type I and type II SN is similar in Sb's and Sc's, indicating that the difference in total SN rate also applies to the specific SN types individually. As it is generally assumed that the Main Sequence population of type II SN progenitors is in a steady state, the factor of ~-4 difference in SN rate between Sb and Sc galaxies

Astrophysics and Space Science 26 (1974) 107-109. All Rights Reserved Copyright �9 1974 by D. Reidel Publishing Company, Dordreeht-Holland

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implies that a similar difference exists in the overall present SN progenitor birthrate (PBR) in these galactic types.

A comparison of the observed mean PBR, as inferred from Tammann's data, with what is predicted on the basis of the Schmidt hypothesis (R. o :~ ) , requires that one integrate the expression for R . over the volume of a galaxy and then average the result for all galaxies of a given type. The resultant expression for the average stellar birthrate for galaxies of type T may be expressed as

( R , ) T or fiT (~o)~r T , (1)

where ( ) refers to the spatial average value of the enclosed quantity for a given galaxy, the subscript T denotes the mean value of the spatial average for all galaxies of type T, and fl=-(~"o)/(qg)'. As can be seen from its definition, fl is a measure of 'clumpiness' or non-uniformity in the gas distribution within the galaxy. At present, there is no observational evidence which indicates that fist is different than flSb, and in the following discussion it is assumed that fiSh--fiSt.

If the gas density is the primary factor in determining R, , Tammann's observations n ~a n require that (Qg)sc--4(~a)Sb" However, a recent study of the mean HI space density

in the disks of galaxies ranging in type from Sb to Irr (Kellman and Black, 1973) has shown that (QH~) does not vary systematically with galactic type over this range of the Hubble sequence. In addition, the results of several investigations to observationally determine the exponent n (Schmidt, 1959; Sanduleak, 1969; Gordon, 1971 ; Hartwick, 1971; Einasto, 1972) are consistent with a single value of n(~-2), independent of galactic type. Thus, " '-~ " (~o)so - (Qg)Sb, implying that, based on available data and subject to the proviso flso--~flSb, the gas density is not the pr imary fac tor in determining R , . This result does not mean that the suggested relation between R. and ~0 is incorrect, only that it is incomplete.

If ~0 is not the primary factor determining R., what is ? Quirk (1972) and Quirk and Tinsley (1973) have proposed that the present rate of star formation may be determined by the rate at which extra-galactic gas falls into a galaxy. To be consistent with the observed difference in PBR between Sb and Sc galaxies, however, this mechanism would require the infall rate into Sc galaxies be, on the average, four times greater than into Sb galaxies. However, there is no a priori reason to expect different infall rates. It is interesting to note that if the primary factor controlling the present value of R . in galaxies is the rate at which gas is injected into the interstellar medium by massive stars, one may have a self-sustaining mechanism for preserving the observed difference between the present PBR in Sb and Sc galaxies.

References

Einasto, J.: 1972, Asttvn. Astrophys. 11, 195. Field, G. B. and Saslaw, W. C.: 1965, Astrophys. J. 142, 568. Field, G. B. and Hutchins, J.: 1968, Astrophys. J. 153, 737. Gordon, K. J.: 1971, Astrophys. J. 169, 235. Hartwick, F. D. ~.: 1971, Astrophys. J. 163, 431. Ilovaisky, S. H. and Lequeux, J. : 1972, Astron. Astrophys. 18, 169.

IS THE PRESENT STELLAR BIRTHRATE REALLY DETERMINED BY GAS DENSITY? 109

Kellman S. A. and Black, D. C.: 1973, Astrophys. J. 184, 753. Larson, R. B.: 1969, Monthly Notices Roy. Astron. 145, 271. Quirk, W. J.: 1972, Astrophys. J. 176, L9. Quirk, W. J. and Tinsley, B. M.: 1973, Astrophys. J. 179, 69. Sanduleak, N.: 1969, Astron. J. 74, 47. Schmidt, M.: 1959, Astrophys. J. 129, 243. Tammann, G.: 1970, Astron. Astrophys. 8, 458.