A model of bimodal star formation is presented, wherein massive stars form in giant molecular clouds (GNC), at a rate regulated by supernovae energy feedback through the interstellar medium, the heat input also ensuring that the initial mass function (IMF) remains skewed towards massive stars. The low mass stars form at a constant rate. The formation of the GMC is governed by the dynamics of the host galaxy through the rotation curve and potential perturbations such as a spiral density wave. The characteristic masses, relative normalizations, and rates of formation of the massive and low mass modes of star formation may be tightly constrained by the requirements of the chemical evolution in the Solar Neighborhood. Good fits were obtained for the age metallicity relation and the metallicity structure of thin disk and spheroid stars only for a narrow range of these parameters

Silk, J.

Wyse, Rosemary F. G.

English

NASA Technical Reports Server

N87- 24317
A SIMPLE THEORY OF BIMODAL STAR FORMATION<>
Rosemary F.G. Wyse 1,2 and J. Silk 2
1. Space Telescope Science Institute, Baltimore, MD 21218
2. Astronomy Dept., University of California, Berkeley, CA 94720
ABSTRACT. We present a model of bimodal star formation, wherein massive stars form in
giant molecular clouds (GMC), at a rate regulated by supernova energy feedback through
the interstellar medium, the heat input also ensuring that the initial mass function (IMF)
remains skewed towards massive stars. The low mass stars form at a constant rate. The
formation of the GMC is governed by the dynamics of the host galaxy through the rotation
curve and potential perturbations such as a spiral density wave. The characteristic masses,
relative normalisations and rates of formation of the massive and low mass modes of star
formation may be tightly constrained by the requirements of the chemical evolution in the
Solar Neighborhood. We obtain good fits to the age metallicity relation and the metallicity
structure of thin disk and spheroid stars only for a narrow range of these parameters.
1. THE MASSIVE STAR FORMATION RATE
The effects of massive stars on the surrounding interstellar medium and subsequent
star formation may be envisaged to be either to suppress further star formation for some
time by destroying the cold (molecular)gas from which stars are presumed to form, or to
induce further star formation through the increase in pressure compressing and destabilising
clouds. These two effects in fact operate simultaneously, leading to self regulated (massive)
star formation (cf. Cox 1983; Franco and Cox 1983; Dopita 1985). The lower mass stars
are effective over much longer timescales and may be neglected for the regulation of the
formation of short-lived stars. Assuming that the most important energy injection process
is due to supernova explosions, which maintain a velocity dispersion in the system of GMC
that governs the cloud-cloud collision time and hence energy dissipation and star formation
time, leads to the following dependence of global massive star formation rate (SFR) per unit
(molecular) gas mass on the surface densities (_) of total material, and gas:
Mo ~ (2,tot ,g.,.co)I/2
Mgas,CO
The self regulation allows one to understand why only a small fraction of GMC cores
have associated HII regions (Solomon, Sanders and Rivolo 1985; Scoville, Sanders and Clemens
1986) ie. why massive star formation is in this sense inefficient.
The massive SFR in external galaxies may be estimated from the UV flux, or the far IR
assuming it is mainly due to dust reradiation of the UV from massive stars. Unfortunately,
large discrepancies in these two estimates exist for the galaxies that have measurements of
the quantities in the above equation, which may indicate either that a significant fraction of
the IRAS flux is due to a cirrus component of dust heated by the general stellar radiation
field, or that extinction problems remain with the quantitative interpretation of the UV, or
both. Thus a direct quantitative testing of this relation is not yet possible.
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Star Formation in Galaxies 339
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R. F. G. WYSE AND J. SILK
2. THE RADIAL DEPENDENCE OF GMC AND MASSIVE STARS.
The dependence of the global massive SFR on total surface density found above sug-
gests that the rotation curve may be of importance. Many models for the formation of GMC
complexes analyse the effect of a spiral density wave and postulate that the potential causes
an increase in the lengthscale which is gravitationally unstable, or simply aids the coagula-
tion of small diffuse clouds of either atomic or molecular gas (eg. Cowie 1980; Balbus and
Cowie 1985). We here present a phenomenological model for GMC, whereby the rate of their
formation, and CO emission, depends on the rate at which a parcel of gas encounters a spiral
perturbation, and on the square of the HI density. We are most interested in understanding
the radial profiles of CO in disk galaxies - why they are so different from the atomic gas
profiles, but similar to the blue light. In this respect it is only important that the progenitors
of GMC have the same radial profile as the HI, as may be the case for the analogs of the small
high latitude CO clouds found by Blitz, Magnani and Mundy (1984). Thus
coCr) - ne), 
where t2 is the local angular frequency, t2p and rn being the pattern speed and number of
arms in the spiral pattern. For situations where no underlying density wave occurs but the
arms are due to a simple shear instability and swing amplifier, we set t2p -- 0, since then
t2(r) mimics the Oort constant of differential rotation, which controls the instability (Toomre
1981). A dependence on the rate of encounters of spiral arms was also postulated by Shu et
al. (1972) in their modelling of the SFR in density wave theory, and by Gfisten and Metzger
(1982) for massive stars in the spiral arms of our Galaxy. The dependence on the square of the
HI density assumes that two-body processes such as binary cloud-cloud collisions dominate.
We are also equating a rate with a luminosity and hence mass.
E
v
E
5 5
''11 .... I .... ]
OMilky Way observed CO
• Predicted CO. normalised
5 i0 15
radius (kpe)
P
E
o
' ' ' ' I ' _ ' ' I ' ' ' ' i ' ' _ '
ONGC 2841 observed CO
• predicted CO, normalised
i 0 Iii i
20 -10 300 10 20
radius (kpc)
Figure 1. Predicted CO emission (filled triangles), arbitrarily normalised, compared to
the observations (open circles) for the Milky Way (Sanders, Solomon and Scoville 1984) and
NGC 2841 (Young and Scoville 1982).
We have made predictions for of order ten galaxies with the necessary observations,
obtaining encouraging results. Interesting features are that galaxies which are believed to
have a density wave are best fit by corotation in the outer regions, as predicted by theory
(Shu et al. 1972) and have a significantly poorer fit if we set t2p = 0, while the galaxies with
more filamentary arms (eg NGC 2841) are well fit by the theory for arbitrary values of the
340
A SIMPLE THEORY OF BIMODAL STAR FORMATION
pattern speed, as may be expected. Results for the Milky Way and NGC 2841 are shown in
Figure 1. We obtain equally good agreement with the CO observations for galaxies with a
CO 'ring' and those with monotonic CO. The radial fall-off of the CO emission to large radii
while the HI remains fiat reflects the near exponential behavior of fl(r) - lip, which in turn
reflects the profile of the stellar disk since disk galaxies are essentially self-gravitating within
a few scale-lengths. Thus fitting an exponential to the CO results in a scale-length close to
that of the stars, or equivalently, the blue light.
3. CHEMICAL EVOLUTION IN A BIMODAL MODEL.
Any reasonable model for the time dependence of the gas mass, together with the regu-
lation equation above, yields a massive SFR that decreases sharply with time. This contrasts
strongly with the derived constant Solar Neighborhood low mass SFR (Twarog 1980) - hence
the star formation process is bimodal in time as well as space (of Larson 1986). Matteucci and
Greggio (1986) showed that a constant SFR for stars of all masses would overproduce oxygen
and other elements due to massive stars. The effect of the new 12C(a,"/)lsO reaction rate
on the chemical yields of massive stars was investigated subsequently (Matteucci 1986) and
silicon and iron are still overproduced. A decreasing massive SFR appears to offer a solution.
We have investigated the chemical evolution in a particular parameterisation, where
the two modes are taken to be 1). 'low mass' mode : Miller-Scalo IMF, all masses, constant
SFR AIM®Gyr -1 and 2) 'massive' mode : only stars above ML2, SFR A2e-t/r2M®Gyr -1.
The lower mass cutoff of the 'massive' mode is made as low as possible, to avoid introducing
a time dependence into isotopic ratios which would arise were the nucleosynthetic properties
of the two modes different and which is not observed. The models are required to fit the
Solar Neighborhood age-metallicity relationship for low mass F stars and also to reproduce
the present day gas content and total disk surface density, 70 M®pc -2 (any dark matter being
stellar remnants). A gas consumption time of at least several Gyr is also required. These
quantities are shown in Figure 2 for a model we deem satisfactory.
-5
r_
• Twarog
e Carlberg et al
0 5 I0
Age (Gyr)
Figure P.. The predicted age metallicity relation
for long-lived F stars in the Solar Neighborhood
(solid line), for a model for the thin disk with ini-
tial metallieity a tenth solar, consistent with the
spheroid model in Figure 3(b), and with low mass
mode SFR 4 M®Gyr -1, high mass mode, with
lower mass of 2 M®, normalisation 20 M®Gyr -1
and e-folding time of 2 Gyr. The observational
data of Twarog (1980) and Carlberg et al. (1985)
are also shown. The model and observations are
in good agreement, and the model output values,
at 15Gyr, for the gas and stellar surface density/_
2
M®pc- and the gas lockup (consumption) time
are entirely satisfactory, although the gas content
is somewhat high.
15
We have also compared model predictions with the cumulative metallicity distributions
of thin disk stars and extreme spheroid stars, allowing for ejecta from the spheroid (leaving
at a rate )_ times the star formation rate) to pre-enrich the thin disk material (see Figure 3).
There is a narrow range of parameter values which provides a good fit to all these observational
constraints.
341
R.F.G.WYSEANDJ.SILK
We are currently working on fully self consistent models, using the equations above for
the time and radial dependences of the massive SFRs. Extension of the model to different en-
vironments such as IRAS galaxies is underway to help understand the starburst phenomenon.
.8
.6
.4
.2
0
0
- - bimodal model, initial [Fe/H]=-I -- -/ /!//'//'_
/// /
/
_ .... thin disk stars
<[Fe/H]>=-0A5, (_2>cr>0 1
I III I i L _ I i i i _ I I i i ,
2 .4 .6 8
N/Nt
I'' I '' ' I ''' I' ' ' I I '
L model : input 1=2; Az=50; At=0 1; Ta=2;
1
spheroid:disk mass = 0.1 /
/
.2 .4 .6 .8 1
N/N1
Figure $ (a). Cumulative metallicity distribution for the low mass stars of our favored model
(solid line) compared to estimates of the true distribution, which are +2a truncated gaussians,
of mean -0.15 dex (dashed lines delimiting range of dispersion 0.1 < a < 0.2 dex).
(b). Cumulative metallicity distribution for spheroid stars. The model (solid line) has
star formation parameters as indicated, with outflow at twice the total SFR, and a total initial
surface density (ai) of 100M®pc -2. The observations are the metal poor spheroid globular
clusters (Zinn 1985). The model predicts reasonable values for the initial enrichment of the
thin disk and for the spheroid to thin disk mass ratio.
REFERENCES
Balbus, S.A. and Cowie, L.L., 1985, Ap. J., 297, 61.
Blitz, L., Magnani, L. and Mundy, L. 1984, Ap. J. (Lett.), 282, L12.
Carlberg, R. et al., 1985, Ap. J., 294, 674.
Cowie, L.L., 1980, Ap. J., 236, 868.
Cox, D.P., 1983, Ap. J. (Lett.), 265, L61.
Dopita, M.A., 1985, Ap. J. (Left.), 295, L5.
Franco, J. and Cox, D.P., 1983, Ap. J., 273, 243.
Gfisten, R. and Metzer, P.G., 1982, Vista in Astr., 26, 159.
Larson, R.B., 1986, M.N.R.A.8., 218, 409.
Matteucci, F., 1986, Ap. J. (I, ett.), 305, L81.
Matteucci, F. and Greggio, L., 1986, Astr. Ap., 154, 279.
Sanders, D.B., Solomon, P.M. and Scoville, N.Z., 1984, Ap. J., 276, 182.
Scoville, N.Z., Sanders, D.B. and Clemens, D.P., 1986, preprint.
Solomon, P.M., Sanders, D.B. and Rivolo, A.R., 1985, Ap. J. (I, ett.), 292, L19.
Toomre, A., 1981. Normal Galaxies, eds. S.M. Fall and D. Lynden-Bell (CUP) plll.
Twarog, B., 1980, Ap. J., 242, 242.
Shu et a/., 1972, Ap. J., 173, 557.
Young, J.S. and Scoville, N., 1982, Ap. J. (Lett.), 260, L41.
Zinn, R., 1985, Ap. J., 293, 424.
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A simple theory of bimodal star formation

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