5.1. Introduction. Star formation rate
Star formation is a combination of complex processes of the interstellar
medium, eventually culminating in fragmentation and collapse of stellar
size clumps (e.g.
McKee & Ostriker
2007).
Most of the steps imply densities where the interstellar gas is
necessarily molecular.
One may thus expect strong correlations between the amount of molecular
gas and the efficiency of star formation at all scales. Indeed, in
external galaxies only massive star formation is detectable from the UV
energy it generates. The star formation rate is therefore directly
characterised by the UV luminosity, or by the induced
H
or far-infrared
luminosities. The derived star formation rate (SFR, in units of
M
/ yr) relies on
usual assumptions about the stellar initial mass function (IMF). The
star formation efficiency is usually defined as the star formation rate
per unit mass of interstellar gas. We will stress in
Section 5.2 that
there are also good reasons to define it as star formation rate per unit
mass of molecular gas. The relevant scale for massive star
formation is indeed that of giant molecular clouds which have the right
mass to eventually form one or several clusters of massive stars. In the
Milky Way, it is well proved that most star formation takes place in
GMCs. In estimating SFRs, dust extinction should be carefully taken into
account for correcting the UV or H luminosities, or estimating the fraction of the UV energy
which is processed into the far-infrared. When this fraction is large,
the far-infrared luminosity, LFIR is a better indicator of
the star formation rate. GMCs are also the right scale for discussing
the various feedback processes associated with massive star formation,
either positive ones propagating star formation by compressing the
interstellar gas by stellar winds or supernovae blast waves; or negative
ones by cloud destruction.
5.2. Star formation and molecular clouds in non-starburst galaxies
Since the first extragalactic CO surveys, it was noticed that there is a
strong correlation between the CO intensity ICO and both the
far-infrared and H
luminosities. However, making this correlation quantitative with SFR
raises several difficulties even for non-starburst galaxies including
the most important case of normal spirals. First, a precise value of SFR
is difficult to estimate from both LFIR and
LH,
although it can be approximately and consistently calibrated on both,
yielding SFR roughly proportional to ICO for normal spirals
(see e.g.
Young 2000,
Gao & Solomon 2004b,
and references therein). The use of LFIR has the advantage to
be very well fitted to the extension to starburst galaxies (see
Section 5.3). But for normal spirals, it is not easy
to estimate the
fraction of the UV radiation emitted by young stars which is absorbed by
dust and reemitted in the far-infrared.
LH
is thus often preferred for normal spirals; however, it must be
corrected for extinction, either by a uniform average factor (e.g.
Kennicutt 1998a)
or, better, individually for each galaxy (e.g.
Boselli et al. 2002).
For galaxies with low CO emission (Section 4.2), it is not surprising that the correlation between SFR and ICO is very poor since CO no longer well reflects the H2 mass. However, if one properly determines MH2 with the right X-factor, the correlation between SFR and MH2 remains at the same level of accuracy as for normal spirals, i.e. with the same average value of the star formation efficiency SFE = SFR/MH2, with a similarly large dispersion.
It has been shown that there is a similar correlation between SFR and the total amount of gas, MH2 + MHI, with the obvious explanation that the average value of MH2 / MHI is roughly constant for spirals (Boselli et al. 2002). Kennicutt (1998a, b) suggested that the total amount of gas surface density is indeed the most fundamental factor for determining SFR. This is certainly plausible for the average star formation rate on cosmological time scales. But the present star formation rate is much more likely related to the amount of molecular gas, and even the amount of dense molecular gas (see Section 5.3), than to MHI. The definition of the star formation efficiency with respect to MH2, SFE = SFR/MH2, could thus be preferable (Boselli et al. 2002, Wong & Blitz 2002).
In the most accurate determinations of SFE, the value of SFE is thus comprised between ~ 10-8 and ~ 10-10 yr-1, irrespectively of the morphological type, for most non-starburst galaxies (see e.g. Fig. 9 of Boselli at al. 2002). Such short timescales, between ~ 108 and 2 × 109 yr, for the consumption of the current molecular gas by star formation, means that it should be renewed at similar rates from the HI reservoirs, first Galactic and eventually extragalactic.
The advent of far-infrared astronomy, mostly with IRAS, has revealed the
existence of galaxies with LFIR one or two orders of
magnitude larger than for normal galaxies: luminous infrared galaxies
(LIRGs) with LFIR > 1011
L and
ultra-luminous ones (ULIRGs) with LFIR > 1012
L (see e.g.
Sanders & Mirabel 1996,
Lonsdale et al. 2006).
These high luminosity galaxies are directly powered by gigantic
starbursts mostly dust enshrouded, with star formation rates of several
ten or hundred
M / yr, which
may be directly inferred from LFIR if the general relation,
SFR 
2 ×
10-10 LFIR
(Kennicutt et al. 1998a),
applies. From their perturbed morphology, especially for the most
luminous ones (LFIR > 1012
L), it is clear
that these starbursts are often triggered by strong interactions with a
close companion, eventually leading to a complete or partial
merging. Their luminosities are dominated by dust heating within
molecular clouds of circumnuclear starbursts. However, some nuclear
activity at a relatively low level is also present in many of them. Both
starburst and AGN activities are fueled by the presence of huge amounts
of molecular gas which has been driven into the merger nucleus. Even if
a large number has been identified by IRAS at z
0.1-0.3, LIRGs
and especially ULIRGs are relatively rare in the local universe, but
they are orders of magnitude more numerous at high redshift (see
Section 9). High-z ULIRGs may represent
important steps in the formation of
elliptical galaxies, and also in the growth of their massive black
holes, and thus in the genesis of quasars.
Up to redshifts of ~ 0.1 for LIRGs and ~ 0.3 for ULIRGs, they are well within the range of sensitivity of the best present facilities for comprehensive studies of the most prominent molecules, CO, HCN and OH masers. In addition, interferometric studies in the radio continuum (e.g. Turner & Ho 1994) may provide high angular resolution diagnosis of the structure of the starburst and hence of the molecular medium through the general extraordinary FIR-radio correlation (Condon 1992) between the star formation power generated in the starburst and the synchrotron radio luminosity of its supernovae.
It is clear that the neutral gas of the central CO-emitting region is
almost entirely molecular. However, it is known that using the Milky Way
value for the molecular gas mass to CO intensity ratio, X =
NH2 / ICO, overestimates the gas mass in ULIRGs
since it may yield a molecular gas mass comparable to and in some cases
greater than the dynamical mass of the CO-emitting region
(Sanders et al. 1986,
Sanders et al. 1991,
Scoville et al. 1991,
Downes et al. 1993,
Solomon et al. 1997,
Solomon & Vanden Bout
2005).
The reason is probably that the structure and the temperature of the
molecular gas in the centers of ULIRGs is different from the individual
virialized clouds of disks of normal galaxies. Extensive high-resolution
mapping of CO emission from ULIRGs shows that the molecular gas is in
rotating disks or rings. Kinematic models
(Downes & Solomon
1998)
in which most of the CO flux comes from a moderate density warm
intercloud medium, have yielded conversion factors for deriving the mass
of molecular mass from CO emission approximately 4-5 times lower
than standard values for the Milky Way; namely X =
NH2 / ICO
0.4 ×
1020 cm-2
(K km s-1)-1. Such a value for X is often used by
observers, even for high-z ULIRGs where such a calibration is more
uncertain (Section 9).
There is a correlation in LIRGs and ULIRGs, as well as in other galaxies, between the CO luminosity LCO and the far-infrared luminosity LFIR which traces the star formation rate (see e.g. Sanders & Mirabel 1996, Kewley et al. 2002). However, such a relation is not linear, and the ratio between LCO and LFIR decreases with increasing LFIR (Sanders & Mirabel, 1996, Solomon et al. 1997, Gao & Solomon 2004b). The reason is probably that CO mainly traces the low density gas of giant molecular clouds (see Section 3 & 4), but not their active star forming hot cores. On the other hand, HCN is a much better tracer of the dense regions and thus of star formation. This has been shown by Gao & Solomon (2004a) who found a tight correlation between the HCN luminosity LHCN and LFIR in a sample of 65 normal spiral and starburst galaxies. The correlation remains almost linear over a factor of 103 in luminosity from normal galaxies to LIRGs and ULIRGs. Wu et al. (2005) have recently shown that the correlation between LHCN and LFIR continues up to the much smaller scale of Galactic dense cores, and they argue that it could be explained if the basic unit of star formation in all galaxies is a dense core similar to Galactic ones. A large CO, HCN multi-transition survey of 30 LIRGs is nearing completion with JCMT and the IRAM 30-m telescopes (Papadopoulos et al. 2007), and the properties of the dense molecular gas have been studied in a sample of 17 nearby LIRGs and ULIRGs through observations of HCO+, HCN, CN, HNC and CS (Gracia-Carpio, J. et al. 2007).
Since luminous infrared galaxies are those where the molecular medium
is the most enhanced, it is not surprising that nearby LIRGs such as M 82
provided the first extragalactic detections of many molecules
(Section 6 and
Table 2). This is true not only
for molecules such as
HCO+ or CS which, together with HCN, are well known tracers
of dense regions, but also for widespread molecules such as
OH. Absorption 18 cm lines of OH were detected very early in M 82
(Weliachew 1971).
Later, OH emission lines were detected
(Nguyen-Q-Rieu et
al. 1976),
with maser amplification of the background radio continuum and
intensities 10 times stronger than bright Galactic OH masers. However,
it was a surprise to discover OH maser emission with many orders of
magnitude higher (~ 108 times that of typical OH Galactic
masers) first in the ULIRG Arp 220 (IC 4553)
(Baan et al. 1982)
and then in many luminous and ultra-luminous infrared galaxies (see
detailed recent review on such OH `mega-masers' by
Lo 2005,
to which we refer, avoiding detailed developments on this important
topic). OH mega-masers taking place in powerful starburst galaxies
present a strong correlation between LOH and LFIR,
with LOH > 104
L associated
with LFIR > 1012
L. A quadratic
dependence between LOH and LFIR was even believed
for a while, LOH
LFIR2; but it is now proved from the combined
analysis of 95 OH mega-masers that the relation is rather LOH
LFIR1.2 ± 0.1
(Darling & Giovanelli
2002).
The main pumping mechanism is thought to be mid-infrared pumping by OH
rotational lines. However, as for other interstellar OH masers, the
whole process of mega-maser emission is very complex, as indicated in
particular by the non understood absence of mega-maser detection in a
large fraction (80%) of infrared luminous galaxies. The possibility of
performing high angular resolution VLBI studies of OH mega-masers
provides important clues about their origin as well as the structure and
physics of the starburst regions where they take place (see e.g.
Lo 2005).
It seems that OH mega-masers could mostly trace compact extreme
starburst regions where the conjunction of very strong infrared and
radio emission may create favourable conditions for mega-maser
emission. Combined high resolution studies of OH and CO in nearby
ULIRGs, such as Arp 220, are consistent with such ideas; however,
further elucidation of the physics involved is required.