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.
5.3. Molecular gas and starbursts in luminous and ultra-luminous infrared galaxies (LIRGs and ULIRGs)
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).
5.4. OH mega-masers.
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.