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the principal way to trace molecular gas in galaxies is with the rotational lines of the co molecule , due to co s relatively high abundance ( about @xmath4 of h@xmath3 ) and low excitation requirements ( @xmath5 k ) .
the high abundance of co generally makes it optically thick , especially in the lowest ( @xmath6 ) transition , with the result that the _ effective _ critical density is quite low , @xmath7 @xmath8 , and the excitation temperature @xmath9 approaches the kinetic temperature in most molecule - rich regions . unlike co , h@xmath3 itself has no permitted rotational transitions , and can only be observed in infrared ( quadrupolar or rovibrational ) lines that require more extreme ( @xmath10 k ) excitation conditions .
the main disadvantage of co is that its high opacity makes it a poor tracer of column density .
indeed , the theoretical basis for using co as a column density tracer is the _ virial hypothesis _ : the co emission comes from an ensemble of virialised clouds that do not shield each other in position - velocity space . for a virialised cloud ,
the size @xmath11 , density @xmath12 , and linewidth @xmath13 are related by : @xmath14 then the co luminosity is proportional to the h@xmath3 mass , assuming roughly constant density and temperature : @xmath15 however , the assumption of virial equilibrium in molecular clouds has been questioned ( e.g.  ballesteros - paredes & mac low 2002 ) , and in regions where co comes predominantly from a diffuse intercloud medium  as has been suggested for starburst galaxies ( solomon et al.1997 , downes & solomon 1998)the linearity between co emission and h@xmath3 column density is likely to break down .
co is also not as self - shielding at h@xmath3 , and might be dissociated even in regions where h@xmath3 is present .
finally , its abundance relative to h@xmath3 will vary according to the metallicity of the interstellar medium ( ism ) , and so it is unlikely to be detectable in very low metallicity regions .
other methods to trace molecular gas include observations of far - infrared and submillimetre emission from dust , and ultraviolet ( uv ) h@xmath3 absorption towards continuum sources .
dust emission is usually optically thin and depends only linearly on temperature in the rayleigh - jeans part of the spectrum , although there are additional uncertainties arising from the adopted grain size distribution and gas - to - dust ratio .
alton et al .  ( 2002 ) show that the 850@xmath16 m dust emission from the disk on ngc 6946 matches the co emission very well .
the uv absorption technique is biased against high gas columns because of extinction , but does provide a powerful tool to study _ diffuse _ h@xmath3 .
tumlinson et al .  (
2002 ) find that the diffuse h@xmath3 fraction in the magellanic clouds is very low , @xmath11% compared to @xmath110% in the galaxy .    for the remainder of this paper ,
we assume that co can be used as a quantitative tracer of h@xmath3 within the disks of normal spiral galaxies .
our general knowledge of the co distribution in galaxies is still based on the single - dish survey of some 300 galaxies conducted with the fcrao 14-m telescope ( young et al .
1995 ) . using multiple - pointing observations for 193 of the galaxies ,
young et al.concluded that co is usually peaked toward galaxy centres : only in 28 galaxies was there an indication of a molecular ring or off - centre co peak . at higher resolution , however , the picture is not so simple .
the bima survey of nearby galaxies ( bima song ) , which imaged the distribution of co emission in 44 nearby spirals at 69  resolution and included single - dish data for full flux recovery , finds that the co distribution in spiral galaxies is generally very heterogeneous ( regan et al .
2001 , helfer et al .
even when azimuthally averaged , large departures from a smooth exponential profile are seen , due to the very clumpy distribution of molecular gas ( which responds strongly to spiral arms , bar perturbations , etc . ) . in addition , only 20 of the 44 song galaxies exhibit their maximum co surface brightness within the central beamwidth , with six galaxies showing no detectable co emission at all in this region ( helfer et al .
2003 ) .    with the higher resolution imaging , the distributions of molecular gas and stars can be compared on scales relevant for studying the effects of internal dynamical processes .
even though many galaxies in bima song do not show central co peaks , the majority do display a co excess in the inner @xmath120  above the exponential profile , where the stellar bulge contributes a similar excess to the stellar light profile ( regan et al .
2001 , thornley et al .
representative profiles are shown in figure 1 .
concentrating on the 27 bima song galaxies with the most extended co detections , thornley et al .
( 2003 ) have found that such co excesses occur in both early and late - type galaxies , and are nearly universal in galaxies with some bar contribution ( type sab or sb ) .
this suggests that at least some of the central excesses are due to bar - driven inflow of molecular gas ( sakamoto et al .  1999 ,
sheth et al .
however , roughly half of the selected galaxies without significant bar contributions also show such central excesses , suggesting that significant bars are not required to produce gas inflow .
it is notable that the hi radial distribution is almost always much flatter than the co , and often shows a central depression , as if the atomic gas has undergone a phase transition to form h@xmath3 .
recent comparisons of single - dish co maps and vla hi imaging by crosthwaite et al .
( 2001 , 2002 ) highlight this dichotomy .
wong & blitz ( 2002 ) found that for seven galaxies with high - resolution co and hi data , the hi / co ratio increases with radius as roughly @xmath17 , consistent with being determined largely by the hydrostatic pressure of the ism , as predicted by elmegreen ( 1993 ) . in this interpretation
, star formation is rarely found in low - pressure regions such as the halo or outer disk because the dominant phase of neutral gas there is atomic .
the fcrao survey indicated that co emission scales roughly linearly with star formation tracers ( e.g. rownd & young 1999 ) except in merging or interacting galaxies ( young et al .
1996 ) , which show enhanced star formation rates .
kennicutt ( 1998 ) , averaging co , hi , and h@xmath18 fluxes within the optical disks of 61 galaxies , found a strong correlation between the sfr and the total gas content , consistent with a schmidt ( 1959 ) law : @xmath19 where @xmath20 and @xmath21 are the surface densities of the star formation rate ( in @xmath22 ) and total gas mass ( in @xmath23 ) respectively .
the correlation of sfr with hi or co individually was much poorer , suggesting that the gas involved in star formation can quickly cycle between atomic and molecular phases .
how does the star formation law behave on smaller scales ?
wong & blitz ( 2002 ) compared co , hi , and h@xmath18 emission in seven galaxies from the bima song sample , and found that the schmidt law continues to hold for azimuthally averaged rings spaced by @xmath11 kpc .
the exact slope of the power law depends on how one chooses to correct for h@xmath18 extinction ; an extinction - free sfr indicator , such as the total ir emission ( kewley et al .
2002 ) might yield a more accurate slope than h@xmath18 .
regardless , the correlation of sfr with co is considerably stronger than that with hi , as the hi profile is often declining or flat in the inner regions , whereas star formation is generally centrally peaked ( figure 2 ) .
it is unclear whether the poor correlation of sfr with co found by kennicutt ( 1998 ) may be due to differences in galaxy selection , as the galaxies studied by wong & blitz ( 2002 ) are relatively strong co emitters .
if sfr generally correlates with molecular rather than atomic gas , then the schmidt law index of @xmath21.5 may derive from a roughly linear relation between sfr and h@xmath3 coupled with a weak dependence of the molecular fraction @xmath24 on @xmath25 : @xmath26 this implies that star formation is a two - step process involving molecular cloud formation , and contrasts with the conventional interpretation that the index results from the free - fall ( dynamical ) time being the natural timescale for star formation : @xmath27 indeed , it has long been known that the star formation timescale is much longer than the free - fall time ; this inefficiency of star formation is reflected in the numerical factor in eq .
[ obeqn ] and @xmath28 in eq .
[ theqn ] .
recently , two studies have tried to explain the observed schmidt law using the density probability distribution function ( pdf ) that results from interstellar turbulence , as revealed in simulations by ( e.g. ) wada & norman ( 2001 ) .
elmegreen ( 2002 ) hypothesises that only that part of the density pdf above @xmath29 @xmath8 proceeds to form stars on a dynamical timescale , whereas kravtsov ( 2003 ) assumes a much lower critical density of 50 @xmath8 but a much longer star formation timescale of 4 gyr . in both cases ,
the presence of a critical density ensures that only a small fraction of the galactic gas is involved in star formation at a given time .
detailed case studies of nearby galaxies such as m33 and the lmc may be able to shed further light on this issue .
we thank eva schinnerer for providing the iram pdb image of ngc 4736 used in the talk , and leo blitz for extensive discussions over the past few years on many of the topics covered here .
this work was supported by a bolton fellowship awarded to t.w . by the csiro atnf .
we review recent observations of molecular gas in nearby galaxies and their implications for the star formation law on large ( @xmath0 kpc ) scales . 
 high - resolution data provided by millimetre interferometers are now adding to the basic understanding that has been provided by single - dish telescopes . 
 in particular , they confirm the good correlation between star formation rate ( sfr ) and molecular gas surface densities , while at the same time revealing a greater degree of heterogeneity in the co distribution . 
 galaxies classified as sab or sb tend to show radial co profiles that peak sharply in the inner @xmath120 , indicative of bar - driven inflow . 
 the observed schmidt law index of @xmath21.5 may result from a nearly linear relation between sfr and h@xmath3 mass coupled with a modest dependence of the molecular gas fraction on the total gas density . 
 the normalisation of the schmidt law , giving the characteristic timescale for star formation , may stem from the generic nature of interstellar turbulence .