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ABSTRACT 1 iona A12,USA CA91125, lifornia, rd,Cri,Wls F4A UK CF24AA, Wales, Cardiff, arade, .Neri R. , 1 ∼ 5 0M 60 .P Kneib J.-P. , nsvrlkydtiso h trfrainpoesi this in process star-formation the galaxy. light of young shed details in to direct key reservoir helped several first gas also on have cold the observations sizeable These providing a LBG. detection of an LBG, only existence an the the of from cB58 evidence emission for CO obtained of (2004) al. et Baker SN,hg-eouinrsfaeU pcrsoycon- a spectroscopy is de- UV cB58 2002) that restframe signal-to-noise cluding inter- (2000, high the cB58 high-resolution al. from et of (S/N), abundances Pettini studies elemental 1996). unique the 1512–cB58 LBGs: al. two rived et of MS of Yee medium subject stellar cB58: the lens: as been cluster has to magni- foreground referred gravitational a (hereafter by by whose boosted LBG an fication is made of example been brightness rare ob- only single, apparent far current are a of so relevant they studies has the through as Progress of address, facilities. limits to servational sensitivity hard the proved beyond have LBGs of typical mass the hence also and and galaxy. dynamics mass host emission its gas the CO of the tracer of mass). unbiased measure stellar an reliable substantial a a both up provides poten- build the the provides to hence gas (and tial dense activity and star-formation cold for this reservoir as observable, key a is 2 .Cox P. , z oee,tepoete ftegsoscmoetin component gaseous the of properties the However, ⊙ 3 = Z yr 3 = . − 7uigtePaeud ueInterferom- Bure de Plateau the using 07 ∼ a anfiain a td “ordinary” study can magnification, nal 1 3 f 2 niaigta h oeua a will gas molecular the that indicating , . p.TeC msini unresolved, is emission CO The kpc. 2 a Smail Ian , 07 × 6 .C Edge C. 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Unfortunately, while these studies of cB58 have provided dow centered on the systemic redshift of the system. In unique insights into the properties of LBGs, it is dangerous Fig. 2 we show the spectrum of the CO(3–2) emission in to draw general conclusions about the whole LBG popu- the brightest pixel of the source in the channel map. lation from this single example. Hence, significant efforts have gone into finding other examples of lensed LBGs and after nearly a decade of searches, several lensed LBGs as bright as cB58 have now been found. Smail et al. (2007) present the discovery of a strongly lensed LBG at z =3.07, 10 LBG J213512.73–010143 (hereafter LBGJ213512), simi- lar to cB58. At rAB = 20.3 this new LBG is brighter in the restframe UV than cB58, owing to the 28× magnifica- 5 tion (Dye et al. 2007). Moreover, the LBG appears as two small arcs (∼ 3′′ in extent) and hence provides a unique opportunity for spatially resolved studies on 100 pc scales across this galaxy. When corrected for the lensing mag- 0 ⋆ [arcsec] nification, the background source appears as an L LBG, ∆δ with a similar intrinsic luminosity to cB58. We thus have a second example of a highly magnified “typical” LBG. In this paper we present interferometric measurements -5 of the CO(3–2) emission and mid-infrared photometric ob- servations of this new lensed LBG. We use the CO(3–2) line luminosity and width to infer the gas and dynami- -10 cal masses and compare these with the stellar mass in- ferred from the rest-frame optical-to-near-infrared pho- 10 5 0 -5 -10 tometry of the system. We also compare our results with ∆α [arcsec] the similar observations of cB58 to investigate the varia- tions within the LBG population and further compare our Fig. 1.— HST ACS F606W image of LBG J213512, centered on results with the growing number of CO observations of the optical position, 21 35 12.73 −01 01 43.0 (J2000), with the CO(3– other high-redshift galaxies (see Solomon & Vanden Bout 2) contours overlaid (contours begin at 1σ and increase in steps of 1σ, negative contours are dashed). We also show two insets, the up- 2005 for a review). We adopt cosmological parameters per inset illustrates the image-plane morphology of the LBG (with from the WMAP fits in Spergel et al. (2003): ΩΛ =0.73, the foreground lens removed; scale in arcseconds) consisting of two −1 −1 Ωm =0.27, and H0 = 71kms Mpc . All quoted mag- bright arcs and two fainter knots (marked B1 and B2). The lower nitudes are on the AB system. inset illustrates the source-plane reconstruction of the LBG from Dye et al. (2007) in kpc. This shows that in the restframe UV the LBG comprises two components (As and Bs) separated by ∼ 2– 2. observations and reduction 3 kpc. Both of the bright arcs are formed from the lensing of As, which is magnified in total by a factor of 28×, while Bs gives rise 2.1. Millimeter Interferometry to B1 and B2 (the magnifications of B1 and B2 are 6.2× and 1.8×, We used the six-element IRAM PdBI (Guilloteau et al. respectively). Comparison of the CO map with the optical morphol- ogy of the system shows the CO emission is offset from the center 1992) to observe LBGJ213512 in the redshifted CO(3– of the LBG, and we mark by a “×” the predicted center of the CO 2) line and in the continuum at 84.87 GHz. The fre- emission if the molecular gas follows the R- or K-band light. We quency was tuned to the CO(3–2) rotational transition conclude that the CO emission is unlikely to follow the restframe at z = 3.0743, the systemic redshift of the system from UV/optical light in this system and instead it appears to coincide with a faint knot (marked as B1 in the top inset). To test this we Smail et al. (2007). Observations were made in D configu- predict the observed centroid of the CO emission if it is associated ration in Director’s Discretionary Time (DDT) between with source Bs and mark this as “+”, this is coincident with the 2006 August 24 and 2006 September 20 with good at- observed centroid supporting the proposed association. See text for mospheric phase stability (seeing = 0.6′′–1.6′′) and rea- a detailed discussion. sonable transparency (pwv = 5–15 mm). We observed LBGJ213512 with a total on-source observing time of 2.2. Mid-infrared Imaging 10hrs. The spectral correlator was adjusted to detect Observations of LBGJ213512 were taken with the the line with a frequency resolution of 2.5 MHz in the Spitzer Space Telescope Infrared Array Camera (IRAC) 580MHz band of the receivers. The overall flux scale in 2005 November using time awarded through DDT. Ob- for each observing epoch was set on 2134+004, 2145+067 servations were taken at 3.6, 4.5, 5.8 and 8.0 µm using two and MWC349. The visibilities were resampled to a ve- cycles of a 10-point dither pattern, each with integration locity resolution of 35.3 km s−1 (10 MHz) providing 1-σ time of 30 s. The total integration time was 0.9 ks pixel−1 line sensitivities of ∼ 1.0mJybeam−1. The correspond- in each band. Further observations were also obtained ing synthesized beam, adopting natural weighting, was at 24 µm with the Multi-band Imaging Photometer for 6.3′′× 5.5′′ at 44◦ east of north. The data were calibrated, Spitzer (MIPS) camera. These observations were made mapped and analyzed in the gildas software package. In- using eight repeats of a nine-point dither pattern, each spection of the velocity datacube shows a significant de- consisting of 30 s exposures, for a total integration time tection of CO(3–2) line emission close to the position of of 2.0ks. We use the Post Basic Calibrated IRAC frames LBG J213512 in the central velocity channels with a ve- generated by the pipelines at the Spitzer Science Center locity width of ∼ 250kms−1. Fig. 1 shows a channel map (SSC) and perform post-processing on the data frames to constructed from the average emission in a 250kms−1 win- remove common artifacts and flatten small and large-scale CO and MIR Emission in the Cosmic Eye 3

−1 gradients using “master-flats” generated from the data. [Oiii] λ5007 emission line (FWHM <∼ 220kms ) as mea- For mosaicking we use the SSC mopex package, which sured by Smail et al. (2007). The velocity integrated line −1 makes use of the supplementary calibration files which are flux is measured to be FCO(3−2) = 0.50 ± 0.07Jykms supplied with the main science set. We align and combine (S/N=7.1). We note that this line flux is comparable the four IRAC images and use this composite image to ex- to the CO flux density measured for cB58: FCO(3−2) = ′′ tract 3.8 -diameter apertures magnitudes at the position ± −1 ′′ 0.37 0.08Jykms (Baker et al. 2004, with an estimated of LBGJ213512 from the IRAC data and 10 -diameter magnification factor for cB58 of µ ∼ 32). aperture magnitudes from the MIPS data. We obtain a Redshift strong detection of the emission from the LBGJ213512 3.065 3.070 3.075 3.080 3.085 3 (with some contribution from the foreground lens) at 3.6– 8µm and a weaker detection at 24 µm. Aperture-corrected 2 photometry for the LBG are reported in Table 1, including 1 gR606K-band photometry from Smail et al. (2007). 0

Table 1. Flux Density [mJy] -1 Aperture-corrected photometry for LBG J213512 -2 -1000 -500 0 500 1000 LBG + Lens Lens LBG Velocity [km s-1] (1) (2) (3) Fig. 2.— The spectrum of CO(3–2) emission in LBG J213512, g ··· ··· 21.47[5] binned into 35.3 km s−1 channels. We detect the line at 7.1-σ signifi- R606 · · · 22.34[15] 20.54[2] cance and the best-fitting Gaussian with a FWHM of 190±24 km s−1 K · · · 19.70[10] 18.90[10] is overlaid. The upper axis indicates the redshift of the CO(3–2) 3.6 µm 18.34[2] · · · 18.74[4] transition. There is a hint of double peak to the CO line, although 4.5 µm 18.19[2] · · · 18.39[4] a double component fit does not provide a better description of the 5.8 µm 18.13[3] · · · 18.33[6] data due to the modest S/N of the detection. We have confirmed that there is no detectable spatial offset between the blue and red µ · · · ′′ 8.0 m 18.30[2] 18.35[4] halves of the line (<∼ 0.1 ). 24 µm 17.78[25] · · · 17.78[25] Next, averaging the emission over a 250kms−1 window, centered on the redshift of the CO emission, we determine a flux of 2.0 ± 0.3mJybeam−1 for a source centered at Note. – (1) The observed photometry for the LBG. Due to the 21 35 12.62, −010143.9 (J2000) corresponding to a ∼ 7- low spatial resolution of IRAC the photometry from the z=0.73 σ detection (we ignore the small correction for primary and z=3.07 galaxies are blended. We remove the contribution of the z=0.73 lensing galaxy to the IRAC channels by fitting beam attenuation given the source is close to the phase the R606&K-band photometry of the foreground lens (column center of the map). We note that no significant continuum 2) with an elliptical galaxy template redshifted to z=0.73 and emission is detected from the line-free region (470 MHz of subtracting the contribution at ≥ 3.6 µm. These corrected LBG bandwidth) down to a 1-σ sensitivity of 0.14 mJy. photometry are given in column 3 (see text). To convert to in- In Fig. 1 we show the Hubble Space Telescope (HST) trinsic magnitudes (corrected for the lensing amplification fac- ACS F606W image of the system from Smail et al. (2007) tor 28 ± 3×) add 3.6 mags to column 3. Values in the [] denote and overlay the contours from the CO(3–2) channel map. the error in the last decimal place and we note that 1 µJy cor- Dye et al. (2007) present a detailed lens model and use it responds to mAB = 23.90. to reconstruct the restframe UV source-plane morphology of the LBG. They show that the system comprises two UV- 3. analysis and results emitting components separated by ∼ 2–3kpc, probably representing two star-forming regions within the galaxy 3.1. CO Emission Properties separated by a dust lane or region of lower activity (see The luminosity, velocity width and spatial extent of the inset in Fig. 1; As and Bs). The intrinsically brighter and CO line emission can be used to place limits on the gas more highly amplified of these, As, lies within the lens and dynamical mass of the system. Fitting a Gaussian caustic and is magnified by a factor of 28 ± 3 (Smail et al. profile to the CO spectrum for the source at the phase 2007), giving rise to the ring-like structure surrounding center of our observations (Fig. 2) we derive a best-fit red- the foreground galaxy. The second UV component, Bs, shift for the CO(3–2) emission of z = 3.0740 ± 0.0002. lies just outside the caustic and gives rise to two images: This is in excellent agreement with the systemic red- B1 and B2 (see Fig. 1 and Fig. 4 of Dye et al. 2007). shift derived from the [Oiii] λ5007 line by Smail et al. The lensing magnifications of the components are 6.2× (2007), with an offset of just ∆ v = −22 ± 14kms−1. and 1.8× respectively, giving a total amplification factor The error on the line parameters are bootstrap esti- of (8.0 ± 0.9) × for Bs (Dye et al. 2007). mates generated by adding noise at random to the chan- The astrometric solution on the HST image is derived nels closest to the spectral peak from the outer-most by comparing the positions of unsaturated stars with the noisy baseline channels 1000× with replacement (e.g. see USNOA-2.0 catalog and we estimate an r.m.s. uncer- Wall & Jenkins 2004). This provides a reasonable esti- tainty in the optical position of the system (21 35 12.73, ′′ mate of the uncertainties provided the noise is not strongly −010143.0, J2000) of <∼ 0.2 . The absolute astrometry correlated between channels. The restframe FWHM of of the CO observations is estimated to be accurate to −1 ′′ the CO line is 190 ± 24kms (or alternatively a dis- <∼ 0.01 , but the centroid for the emission is only accu- −1 ′′ persion of 80 ± 10kms ) which is consistent with the rate to <∼ 0.3 and places the peak of the CO emission 4 Coppin et al. at 21 35 12.62, −010143.9 (J2000) – which is centered ap- observations allow us to place strong constraints on the dy- proximately 1.9 ± 0.4′′ due west of the optical centroid. namical mass, while the Spitzer observations can be used We first test whether the CO centroid is consistent with to constrain the stellar mass and current star formation the expected position if the CO emission traces the rest- rate (SFR) of the galaxy. frame UV/optical light. To achieve this we subtract the For LBG J213512, the line width of the CO emission foreground lensing galaxy from the HST imaging and con- (190 ± 24kms−1) predicts a dynamical mass of (8.4 ± 9 2 volve the resulting image with the PdBI beam, this pre- 1.4) × 10 csc i M⊙, assuming the gas lies in a disk with dicts a centroid for the CO emission approximately 0.4′′ inclination i and a radius of ∼ 1kpc. Based on this NW of the lensing galaxy (marked by the “×” in Fig. 1). we calculate a gas-to-dynamical mass fraction of f = 2 Thus the CO line emission does not appear to be associ- Mgas/Mdyn ∼ 0.30 sin i. For comparison with the to- ated with the most highly magnified and UV-bright com- tal stellar mass, we extrapolate this CO measurement ponent part of the galaxy (As). Instead, the centroid of slightly to give us a total mass within the UV-extent of the CO emission appears to correspond to B1, the more the LBG, a radius of 2 kpc, yielding an enclosed mass of 10 2 magnified of the two images of component Bs. To confirm M(< 2kpc) ∼ 1.7 × 10 csc i M⊙. We note that the mean this, we model the CO emission from Bs using the mag- angle of randomly oriented disks with respect to the sky nifications for the two images from Dye et al. (2007) and plane in three dimensions is i = 30 deg (Carilli & Wang convolve this with the PdBI beam, this yields a centroid 2006), resulting in an inclination correction of csc2i = 4. of 21 35 12.63, −010143.3 (J2000) (marked by the ‘+’ in In order to derive the stellar mass, we adopt the ap- Fig. 1), which is 0.6±0.4′′ due west from the observed peak proach of Borys et al. (2005): first we estimate the rest- and hence consistent with it. Thus, we conclude that the frame K-band luminosity for the galaxy by interpolating CO reservoir appears to be associated with Bs, the fainter the rest-frame spectral energy distribution (SED) and then of the two UV regions in LBGJ213512. We discuss the combine this with estimates of the K-band light-to-mass implications of this further in §4. ratio (LK /M) for a range of plausible ages for the dom- inant stellar population. We exploit the HyperZ pack- 3.2. CO Luminosity and Molecular Gas Mass age (Bolzonella, Miralles & Pello 2000) to fit the observed We calculate the line luminosity and estimate the total gR606K and IRAC 3.6–8.0 µm photometry in Table 1. cold gas mass (H2+He) from the integrated CO line flux. We use solar metallicity stellar population models from ′ The observed CO(3–2) line luminosity is µLCO(3−2) = Bruzual & Charlot (1993) and a Calzetti et al. (2000) (2.4 ± 0.3) × 1010 Kkms−1 pc2, where µ is the amplifi- starburst attenuation to infer the rest-frame optical/near- cation factor. Although the lensing magnification of the infrared SED. At z =3.07, the rest-frame K-band (which entire UV source is ∼ 28×, our association of the molecu- is most sensitive to the underlying stellar population) is lar gas reservoir with component B means we must adopt redshifted to ∼ 8 µm (i.e. into IRAC Channel 4). How- s ever, since the IRAC photometry has a spatial resolution the estimated magnification for this component of (8.0 ± ′′ 0.9) ×. The resulting intrinsic line luminosity is therefore of ∼ 3 comparable to the extent of the lensed LBG, the ′ 9 −1 2 contribution from the z = 0.73 lensing galaxy is blended LCO(3−2) = (3.0±0.5)×10 Kkms pc . We then assume ′ ′ with the LBG, and the lensing galaxy must be subtracted. both a line luminosity ratio of r32 = L − /L − = CO(3 2) CO(1 0) We therefore fit the R606 and K-band magnitudes of the 1 (i.e. a constant brightness temperature) and a CO-to-H2 lens with an early-type (E/S0) galaxy template based on −1 2 −1 conversion factor of α = 0.8 M⊙(Kkms pc ) . These the spectral properties and colors in Smail et al. (2007) values are appropriate for local galaxy populations exhibit- (the template comprises a stellar population for an expo- ing similar levels of star formation activity to LBG J213512 nential star-formation history with a timescale of 1 Gyr) (e.g. local infrared galaxies or LIRGs; Solomon et al. 1997; redshifted to z =0.73 and subtract the expected contribu- see §3.4). We discuss in §4.2 how our conclusions would tion to the IRAC photometry: <∼ 20, 15, 10 & 5 percent at change if we adopted α and r32 values typical of the 3.6, 4.5, 5.0 and 8.0 µm, respectively. The LBG photome- Milky Way. This then yields a total cold gas mass of try with the contribution from the lensing galaxy removed ′ 9 Mgas = M(H2+He) = αLCO = (2.4 ± 0.4) × 10 M⊙. are given in Table 1. Based on the association of the CO emission with source We determine a rest-frame absolute K-band magni- Bs and its extent in the restframe UV we assume the gas tude of MK = −22.2 ± 0.1 (corrected for lens magnifi- is distributed in a disk with a radius no larger than 1 kpc cation using µ = 28). As expected, this is comparable (see Fig. 1) resulting in an inferred gas surface density of to L∗ for z ∼ 3 LBGs (Shapley et al. 2005). To con- −2 8µm Σgas ≃ (760 ± 130)M⊙ pc . vert this to a stellar mass, we need to determine LK /M 3.3. Dynamical and Stellar Mass for the dominant stellar population. To do this, we turn to the Starburst99 stellar population model (Leitherer The next step in our analysis is to compare the mass 1999), which provides estimates for LK /M for models of we derived for the cold gas reservoir to the dynamical bursts of star-formation. We adopt an age for the stel- and stellar masses in this LBG. Whilst in principle the lar population dominating the UV light of ∼ 10–30Myr dynamical masses of LBGs can be derived from optical based on the analysis of the features in the restframe or near-infrared observations of emission line gas in these UV spectrum which show that the UV emission is domi- galaxies, dust obscuration and outflows in the gas may nated by B stars (Smail et al. 2007). Fits using hyperz bias the measurements. In contrast, molecular CO emis- (Bolzonella, Miralles & Pello 2000) to the broadband SED sion is comparatively immune to the effects of obscuration spanning the restframe 0.13–2 µm yield similarly young and outflows and therefore provides a unbiased measure- ages, . 50 Myr with moderate reddening, AV ∼ 1, as do ment of dynamics within the CO emitting region. Our CO CO and MIR Emission in the Cosmic Eye 5 more sophisticated modeling (Shapley et al. 2005). For spatial resolution of our 24 µm image and its modest S/N these ages the Starburst99 models predict LK /M ∼ it is impossible to determine if the emission follows the 2.5 ± 0.5. We note that the average LK /M for LBGs in UV or CO morphology of the source. However, we have Shapley et al. (2005) is LK /M ∼ 2.5. Thus for a stellar confirmed that within the large uncertainty, the integrated population dominated by young stars (< 50 Myr), the pre- R/24 µm color of the LBG is similar to that seen in other 9 dicted stellar mass is ∼ (6 ± 2) × 10 M⊙. This implies a z = 3 LBGs (Reddy et al. 2006), supporting the assump- 10 baryonic mass of Mbary = Mgas+ Mstars <∼ 1 × 10 M⊙, tion that the 24 µm follows the R-band light. with 75 per cent of this in stars. This baryonic mass Assuming the molecular gas reservoir we detect is fu- estimate is consistent with the dynamical mass with a eling the star-formation within this galaxy, then it has 1–2-kpc radius traced by the CO emission: M ∼ 0.8– enough gas to sustain the current star-formation for 10 2 9 −1 1.7 × 10 csc i M⊙, for all inclinations. τdepletion ∼M(H2)/SFR ∼ 2.4 × 10 M⊙/60 M⊙yr ∼ 40 Myrs. Since we also have a stellar mass of LBG J213512, 3.4. Star-Formation Rate and Efficiency we can compare the gas depletion time with the time to form the current stellar mass of the system. At the current Smail et al. (2007) estimate the SFR for LBGJ213512 9 −1 SFR: τformation ∼Mstars/SFR ∼ 6 × 10 M⊙/60 M⊙ yr ∼ from the rest-frame 1500A˚ continuum flux of L1500 ∼ 100Myr, which is comparable to the assumed age of the 30 −1 −1 4.6 × 10 ergs Hz which translates into a SFR (cor- stellar population. rected for lens magnification and dust reddening) of ∼ −1 100 M⊙ yr (assuming a Salpeter initial mass function 4. discussion (IMF) with an upper mass cut off of 100M⊙; Kennicutt 1998). Our observations of LBGJ213512 demonstrate that it is Perhaps more reliably, the 24-µmflux of the LBG can be a relatively massive galaxy hosting an equally massive gas used to estimate the far-infrared luminosity of the galaxy reservoir and has significant on-going star formation. The (e.g. Bell et al. 2005; Geach et al. 2006) which can then majority of the baryons in the central regions of the galaxy be converted into a SFR. Taking the library of dusty, are in the form of stars. We estimate that the stellar pop- star-forming SEDs from Dale & Helou (2002), we calcu- ulation of the LBG could have been formed at the current late the ratio of the 24-µm luminosity to the far-infrared SFR within ∼ 100 Myrs and that if the current SFR con- luminosity integrated over the entire SED (8–1000µm). tinues, then the cold gas reservoir will be exhausted within The SED templates are simply characterized by a power- <∼ 40 Myrs unless it is replenished. Thus, it appears that law distribution of dust mass, with an exponent of 1–2.5 we are seeing the LBG in the last half of its current star for “typical” local star-forming galaxies (Dale et al. 2001). formation episode. We now compare the gas properties of 11 We derive LFIR ∼ 3.4 × 10 L⊙ for an unlensed 24-µm LBG J213512 to other similarly well-studied sources and −1 flux of 10 µJy, corresponding to a SFR of ∼ 60 M⊙yr populations at low and high redshifts. (Kennicutt 1998). This is the average luminosity over the entire library of SEDs, and the extreme SEDs suggest our 4.1. Comparison to other populations estimate is likely to be uncertain by a factor of 3×. This We first compare LBGJ213512 to the only other CO- bolometric luminosity is consistent with the 0.14 mJy up- detected LBG: cB58 Baker et al. (2004). The intrinsic per limit to the 3 mm flux of LBG J213512 and the lumi- CO line luminosity, gas and dynamical masses we derive nosity implies an 850 µm flux of ∼ 0.35 mJy, where we have ′ 9 −1 2 for LBGJ213512 are LCO(3−2) = 3.0 × 10 Kkms pc , estimated this flux by scaling a modified blackbody with 9 Mgas = 2.5 × 10 M⊙ and Mdyn(< 1kpc) = 8.4 × a dust temperature of 40K, and a dust emissivity β =1.5 9 2 (see Blain et al. 2002) to match the 24 µm-predicted bolo- 10 csc i M⊙, with a gas fraction within 1-kpc of fgas = 0.30 sin2 i. Using the same conversion factors for cB58, metric luminosity. Note that S850 ∼ 0.35 mJy is consistent ′ with a mean observed 850 µm flux of 0.5 ± 0.4mJy for α = 0.8 and r32 = 1, we estimate: LCO(3−2) = 0.43 × 9 −1 2 9 typical LBGs (Chapman et al. 2000). Our SFR estimate 10 Kkms pc , Mgas = 0.34 × 10 M⊙ and Mdyn ∼ −1 −2 9 2 −1 yields a SFR density of ΣSFR ∼ 20 M⊙ yr kpc for a 10×10 csc i M⊙ (which has FWHMCO = 175±45kms ), 2 disk radius of 1kpc, and a star-formation efficiency (SFE) with a gas fraction of fgas =0.03 sin i. 11 9 −1 of LFIR/MH2 =3.4×10 L⊙/2.4×10 M⊙ ∼ 140L⊙ M⊙ . We could attempt to reduce the uncertainties due to A related way to present these observations is to roughly the unknown inclination and average the properties of estimate the gas-to-dust mass ratio. Following Blain et al. LBGJ213512 and cB58, deriving a typical dynamical mass 7 10 (2002), we estimate a dust mass of Md ≃ 2.5 × 10 M⊙ of Mdyn ∼ (3.6 ± 0.4) × 10 M⊙ and a gas fraction of from the predicted 850 µm flux of ∼ 0.35 mJy, assuming a fgas ∼ 0.05 ± 0.05 (both for i = 30degrees). However, we 2 −1 dust mass absorption coefficient of κ850µm =0.15 m kg . note that LBGJ213512 has roughly 7× more cold gas than This yields a constraint on the gas-to-dust mass ratio for cB58, demonstrating that there is a significant variation in LBGJ213512 of ∼ 100, with at least a factor of ∼ 6 the gas content of L∗ LBGs at z ∼ 3 and argues against uncertainty accounting for our uncertainty of the dust blindly averaging their properties. Our estimate of the temperature (∆ Td ≃ ±5 K), dust emissivity coefficient SFR for LBGJ213512 is 3–4× higher than cB58’s value of −1 (∆ β ≃ ±0.5), and mass absorption coefficient (about a 24 M⊙ yr (Baker et al. 2004), although this comparison factor of ∼ 3; e.g. Seaquist et al. 2004). uses different indicators in the two LBGs and so is uncer- In terms of the spatial distribution of the star forma- tain. These SFRs suggest comparable gas depletion time tion, if the 24 µm emission traces the R-band light, then scales for LBGJ213512 and cB58: τdepletion <∼ 40 Myrs and 9 we expect that the UV-bright component As will contain τdepletion ∼ 0.34 × 10 /24 ∼ 15Myrs for cB58. The varia- 75 per cent of the current star formation. Given the poor tions in gas mass as well as the short depletion timescales 6 Coppin et al. probably reflects the brevity of the star formation events LBG J213512 is similar to local LIRGs. and hence the strong variation within the population in The CO line widths (and hence dynamical masses the amount of gas consumed at any time. In terms of the for similar radii and inclination angles) for LIRGs (< comparison of LBGJ213512 and cB58: these appear to FWHM >∼ 200kms−1; Sanders, Scoville & Soifer 1991) be similarly massive L∗ LBGs, although LBGJ213512 is are comparable to LBGJ213512 and cB58, suggesting younger, more gas-rich and forming stars at a higher rate that LBGs are simply gas-rich high-redshift analogs of than cB58. LIRGs, but possessing a marginally higher star formation The only high-redshift galaxy population for which efficiency than the range typically seen in local LIRGs −1 −1 there are large numbers of sources with reliable cold (140L⊙ M⊙ compared to ∼ 1–50L⊙ M⊙ for α = 0.8; gas masses are submillimeter galaxies (SMGs). Taking Sanders, Scoville & Soifer 1991). the average CO line luminosity and gas mass for cB58 and LBGJ213512 we find that the “typical” LBG has 11.0 an intrinsic line luminosity ∼ 20× lower than the me- ′ LBGs, This work and see caption dian for SMGs (c.f. < L >= (3.8 ± 2.3) × 1010 and IRGs, Yao et al. (2003) CO 10.5 ULIRGs, Solomon et al. (1997) < M >= (3.0 ± 1.6) × 1010; Greve et al. 2005). Al- ULIRGs, Sanders et al. (1991) gas SMGs, Greve et al. (2005) though, we note that the SMGs studied by Greve et al.

]) 10.0 (2005) are not strongly lensed and hence the sensitivity 2 pc limits of their survey precludes the detection of sources -1 ′ < 10 −1 2 9.5 with LCO ∼ 1 × 10 Kkms pc , and that in addition, the typical SMGs lies at somewhat lower redshifts than [K km s the LBGs (although those SMGs at z ∼ 3 appear com- CO 9.0 '

parable to the general population). The CO line widths (L of LBGJ213512 and cB58 are 3× lower than the median 10 of SMGs (Greve et al. 2005) with this emission arising in log 8.5 a region estimated to be half the size of that in SMGs (Tacconi et al. 2006). The typical gas-to-dynamical mass 8.0 fraction in SMGs is estimated to be ∼ 0.3 assuming a merger model (Greve et al. 2005), while they have SFEs 7.5 −1 9 10 11 12 13 of LFIR/MH2 ∼ 450±170L⊙ M⊙ (Greve et al. 2005), gas- log (L [L ]) to-dust mass ratios of ∼ 200 (with about factor of a few 10 FIR o uncertainty in the dust mass alone) and gas surface den- −1 2 Fig. 3.— A comparison of the CO and far-infrared luminosities sities of Σgas ∼ 3000M⊙ yr pc (Tacconi et al. 2006). for LBGs (including cB58 from Baker et al. 2004 and LBG J213512), Overall, this comparison suggests that LBGs and SMGs and the faint submillimeter-selected source SMMJ16359+6612 from are equally evolved, but that the cold gas reservoir in LBGs Kneib et al. 2005 (listed in order of increasing luminosity), LIRGs, ULIRGs and SMGs. The solid line is the best-fitting relation with a resides in a system which is typically a factor of ∼ 5× less ′ form of log LCO = α log LFIR +β to the LIRGs, ULIRGs and SMGs massive than in SMGs (Swinbank et al. 2004, 2006), that from Greve et al. (2005). The LBGs all lie on the relation within the LBG’s cold gas disks have surface densities 4× lower their uncertainties and lie in the same region of the plot as the than SMGs (if both can be well-described as disks) and LIRGs. Note that this diagram is a particularly useful diagnostic that LBGs appear to be forming stars less efficiently than since it does not depend on the CO-to-H2 conversion factor. typical SMGs, by about a factor of 4×. The two popu- lations do appear to have similar fractions of baryons in 4.2. The physics of star-formation in LBGs cold gas and stars: M /M ∼ 0.2, 0.4 and ∼ 0.3 for gas stars What do our observations tell us about the structure of cB58, LBGJ213512 and SMGs, respectively. the gas disk and the mode of star formation in LBGs? We can also compare the LBGs to local populations. We To investigate the physics of star formation within LBGs first note that our 24-µm detection predicts a far-infrared 11 in more detail, we can first test whether the star formation luminosity for LBG J213512 of L ∼ 3 × 10 L⊙. Even FIR activity within LBG J213512 is consistent with the global with our estimated factor of 3× uncertainty, this indicates Schmidt law (Schmidt 1959). Kennicutt (1998) derives a that the LBG is likely to have a far-infrared luminosity 1.4 > 11 Schmidt law of the form ΣSFR = A (Σgas) , where Σgas comparable to local LIRGs, LFIR ∼ 10 L⊙. −1 −2 −1 −2 ′ and ΣSFR are in units of M⊙yr pc and M⊙yr kpc , Locally, LCO increases with LFIR for (U)LIRGs, with −4 the Greve et al. (2005) sample of SMGs extending this respectively and A = (2.5 ± 0.7) × 10 . In deriving this trend out to the highest far-infrared luminosities (& relationship, Kennicutt (1998) assumed α = 4.6 for all 13 the galaxies (including LIRGs) and noted that the scatter 10 L⊙). For comparison, in Fig. 3 we have plot- ′ around the relation is large, with individual galaxies lying ted LBGJ213512 on the LCO–LFIR diagram along with cB58, SMMJ16359+6612 (with a lensing magnification of up to a factor of 7× off the mean relation. 22× and weak submillimeter emission, making it more Therefore, we follow Kennicutt (1998) and use α = 4.6 for the gas surface densities in this calculation. For similar to LBG J213512 than to the SMG population) +3.2 from Kneib et al. (2005), LIRGs, ULIRGs and SMGs. LBG J213512 we estimate a normalisation of A =1.6−1.1× −4 LBGJ213512, cB58 and SMMJ16359+6612 all lie on the 10 , where the large error accounts for the uncertainty in local relation within the considerable uncertainties in the true SFR. In contrast, cB58 predicts a normalization −4 their far-infrared luminosities, in the same region of the of A ∼ 9.3 × 10 with a similar uncertainty. Thus the plot that the local LIRGs occupy. This suggests that two LBGs bracket the local Schmidt law and are each con- sistent with it within the large scatter and uncertainties. CO and MIR Emission in the Cosmic Eye 7

To determine the likely structure of the gas reservoir, It is difficult to understand this mix of properties, with we use the gas mass and assume a radius of 1kpc to infer immense gas reservoirs in highly unstable, dense gas disks −2 a mass surface density of Σ = 760 ± 130M⊙ pc . If the which are in some respects more extreme than SMGs, but gas is present in a disk, we can test whether the material yet result in star formation occuring with an efficiency will be unstable to bar-formation. The Toomre stability at least an order of magnitude below that in SMGs. We criterion states that Q = σκ/2πGΣ >∼ 1 in order for a therefore conclude that it is hard to reconcile the gas prop- gaseous disk to be stable (e.g. Binney & Tremaine 1987) erties of LBGs if the CO-to-H2 conversion factor is similar where σ and κ are the velocity dispersion and the circular to the Milky Way. Instead, we suggest that the high gas frequency of the disk respectively. For a surface density surface density and low star-formation efficiency is most −2 of 760M⊙ pc , Q < 1 for any realistic value of σ and κ. naturally explained if the gas is distributed in a similar This suggests that if the gas is present in a disk, it will be manner to local ULIRGs and SMGs and the dominant unstable to bar-formation and will collapse on a timescale star-formation mode follows that seen in local luminous of τrot ∼ 60 Myrs, comparable to the estimated remaining starbursts (e.g. ULIRGs). lifetime of the burst. However, the cost of adopting α = 0.8 is that the gas 2 Following Tacconi et al. (2006), we derive the maximal fraction for cB58 drops to just fgas ∼ 0.03 sin i, which SFR and SFR surface density for the average LBG with seems uncomfortably low for a young high-redshift galaxy −1 an inclination angle of i = 30deg to be ∼20 M⊙ yr and which is still forming stars. One potential solution is to −1 −2 ∼7 M⊙ yr kpc , respectively. These are comparable adopt different CO-to-H2 conversion factors in the two to the observed average SFR and SFR surface density of LBGs, with the more active LBGJ213512 having a lower −1 −1 −2 ∼40 M⊙ yr and ∼7 M⊙ yr kpc , respectively. Hence value than cB58. This could reflect a period of bulge- we conclude that LBGs could be maximal starbursts if formation in LBG J213512, while cB58 is currently in a our assumptions of the geometry and star-formation effi- less active phase of star formation. Such a complication ciency are all correct. Our observations appear to point is of course unjustified given the current information we towards the star formation in LBGJ213512 occuring in an have and we must instead look forward to observations of intense central starburst, similar to the activity seen in cold gas in a larger number of LBGs to allow us to place local LIRGs and ULIRGs. Many of the physical proper- limits on α using the same dynamical arguments employed ties we derive for the LBG mirror those of local LIRGs. by Solomon et al. (1997). However, many of these conclusions are sensitive to the conversion factor between the CO and H2 gas masses, α, 5. conclusions and so we must re-examine this choice. −1 2 −1 We have carried out millimeter interferometry and mid- The values of α =0.8 M⊙(Kkms pc ) and r =1 32 infrared imaging of a strongly lensed LBG at z = 3.07. we adopted are derived from luminous local starburst We detect strong CO(3–2) emission with a line width of galaxies in which the molecular gas is distributed in a ex- 190 ± 24kms−1. Although the lensing magnification of tensive intercloud medium (Solomon et al. 1997), rather the entire UV source is ∼ 28×, the position of the CO than as discrete giant molecular clouds (GMCs). Thus emission appears coincident with a UV component in the lower H to CO ratios in these more energetic environ- 2 source plane which has a magnification of ∼ 8×. Correct- ments are potentially an indication of a mode of star ing for the magnification of the CO source, LBGJ213512 formation associated with bulge formation, with higher 9 has an inferred gas mass of (2.4 ± 0.4) × 10 M⊙ and ratios being more prevalent in quiescently star-forming 9 2 a dynamical mass of (8.4 ± 1.4) × 10 csc i M⊙, within disks. A value of α =0.8 is also adopted for high-redshift an estimated radius of ∼ 1 kpc. Fitting to the observed submillimeter galaxies (which are believed to be scaled- gR606K and our Spitzer IRAC 3.6–8.0 µm photometry we up high-redshift analogs of local ULIRGs; Greve et al. 9 derive a stellar mass of ∼ (6 ± 2) × 10 M⊙. We also use 2005; Tacconi et al. 2006). If we had instead assumed Spitzer/MIPS 24µm imaging to estimate a far-infrared lu- that the cold gas is distributed in stable GMCs, as in 11 minosity of ∼ 3 × 10 L⊙ with an uncertainty of a fac- our own galaxy, then the predicted gas masses are 9× −1 2 −1 tor of 3×. From this we derive a star-formation rate of higher (taking α = 4.6 M⊙(Kkms pc ) and r32 = −1 ∼ 60 M⊙ yr , and hence a star-formation efficiency of 0.65; Solomon & Barrett 1991; Mauersberger et al. 1999; −1 Dumke et al. 2001; Yao et al. 2003). ∼ 140L⊙ M⊙ . Based on this star formation rate we esti- We currently cannot constrain α in high redshift galax- mate that the current activity in LBGJ213512 could have ies directly and so we must examine whether adopting formed the current stellar mass in a period of ∼ 100Myrs the Milky Way conversion factors would substantially al- and can continue for a further ∼ 40Myrs before the gas ter our interpretation of the LBGs (c.f. Baker et al. 2004). reservoir is exhausted. We find that the CO line luminosity and inferred gas Adopting α =4.6 and r32 =0.65 increases the gas masses 9 mass for LBGJ213512 are ∼ 7× higher than that mea- for LBGJ213512 to 22 × 10 M⊙, which is comparable to sured for the only other CO-detected LBG, cB58, indicat- the cold gas masses derived for typical SMGs (Greve et al. ⋆ 2005) and exceeds the dynamical mass of the galaxy for ing a significant variation in the gas content of L LBGs at z ∼ 3. In contrast, the two LBGs have effectively iden- inclinations of i >∼ 40 deg. Similarly cB58’s gas mass 9 tical CO line-widths, indicating similar dynamical masses increases to 3 × 10 M⊙. The star formation efficiency, −1 (within the uncertainties of their unknown inclinations). L /M 2 , for LBGJ213512 drops to ∼ 15L⊙ M , while FIR H ⊙ Thus there is a large range in gas-to-dynamical mass ra- the surface density of the gas disk increases dramatically −2 tio between cB58 and LBGJ213512, Mgas/Mdyn ∼ 0.03– to Σgas ∼ 8000M⊙ pc , larger than the values claimed 2 for SMGs (Tacconi et al. 2006). 0.3 sin i, which may reflect the short timescales for star formation in these galaxies. Following Kennicutt (1998), 8 Coppin et al. we use the gas and star-formation surface densities to de- to-H2 conversion factor, α, in LBGs will require either high rive the Schmidt law and find that both LBG J213512 and angular resolution CO mapping (to resolve the gas disks cB58 are consistent with the Schmidt law. and solve for their inclination), which could be within the We compare our observations of LBGJ213512 to far- grasp of the most extended IRAM configurations, or from infrared luminous galaxy populations at low and high red- a statistical study of the gas-to-dynamical mass ratios for shifts. We find that the star-formation efficiency we de- a large sample of LBGs with CO detections. The latter rive for LBG J213512 is slightly above the range of values may have to wait until the advent of ALMA. derived for similarly far-infrared-luminous local galaxies Overall, these observations effectively harness a gravi- (LIRGs), but is significantly below the typical efficiency tational lens to boost the light-grasp of the IRAM and −1 for high-redshift submillimeter galaxies (∼ 450L⊙ M⊙ ). Spitzer telescopes by a factor of up to 30×, whilst im- ′′ The gas and dynamical masses we find are also an order of proving the effective resolution to ∼ 0.2 . The next step magnitude smaller than estimated for SMGs. We suggest is to observe the system at higher resolution with IRAM that LBGJ213512 has many features in common with local (FWHM ∼ 0.3′′) in order to dissect the gas distribution on ′′ LIRGs and hence that the star formation activity in this the smallest scales of ∼ 0.02 (corresponding to ∼ 0.2kpc high-redshift system may be closely related to the mode in the image plane), providing a preview of the capabili- of star formation seen in these galaxies. ties of ALMA. Such observations will allow us to address A major uncertainty in our analysis is the choice of the questions which are drivers of the ALMA, SKA and JWST CO-to-H2 conversion factor (α) we should adopt. The two science cases: yielding insights into the kinematics of the most commonly used assumptions: α = 0.8 and r32 = 1 interstellar medium in a normal, young galaxy seen 12 bil- appropriate for local ULIRGs or α = 4.6 and r32 = 0.65 lion years ago. as measured for the Milky Way, produce a factor of ∼ 9× variation in the expected gas masses and all the associ- This work is based on observations carried out with ated derived properties. We argue that selecting an α and the IRAM PdBI. IRAM is supported by INSU/CNRS r32 similar to comparably far-infrared luminous galaxies (France), MPG (Germany) and IGN (Spain). This work at the present-day yields a system with more easily un- is also makes use of data obtained with Spitzer, which is derstood properties, than the more gas-rich system pre- operated by the Jet Propulsion Laboratory, California In- dicted by α = 4.6 and r32 = 1. However, it is clear that stitute of Technology under a contract with NASA. We a measurement of other CO transitions for LBGJ213512, thank the Spitzer Director, Tom Soifer, for the award of accessible from the GBT or from the PdB, would place a the Spitzer DDT. We thank Max Pettini, Alice Shapley, constraint on the temperature and density of the molecular and Dave Alexander for useful discussions and help, and gas (e.g. Hainline et al. 2006) and allow a more accurate an anonymous referee for a constructive report. KEKC, determination of the line luminosity ratio, r32, and hence AMS and JEG acknowledge support from PPARC. IRS the total gas mass of the system. Placing limits on the CO- acknowledges support from the Royal Society.

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