A&A 423, 867-880 (2004)
DOI: 10.1051/0004-6361:20035740

The Luminosity-Metallicity relation of distant luminous infrared galaxies^,

Y. C. Liang ^1,2 - F. Hammer ¹ - H. Flores ¹ - D. Elbaz ³ - D. Marcillac ³ - C. J. Cesarsky ⁴

1 - GEPI, Observatoire de Paris, Section de Meudon, 92195 Meudon Cedex, France
2 - National Astronomical Observatories, Chinese Academy of Sciences, No. 20A Datun Road, Chaoyang District, Beijing 100012, PR China
3 - CEA, Saclay-Service d'Astrophysique, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
4 - ESO, Karl-Schwarzschild Strasse 2, 85748 Garching bei Munchen, Germany

Received 25 November 2003 / Accepted 26 April 2004

Abstract
One hundred and five 15 $\mu$m-selected objects in three ISO ( $\it Infrared~Space~Observatory$) deep survey fields (CFRS 3$^{\rm h}$, UDSR and UDSF) are studied on the basis of their high-quality optical spectra with resolution R>1000 from VLT/FORS2. $\sim$92 objects (88%) have secure redshifts, ranging from 0 to 1.16 with a median value of  $z_{\rm med}=0.587$.

Considerable care is taken in estimating the extinction properties of individual galaxy, which can seriously affect diagnostic diagrams and estimates of star formation rates (SFRs) and of metal abundances. Two independent estimates of the extinction have been made, e.g. Balmer line ratio and energy balance between infrared (IR) and H$\beta$ luminosities. For most of the sources, we find a good agreement between the two extinction coefficients (within $\pm$0.64 rms in A_V, the extinction in V band), with median values of A_V(IR) = 2.36 and A_V(Balmer)= 1.82 for z>0.4 luminous IR galaxies (LIRGs). At z >0.4, our sample show many properties (IR luminosity, continuum color, ionization and extinction) strikingly in common with those of local (IRAS) LIRGs studied by Veilleux et al. (1995). Thus, our sample can provide a good representation of LIRGs in the distant Universe.

We confirm that most (>77%) ISO 15 $\mu$m-selected galaxies are dominated by star formation. Oxygen abundances in interstellar medium in the galaxies are estimated from the extinction-corrected "strong'' emission line ratios (e.g. [O II]/H$\beta$, [O III]/H$\beta$ and [O III]/[O II]). The derived 12+log(O/H) values range from 8.36 to 8.93 for the z>0.4 galaxies with a median value of 8.67. Distant LIRGs present a metal content less than half of that of the local bright disks (i.e. L^*). Their properties can be reproduced with infall models although one has to limit the infall time to avoid overproduction of metals at late times. The models predict that total masses (gas + stars) of the distant LIRGs are from  $10^{11}~M_{\odot}$ to $\le$ $10^{12}~M_{\odot}$. A significant fraction of distant large disks are indeed LIRGs. Such massive disks could have formed $\sim$50% of their metals and stellar masses since $z\sim1$.

Key words: galaxies: abundances - galaxies: evolution - galaxies: ISM - galaxies: photometry - galaxies: spiral - galaxies: starburst

1 Introduction

The IRAS all-sky survey detected tens of thousands of galaxies with far-infrared (far-IR) radiation luminosities from less than  $10^{6}~L_{\odot}$to $\sim$ $10^{13}~L_{\odot}$ up to a moderate redshift ($z \sim0.3$). However, luminous infrared galaxies (LIRGs) are not typical of local galaxy population, and they account for only $\sim$2% of the local bolometric luminosity density (Soifer et al. 1987; Sanders & Mirabel 1996).

However, the COsmic Background Explorer (COBE) observations imply that there likely exists a very significant contribution of dust-obscured star formation at high redshifts (Puget et al. 1996; Genzel & Cesarsky 2000). The ISO made it possible to study the infrared emission of galaxies at  $z \geq 0.5$, which plays an important role in understanding the co-moving star formation density evolution with look-back time. The ISO mid infrared camera (ISOCAM) (Cesarsky et al. 1996) is $\sim$10³ times more sensitive and has 60 times higher spatial resolution than IRAS. The mid-IR ISOCAM 15 $\mu$m source counts provide evidence for strong IR light density evolution, as revealed by the strong excess of 15 $\mu$m counts above the predictions of non-evolution models at sub-mJy (Elbaz et al. 1999; Aussel et al. 1999). The cosmic infrared background resolved by ISOCAM shows that the co-moving density of infrared light due to the luminous IR galaxies ( $L_{\rm IR}\geq 10 ^{11}~L_{\odot}$) was more than 40 times larger at $z\sim1$ than today (Elbaz et al. 2002). The main driver for this evolution is the luminous infrared starburst galaxies seen by ISO at z>0.4, which form stars at a rate of more than  $50~M_{\odot}$ yr^-1(Flores et al. 1999).

Based on the correlation analysis of deep X-ray and mid-IR observations in Lockman Hole and Hubble Deep Field North (HDF-N), Fadda et al. (2002) found that the active galactic nuclei (AGN) contribution to the 15 $\mu$m background is only $17\pm2$%. They concluded that the population of IR luminous galaxies detected in the ISOCAM deep surveys, and the cosmic infrared background sources themselves, are mostly dust-obscured starbursts (also see Elbaz et al. 2002). Reviews of extragalactic results from ISO can be found in Genzel & Cesarsky (2000), Franceschini et al. (2001) and Elbaz & Cesarsky (2003).

Recently, Flores et al. (2004a) studied the interstellar extinction and SFRs of 16 luminous infrared galaxies in Canada-France Redshift Survey (CFRS) 3$^{\rm h}$and 14$^{\rm h}$ fields using the spectra from the European Southern Observatory (ESO) Very Large Telescope (VLT) and Canada-France-Hawaii Telescope (CFHT). They found that the extinction coefficients obtained from H$\gamma$/H$\beta$ (using the VLT/FORS2 or CFHT spectra) and H$\alpha$/H$\beta$ (combining the VLT/FORS2 and VLT/ISAAC spectra) are in agreement, and that SFRs derived from H$\alpha$ are consistent with those from infrared luminosities, except for the galaxies near the ultra luminous IR galaxy (ULIRG) regime ( $L_{\rm IR} > 10^{12}~L_{\odot}$).

Spectrophotometric properties of IRAS galaxies have been studied in detail, providing a full diagnostic of their ISM properties (Veilleux et al. 1995, hereafter V95; Kim et al. 1995). However, at higher redshifts, studies of ISOCAM sources have mostly focused on source counts and SFRs. Very little is known about chemical properties of distant LIRGs, including their metal content, and the main objective of this paper is to fill this gap.

In the local Universe, metallicity is well correlated with the absolute luminosity (stellar mass) of galaxies over a wide magnitude range (e.g. 7-9 mag) (Zaritsky et al. 1994; Richer & McCall 1995; Telles & Terlevich 1997; Contini et al. 2002; Melbourne & Salzer 2002; Lamareille et al. 2004). Some results have been obtained on the luminosity-metallicity (L-Z) relations in the intermediate-redshift Universe. Kobulnicky & Zaritsky (1999) found that the L-Z relations of 14 intermediate-z emission line galaxies with 0.1<z<0.5 are consistent with those of the local spiral and irregular galaxies studied by Zaritsky et al. (1994), Telles & Terlevich (1997) and Richer & McCall (1995). The 16 CFRS galaxies at $z\sim0.2$ studied by Liang et al. (2004) fall well in the region occupied by the local spiral galaxies (from Zaritsky et al. 1994).

At higher redshifts, Kobulnicky et al. (2003) have obtained the L-Z relations of 64 galaxies from the Deep Groth Strip Survey (DGSS) which have been separated into three redshift ranges ( z =0.2-0.4, 0.4-0.6, and 0.6-0.82). In the highest redshift bin galaxies are brighter by $\sim$1 mag relatively to those in the lowest redshift bin and brighter by $\sim$2.4 mag compared to the local (z <0.1) field galaxies (from Kennicutt 1992a,b, hereafter K92, and Jansen et al. 2000a,b, hereafter J20). Such a result is confirmed by Maier et al. (2004). These studies contrast with the results of Lilly et al. (2003), who have found that the L-Z relation of most of their 66 CFRS galaxies with 0.5<z<1 is similar to that of the local galaxies from J20. However, Lilly et al. (2003) have assumed a constant A_V=1 for accounting for dust extinction. In this study, we investigate the L-Z relation for LIRGs in z>0.4 Universe, after a detailed account for their dust extinction properties.

This paper is organized as it follows. In Sect. 2, we describe the sample selection, the observations and the data reduction and analysis, while the redshift distribution and the spectrophotometric properties are presented in Sect. 3. Sections 2 and 3 are aiming at assessing whether our resulting sample can be used to test the properties of distant LIRGs. Flux measurements, interstellar extinction and SFRs of the galaxies are shown in Sect. 4. It includes a detailed comparison between extinction parameter deduced from Balmer line ratio to that derived from mid-IR luminosity. In Sect. 5, we discuss the diagnostic diagrams to test the AGN contribution as well as the ionization properties. In Sect. 6, we present the luminosity-metallicity relation (based on oxygen abundances) of distant LIRGs which is compared to other galaxy samples. Discussion and conclusion are given in Sects. 7 and 8. Throughout this paper, a cosmological model with  H₀=70 km s^-1 Mpc^-1,  $\Omega _{\rm M}=0.3$ and  $\Omega _\Lambda =0.7$ has been adopted.

2 Sample selection, observations and data reduction

2.1 The fields

Our sample galaxies were selected from three ISO deep survey fields: CFRS 3$^{\rm h}$, Ultra-Deep-Survey-Rosat (UDSR) and Ultra-Deep-Survey-FIRBACK (UDSF) fields.

The CFRS was carried out in five moderate to high galactic latitude ($\mid$b $\mid > 45^{\circ}$) survey fields of area 10 $\hbox{$^\prime$ }\times 10\hbox{$^\prime$ }$ chosen to match the field of view of the MOS multiobject spectrograph on the 3.6 m CFHT. The 14$^{\rm h}$ and 3$^{\rm h}$ fields have been deeply imaged with the ISOCAM. Combining the deep IR observation and the deep optical and radio data, Flores et al. (1999) studied the 78 ISOCAM sources detected in the 14$^{\rm h}$ field down to a 15 $\mu$m flux $\geq$250 $\mu$Jy. In the CFRS 3$^{\rm h}$ field, 70 sources were detected, with the 15 $\mu$m fluxes in the range of 170-2100 $\mu$Jy (Flores et al. 2004a,b, in preparation).

The UDSR field refers to the Marano field (centered at $\alpha$(2000 $)=03^{\rm h}$15$^{\rm m}$09$^{\rm s}$, $\delta$(2000 $)=-55^{\circ}$13 $\hbox{$^\prime$ }$57 $\hbox{$^{\prime\prime}$ }$), which is a deep ROSAT observation field. The deep ($\sim$80 or 120 ks integration time) XMM-Newton observations (Giedke et al. 2001, 2003) and the optical identifications were also done (Lamer et al. 2003). FIRBACK is a deep survey conducted with the ISOPHOT instrument aboard the ISO at an effective wavelength of 175 $\mu$m. The total survey covers more than 4 square degrees located in one Southern and two Northern fields (Puget et al. 1999; Lagache & Dole 2001). For the UDSR and UDSF fields, very deep ISOCAM follow-up have been done (Elbaz et al. 2004) reaching flux limits three times lower than for the CFRS fields.

2.2 The sample

Figure 1: a) The IR luminosity log( $L_{\rm IR}/L_{\odot }$) distribution (bin = 0.25) of 55 ISO-detected sample galaxies with z>0.4 in all of the three fields (the shaded region), with the median IR luminosity of log( $L_{\rm IR}/L_{\odot })=11.32$, which is similar to those of the local IRAS sample of V95 and Kim et al. (1995) (the dotted-line for BGSs, and the dashed-line for WGSs, with the median values of 11.34 and 11.38, respectively). b) The distribution of the corresponding 38 galaxies with z>0.4 in the UDSR and UDSF fields (the solid line), with the median IR luminosity of log( $L_{\rm IR}/L_{\odot })=11.27$, and the distribution of the galaxies in the CFRS 3$^{\rm h}$ field (the dashed-line), with the median IR luminosity of log( $L_{\rm IR}/L_{\odot })=11.55$. Although the ISOCAM survey observations in the UDSR and UDSF fields are three times deeper than in the CFRS 3$^{\rm h}$ field, the total distribution of the galaxies in the 3 fields is a reliable representation of the IR luminous galaxies in z>0.4 Universe.

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In the CFRS 3$^{\rm h}$ field, we selected 25 targets out of the 70 ISO 15 $\mu$m sources according to their ($\alpha$, $\delta$) positions to observe by using VLT/FORS2. Another 9 objects without 15 $\mu$m fluxes were added to these observations to fill the FORS2 mask. In the UDSR field, 29 targets with ISO 15 $\mu$m fluxes were selected to be observed by using VLT/FORS2. Another 6 non-ISO objects were also added. Three slits (numbers 18, 19 and 25) were superposed on more than one object. In the UDSF field, 27 targets out of the ISO sources list were selected to be observed by using VLT/FORS2. Another 9 objects without 15 $\mu$m fluxes were also selected. Three slits (numbers 26, 27 and 29) were superposed on more than one object.

In total, 105 objects were selected for VLT/FORS2 spectral observations from the three fields. The basic data of the target galaxies are given in Tables 1 and 2. The columns are the slit numbers (also CFRS name in Table 1), the 2000 epoch coordinates, redshift z, I or R band photometric and spectral magnitudes in the AB system, aperture correction factor by comparing the photometric and spectral I or R band magnitudes, absolute B band magnitude M_B in the AB system, the spectral types of the objects, and the related infrared data including 15 $\mu$m fluxes, far-IR luminosities and IR-SFRs.

The IR luminosities (and deduced SFRs) have been calculated using the procedure given in Elbaz et al. (2002) and are given in Tables 1 and 2. They are based on mid-IR fluxes which show good correlations with radio and far-IR measurements in the local Universe (Elbaz et al. 2002). In the distant Universe, these estimates agree within a factor of 2 with those based on H$\alpha$ luminosities (Flores et al. 2004a). Figure 1a shows the distribution (the shaded region) of the inferred IR luminosity (8-1000 $\mu$m) of the 55 ISO/15 $\mu$m-detected objects with z>0.4 (the called "high-z'' sample in the following parts of this paper) in the three fields for VLT/FORS2 spectroscopic observation (see Sect. 3 for redshifts) with a median value of log( $L_{\rm IR}/L_{\odot })=11.32$. Figure 1b shows the corresponding distribution of the 38 z>0.4 objects in the UDSR and UDSF fields with a median value of log( $L_{\rm IR}/L_{\odot })=11.27$, and the distribution of the objects in the CFRS 3$^{\rm h}$ field with a median value of 11.55. The difference is simply related to the different flux limits adopted in UDSR and UDSF fields on one side and on the CFRS 3$^{\rm h}$ field, on the other side. However, our high-z sample exhibits IR luminosity distribution very similar to local IRAS galaxies studied by V95 and Kim et al. (1995), in which the median log( $L_{\rm IR}/L_{\odot})=11.34$ for the Bright Galaxies (BGSs) and 11.38 for the Warm Galaxies (WGSs) (in Fig. 1a, the dotted-line for BGSs, and the dashed-line for WGSs). We believe that our sample can be used to probe the properties of distant LIRGs over an IR luminosity range comparable to that of V95.

2.3 Spectroscopic observations and data reduction

Spectrophotometric observations of the 105 targets were obtained during three nights with the ESO 8 m VLT using the FORS2 with R600, I600 at a resolution of 5 Å and covering the possible wavelength range between 5000 and 9200 Å. The slit width is 1.2 $^{\prime\prime}$ and the slit length is 10 $^{\prime\prime}$. Spectra were extracted and wavelength-calibrated using the IRAF package. Flux calibration was done using 15 min exposures of 3 photometric standard stars per field. In addition, for one field (CFRS), we have compared the spectrophotometry to the V and I photometries and found a very good agreement. To ensure the reliability of the data, all spectrum extractions as well as lines measurements were performed by using the SPLOT program.

A rest-frame spectrum of one typical galaxy of our sample, UDSR23, is given in Fig. 2. The strong emission lines (e.g.  $[O {\sc ii]}$ $\lambda$3727, H$\gamma$, H$\beta$,  $[O {\sc iii]}$ $\lambda$5007) and the obvious absorption lines are marked. The continuum has been convolved except at the locations of the marked emission lines using the softwares developed by our group (Hammer et al. 2001; Gruel 2002). The adopted convolution factors are 7 pixels and then 15 pixels.

Figure 2: Rest-frame spectrum of one of the sample galaxies, UDSR23. It is a luminous infrared galaxy with log( $L_{\rm IR}/L_{\odot })=11.38$. The continuum has been convolved except at the location of the emission lines (e.g. [O II] $\lambda$3727, H$\gamma$, H$\beta$ and [O III] $\lambda$$\lambda$ 4959, 5007). The dashed boxes delimit the wavelength regions where strong sky emission lines (e.g.  $[O {\sc i]}$5577, 5891, 6300, 6364 Å and OH 6834, 6871, 7914 Å etc.) and absorption lines (O2 6864, 7604 Å etc.) are located.

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3 Redshift distributions and spectral types

Redshifts are identified by using the emission and/or absorption lines. Column (4) of Tables 1 and 2 gives the z values of the objects. Redshift distributions of the combined and the individual three fields are shown in Fig. 3. The corresponding median redshifts are $z_{\rm med}=0.587$ in the combined sample,  $z_{\rm med}=0.525$ in the CFRS, $z_{\rm med}=0.521$ in the UDSR and  $z_{\rm med}=0.698$ in the UDSF. The redshift peak around z=0.70 in the UDSF field (six galaxies) shows a velocity dispersion of $\sim$1390 km s^-1, a typical value for a galactic cluster. The corresponding six objects are UDSF06, 07, 08, 21, 26a and 26b. In the UDSR  field, four objects (UDSR11, 12, 13 and 16) show a redshift peak around z=0.166, which may correspond to a velocity dispersion of $\sim$129 km s^-1, a typical value for a galactic group.

The redshift distributions are consistent with the results in some other ISOCAM survey fields, e.g., the  $z_{\rm med}=0.7$ in the CFRS 14$^{\rm h}$ field (Flores et al. 1999) and 0.585 in the HDF-N (Aussel et al. 1999). Franceschini et al. (2003) found a peak at $z\sim 0.6$ for their 21 objects in the Hubble Deep Field South (HDF-S) field, which they suggested to be a cluster or a large galaxy concentration. The similarities between the IR luminosities as redshift distribution of our sample to those of other studies lead us to assume that our sample can be used to test the properties of distant LIRGs. About 81% (75/92) of the redshift-identified galaxies show obvious and strong emission line (EL) (see Col. 9 of Tables 1 and 2). The corresponding EL galaxies fraction of ISO-detected objects is $\sim$85%. Table 3 summarizes the redshift identifications and spectral types of the galaxies in our sample.

	Figure 3: Redshift distributions (bin=0.08) of the sample galaxies in the combined and the individual three fields.
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4 Flux measurements, extinction and SFRs

4.1 Flux measurements

The fluxes of the emission lines are measured using the SPLOT package. The stellar absorption under the Balmer lines is estimated from the synthesized stellar spectra obtained using the stellar spectra of Jacoby et al. (1984). To do so, we use the spectra of four stellar types (e.g. A, B, F and G types) to synthesize the "galactic'' continuum and absorption lines. Then, the "pure'' emission Balmer lines are obtained through reducing the underlying stellar absorption. The corresponding error budget of emission line flux is deduced by a quadratic addition of three independent errors: the first one is related to the use of stellar templates to fit stellar absorption lines and continuum; the second one comes from the differences among independent measurements performed by Liang, Flores and Hammer; the third one is from the Poisson noises from both sky and objects, and it actually dominates the error budget. The flux measurements of emission lines and their percent errors are given in Table 4 for high-z galaxies, and in Table 5 for low-z galaxies. Three low-z galaxies are also given in Table 4 for their H$\gamma$ fluxes. To obtain reliable global fluxes of emission lines of the galaxies, we should notice that the 1.2 $\hbox{$^{\prime\prime}$ }$ slit of VLT observations does not always contain the whole galaxy. Thus, the fluxes of the emission lines are corrected by an aperture factor derived by comparing the photometric magnitudes to the spectral magnitudes at  $I_{\rm AB}$ (for CFRS field) or  $R_{\rm AB}$ (for UDSR and UDSF fields) bands. The aperture correction factors are given in Col. 7 of Tables 1 and 2.

4.2 Balmer decrement and extinction

The extinction inside the galaxy can be derived using the decrement between the two Balmer lines: H$\gamma$/H$\beta$ for our high-z galaxies, and H$\alpha$/H$\beta$ for the low-z galaxies. Case B recombination with a density of 100 cm^-3 and a temperature of 10 000 K was adopted, the predicted ratio is 0.466 for  $I_0({\rm H}\gamma)$/ $I_0({\rm H}\beta)$ and 2.87 for  $I_0({\rm H}\alpha)/I_0({\rm H}\beta)$ (Osterbrock 1989). Using the interstellar extinction law given by Fitzpatrick (1999) with R=3.1 ( R=A(V)/E(B-V)), the extinction can be readily determined. Using the Balmer decrement method we find a median extinction of  A_V(Balmer)=1.68 (=1.82 for the z>0.4sample). Extinction corrected Balmer lines (either H$\beta$ or H$\alpha$) can be used to estimate the SFR, which could be then tested by comparison with SFR obtained from infrared flux.

4.3 Comparison between SFRs deduced from mid-IR and from Balmer lines

To compare the SFRs from IR and Balmer lines, we adopt the calibrations from Kennicutt (1998) based on the Salpeter's initial mass function (IMF) (Salpeter 1955) with lower and higher mass cutoffs of 0.1 and 100 $M_{\odot}$. The median SFR$_{\rm IR}$ of our sample galaxies is about 31 $M_{\odot}$ yr^-1 for the z>0.4 galaxies (it is 19 $M_{\odot}$ yr^-1 when the low-z galaxies are included). The obtained median SFR $_{2.87f({\rm H}\beta)}$is about 28 $M_{\odot}$ yr^-1 for z>0.4 galaxies. For most galaxies, SFR $_{2.87f({\rm H}\beta)}$ are consistent with SFRs estimated from infrared luminosities (Fig. 4a).

4.4 A robust estimate of the extinction coefficient

Figure 4: a) The SFRs estimated from the extinction corrected Balmer lines (Io(H $\alpha )\approx 2.87I_o$(H$\beta$)) (also see Tables 6, 7), compared with the SFRs estimated from infrared fluxes. The small zoomed figure on the bottom right is for the low-z sample. Relative error bars ($\Delta$SFR$_{\rm IR}$/SFR$_{\rm IR}$) are quoted in Tables 1 and 2, and average to 30% (see however a discussion by Cardiel et al. 2003). b) The relation between the extinction AV values derived from Balmer decrement and by the energy balance between the IR radiation and the optical H$\beta$ emission line luminosities. The two dashed lines refer to the results with $\pm$0.64 rms. The different kinds of symbols in the two figures roughly show whether the infrared fluxes of the galaxies are affected by nearby objects according to their images from the VLT and the ISOCAM: the  $\it filled~squares$ represent the objects for which the IR fluxes are possibly affected by other nearby ISO objects; the  filled circles show the objects for which no contamination is expected; the  $\it asterisks$ mark the objects which are not detected by ISO, and their AV(IR) are just upper limits.

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Because of the large uncertainties related to the measurements of the H$\gamma$ line, we need to verify the quality of our derived extinction. This can be done assuming that the infrared data provide a robust SFR estimate for IR-luminous galaxies (Elbaz et al. 2002; Flores et al. 2004a). We estimate a new dust extinction coefficient, A_V(IR), by comparing the infrared SFR with the SFR calculated from the optical H$\beta$ emission line: the energy balance between IR and H$\beta$ luminosities. Figure 4b shows that the derived A_V(IR) is consistent with A_V(Balmer) for most galaxies, most of them falling in the $\pm$0.64 rms discrepancy. Few objects however lie outside the $\pm$0.64 rms as shown in Fig. 4b (also see Table 6). For three of them (filled squares, CFRS10, CFRS19 and UDSF13) showing A_V(IR) much larger than A_V(Balmer), we believe that the discrepancy could be related to a possible overestimate of the IR flux due to contamination by neighboring ISO sources (the "possible flux blending'' sources).

The derived median value of A_V(IR) is 2.18 (=2.36 for z>0.4 galaxies) for our sample, which is slightly larger than the extinction derived from optical Balmer lines. This trend might be related to the fact that infrared radiation includes fluxes from the optical thick H II regions, which might be obscured to contribute to the detected optical emission lines. An extreme example is CFRS25, CFRS03.0932, which shows A_V(Balmer)= 1.04 and A_V(IR)= 3.77. It is an extreme edge-on disk galaxy with an inclination of $\sim$79$^{\circ}$ (Zheng et al. 2004). Most of the optical light of the whole galaxy is strongly hidden by dust (screen effect), and the detected optical Balmer lines just trace the star formation of a few optical-thin H II regions lying on the edge of the galaxy.

The median extinction in our sample is lower than those of the local IRAS sample by V95 who obtained the median E(B-V) (= A_V/3.1) values 0.99 for the H II LIRGs, and 1.14 for the LINERs. This could be due to the fact that V95 only studied the central $\sim$2 kpc parts of the IRAS galaxies, which could be more affected by dust than the whole galaxy light as studied in distant galaxies. The derived median extinction of our galaxies is comparable to that of radio-detected Sloan Digital Sky Survey (SDSS) galaxies ( $A_{{\rm H}\alpha}=A_{V}$/1.25=1.6, Hopkins et al. 2003). It is much higher than those of the local normal star forming galaxies for which the median $A_V \approx 0.86$ (K92 and J20).

Comparison between the extinctions derived from IR and optical Balmer lines (Fig. 4b) provides a significant reduction of the error bars derived from the single H$\beta$/H$\gamma$ ratio, to $\sim$0.64 for A_V. This might also provide a useful diagnostic for the dust and star formation properties in individual galaxies. In the following, we have to adopt a reliable A_V which describes as best as possible the global properties of each individual galaxy. The one based on the H$\beta$/H$\gamma$ ratio shows a large uncertainty because it is based on the faint H$\gamma$ emission line. Diagnostic diagrams and metal abundance determination often depend on the [O II] $\lambda$3727/H$\beta$ ratio and then on the adopted extinction coefficient. It is uncertain whether such a ratio can be obtained as a global parameter for a given galaxy. On the other hand, using A_V(IR) could lead to overestimates of the extinction (and then to underestimates of the metal abundance) since it accounts for the most obscured regions. However the good correlation found by Flores et al. (2004a) between SFR$_{\rm IR}$ and SFR $_{{\rm H}\alpha }$ for LIRGs implies that strong obscuration are not preponderant in the energy balance for these galaxies. Because our study of the metal abundances is only based on starbursts and LIRGs (no ULIRGs), we adopt in the following A_V(IR) for estimating the extinction, while paying attention to how our results would be affected if using A_V(Balmer).

Figure 5: The far-IR luminosities and color excesses (extinction) as functions of continuum colors for our sample galaxies: a) IR luminosities, b) extinction for the high-z sample, c) extinction for the low-z sample. The continuum colors are defined as the ratios of the continuum levels close to the lines (no extinction correction) (on both sides $\sim$4 Å around the line), with a typical uncertainty 0.03.

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4.5 Continuum colors

The continuum colors of our sample galaxies are determined by the ratios of the continuum levels at 4861 Å and 3660 Å (C4861/C3660, for the high-z sample) and at 6563 Å and 4861 Å (C6563/C4861, for the low-z sample) (no extinction correction). We use the same three IR luminosity bins as V95 for log( $L_{\rm IR}$/$L_{\odot}$) ($\leq$11, between 11 and 12, and $\geq$12) in the following studies. Figure 5a shows the IR luminosity against the C4861/C3660 color for our sample galaxies. It seems that this plot shows that the more IR luminous galaxies with log( $L_{\rm IR}$/ $L_{\odot})>11$ have redder colors than the less luminous galaxies with log( $L_{\rm IR}$/ $L_{\odot})\leq 11$. However, the trend is very weak(less than 1$\sigma$) and similar to the result of V95 (their Fig. 17, for C6563/C4861 vs. IR luminosity). Figure 5b shows the color excess (extinction) against the C4861/C3660 color for our sample. It shows a weak positive correlation, i.e., the redder color, the higher dust extinction, which is similar to that of the local IRAS sample shown by Fig. 5 of V95 (with C6563/C4861 color). Figure 5c shows the color excess against the C6563/C4861 color for the low-z sample. It seems that a weak correlation exists as well, similar to that of V95 (on their Fig. 5). The median color C6563/C4861 value is about 0.4. If the dust extinction is considered to correct the continuum color roughly, the median color (C6563/C4861)₀ ("0'' means extinction correction) is about 0.35, which is similar to the value 0.4 obtained by V95 for their local IRAS sample (their Fig. 16).

5 Diagnostic diagrams

5.1 High redshift galaxies

The diagram of log([O II] $\lambda$3727/H$\beta$) vs. log([O III]  $\lambda\lambda$4959, 5007/H$\beta$) can be used to distinguish the H II region-like objects from the LINERs and Seyferts. The H II region-like objects can be H II region in external galaxies, starbursts, or H II region galaxies, objects known to be photoionized by OB stars.

Figure 6a gives the diagnostic diagram for our z >0.4 galaxies, and shows that most of the objects are H II region galaxies, and are consistent with the theoretical fitting of the local extragalactic H II regions (the solid line, from McCall et al. 1985). The dashed line shows the photoionization limit for a stellar temperature of 60 000 K and empirically delimits the Seyfert 2 area from the H II region area (also see Hammer et al. 1997). From this plot, eight objects are identified to be AGNs, including five LINERs (CFRS17, 32, 33, UDSR04 and UDSF32) and three Seyfert 2 galaxies (UDSR09, UDSF13, 28). An AGN fraction of $\sim$23% is identified from the diagnostic diagram. However, this ratio can be decreased to 11% when A_V(Balmer) instead of A_V(IR) is used to correct the emission line fluxes. One reason for this is the higher extinction of A_V(IR) results in higher [O II] emission line flux corrected by extinction, hence, a higher LINER fraction. The AGN fraction is consistent with previously reported results (17%, Fadda et al. 2002).

Figure 6: a) Diagnostic diagram for our high-z sample. The solid line shows the theoretical sequence from McCall et al. (1985), which fits the local extragalactic H II regions well with metallicity decreasing from left to right. b), c) Diagnostic diagrams for the low-z sample, with symbols as in Fig. 5, and the long-dashed lines are taken from Kewley et al. (2001), others are from Osterbrock (1989).

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5.2 Low redshift galaxies

For the low-z galaxies, the diagnostic diagrams of [O III] $\lambda$5007/H$\alpha$ vs. [S II] $\lambda$$\lambda$6716, 6731/H$\alpha$ and [O III] $\lambda$5007/H$\alpha$ vs. [N II] $\lambda$6583/H$\alpha$ are available to diagnose their source of ionization (Veilleux & Osterbrock 1987; Osterbrock 1989). Figures 6b and c show these properties of the sample galaxies.

From the [S II]/H$\alpha$ vs. [O III]/H$\beta$ relations, most of the galaxies are LINERs with low ionization levels. However, from the [N II]/H$\alpha$ vs. [O III]/H$\beta$ relations, most of the galaxies are H II region galaxies since only two objects (20%) show the LINER character (UDSR06, 11). Also, most of them will be classified to be "Star Forming'' galaxies by using the corresponding diagnostic for the SDSS sample (Kauffmann et al. 2003; Brinchmann et al. 2003). Thus, to study the diagnostic diagrams of such emission line galaxies, these two diagrams are needed simultaneously (also see Liang et al. 2004). Considering the limits given by Kewley et al. (2001) (the long-dashed lines in Figs. 6b and c), most of the low-z galaxies would be classified as H II regions. It may infer that most of them occupy a region intermediate between LINERs and H II regions.

5.3 [O III]/H$\beta$ versus [O II]/[O III] diagram for high-z galaxies

The ([O II] $\lambda$3727/[O III] $\lambda$5007) emission line ratio follows a sequence from low-excitation H II regions to high-excitation H II regions (Baldwin et al. 1981). Figure 7 shows the log([O III] $\lambda$5007/H$\beta$) vs. log([O II] $\lambda$3727/[O III] 5007) diagnostic relation for our sample, compared with that for local IRAS LIRGs of V95. Most of our galaxies lie in the bottom right region indicating low ionization levels ([O III]/H$\beta <3$). The apparent excess of high ionization objects in V95 could be attributed to the fact that they only studied the central $\sim$2 kpc of the IRAS galaxies, and that they could be more sensitive to a possible high ionization central AGN. Another possible selection bias in V95 might also contribute to this excess, since they have been able to detect [O II] $\lambda$3727 line only in their brightest and more distant sources, which likely include more objects with high ionization levels.

Figure 7: [O III]$\lambda$5007/H$\beta$ versus [O II]$\lambda$3727/[O III]$\lambda$5007 emission line flux ratios of our sample galaxies, compared with the local IRAS sample from V95. The typical (median) uncertainties of the two parameters in logarithm are 0.08 and 0.12 dex, respectively. The  $\it squares$ are the IRAS data: the  open squaresrepresent the galaxies with log( $L_{\rm IR}/L_{\odot })<11$, the  $\it squares$ $\it with$ a $\it cross$ $\it in$ $\it the$  $\it middle$ are the galaxies with $11\leq \log(L_{\rm IR}/L_{\odot})\leq 12$, and the  $\it filled~squares$ are the galaxies with log( $L_{\rm IR}/L_{\odot })>12$. Most of our sample galaxies have relatively low ionization levels ([O III]/H$\beta <3$).

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6 Abundances in interstellar medium and luminosity-metallicity relation

Chemical properties of gas and stars within a galaxy are like a fossil record chronicling its history of star formation and its present evolutionary status. The high quality optical spectra from VLT/FORS2 make it possible, for the first time, to obtain the chemical abundances in ISM for such a large sample of high-z LIRGs.

6.1 Metallicities estimated from diagnostic diagram

On the diagnostic diagram of log([O II]  $\lambda {3727}$/H$\beta$) vs. log([O III]  $\lambda \lambda {4959,5007}$/H$\beta$), the local H II region samples with different metallicities lie in different areas. Moreover, they follow the empirical sequence from McCall et al. (1985), which fits the local H II galaxies well with metallicity decreasing from the left to the right (see Fig. 12 of Hammer et al. 1997). The corresponding relations for our galaxies are given in Fig. 8a (the larger points), together with the local H II regions with different metallicities (the smaller points, the representative metallicities of the different symbols are shown in the box on the bottom right, Z₀ is the solar metallicity). The solid line shows the theoretical sequence from McCall et al. (1985). This diagram shows that our high-z H II region galaxies fall in the local sample well, and have metallicities of 0.5  $Z_{\odot} < Z < Z_{\odot}$. One non-ISO galaxy, UDSF26a, perhaps has low metallicity with  $Z < 0.25~Z_{\odot}$. It seems that there is no obvious difference in metallicities between the more luminous infrared H II galaxies (log( $L_{\rm IR}/L_{\odot})>11$) and other less luminous infrared samples (log( $L_{\rm IR}/L_{\odot})\leq11$).

This plot shows that the horizontal-axis parameter, log([O III]  $\lambda \lambda {4959,5007}$/H$\beta$), can trace the metallicities of the H II galaxies roughly, following a trend that increasing values (up to $\sim$1.0) corresponds to lower metal abundances. Also, this ratio is almost independent of extinction. Therefore, we further obtain the log( $L_{\rm IR}/L_{\odot }$) vs. log([O III]  $\lambda \lambda {4959,5007}$/H$\beta$) (no extinction correction) relation shown by Fig. 8b, in which more data points are included though their H$\gamma$ emission lines (for extinction) and/or [O II] $\lambda$3727 shift out of the rest-frame spectra. Figure 8b indicates that there is almost no obvious correlation between the two parameters, if one exists, a very weak correlation may show the decreasing [O III]/H$\beta$ ratio following the increasing IR luminosity for the high-z galaxies when the three Seyfert 2 galaxies (with log([O III]  $\lambda \lambda {4959,5007}$/H $\beta)>1.0$) are excluded.

6.2 Oxygen abundances estimated from strong emission lines

The "direct'' method to determine chemical compositions requires the electron temperature and the density of the emitting gas (Osterbrock 1989). In a best-case scenario, the electron temperature of the ionized medium can be derived from the ratio of a higher excitation auroral line, such as [O III]  $\lambda{4363}$ to [O III]  $\lambda \lambda {4959,5007}$. However, [O III]  $\lambda{4363}$ is too weak to be measured except in extreme metal-poor galaxies, and becomes extremely weak in more metal-rich environments due to abundant heavy elements reducing collision excitation of the upper levels. In this case, the oxygen abundances may be determined from the ratio of [O II]+[O III] to H$\beta$ lines ("strong line'' method). The general parameter is R₂₃: $R_{23}=({[O {\sc ii]}\lambda{3727}+[O {\sc iii]}\lambda{4959}+[O {\sc iii]}\lambda{5007}})/{H\beta}.$

Figure 8: a) The relation between log([O II]  $\lambda {3727}$/H$\beta$) and log([O III]  $\lambda \lambda {4959,5007}$/H$\beta$) for z> 0.4 galaxies, compared with a sample of local H II regions and H II galaxies with different metallicities (see Fig. 12 of Hammer et al. 1997 for references of H II samples). The solid line shows the theoretical sequence from McCall et al. (1985), same as in Fig. 6a. b) The relation between the infrared luminosities and the log([O III]  $\lambda \lambda {4959,5007}$/H$\beta$) (not corrected by extinction), which includes more data points than figure a) panel since some galaxies can be added according to their [O III] to H$\beta$ ratios which are almost independent of extinction.

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Many researchers have developed formula for converting R₂₃into oxygen abundance. The different calibrations have been checked by Kobulnicky & Zaritsky (1999) and Kewley & Dopita (2002). Recently, using the calibration given by McGaugh (1991), Kobulnicky et al. (1999) presented two analytic formulae to convert R₂₃ into 12+log(O/H) for the metal-rich and metal-poor branches, respectively. Here we only adopt the calibration for the metal-rich branch since the related sample includes only luminous galaxies (M_B <-18) (Kobulnicky et al. 1999):

$$12+\log({\rm O/H})=$$ 12-2.939-0.2x-0.237x²- 0.305x³

$$-0.0283x^4- y\big(0.0047-0.0221x$$

$$- 0.102x^2-0.0817x^3 -0.00717x^4\big),$$ (1)

where x refers to logR₂₃, and y refers to logO₃₂: ${\rm log}(O_{32})={\rm log}(([O {\sc iii]}\lambda{4959}+[O {\sc iii]}\lambda{5007})/[O {\sc ii]}\lambda{3727}).$To translate R₂₃ to be $12 + {\rm {log(O/H)}}$, the different calibrations will cause slightly different oxygen abundances. In fact, it is not important which calibration is used here since we are interested in the relative abundances between local and distant galaxy samples analyzed in the same manner. For the comparison samples in Fig. 9 (K92; J20; Kobulnicky et al. 2003; Lilly et al. 2003), the same calibration (Kobulnicky et al. 1999) has been adopted.

Figure 9: The MB-metallicity relation of our distant LIRGs (with the typical uncertainty of 0.08 dex on metallicity), compared with other samples and Pegase2 models: a) with the local galaxies from K92 and J20; the vertical arrow connecting with the solid fit line shows the maximal extinction effect on MB, assuming an average extinction correction of AV=2.36. b) Pegase2 infall models are superimposed assuming a total mass of  $10^{11}~M_{\odot}$ and infall times of 5 Gyr and 1 Gyr (the solid and dashed lines with pentagons, respectively); the different timescales are indicated below pentagons. c) With the galaxies with 0.4< z <0.82 from Kobulnicky et al. (2003). d) With the galaxies with 0.47< z <0.92 from Lilly et al. (2003); solid triangles represent the LIRGs in the Lilly et al. sample for which we suspect that their location should move to lower metal abundance values (see text), reconciling their results to ours and those of Kobulnicky et al. The linear least-squares fits of the samples are given: the  $\it solid~line$ is for our distant LIRGs, the $\it short$- $\it dashed~line$ for the local sample, and the $\it long$- $\it dashed~lines$ for the other two high-z samples.

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Due to the limits of wavelength ranges, [O II] $\lambda {3727}$ emission lines shift out of the visible wavelength in the low-z galaxies. Oxygen abundances in ISM of these galaxies can be estimated by R₃ parameter for this case (Edmunds & Pagel 1984): $R_3=1.35\times ([O {\sc iii]}\lambda{5007}/{\rm H}\beta).$Then, their $12 + {\rm {log(O/H)}}$ values can be obtained using the empirical relation proposed by Vacca & Conti (1992) (also see Coziol et al. 2001):

$$\log({\rm O/H})=-0.69\times \log R_3 - 3.24, ~~~~~(-0.6\leq \log R_3 \leq 1.0).$$

The derived $12 + {\rm {log(O/H)}}$ values of the galaxies are given in Col. 12 of Table 6 (for high-z sample) and Col. 8 of Table 7 (for low-z sample), which show that our high-z H II region galaxies have $12 + {\rm {log(O/H)}}$ from 8.36 to 8.93, with a median value of 8.67. Two low-z galaxies have higher metallicities than 9.0. We should notice that here and hereafter the mentioned "oxygen abundance'' or "metallicity'' refers to "gas-phase'' value in the ISM.

For the solar metallicity, Anders & Grevesse (1989) obtained a value of $12 + {\rm {log(O/H)}}=8.90$, Grevesse & Sauval (1998) got 8.83, whereas Allende Prieto et al. (2001) gave a preferred solar value of 8.68. Therefore, in the following, our discussion is based wherever possible on $12 + {\rm {log(O/H)}}$ values rather than metallicities relative to solar, in order to avoid confusion.

6.3 Luminosity-metallicity relation

In the local Universe, metallicity is well correlated with the absolute luminosity of galaxies (Zaritsky et al. 1994; Contini et al. 2002; Melbourne & Salzer 2002; Lamareille et al. 2004). Based on the current understanding of cosmic evolution, the volume-averaged star formation rate was higher in the past (Madau et al. 1996; Lilly et al. 1996; Flores et al. 1999) and the overall metallicity in the Universe at earlier times was correspondingly lower. We might expect galaxies to be considerably brighter at a given metallicity (i.e. luminosity evolution) if they are forming stars at higher rates. A high or intermediate redshift galaxy sample ought to be systematically displaced from the local sample in the L-Z plane if individual galaxies reflect these cosmic evolution processes. However, if local effects such as the gravitational potential and "feedback'' from stellar winds and supernova regulate the star formation and chemical enrichment process, the L-Z relation might be less dependent on the cosmic epoch. In fact, feedback could confuse the use of metallicity as a simple metric (Garnett 2002).

Figure 9 presents the M_B vs. $12 + {\rm {log(O/H)}}$ relations for our LIRG sample, compared with the local (from K92 and J20) and the other two high-z samples (from Kobulnicky et al. 2003 and Lilly et al. 2003). The M_B values of the compared samples have been corrected to be the same cosmological model as ours and in the AB system. The linear least-squares fits for the corresponding galaxy samples are also given by considering the metallicity as an independent variable.

6.3.1 Comparison with local disks

Figure 9a compares the L-Z relation for the LIRGs to that of local disks (K92 and J20), which are restricted to moderately star forming galaxies (EW(H $\beta )<20$ Å) following Kobulnicky et al. (2003). For the local disks, there is a correlation between L_B and Z, with some dispersion at low luminosity, which could be related to different star formation histories at different epochs. For the brightest/more abundant disks, this might be translated into a mass-abundance relation, assuming that their B lights are dominated by emissions from intermediate or old stellar populations. Most of the low redshift sample galaxies (the triangles) lie in the disk locus, which could be simply related to the fact that they show moderate SFRs, and are not so different from the local disks. Two of the low-z galaxies (CFRS09, 13) show high metal abundances $12 + {\rm {log(O/H)}}>9.0$). They are the so-called "CFRS H$\alpha$-single'' galaxies studied by Liang et al. (2004), and are over-abundant spirals. The situation for distant LIRGs is far more complex. At a given metal abundance, all of them show much larger B luminosities than local disks, which corresponds to $\delta M_B= 2.5$ mag at the median $12 + {\rm {log(O/H)}}= 8.67$ (with the median M_B = -21.24). These galaxies show $\sim$0.3 dex lower metallicity than that of the local disks with the similar B luminosity (e.g. the median  M_B=-21.24). Adopting A_V(Balmer) instead of A_V(IR) would move the median metal abundance value of our galxies by +0.03 dex.

The small M_B variation with metallicity is probably related to selection effect because distant ISOCAM sources likely correspond to luminous (and massive?) systems (also see Franceschini et al. 2003). As an aside, they are also consistent with an infall model (single-zone Pegase2 from Fioc & Rocca-Volmerange 1999) as displayed in Fig. 11 of Kobulnicky et al. (2003) for a  $10^{11}~M_{\odot}$ galaxy (our Fig. 9b). The model assumes a SFR proportional to the gas mass where the galaxy is built by exponentially decreasing infall of primordial gas with an infall timescale of 5 Gyr (the solid line with pentagons). Here the nucleosynthesis yields of stars (from the B-series models of Woosley & Weaver 1995) have been arbitrarily reduced by a factor of 2 to avoid overproduction of metals at late times (see Kobulnicky et al. 2003). The dispersion of the points around this relation may be reproduced by adding singular burst of star formation of  $10^{6-7}~M_{\odot}$ on the model galaxy.

However, we believe that Fig. 9a does not tell us all of the story. Indeed, distant LIRGs show SFRs extending from 30 to several hundreds of $M_{\odot}$ yr^-1 and high gas extinctions. Conversely to local quiescent disks, their B luminosities are dominated by young stars, and as such, are strongly affected by dust effects. The latter cannot be accurately estimated from their spectral energy distribution, without a careful modelling of stellar populations, IMF and of the dust geometry. We can estimate the maximal B luminosity of distant LIRGs, which can be reached if all blue stars were embedded in the ionized gas. This "maximal'' dust correction is represented in Fig. 9a by a big vertical arrow connecting with the linear least-squares fit of our high-z LIRGs sample, assuming an average extinction correction A_V(IR)=2.36 (or 3 mag at 4350 Å). Then, at a given metal abundance, LIRGs have B luminosities by far larger than those of the local disks, which excess  $\delta M_B$ ranging from 2.5 mag to more than 5 mag at the median $12 + {\rm {log(O/H)}}= 8.67$. Assuming an infall gas model, distant LIRGs could be interpreted as forming very massive systems with total mass ranging from  $10^{11}~M_{\odot}$ to $\le$ $10^{12}~M_{\odot}$, which extend from massive disks to massive ellipticals.

It is valuable to notice that, at the given magnitude (the median value), the metallicity of the distant LIRGs are also lower by $\sim$0.3  dex than those of other local samples (Contini et al. 2002; Lamareille et al. 2004; Melbourne & Salzer 2002). Because the above studies are based on UV or H$\alpha$ emission, they mostly include low luminosity (mass?) systems in the local Universe. In Fig. 9a we have chosen to compare our results to those of more massive objects, i.e. the spiral galaxies from K92 and J20, because this provides us a better tool to understand evolutionary effects.

6.3.2 Comparison with other high-z samples

Figure 9c compares the distant LIRGs with the high-z galaxies from Kobulnicky et al. (2003) with  0.4<z<0.82 (EW(H$\beta )<20$ Å). Kobulnicky et al. estimated the O/H values using R₂₃ and O₃₂ parameters obtained from the corresponding equivalent widths of the lines, which are believed to be less affected by dust extinction (see Kobulnicky & Phillips 2003). The metallicities of their galaxies are in similar range to ours, but the galaxies are fainter at a given metallicity. The median (M_B, $12 + {\rm {log(O/H)}}$) of their sample is about (8.64, -20.08). The difference between the two samples decreases at increasing metallicity, from  $\delta M_B=2.3$ mag at $12 + {\rm {log(O/H)}}\sim 8.42$ to  $\delta M_B= 0$ at  $12 + {\rm {log(O/H)}}\sim 8.85$. The  $\delta M_B$ is $\sim$1 mag at the median abundance of 8.67 of our LIRGs. This discrepancy in M_B reflects that our sample galaxies are brighter and possibly more massive than the rest-frame blue selected sample of DGSS galaxies.

Figure 9d compares the distant LIRGs with the distant CFRS sample studied by Lilly et al. (2003). The M_B values of the two galaxy samples are very similar, from about -19.8 to -22.5. The linear least-squares fits of the two samples (the solid line is for our sample, and the long-dashed line is for Lilly's sample) show a non-significant difference in L-Z relation:  $\delta M_B \sim0.4$ mag. For reasons of clarity, we have restricted the sample of Lilly et al. (2003) to the CFRS 3$^{\rm h}$ and 14$^{\rm h}$ fields, which have been surveyed by ISOCAM. Among this subsample of 42 galaxies, 10 have been identified to be LIRGs by ISO (shown as  $\it filled ~triangles$ in Fig. 9d). The derived oxygen abundances by Lilly et al. for these 10 ISO-galaxies show a median value of $12 + {\rm {log(O/H)}}=8.98$, which is $\sim$0.3 dex higher than the median value of our distant LIRG sample. Indeed, Lilly et al. (2003) assumed a constant extinction of A_V=1 for all their galaxies, which strongly underestimates the average extinction for LIRGs, and then, leads to underestimated [O II] $\lambda{3727}/H\beta$ ratios, hence the overestimated oxygen abundances. This effect has been checked by us in investigating the properties of two common galaxies in the two samples. For CFRS02 (A_V=3.24) and CFRS06 (A_V=2.74), Lilly et al. (2003) found the 0.5 dex and 0.3 dex larger $12 + {\rm {log(O/H)}}$ values than our estimates, respectively. If one assumes an average  A_V=2.36 for LIRGs in the Lilly et al. sample, this would move all the corresponding points (full triangles) towards a lower metallicity by $\sim$0.3 dex. Extinction effects could thus reconcile Lilly et al.'s results with those of Kobulnicky et al. (2003).

7 Discussion

We have gathered a sample of 105 ISOCAM galaxies for which we present detailed optical spectroscopic properties. The sample, although slightly biased towards high IR luminosity, shows several strikingly similar properties with the local sample of IRAS galaxies studied by V95 and Kim et al. (1995). This includes a similar IR luminosity distribution, continuum color, extinction and ionizing properties. We believe that our sample provides a good representation of distant LIRG properties. We also confirm that, for >77% of the distant LIRGs selected by ISOCAM at 15 $\mu$m, star formation is responsible for most of their IR emission.

ISO distant galaxies present a L-Z diagram strikingly different from that of local disks. Distant LIRGs are forming stars at very large rates, and their L-Z diagram is almost an horizontal line reaching the local disk L-Z correlation: they are the systems actively building up their metal content. At the median luminosity ( M_B = -21.24), their median  $12 + {\rm {log(O/H)}}$ is about 0.3 dex smaller than the local disk value, and even less if we correct the M_B value for extinction. It is unlikely that this discrepancy is related to our determination of metallicity, because we have adopted the conservative assumption that all distant LIRGs lie on the upper branch of the R₂₃ - O/H diagram, i.e. with $12 + {\rm {log(O/H)}} \ge 8.35$. In the following, we investigate the relation between distant LIRGs and present-day disk galaxies.

LIRGs can reach the local disk locus by either a progressive enrichment of their metal content or fading. Both cases are somewhat extreme. Single-zone infall models with infall time from $\tau=1$ to 5 Gyr could easily reproduce the link between distant LIRGs, the distant large disks, and the local massive disks (see Fig. 9b). These models predict the total masses of galaxies range from  $10^{11}~M_{\odot}$ to $\le$ $10^{12}~M_{\odot}$. The latter mass value comes from the maximal B band luminosity (see Sect. 6.3.1). As noticed by Kobulnicky et al. (2003), reducing the infall time (to values down to few 10⁸ years) would lead to overproduction of metal at later times. However, we believe that simple infall models cannot apply during the whole history of the galaxy: several factors can prevent the star formation from being held at very large rates, including disk self regulation (Silk 1997), gas consumption or small timescales related to merging events.

A major problem is the uncertainty about the characteristic infall time: if much smaller than 1 Gyr, distant LIRGs might fade away after the burst and be progenitors of low mass disks. It is likely that LIRGs correspond to specific events of strong star formation in galaxy history: if associated to mergers, such events should be rather short, within few 10⁷ to 10⁸ years, leading to relatively small amounts of formed stellar mass and metals. Indeed, several consecutive bursts are predicted by merging simulations. Several minor merger events may occur in a Hubble time. The study of the Balmer absorption lines of these LIRGs will be presented in a forthcoming paper (Marcillac et al. 2004), in which they will be used to quantify the mass fraction of stars born during the starbursts as well as the duration of these bursts.

LIRG morphologies suggest that a noticeable amount of them are intimately linked with the population of large disks. Using HST color maps of 34 distant LIRGs drawn from the CFRS sample, Zheng et al. (2004) showed that 36% of the LIRGs have disk morphologies and only 17% are major mergers of two galactic disks, which confirms the preliminary study in Flores et al. (1999). Lilly et al. (1998) have gathered a small but representative sample of large disks ( $r_{\rm disk}\ge 4~h_{50}^{-1}$) at $z\ge 0.5$, which appears in number density comparable to that of local large disks. Restricting this sample to the two CFRS fields surveyed by ISO (3$^{\rm h}$ and 14$^{\rm h}$), 6 (30%) of the 19 large disks are LIRGs ( $L_{\rm IR}$ from 3 to   $18 \times 10^{11}$ $L_{\odot}$) detected by ISO (4 of them are indeed detected by ISO but 2 of them are in the supplementary catalog of Flores et al. 1999; also see Zheng et al. 2004). If we assume that the sample of Lilly et al. (1998) is a good representation of massive disks in the 0.5< z <1 volume, and that a large fraction of them are experiencing strong star forming episodes (LIRGs), this could constraint the amount of metal/stellar mass they have formed. The elapsed time between z=1 and z=0.5 is $\sim$2.7 Gyr, and if 30% of distant disks are experiencing strong star formation episodes (LIRGs), infall time likely averages to a value close to 1 Gyr: this would suffice to produce an amount of metal to reach the upper metal branch of local massive disks.

Unfortunately, at present, we only have a few K band measurements for the sample galaxies studied here to estimate their stellar masses. However, Zheng et al. (2004) has derived rest-frame K-band luminosities ranging from $1.4\times 10^{10}~L_{\odot}$ to  $2.9\times 10^{11}~L_{\odot}$ for 24 of their distant LIRGs. The characteristic time for doubling the stellar masses of the distant LIRGs ranges from 10⁸ to 10⁹ years. Since in the very simple model (1 Gyr infall) described above, a noticeable fraction of the gas was not converted into stars, this supports our view that LIRGs are related to the formation of massive systems ($\sim$ $10^{11}~M_{\odot}$, mostly large disks). On average, $z\sim1$ large disks could double their metal content and their stellar mass to reach the massive spiral locus at z<0.5. This is consistent with Franceschini et al. (2003), who found that the distant IR sources in the HDF-S are hosted by massive galaxies ( $M\sim 10^{11}~M_{\odot}$), with an observed median star forming activity parameter,  $M/{\it SFR}\sim1$ Gyr.

Our result is globally in agreement with that of Franceschini et al. (2003) who found that the host galaxies of ISO sources are massive members of groups with typically high rates of star formation ( ${\it SFR}\sim 10$ to 300 $M_{\odot}$ yr^-1), and suggested that the faint ISOCAM galaxies appear to form a composite population, including moderately active but very massive spiral-like galaxies, and very luminous ongoing starbursts, in a continuous sequence.

8 Conclusion

A large sample (105) ISO/15 $\mu$m-selected sources in three ISO deep survey fields (CFRS 3$^{\rm h}$, UDSR and UDSF) are studied on the basis of their high quality VLT/FORS2 spectra and the infrared data from ISO. Among the 92 redshift-identified objects, 75 (64 with z>0.4) are classified to be EL galaxies. 66 (55 with z>0.4) objects are EL galaxies out of the 77 ISOCAM 15 $\mu$m detected sources. This is by far the largest sample of spectra of distant ISO galaxies. We present here their properties derived from the emission lines. The redshift distribution ( $z_{\rm med}=0.587$) is consistent with that of previous studies, and some galaxies belong to a  $z \sim0.70$ cluster (in the UDFS field) or to a  $z \sim0.166$ galaxy group (in the UDSR field). This study provides us:

• An accurate calculation of the extinction coefficient from Balmer emission lines, which properly account for underlying Balmer absorption (A_V(Balmer), median value of 1.82 for z >0.4 sample galaxies).

• An energy balance between IR and Balmer luminosities which provides us with an original way to calculate an IR-based extinction coefficient (A_V(IR), median value of 2.36 for z>0.4 galaxies).

• A good correlation between the above-mentioned two extinction coefficients, which, for the first time, allows us to reliably obtain the chemical properties of distant galaxies with considering interstellar extinction; this diagram could also be used as a diagnostic of their dust geometry and star formation history.

• The very similar general properties of z>0.4 ISO sources to those of the local IRAS LIRGs studied by V95, including IR luminosity distribution, continuum color, ionization and extinction properties, which ensures that our sample is representative of LIRGs in the distant Universe.

• An extinction-corrected diagnostic diagram based on [O II]/H$\beta$ and [O III]/H$\beta$ ratios, which confirms the small fraction ($\sim$23%) of Seyferts and LINERs for ISOCAM 15 $\mu$m sources found in other studies (Flores et al. 1999; Fadda et al. 2002; Elbaz et al. 2002).

• A determination of O/H metallicity, which ranges from 8.36 to 8.93 in  $12 + {\rm {log(O/H)}}$ for the z>0.4 sample; no obvious trend is found between the IR luminosity and the metallicity.

This study shows that distant LIRGs form a peculiar sequence in the M_B-O/H diagram, which is a broad L-Z relation at bright B absolute luminosities. When compared to local bright disks, at constant metallicity ( $12 + {\rm {log(O/H)}}= 8.67$, median value), LIRGs are from 2.5 to 5 mag more luminous, and at constant M_B( M_B = -21.24, median value), they are more than two times deficient in metal. These properties can be reproduced with infall models though one has to limit the infall time to avoid overproduction of metals in late time. Models predict a total mass ranging from  $10^{11}~M_{\odot}$ to $\le$ $10^{12}~M_{\odot}$, which can be twice of the stellar masses of distant LIRGs derived by Zheng et al. (2004) on the basis of the K band luminosities. In a forthcoming paper (Hammer et al. 2004) we investigate whether LIRG properties could be related to a recent and significant star formation in massive galaxies, including spirals.

Acknowledgements

We are very grateful to Dr. Jarle Brinchmann for the very detailed and valuable comments which have greatly helped us in improving this paper. We thank Dr. Nicolas Gruel for providing us an up-dated version of his software; we are grateful to Dr. Xianzhong Zheng for his comments and suggestions. We thank Dr. David Koch for his help to improve the English language in the text. We also thank Dr. Xiang-Ping Wu for valuable discussions about the cosmological parameters. This work has been supported by grants of the French Ministry of Education and of the K. C. WONG Education Foundation and CNRS.

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Online Material

Table 1: Basic data of the sample galaxies in CFRS 3$^{\rm h}$ field.

Table 2: Basic data of the sample galaxies in UDSR and UDSF fields.

Table 3: Redshift-identification and spectral types of the galaxies in the three fields. "ELGs'' means "Emission Line Galaxies'', "ETGs'' means "Early-Type Galaxies'', "z-poor'' means the redshift can be gotten even the Type is not clear from the spectrum.

Table 4: Measured emission line fluxes (F$_\lambda$) in unit of 10^-17 (ergs cm^-2 s^-1) and the errors in percent for the high-z EL galaxies. "9997'' means the line is blended with strong sky line, "9998'' means there is no corresponding emission line detected at the line position, and "9999'' means the line is shifted outside of the rest-frame wavelength range. "o5'' means [O III]₅₀₀₇, and "o4'' means [O III]₄₉₅₉.

Table 5: Measured emission line fluxes ($F_\lambda$) in unit of 10^-17 (ergs cm^-2 s^-1) and the errors in percent in the low-z EL galaxies in CFRS/UDSR/UDSF fields (C/R/F).

Table 6: The extinction A_V(Balmer), A_V(IR), the SFR $_{{\rm H}\alpha }$, "flux blending'' factor "FB'', the continuum colors, some important emission line ratios, the oxygen abundance in ISM and the spectral types from the diagnostic diagrams ("H'' for H II region galaxies, "L'' for LINERs and "S'' for Seyfert 2) for the sample galaxies. [O II] = [O II] $\lambda$3727, [O III] = [O III] $\lambda$4959 + [O III] $\lambda$5007, and [O III]₅ = [O III] $\lambda$5007. "FB'' (Col. 4) refers to the possible flux blending: "3'' means "possible flux blending'', "1'' means "isolated'', "0'' means "non-ISO detected''. For oxygen abundances (Col. 12), the right up-description "L'' means the values are determined from R₃ parameter. The uncertainties of the line ratios and metallicity are from the uncertainties of extinction and emission line flux measurements. The typical 30% uncertainty of  SFR$_{\rm IR}$ will result in a typical 0.03 dex discrepancy on the derived values.

Table 7: The extinction A_V from Balmer decrement, SFRs, important emission line ratios, oxygen abundance in ISM and continuum colors of the low-z galaxies. "nc'' means no extinction correction for the emission line fluxes. The uncertainties of the line ratios and metallicity are from the uncertainties of extinction and emission line flux measurements.