CO emissions from optically selected galaxies at z  ∼ 0.1–0.2: Tight anti-correlation between molecular gas fraction and 4000 Å break strength

Abstract

We performed ¹²CO(J = 1–0) (hereafter, CO) observations toward 12 normal star-forming galaxies with stellar masses of M_⋆ = 10^10.6–10^11.3 M_⊙ at z = 0.1–0.2 with the 45 m telescope at the Nobeyama Radio Observatory. The samples were selected with D_n(4000), that is, the strength of the 4000 Å break, instead of the commonly used far-infrared (FIR) flux. We successfully detected the CO emissions from eight galaxies with signal-to-noise ratio larger than three, demonstrating the effectiveness of the D_n(4000)-based sample selection. For the first time, we find a tight anti-correlation between D_n(4000) and molecular gas fraction (f_mol) using literature data of nearby galaxies in which the galaxies with more fuel for star formation have younger stellar populations. We find that our CO-detected galaxies at z ∼ 0.1–0.2 also follow the same relation as nearby galaxies. This implies that the galaxies evolve along this D_n(4000)–f_mol relation, and that D_n(4000) seems to be able to be used as a proxy for f_mol, which requires many time-consuming observations. Based on the comparison with the model calculation with a population synthesis code, we find that star formation from metal enriched gas and its quenching in the early time are necessary to reproduce galaxies with large D_n(4000) and non-zero gas fraction.

1 Introduction

The redshift range of z < 1 is the key epoch for revealing the formation and evolution of disk galaxies. Large surveys in the optical and near-infrared (NIR) wavelengths have revealed important observational evidence for the dependence of galaxy evolution on its stellar mass: (1) the bimodal distribution in color with the boundary mass of M_⋆ = 10^10.5 M_⊙ (e.g., Strateva et al. 2001; Kauffmann et al. 2003); (2) galaxies with M_⋆ < 10^10.5 M_⊙ and M_⋆ > 10^10.5 M_⊙ consist of the later- and earlier-type galaxies, respectively (e.g., Conselice 2006); (3) massive galaxies with M_⋆ > 10¹¹ M_⊙ acquired most of their stellar mass before z = 1 while less massive galaxies with M_⋆ < 10¹⁰ M_⊙ acquired most of their stellar mass after z = 1 (e.g., Leitner 2012); (4) for Milky Way-sized galaxies, only galactic disks have evolved in z < 1 and both bulges and disk had been formed by z > 1 (e.g., van Dokkum et al. 2013). These indicate that the redshift range of z < 1 is the growing period for disk galaxies in terms of stellar mass. In addition, local disk galaxies have evolved their galactic disks in this epoch.

Understanding of the stellar component of galaxies at z < 1 has progressed, but there is only a very small number of studies on molecular gas of normal galaxies at this redshift range¹ (Geach et al. 2011; Matsui et al. 2012; Bauermeister et al. 2013). The next most abundant molecule after H₂, carbon monoxide (CO), has been widely utilized to measure molecular gas mass, since the H₂ molecule does not radiate a line emission in a cold environment such as molecular clouds, whose typical temperature is a few tens Kelvin. One of the reasons for the small number of CO observations in z < 1 is the limitation of the atmospheric window. The so-called 3 mm window restricted by the O₂ of atmosphere of the Earth is opened around ∼ 80–115 GHz, which constrains the redshift to z < 0.44 in the case of observations in CO(J = 1–0), whose rest-frame frequency is 115.271 GHz.

The sample selection with far-infrared (FIR) flux also prevents the number of CO observations toward normal galaxies from increasing in z < 1. For the time-consuming CO observations, it is preferred to observe galaxies with the coordinate, spectroscopic redshift, and expected intensity. Although the catalogue of a large optical survey contains data on the coordinates and redshifts of many galaxies (e.g., ∼ 10⁹ for SDSS Date Release 9: Ahn et al. 2012), the number drastically decreases if the candidates are cross-matched with the FIR catalogue. In addition, sample selection based on FIR flux obviously biases to IR-bright objects such as ultra-luminous infrared galaxies (ULIRGs) whose IR luminosities are L_IR > 10¹² L_⊙ (Sanders & Mirabel 1996). The majority of local ULIRGs are reported as mergers with tidal features (Sanders et al. 1988). Therefore, to select normal galaxies, sample selection based on FIR flux is not an optimal choice.

We performed ¹²CO(J = 1–0) (hereafter, CO) observations toward normal galaxies at z ∼ 0.1–0.2 with the 45 m telescope at the Nobeyama Radio Observatory (NRO)² to fill the observational gap in 0.1 < z < 1.0. For the sample selection, we used optical data instead of FIR data to increase the number of candidates and select normal galaxies rather than IR-bright galaxies.

The structure of this paper is as follows: The observational information and data reductions are described in section 2. The CO spectra obtained and the relations between molecular gas fraction and optical indices are shown in section 3. We investigate the relation between the star-formation history and gas fraction with a model calculation in section 4. Finally, we summarize this work in section 5. We adopt H₀ = 71 km s⁻¹, Ω_M = 0.27, and Ω_M = 0.73.

2 Observations

2.1 Sample selection

Sample galaxies were selected by using SDSS DR9 (Ahn et al. 2012), which contains the photometric or spectroscopic data of ∼ 10⁹ objects.³ The basic criteria for the sample selection are as follows: (1) −20° < Dec < +30°, (2) 0.1 < z < 0.23, (3) apparent size: Petrosian radius > 4″, (4) nuclear activity: H ii, (5) morphology: disk galaxy, (6) D_n(4000) < 1.4.

The declination range was determined so that the objects are observable with ALMA as well as with the 45 m telescope at NRO for a further investigation of gas distribution and kinematics, which are important for understanding the detailed physical properties of the gas component in galaxies. We used the criterion of apparent disk size to check the morphology of the disk galaxy (higher likelihood in fitting of galaxy light profile with exponential than de Vaucouleurs, Strateva et al. 2001). Active galactic nuclei (AGN) were excluded from our samples using a set of nebular emission line diagrams [Baldwin, Phillips, and Terlevich (BPT) diagram: Baldwin et al. 1981] to reduce the contamination of light from AGN and estimate star-formation rate (SFR) accurately.

We did not use FIR fluxes but D_n(4000) to select sample galaxies. D_n(4000) is a measure of the strength of the 4000 Å break and is defined as

\begin{equation} D_n(4000) = \frac{(\lambda ^-_2 - \lambda ^-_1) \int ^{\lambda ^+_2}_{\lambda ^+_1} F_\nu \ d\lambda }{(\lambda ^+_2 - \lambda ^+_1) \int ^{\lambda ^-_2}_{\lambda ^-_1} F_\nu \ d\lambda }, \end{equation}

(1)

where |$(\lambda ^-_1,\lambda ^-_2,\lambda ^+_1,\lambda ^+_2)$| = (3850, 3950, 4000, 4100) Å (Balogh et al. 1999). This value allows us to constrain the mean stellar age of a galaxy, where lower D_n(4000) indicates a younger stellar population and vice versa (Kauffmann et al. 2003). If we consider single-burst populations, the 4000 Å break, which is characteristic of cooler stars with types later than about G0, becomes dominant at older ages. This is due to the sudden onset of absorption features bluewards of 4000 Å, produced notably by Ca ii, H, K, and CN lines. Kauffmann et al. (2012) showed that CO-detected galaxies in the COLD GASS project (Saintonge et al. 2011) have lower values of D_n(4000) (< 1.4). We used this empirical criterion for the sample selection instead of the commonly used FIR flux. The SDSS images of the sample galaxies are shown in figure 1 .

Fig. 1.

SDSS optical three-color images of the sample galaxies. The image size is 20″ × 20″. (Color online)

2.2 Observations with the 45 m telescope at NRO

We observed 12 disk galaxies at z ∼ 0.1–0.2 in the CO (J = 1–0) line during the observing periods of 2012/2013 and 2013/2014 winter seasons in Japan. The line frequency was shifted to between 93.638 GHz and 104.749 GHz from the rest frequency of 115.271 GHz according to the redshifts of the sample galaxies. We used a new two-beam, two-polarization, sideband-separating SIS receiver, TZ (Two-beam sideband-separating SIS receiver for Z-machine: Nakajima et al. 2013) and SAM45 (Spectral Analysis Machine for the 45 m telescope), which is a copy of a part of the FX-type correlator for the Atacama Compact Array (ACA). The image rejection ratios (IRRs) of TZ were measured at each observing frequency in every observation. The values of the IRRs were 8–20 dB at the center of the intermediate frequency (IF) throughout the observations. The system noise temperature, T_sys, was typically 150–240 K during our observations. Telescope pointing was checked every 50 min through observing SiO maser sources close to our target galaxies at 43 GHz. We used the data that were observed with pointing accuracy better than 5″. The main beam size, θ_B, is ∼ 18″ around 100 GHz, which corresponds to ∼ 31 kpc at the lowest redshift of the sample galaxies (z = 0.10), and to ∼ 66 kpc at the highest (z = 0.23). All data were calibrated by the standard chopper wheel method, and converted from the antenna temperature |$T^*_{\rm a}$| scale into main-beam brightness temperature by |$T_{\rm {mb}}=T^*_{\rm a}/\eta _{\rm {mb}}$|⁠. The main beam efficiencies, η_mb, in the 2012/2013 and 2013/2014 seasons at the observing frequencies were 0.33–0.35 and 0.37–0.41, respectively.

2.3 Data reduction

Data reduction was performed using the NEWSTAR software, which was developed by NRO based on the Astronomical Image Processing System (AIPS) package. The integration time of each galaxy was typically six hours, summed for both polarizations, and the typical rms noise temperature was in the range of 1–8 mK in the T_mb scale after binning up to 40 km s⁻¹ resolution. Integrated intensity, I_CO, was calculated according to I_CO = ∫T_mb dv. The error in I_CO, ΔI_CO, was estimated as |$T_{{\rm rms}} \sqrt{\Delta V_{\rm e} \Delta v}$|⁠, where T_rms is the rms noise temperature at a velocity resolution of Δv, which is the velocity resolution of the final spectrum. ΔV_e is the full line width within which the integrated intensity was calculated. In the case where the peak temperature of the emission line has a signal-to-noise ratio (S/N) of less than three, the upper limit of 3 ΔI_CO was adopted as I_CO.

CO line luminosity, |$L_{\rm {CO}}^{\prime }$|⁠, was calculated from the integrated intensity and beam solid angle |$\Omega _{\rm b}=\pi \theta _{\rm {B}}^2/4 \ln {2}$| (θ_B in radians) as

\begin{equation} L_{\rm {CO}}^{\prime } = \frac{\Omega _{\rm b} I_{\rm {CO}} D_L^2}{(1+z)^3}\ \ (\rm {K\,km\,s^{-1}\,pc^2}), \end{equation}

(2)

where D_L is the luminosity distance.

The molecular gas mass, M_mol, was calculated with |$L_{\rm CO}^{\prime }$| and a CO-to-H₂ conversion factor, α_CO, as |$M_{\rm mol} = 1.36\ \alpha _{\rm CO} L_{\rm CO}^{\prime }$|⁠, where 1.36 is a factor to account for the contribution of He by mass. We adopted the typical Galactic value of α_CO = 3.2 M_⊙ (K km s⁻¹ pc²)⁻¹ [corresponding to X_CO = 2 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹], which is widely used for star-forming galaxies in the high-z universe (Tacconi et al. 2013) as well as local normal galaxies (Bolatto et al. 2013).

3 Results

3.1 CO spectra

Figure 2 shows the CO spectra obtained, binned with a velocity resolution of 40 km s⁻¹. We successfully detected CO emission from six galaxies with S/N (peak temperature) larger than four, and tentatively from two galaxies with 3 ≤ S/N < 4, while the remaining four galaxies did not show significant CO emission (S/N < 3). This high detection rate (67%) indicates the effectiveness of the sample selection based on D_n(4000). The fitting result with a Gaussian is also plotted with a blue solid line for the emission lines with S/N ≥ 3. I_CO, full width at half maximum (FWHM), molecular gas mass (M_mol), and molecular gas fraction [f_mol, equation (3)] are presented in table 1. I_CO was calculated by summing the intensity within the velocity range colored in red in figure 2. FWHM in this table is estimated with a Gaussian fitting. Although the line profiles of the galactic CO spectra are not well described by a Gaussian as in figure 2, we present here the FWHM for reference; they are not used in the following analysis.

Fig. 2.

CO spectra obtained with the 45 m telescope at NRO. The unit of the vertical axis is antenna temperature T_a* and the velocity resolution is 40 km s⁻¹. I_CO is calculated by summing the intensity within the velocity range colored in red. The fitting results with a Gaussian are also shown in blue lines in the case of S/N ≥ 3. (Color online)

Table 1.

General information and observed results of the sample galaxies.

SDSS name	z	M⋆*	SFR*	Dn(4000)*	ICO	FWHM	Mmol	fmol
		log (M⋆/M⊙)	(M⊙/yr)		(K km s−1)	(km s−1)	(109 M⊙)	(%)
J031648.71+000502.5	0.1315	10.79	10.8	1.27 ± 0.02	1.35 ± 0.18	185 ± 53	11.8 ± 1.5	16.1 ± 1.8
J083045.65+203221.9	0.1021	10.55	16.1	1.27 ± 0.02	1.14 ± 0.14	174 ± 50	6.03 ± 0.77	14.6 ± 1.6
J092126.50+155225.8	0.1097	10.94	18.7	1.24 ± 0.01	1.37 ± 0.24	214 ± 53	8.32 ± 1.47	8.7 ± 1.4
J113445.68+134850.6	0.2310	10.88	21.8	1.25 ± 0.03	< 0.48	—	< 12.8	< 14.4
J124517.89+045235.3	0.1800	10.75	19.0	1.23 ± 0.03	< 0.67	—	< 10.9	< 16.2
J130336.12+140328.2	0.1369	10.92	8.47	1.45 ± 0.03†	< 2.46	—	< 23.3	< 21.7
J141212.60+204703.4	0.1925	11.09	18.0	1.32 ± 0.02	0.73 ± 0.12	209 ± 89	13.5 ± 2.3	9.9 ± 1.5
J143838.54−004710.2	0.1940	10.62	13.4	1.21 ± 0.02	0.76 ± 0.16	127 ± 30	14.4 ± 3.0	25.8 ± 4.0
J144044.31−023623.4	0.1050	10.89	18.9	1.29 ± 0.03	2.45 ± 0.29	159 ± 28	9.18 ± 1.10	10.7 ± 1.1
J151414.57−023351.4	0.1005	10.73	11.0	1.26 ± 0.02	1.75 ± 0.16	240 ± 46	8.93 ± 0.82	14.3 ± 1.1
J154336.33+031834.4	0.1109	10.66	21.0	1.22 ± 0.02	3.28 ± 0.25	287 ± 84	20.4 ± 1.6	30.8 ± 1.6
J235529.78+141132.9	0.2015	11.31	48.4	1.34 ± 0.03	< 0.76	—	< 15.4	< 7.0

*M_⋆, SFR, and D_n(4000) are retrieved from SDSS SkyServer DR10 〈http://skyserver.sdss3.org/dr10/en/〉. M_⋆ is derived by fitting SDSS ugriz photometry to models spanning a wide range of star formation histories. SFR is derived by fitting the fluxes of no less than five emission lines (Brinchmann et al. 2004). The infrared luminosity (L_IR) is inferred from SFR ranges (5.67–32.1) × 10¹⁰ L_⊙ using log  SFR(M_⊙ yr⁻¹) = log  L_IR(erg s⁻¹) −43.41 [equation (12) of Kennicutt & Evans 2012], confirming that they are not ULIRGs.

^†D_n(4000) for this galaxy was listed as 1.30 ± 0.02 in DR9 but was changed to 1.45 ± 0.03 in DR10.

3.2 Star-formation history

The optical spectrum of a galaxy is the sum of the continuum and absorption spectra of its stellar components and nebular emissions from ionized gas. In addition, the stellar spectrum is different according to the stellar type. Stellar types that dominate the galactic optical light change with time and then the characteristic spectral features accordingly change with time (e.g., Fioc & Rocca-Volmerange 1997; Bruzual & Charlot 2003). Therefore, previous studies have investigated the mean stellar ages and star-formation history of galaxies with these characteristic spectral features.

A tight anti-correlation between D_n(4000) and Hδ absorption has been studied to investigate the mean stellar age and star-formation history of galaxies (e.g., Balogh et al. 1999; Kauffmann et al. 2003). Measuring the strength of hydrogen Balmer lines in the galactic spectrum is one of the standard methods to derive luminosity-weighted mean ages from the integrated light of galaxies. Once O- and B-type stars have completed their evolution, Balmer lines become most outstanding in A-type stars and weaken as the stellar population gets older. Kauffmann et al. (2003) investigated the mean stellar age and star-formation history statistically using SDSS data combined with model calculations. They showed that D_n(4000) constrains the mean stellar age of galaxies as described above and that the Balmer absorption-line index, Hδ_A, can constrain the fractional stellar mass formed in starburst events over the past few Gyr.

We retrieved catalogued data of D_n(4000), Hδ equivalent width (EW), stellar mass (M_⋆), SFR, and metallicity [12 + log (O/H)] of nearby galaxies and our observed galaxies from SDSS DR10 (Ahn et al. 2014; Brinchmann et al. 2004; Tremonti et al. 2004). Hδ EW is used as a measure of the strength of Hδ absorption, where a larger Hδ EW indicates stronger absorption. The data for nearby galaxies was retrieved from COLD GASS (Saintonge et al. 2011), which is the largest unbiased CO survey toward nearby galaxies (0.025 < z < 0.05). Mass–metallicity and mass–specific SFR (sSFR = SFR/M_⋆) relations for these samples are shown in figures 3 and 4, respectively. Reference data are also plotted in gray scales, selected based on the redshift criteria, 0.025 < z < 0.050 for the COLD GASS samples and 0.1 < z < 0.2 for our observed galaxies, and the criteria that their stellar mass, SFR, and metallicity are properly calculated (i.e., not −999). In total, 42532 and 51157 galaxies were left as the reference samples. The green solid lines in figures 3 and 4 are empirical relations presented in Tremonti et al. (2004) and Bauermeister et al. (2013), respectively. The green dashed line in figure 4 represents the boundary between star-forming galaxies and starburst galaxies. In figure 3, COLD GASS samples and our observed galaxies are found in the plateau at the high mass range of the mass–metallicity relation. Therefore, the variety in metallicity among these galaxies is expected to be small. In figure 4, our observed galaxies are all star-forming galaxies, whereas the COLD GASS samples include quenched galaxies as well.

Fig. 3.

Mass–metallicity relation of COLD GASS samples (Saintonge et al. 2011, blue open circles) and our observed galaxies at z ∼ 0.1–0.2 (red open circles). An empirical mass–metallicity relation of local galaxies obtained in Tremonti et al. (2004) is shown as a green solid line, as 12 + log (O/H) = −1.492 + 1.847(log M_⋆/M_⊙) − 0.08026(log M_⋆/M_⊙)². The background gray scale shows the distribution of 42532 and 51157 galaxies at 0.025 < z < 0.050 and in 0.1 < z < 0.2 as a reference. (Color online)

Fig. 4.

Mass–sSFR relation of COLD GASS samples (Saintonge et al. 2011, blue open circles) and our observed galaxies at z ∼ 0.1–0.2 (red open circles). An empirical mass–sSFR relation of star-forming galaxies obtained in Bauermeister et al. (2013) is shown as a green solid line, as sSFR_SF(Gyr⁻¹) = 0.07 (1 + z)^3.2 (M_⋆/10¹¹ M_⊙)^{− 0.2}. The green dashed line represents the boundary between star-forming galaxies and starburst galaxies (sSFR_SB > 4 × sSFR_SF). The background gray scale shows the distribution of 42532 and 51157 galaxies at 0.025 < z < 0.050 and in 0.1 < z < 0.2 as a reference. (Color online)

In figure 5, we compare D_n(4000) and Hδ EW of our sample galaxies at z ∼ 0.1–0.2 (filled star) with those of COLD GASS galaxies (open circle), confirming the anti-correlation reported in previous studies (Kauffmann et al. 2003). Moreover, the COLD GASS galaxies are distributed in a sufficiently wide range of D_n(4000) for investigation of various galaxy star-formation histories.

Fig. 5.

Correlation between D_n(4000) and Hδ EW. The observed galaxies at z ∼ 0.1–0.2 and local galaxies (COLD GASS: Saintonge et al. 2011) are shown as filled and open circles, respectively. The color is determined according to f_mol, with f_mol > 15% blue, 10% < f_mol < 15% green, 5% < f_mol < 10% orange, and f_mol < 5% red. (Color online)

3.3 Molecular gas fraction

In figure 5, we change the colors of the symbols according to their molecular gas fractions: f_mol < 5% as red, 5% < f_mol < 10% as orange, 10% < f_mol < 15% as green, and f_mol > 15% as blue. Here, molecular gas fraction is defined as

\begin{equation} f_{\rm mol} (\%) = \frac{M\,_{\rm mol}}{M\,_{\rm mol}+M\,_\star }\times 100. \end{equation}

(3)

It is clearly seen that the COLD GASS galaxies with higher Hδ EW and lower D_n(4000) have higher gas fraction. In other words, more gas-rich galaxies have younger stellar components compared to the gas-poor galaxies. Our sample galaxies at z ∼ 0.1–0.2 seem to follow the same D_n(4000)–Hδ EW–f_mol relation. This clear trend indicates the existence of the relation between D_n(4000) and f_mol.

Figure 6 shows the relation between D_n(4000) and f_mol for our samples with CO detection (S/N > 3) and the COLD GASS galaxies. The symbols are the same as figure 5. As expected, a tight anti-correlation between D_n(4000) and f_mol is seen in this figure and the z ∼ 0.1 galaxies follow the same relation of the local galaxies, suggesting that D_n(4000) could be used as a proxy for f_mol, which requires much telescope time to be measured. Since D_n(4000) is calculated as a ratio of fluxes with 100 Å widths, D_n(4000) is easily measured compared to the normal spectral line indices such as Hδ EW that require higher spectral resolution and the S/N of each spectral channel. Therefore, D_n(4000) might be a powerful tool to investigate the molecular gas fraction of high-z galaxies (see also Tacconi et al. 2013).

Fig. 6.

Correlation between D_n(4000) and f_mol. The symbols are the same as figure 5, but the color is determined according to stellar mass, with M_⋆(M_⊙) > 10¹¹ red, 10^10.75 < M_⋆(M_⊙) < 10¹¹ orange, 10^10.50 < M_⋆(M_⊙) < 10^10.75 green, and M_⋆(M_⊙) < 10^10.5 blue. (Color online)

We checked the effect of the difference in the apparent size of galaxies on the D_n(4000)–f_mol relation. D_n(4000) is calculated with data taken within the 3″ fiber in SDSS. The observed region is different according to the apparent galactic sizes. Therefore, we compare the apparent size of galaxies and D_n(4000) of the COLD GASS sample. Even though there is no tight correlation between the apparent size of galaxy and D_n(4000) (correlation factor of 0.07), galaxies larger than 18″ and smaller than 6″ seem to have higher and lower D_n(4000), respectively. We exclude these larger and smaller samples but confirm the same trend seen in figure 6. Hence we conclude that the tight anti-correlation between D_n(4000) and f_mol is not affected by the difference in the apparent galactic sizes.

The colors of the symbols in figure 6 are determined according to the stellar mass. The anti-correlation between D_n(4000) and f_mol is still seen even if we divide thegalaxies into four categories according to their stellar masses. Kauffmann et al. (2003) reported a bimodal distribution in stellar mass (M_⋆)–D_n(4000) plot of galaxies: the first peak is found at D_n(4000) ∼ 1.3 and the second peak at D_n(4000) ∼ 1.85. They also showed that transition mass range (10¹⁰–10¹¹ M_⊙) has a large dispersion in D_n(4000). Our result suggests that the large dispersion of D_n(4000) seen in M_⋆–D_n(4000) is due to the difference in the molecular gas fraction, i.e., the amount of fuel for the future star formation. It is notable that this result also indicates the stellar mass-dependent star-formation history is attributed to the difference in the amount of molecular gas in galaxies. The stellar mass dependence of f_mol evolution will be investigated in our forthcoming paper (K. Morokuma-Matsui et al. in preparation).

Figure 7 shows the variations of (a) gas phase metallicity 12 + log (O/H), (b) sSFR, and (c) concentration parameter in the D_n(4000)–f_mol plot. The concentration parameter, C, is defined as the ratio C = R90/R50, where R90 and R50 are the radii enclosing 90% and 50% of the Petrosian r-band luminosity (Petrosian 1976) of galaxies (Shimasaku et al. 2001). C is strongly related to the Hubble type, where early- and late-type galaxies have C ≥ 2.6 and C < 2.6, respectively (Strateva et al. 2001). In figure 7a, we can see that 12 + log (O/H) was successfully measured only in star-forming galaxies whose optical spectra contain the strong nebular emissions that are used to calculate 12 + log (O/H). However, the metallicity variation is expected to be small among COLD GASS and our samples, taking into account that these sample galaxies have stellar mass >10¹⁰ M_⊙ and that the plateau of the mass–metallicity relation is located at >10¹⁰ M_⊙ as well. We can see the anti-correlation between sSFR and D_n(4000) in figure 7b, as already reported in Brinchmann et al. (2004). Considering that sSFR is a measure of current versus past star formation, the relation between sSFR and D_n(4000) is not surprising. f_mol is related to sSFR as f_mol = 1/[1 + (t_depsSFR)^{− 1}] (e.g., Tacconi et al. 2013), where t_dep is the depletion timescale of molecular gas by star formation ( = M_mol/SFR). If t_dep can be assumed to be constant, f_mol is a function of sSFR. Therefore the anti-correlation between D_n(4000) and f_mol is also a logical conclusion. Figure 7c shows the morphological dependence on the D_n(4000)–f_mol relation, where late-type galaxies tend to have smaller D_n(4000) and larger f_mol.

Fig. 7.

As figure 6, but with color coding for (a) gas phase metallicity [12 + log (O/H)], (b) specific SFR (sSFR = SFR/M_⋆), and (c) concentration parameter (C = R90/R50). Galaxies without metallicity measurement are shown as gray symbols in (a). (Color online)

4 Discussion

4.1 Comparison with model predictions

In this section, we compare the observed D_n(4000)–f_gas relationship and the evolutionary path in this parameter space predicted by a population synthesis code, PEGASE.2 (hereafter PEGASE; Fioc & Rocca-Volmerange 1997). PEGASE allows us to consistently calculate the chemical and mass evolution (both gas and stellar components) of galaxies. We calculated the evolution of nine different types of galaxy (starburst: Burst; early-type galaxies: E, S0; spiral galaxies: Sa, Sb, Sbc, Sc, Sd; irregular galaxies: Im) according to template evolutionary scenarios for them (Fioc & Rocca-Volmerange 1997, 1999; Le Borgne & Rocca-Volmerange 2002; Tsalmantza et al. 2007). In Fioc and Rocca-Volmerange (1999), the observed spectral energy distributions (SED, from optical to NIR) of ∼ 800 nearby galaxies were used to compute the template SEDs for eight different morphological types (E, S0, Sa, Sb, Sbc, Sc, Sd, Im). The SFRs for the eight types were assumed to be proportional to gas mass as |${\rm SFR}(t)=\frac{1}{\rm p2}M_{\rm gas}(t)^{\rm p1}$|⁠. In addition, the SFR of starburst galaxies was modeled to be instantaneous, i.e., δ(t) (Tsalmantza et al. 2007). Exponential gas infall and galactic outflow were also considered. Galactic outflow was modeled to blow out all the existing gas in a galaxy at the specified time. Rana and Basu (1992) was adopted as the initial mass function (IMF). In this IMF, the slope in massive star range (> 6 M_⊙) is ∼−1.7, which is steeper than the Salpeter IMF (−1.35: Salpeter 1955). The parameters used for the calculation are summarized in tables 2 and 3.

Table 2.

Common parameters for all template galaxies in PEGASE.2 (Fioc & Rocca-Volmerange 1997).

Parameter	Value
SNII ejecta of massive stars	Model B of Woosley and Weaver (1995)
Stellar winds	Yes
Initial mass function	Rana and Basu (1992)
Lower mass	0.09 M⊙
Upper mass	120 M⊙
Fraction of close binary systems	0.05
Initial metallicity	0.00
Metallicity of the in-falling gas	0.00
Consistent evolution of the stellar metallicity	Yes
Mass fraction of substellar objects	0.00
Nebular emission	Yes

Table 3.

PEGASE.2 parameters* for each template galaxy.

Type	p1	p2	Infall	Galactic winds	Extinction	Age
		(Myr/M⊙)	(Myr)	(Gyr)		(Gyr)
Burst	—	—	—	—	Inclination-averaged disk geometry	2
E	1	|$\phantom{00}$|300	300	1	Spheroidal geometry	13
S0	1	|$\phantom{00}$|500	100	5	Spheroidal geometry	13
Sa	1	|$\phantom{0}$|1408.5	2800	—	Inclination-averaged disk geometry	13
Sb	1	|$\phantom{0}$|2500	3500	—	Inclination-averaged disk geometry	13
Sbc	1	|$\phantom{00}$|5714.3	6000	—	Inclination-averaged disk geometry	13
Sc	1	10000	8000	—	Inclination-averaged disk geometry	13
Sd	1	14286	8000	—	Inclination-averaged disk geometry	13
Im	1.5	15385	8000	—	Inclination-averaged disk geometry	9

*Burst model assumes δ(t) for star-formation history; the other models assume SFR as |${\rm SFR}(t)=\frac{1}{\rm p2}M_{\rm gas}(t)^{\rm p1}$|⁠. “Infall” represents the starting time of the gas accretion in Myr. If there are numbers in the “Galactic winds” column, the mass of gas in the galaxy becomes zero at that time. “Age” corresponds to the age of the galaxy at z = 0.

PEGASE does not calculate evolution of molecular gas but total gas. Therefore we only use COLD GASS samples combined with available H i data (Cantinella et al. 2010), since our observed galaxies at z ∼ 0.1–0.2 do not have H i data. The total gas fraction is calculated as

\begin{equation} f_{\rm gas}(\%) = \frac{M_{\,\rm H\,{\scriptstyle\small I}}+M_{\,\rm H_2}}{M_{\,\rm H\,{\scriptstyle\small I}}+M_{\,\rm H_2}+M_{\,\star}}\times 100. \end{equation}

(4)

Figure 8a shows a comparison between the observed D_n(4000)–f_gas and the results of model calculations for each galaxy type. Even though the dispersion of the relation is enlarged, there is the same trend in the D_n(4000)–f_gas relation of COLD GASS samples, such as the one found in figure 6, where galaxies with a higher gas fraction have a lower D_n(4000). We can see that the template models reproduce the observed trend where gas-rich galaxies tend to have lower D_n(4000) in figure 8a. In addition, the later-type galaxies tend to be distributed in the upper-left in this plot (see figure 7c). This qualitative consistency roughly supports the different evolutional scenarios (gas accretion and star-formation timescale) for different types of galaxies proposed in a previous study based on optical SED, where later-type galaxies tend to have longer star-formation timescale normalized by total baryonic mass, and longer infall timescale, i.e., more recent gas accretion (Fioc & Rocca-Volmerange 1999). However, there is a significant and qualitative difference between the observations and the model predictions, especially in D_n(4000). Although the predicted gas fractions in spiral models (Sa–Sd) is almost consistent with the observed values, D_n(4000) is too low compared to the observed values. In early-type galaxy (ETG) models, D_n(4000) evolves to 1.6 but is still lower than the observed values (∼ 1.9) for ETG in figure 8a.

Fig. 8.

Comparison between the observed D_n(4000)–f_mol relation and the results of the PEGASE calculations in the case where the initial mass function is (a) Rana and Basu (1992): template scenario in PEGASE; (b) Salpeter (1955); and (c) Chabrier (2003). Filled circles represent COLD GASS galaxies from which both CO and H i emissions are detected (Cantinella et al. 2010; Saintonge et al. 2011). The color coding of the lines are as follows: Burst in pink, E in light green, S0 in orange, Sa in red, Sb in blue, Sbc in light blue, Sc in brown, Sd in dark brown, and Im in green. From f_gas = 0% to 1%, the plot has a linear scale; from f_gas = 1% to 100%, the plot has a log scale. (Color online)

4.1.1 Dependences on IMFs

We also calculated galaxy evolution with the same parameters, except for the IMF. In the previous studies with PEGASE, Rana and Basu IMF (Rana & Basu 1992) was used to investigate the other parameters of galaxy evolution, such as star-formation law and gas infall timescale, which reproduce the observed optical spectra of each type of galaxy (Fioc & Rocca-Volmerange 1997, 1999; Le Borgne & Rocca-Volmerange 2002; Tsalmantza et al. 2007). Figures 8b and 8c show the evolutionary path on the D_n(4000)–f_gas plane in cases of two more widely used IMFs, Salpeter IMF (Salpeter 1955) and Chabrier IMF (Chabrier 2003), respectively. Although these two models also fail to reproduce the observed relation, there are slight but important differences among the three models. First, gas fractions of spiral models at 13 Gyr with Chabrier IMF are larger than those with Salpeter and Rana and Basu IMFs. In addition, D_n(4000) of ETG models at 13 Gyr with Chabrier IMF are larger than those with Salpeter and Rana and Basu IMFs. These results show that shape of IMF can change the D_n(4000)–f_gas relation. We discuss how the choice of IMF changes the evolution of the D_n(4000)–f_gas relation in the following paragraphs.

First of all, the difference in the shape of IMF changes the return gas mass from massive stars when they die. Compared to less-massive stars, massive stars end their lives instantly from their births. Therefore, an IMF with a larger fraction of massive stars results in a larger gas fraction of the galaxy at the time. The fraction of massive stars is larger in Chabrier IMF than Salpeter and Rana and Basu IMFs. This explains the differences seen in the gas fractions of spiral models at 13 Gyr among the three models.

Chemical evolution is one of the important factors affecting D_n(4000) evolution. Current galactic D_n(4000) is determined by the gas phase metallicity when the major portion of stars were formed, and by the elapsed time since the major star-formation event occurred.

This is because the 4000 Å feature of galactic SED is formed by the metal absorptions of old stellar populations. Poggianti and Barbaro (1997) investigated the behavior of the 4000 Å index for a single star and for a single stellar population (SSP) as a function of age and metallicity. They explicitly showed that the strength of the 4000 Å break becomes larger as the metallicity of the star and SSP gets large. Different D_n(4000) evolutions of galaxies according to metallicity were reported in Kauffmann et al. (2003), where a higher metallicity results in larger D_n(4000) using the population synthesis code of Bruzual and Charlot (2003). Kriek et al. (2011) reported a relation between D_n(4000) and Hα EW and showed that the observed relation is reproduced by the code of Bruzual and Charlot (2003) with a fixed metallicity of solar value through the evolution. Therefore, it is important to enlarge the metallicity ofthe gas from which the stars are formed to increase the D_n(4000) of stars to the observed values.

The difference in the shape of IMF changes the chemical evolution. The gas released from dead stars is metal enriched, thus the IMF with a larger fraction of massive stars results in earlier evolution of metallicity. Figure 9 shows the evolutions of gas phase and stellar metallicities with different IMFs. We can see that the model with Chabrier IMF has metal enriched at an earlier time. Gas phase and stellar metallicities of ETGs respectively become zero and almost constant (but gradually decreasing with time) after the galactic wind blows out all the existing gas.⁴ Thus, the ETG model using the IMF with a larger fraction of massive stars results in larger D_n(4000).

Fig. 9.

Evolution of gas phase (upper panels) and stellar metallicities (lower panels) normalized by the solar value (Z_⊙ = 0.0134: Asplund et al. 2009). The dashed lines indicate 2, 9, and 13 Gyr, which are the ages of each type of galaxy specified in table 3. The color coding is the same as figure 8. (Color online)

Higher metallicity of gas from which a major portion of stars is formed can increase D_n(4000) as described above. However, at the same time, f_gas must go to zero at the early epoch to increase D_n(4000) in the existing condition. In the next subsection, we discuss the possible reasons for the difficulty in reproducing the observed D_n(4000)–f_gas relation quantitatively with the models.

4.2 Possible reasons for the discrepancy between observation and model calculation

In this section, we discuss possible reasons for the difficulty in reproducing the observed D_n(4000)–f_gas relation on both sides of the model calculation and observation.

4.2.1 From the model-calculation side

One possibility is the star-formation model in which stars are formed as long as gas exists regardless of the properties of the gas component. According to the studies on star formation of the local universe, SFR is more closely related with dense molecular gas rather than total gas (e.g., Wong & Blitz 2002; Bigiel et al. 2008). Accreting gas is expected to be diffuse and with high temperature from cosmological simulation of galaxy evolution (Duffy et al. 2012). However, there is no model on transition from diffuse and hot gas to dense and cold gas in PEGASE. Once stars are newly formed, D_n(4000) decreases because the luminosity-weighted SED becomes dominated by young and massive stars, taking into account the mass–luminosity relation of main-sequence stars as L ∝ M^3–4 (e.g., Popper 1980; Andersen 1991; Henry & McCarthy 1993). To increase D_n(4000), it is necessary to form stars from metal-enriched gas and quench the star formation early in the galaxy evolution. Therefore, it is difficult to reproduce galaxies with larger D_n(4000) and non-zero gas fraction with the existing conditions in the model.

Morphological quenching (MQ) is an important process that can quench star formation even with a gas component, but which is not implemented in PEGASE. Martig et al. (2009) showed that once the central bulge becomes massive enough to stabilize the galactic disk against local gravitational instability, star-formation quenching occurs. Central concentration of ETGs leads to a large epicyclic frequency κ, which is linked to the depth of the gravitational potential, and results in large Toomre's Q (Toomre 1964). As a result, the star formation in ETGs is quenched without removal of the gas component. We show the concentration parameters of the COLD GASS sample in figure 7c. We can see that galaxies distributed in the lower-right corner of figure 7 mainly consist of ETGs. Therefore, our results suggest that they have large D_n(4000) and non-zero gas fraction because MQ may work in these systems.

Re-accretion of the enriched gas in the halo is also an important process for galaxy evolution, especially in terms of chemical evolution, which is not modeled in PEGASE. Shen et al. (2012) investigated the metal-enriched circumgalactic medium (CGM) of a massive galaxy at z = 3 (M_⋆ = 2.1 × 10¹⁰ M_⊙). They listed three sources of heavy elements in CGM in order of the fraction: (1) galactic wind from the main host, (2) “satellite progenitors” accreted by the main host before z = 3, and (3) “nearby dwarfs” orbiting outside the virial radius. According to their result, the metallicity of accreting gas increases with time as a consequence of re-accretion of the metal-enriched gas in a “halo fountain” (Oppenheimer et al. 2010). Re-accretion of the enriched gas is likely to promote chemical evolution and increase the D_n(4000) of modeled spiral galaxies. In addition, since re-accretion is reported to be promoted more in more massive systems due to the deceleration by the interaction with dense halo gas (Oppenheimer & Davé 2008; Oppenheimer et al. 2010), the larger discrepancy in D_n(4000) of more massive galaxies may be compensated.

4.2.2 From the observation side

The result of the PEGASE calculation is a galactic D_n(4000)–f_gas relation, since PEGASE assumes that a galaxy is a one-zone system. However, the gas mass of galaxies by used in this study is a total mass, and D_n(4000) is calculated using data obtained within the SDSS 3″ fiber. Therefore it is not clear whether the obtained D_n(4000)–f_gas relation is a relation between galactic star-formation history and galactic gas fraction or the star-formation history of the central bulge and galactic gas fraction. Also, the much larger D_n(4000) obtained through observation than those from model prediction may be partly attributed to this situation, since most galaxies have metallicity gradients (e.g., Sanchez et al. 2014). Considering that most disk galaxies have an exponential profile of molecular gas distribution and most ETGs have molecular gas distribution with a relatively small extent (e.g., Davis et al. 2013; Alatalo et al. 2013), the contribution of CO emission from the central part to the total CO flux is large in both cases. Thus, it may be a relation indicating the evolution of the central bulge. To understand the physical background of this relation, it is important to compare spatially disaggregated D_n(4000) and gas fraction.

The universality of this relation should be investigated with higher-z galaxies. Recent CO observations towards galaxies at z = 1–2 revealed extremely high molecular gas fractions (∼ 50%) in those systems (e.g., Tacconi et al. 2013). The measurement of D_n(4000) of those systems allows us to enlarge the f_mol as well as the redshift ranges at the same time. Although the reported D_n(4000)–f_mol relation in this study has already given the important suggestion, once the observational assessments for the tasks described above are completed, this relation would be one of the strict observational constraints on the models for galaxy formation and evolution.

5 Summary

We observed 12 normal galaxies at z ∼ 0.1–0.2 with the 45 m telescope at NRO to measure the molecular gas mass and investigate the relation between star-formation history and molecular gas fraction f_mol. The sample galaxies were selected with D_n(4000) instead of the widely used FIR flux. The main results obtained in this paper are as follows:

• We detected the CO emissions from six galaxies with S/N > 4 and two galaxies with 3 < S/N < 4 out of 12 samples, and have shown the validity of the sample selection based on D_n(4000).

• Using the literature data of nearby galaxies (Saintonge et al. 2011), we found a tight anti-correlation between D_n(4000) and f_mol indicating that more gas-rich galaxies tend to have younger stellar populations than gas-poor galaxies for the first time.

• We have shown that our sample galaxies at z ∼ 0.1–0.2 follow the same D_n(4000) relation as the nearby galaxies. This suggests that galaxies might evolve along this relation and that D_n(4000) might be used as a proxy for f_mol, which requires much telescope time to be measured.

• We calculated the galaxy evolution with a population synthesis code PEGASE (Fioc & Rocca-Volmerange 1997) to investigate the observed D_n(4000)–f_gas relation. We calculated the total gas fraction f_gas with literature data of nearby galaxies and compared it with the model calculations. As a result, any template scenarios for different morphological types which have been constructed so as to reproduce optical SED, cannot reproduce the observed relation.

• Our results suggest that star formation from metal-enriched gas and star formation quenching in the early time are necessary to form galaxies with the observed large D_n(4000) and non-zero gas fraction.

We would like to thank an anonymous referee for very productive comments. KMM thanks Kouji Ohta, Tadayuki Kodama, Takashi Okamoto, Yoichi Tamura, Shinya Komugi, Nick Scoville, Tomoki Morokuma, and all members of NRO for their support and fruitful discussions.

PEGASE calculations were carried out on computers at the Center for Computational Astrophysics, National Astronomical Observatory of Japan. JB was supported by JSPS Grant-in-Aid for Young Scientists (B) Grand Number 26800099.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is 〈http://www.sdss3.org/〉. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

1

There are studies on ultra-luminous infrared galaxies in this redshift range (Solomon et al. 1997; Chung et al. 2009; Combes et al. 2013), showing that both the molecular gas fraction and star-formation efficiency play an important role in cosmic star-formation rate evolution (Combes et al. 2013). However, most of them have signs of merging (e.g., a close pair of galaxies and tidal features), thus they are not expected to be normal galaxies.

2

Nobeyama Radio Observatory is a branch of the National Astronomical Observatory of Japan, National Institutes of Natural Sciences.

3

〈http://skyserver.sdss3.org/dr9/en/〉.

4

The gradual decrease of stellar metallicity in the ETG models in figure 9 is likely to be due to a small amount of accretion of metal-zero gas.