THE STAR FORMATION MASS SEQUENCE OUT TO z = 2.5

Galaxies show a strong correlation between their star formation rate (SFR) and stellar mass (M_⋆) from z = 0 to the earliest observed epoch, z = 7 (e.g., Brinchmann et al. 2004; Noeske et al. 2007; Elbaz et al. 2007; Daddi et al. 2007; Pannella et al. 2009; Magdis et al. 2010; González et al. 2010). On average, galaxies on this "star formation sequence" were forming stars at much higher rates in the distant universe relative to today (e.g., Madau et al. 1996); for a given mass, the SFR has been decreasing at a steady rate by a factor of ∼30 from z ∼ 2 to z = 0 (Daddi et al. 2007), although it appears to be roughly constant from z ∼ 7 to z ∼ 2 (González et al. 2010). The star formation sequence is observed to have a roughly constant scatter out to z ∼ 1 (e.g., Noeske et al. 2007).

Generally, star formation is thought to be regulated by the balance between the rate at which cold gas is accreted onto the galaxy and feedback (e.g., Dutton et al. 2010; Bouché et al. 2010), whereas the relation between gas surface density and SFR surface density does not appear to change, at least out to the highest redshifts accessible to molecular gas studies (Tacconi et al. 2010; Daddi et al. 2010; Genzel et al. 2010). The star formation sequence may be a natural consequence of "cold mode accretion" (e.g., Birnboim & Dekel 2003), as the SFR is approximately a steady function of time and yields a relatively tight relationship between SFR and M_⋆. Feedback may effect the slope of the star formation sequence, whereas the evolution of the normalization is thought to result from evolution in gas densities with redshift. The scatter in the star formation sequence may reflect variations in the gas accretion history and is predicted to be insensitive to stellar mass, redshift, and feedback efficiencies (Dutton et al. 2010).

With a wealth of multi-wavelength data, including ultraviolet (UV) to near-infrared (NIR) photometric surveys, Hα spectroscopic surveys, and mid- to far-infrared photometry from Spitzer/MIPS at 24 μm, Herschel/PACS 70–160 μm, and Herschel/SPIRE 250–500 μm, much work has been done to calibrate different SFR indicators over broad redshift ranges (e.g., Elbaz et al. 2010; Nordon et al. 2010; Hwang et al. 2010; Muzzin et al. 2010; Wuyts et al. 2011a, 2011b; Reddy et al. 2012). Uncertainties in the star formation sequence may now be dominated by selection effects and observational biases. Selection effects can be important, as it is well known that a significant fraction of galaxies have very low SFRs, well below the star formation sequence. Furthermore, there exists a population of dusty star-forming galaxies with similar rest-frame optical colors to these quiescent galaxies (e.g., Brammer et al. 2011). The selection of star-forming galaxies and the treatment of quiescent galaxies can influence the measured relation and its scatter.

With the accurate photometric redshifts and photometry of the NEWFIRM Medium-Band Survey (NMBS; Whitaker et al. 2011), we can now extend studies of the star formation sequence out to z = 2.5 for the largest mass-complete sample of galaxies to date. In this Letter, we study the evolution of the log(SFR)–log(M_⋆) relation from 0 < z < 2.5, selecting star-forming galaxies in a way that is independent from the SFR indicator. We show for the first time that star-forming galaxies with different colors and L_IR/L_UV ratios occupy different regions of the log(SFR)–log(M_⋆) plane.

We assume a ΛCDM cosmology with Ω_M = 0.3, Ω_Λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹ throughout the Letter.

Our sample of 28,701 galaxies is drawn from the NMBS (Whitaker et al. 2011). This survey employs a new technique of using five medium-bandwidth NIR filters to sample the Balmer/4000 Å break from 1.5 < z < 3.5 at a higher resolution than the standard broadband NIR filters. The combination of the medium-band NIR images with deep optical medium and broadband photometry and Infrared Array Camera imaging over 0.4 deg² in the AEGIS and COSMOS extragalactic fields results in accurate photometric redshifts (Δz/(1 + z) ≲ 2%), rest-frame colors, and stellar population parameters. The SFRs presented in this Letter are based in part on Spitzer–MIPS fluxes at 24 μm that are derived from the S-COSMOS (Sanders et al. 2007) and FIDEL⁴ surveys. A comprehensive overview of the survey can be found in Whitaker et al. (2011). The stellar masses used in this work are derived using FAST (Kriek et al. 2009), with Bruzual & Charlot (2003) models that assume a Chabrier (2003) initial mass function (IMF), solar metallicity, exponentially declining star formation histories, and dust extinction following the Calzetti et al. (2000) extinction law.

The SFRs are determined by adding the UV and IR emission, SFR_{UV + IR} = 0.98 × 10⁻¹⁰(L_IR + 3.3 L₂₈₀₀) (Kennicutt 1998), adapted for the Kroupa IMF by Franx et al. (2008), accounting for the unobscured and obscured star formation, respectively. We adopt a luminosity-independent conversion from the observed 24 μm flux to the total IR luminosity (L_IR ≡ L(8–1000 μm)), based on a single template that is the log average of Dale & Helou (2002) templates with 1 < α < 2.5, following Wuyts et al. (2008), Franx et al. (2008), and Muzzin et al. (2010), and in good median agreement with recent Herschel/PACS measurements by Wuyts et al. (2011a). The luminosities at 2800 Å (L₂₈₀₀) are derived directly from the best-fit template to the observed photometry, using the same methodology as the rest-frame colors (see Brammer et al. 2011).

With accurate rest-frame colors, it is possible to isolate "clean" samples of star-forming and quiescent galaxies using two rest-frame colors out to high redshifts (Labbé et al. 2005; Wuyts et al. 2007; Williams et al. 2009; Ilbert et al. 2009; Brammer et al. 2011; Whitaker et al. 2011). The quiescent galaxies have strong Balmer/4000 Å breaks, characterized by red U − V colors and bluer U − V colors relative to dusty star-forming galaxies at the same U − V color.

Whitaker et al. (2011) demonstrated that there is a clear delineation between star-forming and quiescent galaxies with the NMBS data set. Using the criteria U − V > 0.8 × (V − J) + 0.7, U − V > 1.3, and V − J < 1.5, 5885 quiescent galaxies are identified and they are excluded from the bulk of this analysis. The sample of 22,816 star-forming galaxies at 0 < z < 2.5 is selected independent of the SFR indicator and stellar population synthesis model parameters, enabling an unbiased measurement of the star formation sequence.

Complementary to many previous studies, Figure 1 shows the star formation sequence, log(M_⋆)–log(SFR), in five redshift bins out to z = 2.5. The gray scale represents the density of points for star-forming galaxies selected in Section 2, with the running median and biweight scatter color-coded by redshift. The mass-completeness limits are estimated from the 90% point-source completeness limits derived from the unmasked simulations by Whitaker et al. (2011). The SFR completeness limits correspond to the 3σ 24 μm detection limit (17.6 μJy) at the highest redshift of each bin. 15,502 galaxies at 0 < z < 2.5 are significantly detected at 24 μm (>3σ), a factor of 12 larger than the Wuyts et al. (2011a) sample. All 24 μm detections <1σ are replaced with the 1σ upper limit, resulting in a flattened tail of the log(SFR)–log(M_⋆) relation at low M_⋆, where the samples are incomplete.

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3.1. Quantifying the Star Formation Sequence

The running medians and dispersions are measured for all star-forming galaxies, and those above the mass and SFR completeness limits are indicated with filled symbols in Figure 1 and fit with a power law,

$$\begin{equation} \log (\mathrm{SFR})=\alpha (z)(\log {M}_{\star }-10.5)+\beta (z). \end{equation} \tag{ 1 }$$

We find that the slope α gradually evolves with redshift, while the normalization β has a stronger evolution:

$$\begin{eqnarray} \alpha (z) &=& 0.70-0.13z \hspace{40pt} \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} \beta (z) &=& 0.38+1.14z-0.19z^2. \end{eqnarray} \tag{ 3 }$$

Previous studies have found hints of a similar trend for the slope to flatten toward z ∼ 1 or high M_⋆ (e.g., Noeske et al. 2007; Karim et al. 2011; Wuyts et al. 2012). Although the slope is consistent with a gradual evolution toward shallower values, we note that the highest redshift bins are only for galaxies with stellar masses  >  10^10.7 M_☉, due to incompleteness at lower masses. We will address this issue in Section 3.2.

The average SFR of star-forming galaxies steeply declines from z = 2.5 to the present day, changing by roughly 0.2 dex Gyr⁻¹, confirming the results of previous studies (e.g., Noeske et al. 2007; Elbaz et al. 2007, etc.). The normalization β decreases by a factor of four from z = 2 to z = 0, while the global SFR density has decreased a factor of six over the same interval (Hopkins & Beacom 2006). We note that β(z) is the evolution in the specific SFR (sSFR ≡ SFR/M_⋆) at log(M_⋆) = 10.5 (consistent with Elbaz et al. 2007; Pannella et al. 2009; Damen et al. 2009; Magdis et al. 2010, etc).

Interestingly, the scatter in the star formation sequence is observed to be roughly constant at ∼0.34 dex, both with redshift and stellar mass, consistent with the idea that it may reflect variations in the gas accretion history. The observed scatter agrees with results from Noeske et al. (2007) at z < 1, although we note that there are hints of a lower scatter for the most massive galaxies in our highest redshift bin. We find that these results are robust against changes in sample selection. If we include all galaxies (quiescent and star forming) with >1σ detections, the scatter increases by 0.07–0.11 dex.

3.2. The Effects of Dust Attenuation

Previous studies have noted that dust attenuation is a strong function of stellar mass (e.g., Reddy et al. 2006, 2010; Pannella et al. 2009; Wuyts et al. 2011b), where the most massive galaxies are more highly obscured. We find a similar trend with the NMBS data in Figure 2; higher mass galaxies have larger L_IR/L_UV ratios. The SFRs derived from L₂₈₀₀ alone exhibit a flat trend with stellar mass (or even hints of less UV flux toward higher M_⋆), whereas SFRs derived from L_IR show a strong trend with M_⋆. The star formation–mass relation only materializes when dust attenuation is properly taken into account.

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From Figure 2, we also see that the average rest-frame U − V color of star-forming galaxies becomes redder with increasing stellar mass (and increasing L_IR/L_UV). The red colors may be attributed to dust, although older stellar populations have similarly red colors. It is notoriously difficult to differentiate between subtle age and dust effects with a single color alone. However, because L_IR is independent of the rest-frame color measurements, we can isolate galaxies with red colors predominantly due to dust.

The strong dependence of L_IR/L_UV and the rest-frame U − V color on stellar mass raises the question of whether the star formation sequence can be "resolved" into distinct populations of star-forming galaxies. We first consider the following two samples at 1.0 < z < 1.5 (where we have a large number of galaxies at the high-mass end while maintaining a modest mass-completeness level): (1) blue star-forming galaxies with little dust obscuration (U − V < 1.3, log(L_IR/L_UV) < 1.5), and (2) dusty red star-forming galaxies (U − V > 1.3, log(L_IR/L_UV) > 1.5).

When we select blue star-forming galaxies, similar to Peng et al. (2010), the slope of the star formation sequence is close to unity and the observed scatter decreases to 0.25 dex (left panel, Figure 3). However, dusty red star-forming galaxies are an increasing fraction of the massive galaxy population toward z = 2 (e.g., Whitaker et al. 2010). The middle panel of Figure 3 shows the star formation sequence for galaxies with red colors that we attribute to dust due to the high L_IR/L_UV ratios. This population of galaxies has a similarly small observed scatter of 0.25 dex, but a shallower slope of ∼0.8.

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While it has been shown that higher mass galaxies tend to have lower sSFRs (e.g., Zheng et al. 2007), previous studies have not always distinguished between actively star-forming and passive stellar populations. Here, we find that among actively star-forming galaxies, the star formation sequence for red dusty (high-mass) galaxies has a shallower slope, as compared to that for blue low-dust (low-mass) galaxies. This result implies that both massive quiescent and star-forming galaxies have lower sSFRs and hence older ages.

3.3. What Causes Galaxies to be Outliers on the Star Formation Sequence?

We find that star-forming galaxies occupy a tight sequence in the SFR–M_⋆ plane, confirming many previous studies (e.g., Elbaz et al. 2007; Pannella et al. 2009; Wuyts et al. 2011a). We show that the star formation sequence is not linear, with SFR∝M^0.6_⋆ and a constant observed scatter of 0.34 dex. If we only select blue galaxies, however, we do find a linear relation, similar to Peng et al. (2010). This selection removes red, dusty star-forming galaxies at the high-mass end, which have a shallower slope. We note that Pannella et al. (2009) also find a slope close to unity at z ∼ 2. We find a shallower slope when we apply the same "BzK" selection criteria; the discrepancy may be explained by the different SFR measurement methods. Here, we are able to analyze the star formation sequence with a mass-complete sample of galaxies.

By accounting for the ratio of L_IR/L_UV (a proxy for dust) and the rest-frame U − V colors of star-forming galaxies, we develop a simple picture that describes how galaxies populate the log(SFR)–log(M_⋆) plane. We have identified four distinct populations: (1) quiescent galaxies (28% for log (M_⋆) > 10 at 1.0 < z < 1.5), (2) actively star-forming galaxies with "normal" colors and associated L_IR/L_UV ratios (54%), (3) red star-forming galaxies with low L_IR/L_UV ratios and low sSFRs (11%), and (4) blue star-forming galaxies with high L_IR/L_UV ratios and sSFRs (7%).

Among the galaxies that populate the "normal" star formation sequence, we see a continuous sequence of increasing levels of dust attenuation with increasing stellar mass and a decreasing slope in the log(SFR)–log(M_⋆) relation, implying decreasing sSFRs with stellar mass (Figure 4). Wuyts et al. (2011b) observed similar trends across the SFR–M_⋆ plane, where L_IR/L_UV increases along the sequence and at a given M_⋆ toward high SFRs. The dependence of sSFR on M_⋆ appears to introduce a slight curvature to the star formation sequence, consistent with previous sSFR studies (e.g., Gilbank et al. 2011). A power-law fit to all star-forming populations results in an observed scatter that is 0.09 dex larger than that of the "normal" sequence, with a significantly shallower slope of ∼0.6. We note that some models predict slopes that are too steep compared to the observations (e.g., Bouché et al. 2010; Dutton et al. 2010); it is possible that discrepancies between the inferred SFRs may be alleviated if the stellar IMF is systematically weighted toward more high-mass star formation in rapidly star-forming galaxies (Narayanan & Davé 2012).

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The observed scatter of the "normal" star formation sequence is 0.25 dex, which includes contributions from both random and systematic errors. We estimate the average random scatter by perturbing the 24 μm photometry and photometric redshifts within the 1σ error bars for 100 realizations, finding a small contribution of ∼0.05 dex. Additionally, about 0.08 dex scatter is introduced because the average SFR evolves within the redshift bin. A significant contribution to the observed scatter might also be the conversion from 24 μm flux to L_IR, which may be as high as 0.25 dex (Wuyts et al. 2011a). It is unknown, however, whether this scatter correlates with the sSFR as derived from 24 μm imaging.

To bolster the cartoon view presented in Figure 4, we additionally consider the composite SEDs of normal star-forming galaxies in bins of stellar mass. Due to the increasing levels of dust attenuation, we see a clear evolution of the composite SEDs in Figure 5. On average, the most massive star-forming galaxies have characteristically dusty spectral shapes, with a 2175 Å dust feature evident, whereas lower stellar mass galaxies have decreasing amounts of dust obscuration. We note that we see similar trends at higher and lower redshifts, but are unable to make robust statements due to incompleteness.

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Few dusty, blue galaxies appear to be associated with X-ray sources. Remarkably, we see that the spectral shapes of these galaxies are very similar, irrespective of stellar mass (upper right panel, Figure 5). This suggests that the same physical process is dominating the stellar light.

While 28% of galaxies with log(M_⋆) > 10 have already quenched their star formation at 1 < z < 1.5, we find that 11% may be in the process of shutting down star formation. These galaxies have red colors and low L_IR/L_UV ratios, occupying the lower envelope of the star formation sequence. We compare the composite SEDs of these red, low-dust star-forming galaxies to that of quiescent galaxies at the same stellar mass and redshift (solid lines in bottom right panel, Figure 5). These galaxies have similar rest-frame V − J colors to quiescent galaxies, but somewhat bluer rest-frame U − V colors, consistent with the idea that they are in the process of shutting down star formation and may soon migrate to the red sequence.

By studying four distinct populations of galaxies selected from the NMBS, we have demonstrated that quantifying the observed properties of the star formation sequence and how the sequence evolves with time requires a thorough understanding of the selection techniques and biases. A consequence of the strong dependence of dust attenuation on stellar mass is that measurements of the star formation sequence will depend critically on the sample selection. The gradual evolution we measure of the slope of the star formation sequence toward shallower values at high-z is driven by the combination of the curvature of the "normal" star formation sequence and the evolution of the mass-completeness limits with redshift. An in-depth analysis of the physical properties of these galaxies and comparisons between the observations and models will help constrain the physical mechanism driving this potential curvature and the outliers from the star formation sequence.

We thank the anonymous referee for useful comments. We thank the NMBS collaboration for their contribution to this work, and the COSMOS and AEGIS teams for the release of high-quality multi-wavelength data sets to the community. Support from NSF Grant AST-0807974 and NASA Grant NNX11AB08G is gratefully acknowledged.

Facility: Mayall (NEWFIRM) - Kitt Peak National Observatory's 4 meter Mayall Telescope