THE OPACITY OF GALACTIC DISKS AT z ∼ 0.7

After a long-lasting controversy on whether galactic disks are optically thick or thin (e.g., Disney et al. 1989; Burstein et al. 1991), a consensus emerged during the last decade that disks in the local universe (1) behave like optically thick systems as far as integrated photometric properties in the ultraviolet (UV) and visual are concerned (e.g., Shao et al. 2007; Driver et al. 2007; Maller et al. 2009), while at the same time (2) peripheral and inter-arm regions in spiral galaxies are more transparent than spiral arms or the core of the disk (e.g., White et al. 2000; Holwerda et al. 2005, and references therein).

Beyond the nearby universe, observational constraints on the extinction in disk galaxies have been hard to obtain (see, e.g., the review by Calzetti 2001) as (1) some of the locally employed measurement techniques can only be gainfully applied over a limited redshift range (e.g., Holwerda et al. 2007); (2) the spectral energy distribution (SED) of distant galaxies between the UV and infrared (IR) is often only partially sampled; and (3) statistical tests—such as attenuation–inclination relations—could only be applied to fairly small samples (e.g., Lilly et al. 1998).

Pan-chromatic wide field surveys like COSMOS in principle provide both the necessary multi-wavelength information, as well as the means to select a statistically significant and (morphologically) well-defined sample of disk galaxies thanks to high-resolution Hubble Space Telescope (HST) imaging. Here we perform a comparative study of the surface brightness–inclination relation in a sample of local and distant (z ∼ 0.7) pure disk galaxies with the aim of testing if their average opacity has evolved in the past 6.5 Gyr. Our galaxy samples are described in Section 2, followed by results (Section 3) and conclusions (Section 4).

We adopt a concordance cosmology with Ω_m = 0.25, Ω_Λ + Ω_m = 1, and H₀ = 70 km s⁻¹ Mpc⁻¹. Magnitudes are given in the AB system of Oke (1974).

2.1. Strategy

2.2. COSMOS Disks at 0.6 < z < 0.8

2.3. SDSS Reference Sample

In the following, we consider the surface brightness–inclination relation in the rest-frame B band. This has the twofold advantage of bordering on the SED region (g band) sampled by our SDSS and COSMOS imaging, and of providing results that are readily comparable with predictions and previous findings in the literature.

The average surface brightness is obtained by distributing half (hence the second term in Equation (1)) of the total I-band flux over an ellipse with a semi-major axis R_1/2 (in arcseconds). The semi-minor axis follows from the Gim2d value of the axis ratio:

$$\begin{eqnarray} \mu (B) &=& I+2.5\,\hbox{log}\left(2\right)+2.5\,\hbox{log}\left(\pi R_{1/2}^2\right)+2.5\,\hbox{log}\left({b/a}\right) \nonumber \\ &&-10\,\hbox{log}\left(1+z\right)-K_{F814W,B}(z). \end{eqnarray} \tag{ 1 }$$

The K-correction K_F814W,B(z) is determined using the best-fit SED in the template library of the ZEBRA package (Feldmann et al. 2006). The relation between μ(B) and that of the system when viewed face-on (μ^fo) is often parameterized as

$$\begin{equation} \mu (B) \equiv \mu ({\rm cos}(i))= \mu ^{\rm fo} + C\times 2.5\,{\rm log}({\rm cos}(i)). \end{equation} \tag{ 2 }$$

Here i is the inclination angle (i = 0 for face-on and π/2 for edge-on systems). The amount of attenuation is parameterized by the opacity constant C which ranges from unity for transparent disks to zero for opaque disks. For a non-zero C, the apparent surface brightness of an inclined disk is thus always more intense than in the face-on object.

The distribution of axis ratios b/a can be an indication of the opacity of disks (e.g., Jones et al. 1996). In Figure 1, we plot the axis ratios for our COSMOS disks (right ) and the SDSS_{z = 0.7} sample (left ). Instances of b/a ∼ 1 and 0 are rare due to intrinsic disk ellipticity (Ryden 2004) and the finite thickness of edge-on systems. A one-sided Kolmogorov–Smirnov (K–S) test indicates that—within the errors shown—there is a non-negligible probability that the measured axis ratios in the entire samples are drawn from a flat distribution (SDSS_{z = 0.7}: p = 0.19; COSMOS: p = 0.16), as illustrated by the cumulative distribution function (CDF) crossing both panels on an approximate diagonal. Figure 1 also shows the histograms (in gray) of b/a for the subset of disks with physical half-light radii r_1/2 ⩾ 5 kpc. We introduce this restriction in order to obtain a complete¹² sample of disks for the final analysis. While the axis ratio distribution of large SDSS_{z = 0.7} disks remains flat (K–S probability p = 0.99), that of the corresponding COSMOS population is skewed toward elongated objects (p < 10⁻⁵ for the distribution being flat). The different behavior hints at opacity variations which we quantify in the following paragraph.

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Axis ratios are related to inclination (see also the scale along the upper edge of Figure 1) by the Hubble (1926) formula:

$$\begin{equation} {\rm cos}^2(i) = \frac{{(b/a)^2}-({b/a})^2_{\rm min}}{1-({b/a})^2_{\rm min}}, \end{equation} \tag{ 3 }$$

with (b/a)_min = 0.15, in keeping with measurements of the minimal flattening in late-type spirals (e.g., Guthrie 1992; Yuan & Zhu 2004).

We present the surface brightness–inclination relation for large SDSS_{z = 0.7} and COSMOS disks (51 and 611 objects, respectively) in Figure 2. The error bars on the median surface brightness values in bins of increasing inclination (see also Table 1) span the 95% confidence region, estimated with N_cos(i)× 100 bootstrap realizations (N_cos(i) is the number of disks in a given bin of inclination). The uncertainties on the COSMOS median are significantly smaller, in agreement with the expectation that they should scale roughly as ${1/\sqrt{N_{{\rm cos}(i)}}}$.

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Table 1. Median Values of Inclination (Column 2) and of the Associated Average Rest-frame B-band Surface Brightness (Column 3; cf. also Figure 2)^a

Sample/Redshift	$1-\overline{{\rm cos}(i)}$	$\overline{\mu }(B)$
SDSSz = 0.7	0.148+0.062−0.018	22.237+0.082−0.511
	0.310+0.058−0.036	21.866+0.269−0.187
	0.551+0.034−0.037	21.728+0.213−0.307
	0.793+0.058−0.018	21.432+0.393−0.165
COSMOS	0.212+0.021−0.019	21.281+0.138−0.142
(z ∼ 0.7)	0.438+0.018−0.015	21.110+0.054−0.078
	0.603+0.013−0.018	21.031+0.073−0.087
	0.746+0.007−0.009	21.042+0.082−0.070
	0.883+0.017−0.018	21.109+0.089−0.102

Note. ^aErrors span the 95% confidence interval.

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The dashed blue line in Figure 2 (left ) marks the surface brightness–inclination relation for a B-band central face-on optical depth of τ^fo_B = 3.8, the average opacity of nearby disks recently determined by Driver et al. (2007). The plotted line is taken from the predictions¹³ of Möllenhoff et al. (2006), based on radiative transfer models of stable local disks (Popescu et al. 2000; Tuffs et al. 2004). The good agreement with our measurements demonstrates that we correctly recover the attenuation properties of local disks even when they are redshifted to z ∼ 0.7.

We now determine the average correction between face-on and observed surface brightness. At first sight, Figure 2 might suggest that—within uncertainties—the surface brightness–inclination relation is flat both for SDSS_{z = 0.7} and COSMOS disks (see the dotted horizontal line marking the global surface brightness average). However, as we will now show, the opacity constants describing local and z ∼ 0.7 disks turn out to be significantly different.

To properly account for strongly asymmetric error bars (see Figure 2), we interpret the distribution of bootstrapped medians as a probability distribution and accordingly draw pairs of medians ($\overline{{\rm cos}(i)}$, $\overline{\mu }(B)$) in all bins of inclination. We then fit Equation (2) to each of the sets of resampled medians and subsequently locate the peak of the resulting distributions of the free parameters C and μ^fo.

Figure 3 (main window) shows the best-fitting parameter pairs (〈μ^fo(B)〉, C) from 10,000 realizations. The cores of the point clouds are highlighted with (smoothed) equal density contours that enclose 68%, 90%, and 95% of the points. By projecting the scatter plots along the vertical and horizontal axes, we obtain 95% confidence intervals¹⁴ for the free parameters 〈μ^fo(B)〉 and C for the local and high-z disk samples (Table 2). The average surface brightness of face-on disks, 〈μ^fo(B)〉, increases by ∼1 mag between z ∼ 0 and 0.7 (see also Lilly et al. 1998; Barden et al. 2005). For the opacity constant we find C(z ∼ 0.7) ∈ [0.18, 0.62] and C(z ∼ 0) ∈ [0.01, 0.13], and for the most probable values¹⁵ C(z ∼ 0) = 0.47 and C(z ∼ 0.7) = 0.07. The corresponding surface brightness–inclination dependence (Equation (2)) is indicated in red in Figure 2.

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We note that by using the "unbrightened" sample of Kampczyk et al. (2007; see Section 2.3) only the most luminous local disks satisfy the selection criterion I ⩽ 22.5 when redshifted to z ∼ 0.7. The general luminosity evolution of the disk galaxy population (e.g., Scarlata et al. 2007) implies that only the brightest COSMOS disks at 0.6 < z < 0.8 have masses similar to those of the SDSS_{z = 0.7} sample. As the degree of extinction depends on the amount of attenuating material (e.g., Masters et al. 2010), this could be partly responsible for the derived difference in the opacity constant C. We can generate a sample of COSMOS disks that, to first order, have masses similar to the SDSS_{z = 0.7} galaxies by brightening the selection limit for COSMOS galaxies by ∼Δz magnitudes to I ≈ 21.8. This restriction does not change our finding of a nearly flat (C(z ∼ 0.7) = 0.05^+0.08_−0.14, in this case) surface brightness–inclination relation at z ∼ 0.7.

We have investigated the average opacity of distant (0.6 < z < 0.8) COSMOS spiral galaxies by direct comparison with local disks artificially redshifted to z ∼ 0.7. The outcome of inclination-based attenuation measurements is susceptible to selection effects (e.g., Davies et al. 1993; Jones et al. 1996). By processing our two samples identically and by applying a morphologically and photometrically consistent sample selection, we have taken the necessary precautions to reduce such systematic biases. We recover the expected surface brightness–inclination relation for nearby disks even after the simulated shift to z ∼ 0.7 (in the parameterization of Equation (2) this implies an opacity constant C(z ∼ 0) = 0.47^+0.16_−0.28). For high-z COSMOS disks, a significantly lower value of C(z ∼ 0.7) = 0.07 ± 0.06 is found, implying, on average, a nearly constant relation between surface brightness and inclination as is expected for optically thick spiral galaxies.

Previous studies suggest that the extinction laws in star-forming galaxies at similar redshifts as our COSMOS sample do not differ strongly from those in local systems (e.g., Conroy 2010 or Calzetti 2001, and references therein). It thus seems unlikely that the increased opacity of our z ∼ 0.7 COSMOS disks is due to a different chemical composition of the dust. Given that our low- and high-z disk samples have similar luminosities we can also rule out that the evolution is due to the locally observed scaling of dust opacity with the blue luminosity of galaxies (Wang & Heckman 1996).

Other possible explanations for the flat surface brightness–inclination relation at z ∼ 0.7 are the presence of more attenuating material or a different spatial arrangement thereof. Evidence that both factors might contribute exists: Genzel et al. (2008) report stronger turbulent motion in disk-like systems at high redshift that could increase the scale height of the dust, and recent measurements of molecular line emission in typical late-type galaxies at z ∼ 1.5 have revealed large gas fractions in excess of 50% of the baryonic mass (Daddi et al. 2010). The measurements presented here are not sufficient to infer the relative importance of such potential contributions. Additional constraints from complementary measurements or different wavelength regions are thus indispensable to determine the causes for the opacity evolution we observe between z ∼ 0 and 0.7.

We gratefully acknowledge the anonymous referee's helpful suggestions and the contribution of the COSMOS collaboration and its more than 100 scientists worldwide. P.K., P.A.O., C.S., and M.T.S. acknowledge support from the Swiss National Science Foundation. This research was also financed by DFG grant SCHI 536/3-2. The HST COSMOS Treasury program was supported through NASA grant HST-GO-09822.

Facilities: HST (ACS) - Hubble Space Telescope satellite, Subaru (SuprimeCam) - Subaru Telescope