THE CHANGING Lyα OPTICAL DEPTH IN THE RANGE 6 < z < 9 FROM THE MOSFIRE SPECTROSCOPY OF Y-DROPOUTS

We apply the method introduced by Treu et al. (2012) to constrain the distribution of equivalent widths of Lyα given a sample of LBGs, exploiting all information available. Only a brief summary of the method is given here. The reader is referred to Treu et al. (2012) for details and analytic expressions of the likelihood.

As in our previous work, we describe the intrinsic rest-frame distribution in terms of the one measured at z ∼ 6 by Stark et al. (2011), p₆(W):

$$\begin{equation} p_6(W)=\frac{2 A}{\sqrt{2 \pi }W_{c}}e^{-\frac{1}{2}\left(\frac{W}{W_{c}}\right)^2}H(W)+(1-A)\delta (W), \end{equation} \tag{ 1 }$$

with W_c = 47 Å, A = 0.38 for sources with −21.75 < M_UV < −20.25 and W_c = 47 Å, A = 0.89 for sources with −20.25 < M_UV < −18.75. A is the fraction of emitters and H is the step function. As discussed below, 1 − A includes the fraction of interlopers. Following Treu et al. (2012), we consider two extreme cases which should bracket the range of possible scenarios. In the first ("patchy") model, no Lyα is received from a fraction _p of the sources, while the rest is unaffected. The probability distribution of the equivalent width is then given by

$$\begin{eqnarray} p_{p}(W) &=& \epsilon _{p}p_6(W)+(1-\epsilon _{p})\delta (W)\nonumber\\ &=& \frac{2A\epsilon _{p}}{\sqrt{2\pi }W_{c}} e^{-\frac{1}{2}\left(\frac{W}{W_{c}}\right)^2}H(W)+(1-A\epsilon _{p})\delta (W). \qquad \end{eqnarray} \tag{ 2 }$$

In the second ("smooth") model, Lyα is attenuated by a factor _s, yielding

$$\begin{eqnarray} p_{s}(W)&=&p_6(W/\epsilon _{s})/\epsilon _{s}\nonumber\\ &=&\frac{2A}{\sqrt{2\pi }\epsilon _{s}W_{c}} e^{-\frac{1}{2}\left(\frac{W}{\epsilon _{s}W_{c}}\right)^2}H(W)+(1-A)\delta (W). \qquad \end{eqnarray} \tag{ 3 }$$

Bayes's rule gives the posterior probability of _p and _s (collectively ) and z given an observed spectrum and continuum magnitude m:

$$\begin{equation} p(\epsilon,z_i|\lbrace f\rbrace,m)\propto \left[\!\Pi _j\!\int\! dW p(f_j,m|W,z_i)p(W|\epsilon)\!\right] p(\epsilon)p(z_i), \end{equation} \tag{ 4 }$$

where the term within square brackets is the likelihood p({f}|,z_i,m), f_j ∈ {f} are the flux measurements in each spectral pixel and z_i = λ_i/λ₀ − 1. We adopt a uniform prior p() between zero and unity, while the prior p(z_i) is given by the photometric redshift. By construction, our method takes into account the strong wavelength dependence of the sensitivity typical of near-IR spectroscopic data. The inference is carried out for each spectral pixel, using its noise properties including the effects of atmospheric transmission and absorption.

The posterior on is obtained by summing over z_i in the range where p(z_i) is non-zero. Our formalisms properly take into account the effects of incomplete wavelength coverage, in deriving limits on and z_i. For example, if the wavelength range only covers an interval [z_min, z_max], and the prior on is uniform, then the posterior will be

$$\begin{eqnarray} &&p(\epsilon |\lbrace f\rbrace,m)\propto \sum _{z_i\in [z_{\rm min},z_{\rm max}]}p(\lbrace f\rbrace |\epsilon,z_i,m) p(z_i) \nonumber\\ &&\quad + p(\lbrace f\rbrace |\epsilon =0)p(z_i\notin [z_{\rm min},z_{\rm max}]). \end{eqnarray} \tag{ 5 }$$

The normalization factor Z is the Bayesian evidence and quantifies how well the model describes the data. It can be used for selection, by comparing the evidence ratio between two models, or to decide whether additional parameters are warranted by the data. In comparison to other standard model selection techniques such as the likelihood ratio, the advantage of the evidence is that it takes into account the entire parameter space, thus avoiding issues of fine tuning.

The formalism described above is for an individual galaxies. For a sample of galaxies, or for multiple independent spectra of the same galaxies, it is sufficient to multiply the likelihoods to obtain the total likelihood.

The key result of this Letter is the posterior probability densities of the _p and _s parameters given the data, shown in Figure 3. This posterior probability distribution function is based on the eight non-detections of the primary sample presented here, plus the three non-detections presented by Treu et al. (2012) and Schenker et al. (2012).⁵ The non-detections imply that Lyα emission is significantly suppressed between z ∼ 6 and z ∼ 8. The 68% credible intervals, obtained by integrating the posterior, are _p < 0.31 and _s < 0.28, i.e., Lyα emission from LBGs is less than one-third of the value at z ∼ 6. The parameters _p and _s can be physically interpreted to be the average excess optical depth of Lyα with respect to z ∼ 6, i.e., $\langle e^{-\tau _{{\rm Ly}\alpha }}\rangle$. As expected for a sample of non-detections, the data are insufficient to distinguish between the two models. We will thus refer primarily to the patchy model for easier comparison with previous work (this is the model implicitly assumed by Fontana et al. 2010; Pentericci et al. 2011; Ono et al. 2012; Schenker et al. 2012).

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Before discussing the interpretation of our findings, we need to consider the role of contamination. The parameter _p relates the number of LBG-selected galaxies with Lyα emission at z ∼ 8 to the same quantity at z ∼ 6. In order to transform this into a Lyα optical depth, one has to account for the fraction of contaminants in both samples:

$$\begin{equation} n_{{\rm Ly}\alpha,z=8}=\epsilon _{p}n_{{\rm Ly}\alpha,z=6}\frac{1-f_6}{1-f_8}, \end{equation} \tag{ 6 }$$

where f₆ and f₈ are the fraction of contaminants in the z ∼ 6 and z ∼ 8 LBG-selected samples, respectively. A simple estimate of the number of contaminants can be obtained from the posterior probability distribution functions of the photometric redshifts and by computing the total probabilities that the source is outside the fiducial window. This probability is low and does not change our conclusions in any significant way: Stark et al. (2011) estimate f₆ < 0.1 with this method, while for our method it is in the range 0.1–0.2 and already taken into account by our formalism as described by Treu et al. (2012). A more insidious form of contaminants is represented by the "unknown unknowns," like the faint emission line objects discussed above.

In the case of BoRG, this additional contribution is estimated to be f₈ ∼ 0.2, (bringing the total to 0.33–0.42; Bradley et al. 2012). In the case of the i-dropouts selected from GOODS (Stark et al. 2011), the additional contamination is probably somewhat less, given the higher quality of the dithering strategy and larger number of blue bands available. To be conservative, we thus consider the ratio (1 − f₆)/(1 − f₈) to be in the range 1–1.25, that is, from equal contamination—after accounting for known losses inferred from photo-zs—to higher contamination in the z ∼ 8 sample.

With this estimate in hand, we can proceed to compute the fraction of LBGs with Lyα emission above the standard threshold of 25 Å equivalent width. Our measurement at z ∼ 8 is shown in Figure 4 together with data from the literature at lower redshift (see the figure caption). In the patchy model, the fractions for Y-dropouts are <0.07–0.08 for galaxies with M_UV < −20.25 and <0.17–0.21 for galaxies fainter than this limit (the two numbers are for minimal and maximal contamination). In the smooth model, the same fractions are <0.03–0.05 and 0.06–0.12. Note that these bounds include the uncertainty on the z ∼ 6 fraction and thus the uncertainties on the points beyond z ∼ 6 are correlated. If the fractions at z ∼ 6 move up or down, so do the points at higher redshift, but the trend will remain the same. Even considering the more conservative upper limits from the patchy model, the drop in the fraction of Lyα emitters amongst LBG in just 300 Myr is at least a factor of ∼3.

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There are three possible explanations for our finding, ranging from the mundane to the very interesting. The first and most mundane explanation is that samples of Y-dropouts suffer from a much higher rate of contamination than similar LBG samples at lower redshift. A breakdown of the Lyman break technique could occur if there were exotic populations of galaxies that are missing from our current templates and models used to estimate color cuts and compute photo-zs. While this cannot be ruled out with present data, it would certainly be a surprise to see the Lyman break selection breaking down so abruptly over a relatively small change in wavelength and magnitudes. The second explanation could be related to the special environment of the BoRG galaxies. As expected for the most luminous galaxies at every redshift, the BoRG sources are bright and strongly clustered, especially those that we selected for spectroscopic follow-up (Hildebrandt et al. 2009; Overzier et al. 2009). Thus, we may be comparing galaxies in protoclusters with field galaxies, and perhaps this could bias our interpretation. However, we expect the higher density regions to completely reionize earlier and therefore to have a smaller Lyα optical depth, not larger (Barkana & Loeb 2004). Thus, this second explanation of the large Lyα optical depth at z ∼ 8 as the result of a selection bias would also be surprising. The third explanation is that the average Lyα optical depth of the universe increases significantly in this small amount of cosmic time. This third explanation would be very exciting, implying that we have reached an epoch where the properties of the intergalactic and circumgalactic medium are changing dramatically, presumably owing to rapid changes in the degree of cosmic reionization or in the physics of the first generations of star-forming regions.

Observationally, the big question is then how to test these three hypotheses. Searches for Lyα to greater depth than ours would provide useful information, hopefully including detections. However, additional deeper non-detections would certainly help tighten the upper limits derived here. This is possible with longer MOSFIRE integrations or by using the WFC3 grism on board the HST. Systematic studies of many gravitationally lensed sources should be a particularly powerful way to probe very faint sources and thus also help to test the second hypothesis (e.g., Bradač et al. 2012). However, it is likely that some fraction of LBGs at z ∼ 8 and above will remain undetected in Lyα even with heroic efforts. In order to quantify the amount of contaminants and thus test the first and third hypotheses, one needs detections of other lines or of the continuum. We hope that IR lines can be detected with pointed observations with ALMA (Carilli & Walter 2013) although this is non-trivial (Ouchi et al. 2013). Detection of the continuum will be hard and might require several hours of integrations with the James Webb Space Telescope (Treu et al. 2012) or an extremely large telescope like the Thirty Meter Telescope, unless the sources are highly magnified by a foreground gravitational lens.