# Harvard Astronomy 201b

## ARTICLE: Evolution of the Intergalactic Opacity: Implications for the Ionizing Background, Cosmic Star Formation, and Quasar Activity

In Journal Club, Journal Club 2011 on April 26, 2011 at 4:30 pm

### Read the paper by Faucher-Giguère et al. (2008)

Summary by: Aaron Meisner & Ragnhild Lunnan

Abstract:

“We investigate the implications of the intergalactic opacity for the evolution of the cosmic UV luminosity density and its sources. Our main constraint is our measurement of the Ly$\alpha$ forest opacity at redshifts $2$ $\leq$ $z$  $\leq$ $4.2$ from $86$ high-resolution quasar spectra. In addition, we impose the requirements that H I must be reionized by $z=6$ and He II by $z \sim 3$ and consider estimates of the hardness of the ionizing background from H I-to-He II column density ratios. The derived hydrogen photoionization rate is remarkably flat over the Ly$\alpha$ forest redshift range covered. Because the quasar luminosity function is strongly peaked near $z \sim 2$, the lack of redshift evolution indicates that star-forming galaxies likely dominate the photoionization rate at $z$ $\gtrsim$ $3$. Combined with direct measurements of the galaxy UV luminosity function, this requires only a small fraction $f_{esc} \sim 0.5\%$ of galactic hydrogen-ionizing photons to escape their source for galaxies to solely account for the entire ionizing background. Under the assumption that the galactic UV emissivity traces the star formation rate, current state-of-the-art observational estimates of the star formation rate density appear to underestimate the total photoionization rate at $z$ $\sim$ $4$ by a factor of $\sim$ $4$, are in tension with recent determinations of the UV luminosity function, and fail to reionize the universe by $z \sim 6$ if extrapolated to arbitrarily high redshift. A theoretical star formation history peaking earlier fits the Ly$\alpha$ forest photoionization rate well, reionizes the universe in time, and is in better agreement with the rate of $z \sim 4$ gamma-ray bursts observed by Swift. Quasars suffice to doubly ionize helium by $z \sim 3$ and likely contribute a nonnegligible and perhaps dominant fraction of the hydrogen-ionizing background at their $z \sim 2$ peak.”

### Big Questions

• What dominates the hydrogen photoionizing background: stars or quasars? How does the answer vary with redshift?
• What is the global rate of star formation and how does it evolve with redshift?
• Do Ly$\alpha$ opacity-based star formation rate estimates agree with inferred star formation histories based on other types of data?
• Is the star formation history inferred (from Ly$\alpha$ opacity or otherwise) consistent with reionization by $z = 6$?
• What is the escape fraction, $f_{esc}$, of hydrogen photoionizing photons for galaxies and quasars?

### Relation to Gunn & Peterson 1965

In an ancillary paper, the authors use a sample of previously published Keck (Vogt et al. 1994, Sheinis et al. 2002) and Magellan (Bernstein et al. 2003) high-redshift quasar spectra to constrain the IGM Ly$\alpha$ opacity $\tau(z)$ by measuring intervening neutral hydrogen absorption. Whereas Gunn & Peterson 1965 discussed (what they considered a lack of) Ly$\alpha$ absorption in the spectrum of a single quasar, 3C 9 at $z$ $\sim 2$, Faucher-Giguere et al. 2008 use a sample of $86$ objects, most with appreciably higher redshifts (see Fig. 1). The resulting determination of $\tau(z)$ is substantially improved relative to previous results, in part because the quasar sample employed is a factor of $\sim 2$ times larger than in any prior analysis.

Figure 1: Quasar sample used by Faucher-Giguere et al. 2008 to determine the IGM neutral hydrogen opacity. Blue refers to Keck HIRES data, red to Keck HIRES+ESI data, and black to all HIRES+ESI+Magellan MIKE data.

### Relation to AY201B themes: star formation, dust obscuration

The authors use the IGM Ly$\alpha$ opacity to constrain the total UV emissivity as a function of redshift, which can in turn constrain the amount of star formation as a function of redshift, quantified as $\dot{\rho}_{\star}^{com}(z)$, the comoving star formation rate density (units of solar masses per year per comoving cubic megaparsec). This means of constraining star formation history is complementary to more direct approaches, for example those using photometric surveys trace the amount of UV light and hence star formation as a function of redshift (see $\S$Comparison with Prior Results below).

Inferring absolute scale of the star formation rate as a function of redshift requires appropriate corrections for the absorption of UV photons between their emission and entry into the diffuse IGM. Thus, dust extinction should be accounted for. If dust extinction in galaxies evolves with redshift, this impacts determinations not only of the absolute scale of star formation, but also of its evolution. It turns out that the redshift evolution of dust corrections is poorly constrained at present, and therefore authors assume a dust correction that is independent of redshift.

### The 10 second derivation of key star formation results

The authors go into tremendous detail in explicitly stating and justifying the assumptions necessary to get from their starting point, $\tau(z)$, to the eventual star formation results $\dot{\rho}_{\star}^{com}(z)$ (hence why the paper cites a total of 200 references!). The basic idea is that $\tau(z)$ translates into a certain breakdown of neutral versus ionized hydrogen as a function of $z$, which implies a particular photoionization rate $\Gamma(z)$. $\Gamma(z)$ requires a particular intensity $J_{\nu}$ of the photoionizing background, which in turn derives from an intrinsic emissivity of astrophysical sources $\epsilon_{\nu}^{com}(z)$. At least some of these sources must be young stars, so that the star formation history $\dot{\rho}_{\star}^{com}(z)$ can be inferred from the emissivity. Of course, each step in this reasoning involves many cosmological assumptions. However, the collective assumptions made by the authors allow a remarkably simple (“10 second”) derivation to proceed between $\tau(z)$ and $\dot{\rho}_{\star}^{com}(z)$:

$1/\tau(z) \propto \Gamma(z) \propto J_{\nu} \propto \epsilon_{\nu}^{com}(z)/(1+z) \propto \dot{\rho}_{\star}^{com}(z)/(1+z)$

• $\tau(z)$ the optical depth as given in eq. (2), $\tau(z)=-ln(\langle F \rangle (z))$, where $F$ is the transmission
• $\Gamma(z)$ is the photoionization rate
• $J_{\nu}$ is the ionizing background intensity
• $\epsilon_{\nu}^{com}(z)$ is the comoving specific emissivity
• $\dot{\rho}_{\star}^{com}(z)$ is the comoving star formation rate (SFR) density

Note that the first proportionality involves implicit $z$ dependence, but all $z$ dependence in the remaining proportionalities is explicit. That’s why the authors’ plots of inferred $\Gamma(z)$, $\epsilon(z)$, $\dot{\rho}_{\star}^{com}(z)$ look identical up to a factor of $(1+z)$, as shown in Fig. 2 below.

One thing to notice immediately in writing the last proportionality is that the authors are assuming that all of the emissivity is due to star formation in galaxies, neglecting quasars. Other more subtle assumptions are also involved, for example the last proportionality would also be violated if dust corrections evolved with redshift.

Figure 2: Fig. 1, Fig. 11, and Fig. 12 of Faucher-Giguere et al. 2008. In all cases the black points with black error bars are the quantities inferred by the authors; the fact that the shape traced by the points in successive plots is so similar (the same up to factors of (1+z)) arises from the simple chain of proportionalities discussed above.

### Comparison to prior work

Throughout the text, the authors make extensive comparison of their star formation results to those of one particular paper, Hopkins & Beacom 2006. This paper is considered by the authors to be the most thorough SFR history analysis to date , as it makes use of essentially all cosmological probes of star formation other than Ly$\alpha$ opacity, going so far as to include astrophysical neutrino limits from Super-Kamiokande. However, the results of Hopkins and Beacom 2006 have known deficiencies; in particular their best-fit star formation rate falls rapidly beyond $z \sim 3$, so fast in fact that star formation fails to reionize the Universe by $z = 6$.

The results of Faucher-Giguere et al. 2008 are in tension with the results of Hopkins and Beacom 2006 insofar as the Ly$\alpha$ opacity inferred SFR declines less rapidly at high $z$ (see bottom panel of Fig. 2 above, where “H&B (2006) fit” shows the SFR history of Hopkins & Beacom 2006). The SFR history of Faucher-Giguere et al. 2008 remains constant enough out to $z \gtrsim 4$ that the authors claim its extrapolation can reionize the Universe in time. Hence, this disagreement with prior work actually appears to be a virtue of the Ly$\alpha$ opacity inferred SFR.

### Remaining issues: quasar contribution

As noted in $\S$5.2.1, when the quasar contribution to the hydrogen photoionizing background is estimated from the bolometric luminosity function of Hopkins et al. 2007, at $z \lesssim 3$, the quasar contribution alone overproduces the photoionizing background. That’s why in Fig. 5 of the text the quasar contribution has been scaled down by factors ranging from 0.1 to 0.35.

However, the quasar contribution (see Fig. 5 of the paper) falls off too rapidly with $z$ to be able to explain the Ly$\alpha$ opacity measurements over the full redshift range considered. In $\S$5.5.2 the authors use an alternative to the bolometric luminosity function to estimate the quasar contribution to the Ly$\alpha$ photoionizing background. To do so, they impose the constraint that He II be reionized by $z = 3$. Since only quasars can contribute the $\sim 50$ eV photons necessary to doubly ionize He II, this requirement roughly fixes the normalization of the quasar luminosity function at the $\sim 50$ eV energy. Assuming a quasar spectral index then allows the authors to infer the fraction of the photoionizing background at energies relevant to H I ionization. The result is that perhaps $\sim 20\%$ of the H I photoionizing background derives from quasar emission. Clearly, there are disagreements yet to be resolved.

### Important Findings

• The photoionizing background must be dominated by star formation for z$\gtrsim$3, and star formation may dominate over quasars at all redshifts considered.
• The quasar bolometric luminosity function overproduces the photoionizing background with quasar emission alone, while He II reionization arguments suggest quasars make up some non-negligible (but less than unity) fraction $\sim$20% of the photoionizing background.
• $f_{esc}$ need only be $\sim$0.5% for galaxies in order to match the photoionizing background. This $f_{esc}$ value is lower than but possibly consistent with previous $f_{esc}$ estimates.
• The inferred SFR history in this work peaks earlier than the SFR history of prior works, allowing star formation to reionize the Universe in time, by $z = 6$.