# Harvard Astronomy 201b

## Outline

1. What are the characteristics of the first stars? (hot and massive!)
2. Can the first stars and galaxies provide enough ionizing photons to account for reionization? (probably)
3. How can IR observations of distant galaxies confirm these predictions? (gimme JWST)

## Introduction

The setting for the formation of the first stars and galaxies is the early universe. The farthest source of radiation we can observe today is the Cosmic Microwave Background (CMB) at the surface of last scattering, which corresponds to emission during the era of recombination ~370,000 years after the Big Bang. At that time there were not yet stars or galaxies and so light sources were rare in the universe. The period between this time and the formation of the first stars and galaxies is termed the Dark Ages. About 10 Myr after the Big Bang, the gas in the universe was dominated by cooling due to universal expansion (heating due to Compton scattering became negligible) and, similarly, the particle density was dropping. The prospects for life looked pretty grim. Luckily, dark matter halos were merging together and forming large gravitational potential wells that would eventually become the sites of gas coalescence for the formation of the first stars and galaxies.

Recent work in this field is fueled in part by the first ever detection of a Gunn-Peterson trough, predicted in 1965, by Becker et al. (2001) in SDSS data. The trough is formed by a forest of Lyman $\alpha$ absorption lines blueward of the Lyman $lates \alpha$ emission of the source made by neutral Hydrogen in the intergalactic medium (IGM). Becker et al. observed four quasars at z=[5.80,5.82,5.99,6.28] and observed the Gunn-Peterson trough only in the z=6.28 quasar. This suggests that the epoch of reionization occurred between z=5.99 and 6.28 (about 900 Myr after the Big Bang). Furthermore, the WMAP CMB polarization data indicates that ~9% of CMB photons were scattered by free electrons (after reionization), indicating that reionization occurred at z~10 (about 500 Myr after the Big Bang). This suggests a timescale for reionization of order 100 Myr.

Cosmological timeline from Robertson et al. 2010. The history of the universe in one sentence: the universe was neutral, dark, and boring from z~1100 (~370,000 years after the Big Bang) to z~6 (~1 billion years after) and is now ionized, bright, and interesting.

## Forming the first stars

During the expansion-dominated phase ($t\sim100$ Myr), the gas temperature was approximately equal to the CMB temperature Jeans mass stood independent of redshift at $M_J\sim10^5 M_\odot$. Gas condenses and cools within dark matter halos with masses of this order. Tidal torques due to nearby clumps cause these condensing clouds to form disks, in which smalled clumps fragment to form the first stars.

In order for stars to form, these collapsing gas clouds must also cool. However, the heavy elements which are abundant in the modern universe and their radiatively efficient line cooling mechanisms did not yet exist. Moreover, the virial temperature of the gas was $<<10^4$ K and therefore collisions were too rare for atomic line cooling to be plausible. The only available cooling mechanism in these collapsing clouds would have been transitions of molecular hydrogen, which could form through the following chemical reaction.

$H + e^{-} \to H^{-}+\mbox{photon}$
$H^{-} + H\to H_2+e^{-}$

This reaction is catalyzed by the free electrons which were rare, but present in the cloud. This $H_2$ mechanism succeeded in cooling the gas to a few hundred K. In fact, because the timescale for molecular hydrogen formation (and therefore the cooling process) is much longer than the timescale for collapse, the gas will reach an unstable equilibrium at conditions of $T\sim500$ K and $n_e\sim10^4\mbox{cm}^{-3}$, corresponding to $M_J\sim 200M_\odot$.

The first, “Population III” stars are predicted to have been much more massive that typical stars formed in the modern universe. The $M_J\sim 200M_\odot$ clouds described above undergo little fragmentation. The primary reason for this is the much higher temperatures in these gas clouds in the early universe ($T\sim 200-300$ K) as compared to modern star forming regions with metal line cooling ($T\sim 10$ K). By dimensional analysis, we can show that the mass accretion rate is sensitive to this temperature: $\dot{M}\sim c_s^3/G\sim T^{3/2}$.

It is expected that the first stars would have been much more massive than typical O and B stars in the present Milky Way: $30 \lesssim M \lesssim 1000 M_\odot$. Stars of this mass would have had a surface temperature $T_{eff}\sim10^5$ and would be radiating near the Eddington limit, corresponding to a radius of $R\sim6R_\odot$.

However, as soon as the first stars formed, they would have produced UV photons that would have dissociated the surrounding gas, making the next generation of stars more difficult to form. Avi calls these first stars “suicidal.” Moreover, heavy element enrichment to the point of even $Z\sim10^{-3}Z_\odot$ would be sufficient for metal line cooling to begin to dominate over $H_2$ cooling. Therefore we should expect stars formed after the first few generations to have a much less top-heavy initial mass function (IMF) – in other words, only the first few generations of stars would be been supermassive..

## Reionization by the first stars

In the Introduction, we argued for observational evidence that constrains the reionization timescale to a few hundred Myr. We can compare this to the ionization efficiency of different processes to evaluate the probability that they might be responsible for reionization.

Is it plausible that stars could be responsibly for ionizing all of the neutral hydrogen in the universe? Population II stars produce $\sim4000$ ionizing photons per proton. For stars of this type to be responsible for reionization, $\sim0.025$% of all H would need to be incorporated into stars in a short timescale. For reference, at z=0 $\sim10$% of all baryons are incorporated into stars.

If the first stars were truly this hot ($T_{eff}\sim10^5$) and massive, they would have emitted many ionizing photons ($13.6 \mbox{eV} = 1.6\times10^5$ K). Stars such as these would produce $\sim10^5$ ionizing photons per proton, so they could successfully reionize the IGM if only $\sim 10^{-5}$ of all hydrogen atoms in the early universe made it into these stars. The actual star formation efficiency would have been regulated by the cooling mechanisms described above, the ionizing radiation from the first stars, and by the dynamical and chemical contributions of (pair-instability, $10^{53}$ ergs!) supernovae winds.

Numerical simulation by Wise & Abel of a Population III star excavating an HII bubble. Not only does it produce ionizing radiation which causes far-reaching ionization, but it also has strong winds which evacuate ~300 pc to a density of n~0.1.

In the beginning, the universe was full of bubbles. The efficiency with which photons with energy greater than 13.6 eV ionizes hydrogen is very high, so the early ISM would have had two distinct phases: ionized regions around the first stars, and neutral regions elsewhere. Once these ionized bubbles begin overlapping, the intensity of ionizing radiation becomes great enough that even dense pockets of gas cannot stay neutral. This is called the “overlap phase.” The end of the overlap phase, when only the most dense regions of the IGM remain neutral, marks the end of reionization.

More detailed analytic analyses suggest that stars could be responsible for reionization, but observational evidence is required to place firmer limits on the uncertain quantities that underlie this assessment. If star-forming galaxies are not responsible for reionization, it is possible that it was caused by accretion onto primoridal supermassive black holes or perhaps even by the decay of elementary particles.

## IR observations of the first galaxies

To establish that the first stars reionized the universe, observers seek to quantify the number of galaxies at z>6, the first billion years of the universe during which reionization occurred. The basic idea is to constrain the star formation rate in the early universe by measuring its time integral (the stellar density) at various times by observing the total luminosity of galaxies as a function of z.

The “drop-out” technique is used to find high-redshift galaxy candidates. Because photometry is more efficient than spectroscopy for large surveys, observers look for galaxies that are easily detectable in some filters, but then drop out of (are not detectable) bluer filters probing the redshifted Gunn-Peterson trough.

The IR (850-1700 nm) detector of HST’s new (2009) Wide-Field Camera 3 (WFC3, 40x faster than HST’s old NICMOS for surveys) has revolutionized the search for these high-z galaxies. Deep imaging in the 4.7 square arcminute Hubble Ultra Deep Field (UDF) has reached to 29th magnitude, revealing >50 candidates with photo_z > 7 (as of Robertson et al., November 2010). Follow up Spitzer observations of some of these candidates confirms that they have significant stellar populations of $\sim10^{10}M_\odot$.

Panel a shows the star formation rate as derived from volume-limited HST observations of the rest-frame ultraviolet luminosity of ionizing photons. Panel b shows the ionization history history implied by this model, which roughly reproduces (roughly) the expected timing of the epoch of reionization. From Robertson et al. 2010.

The next quantities to be measured are $f_{esc}$, the fraction of ionizing photons which escape into the IGM, and $\eta_Q$, the number of ionizing photons per unit of star formation. We would know the escape fraction if we could simply measure Lyman $\alpha$ flux of these galaxies, but at high redshift the intervening IGM makes this impossible. Another possibility is to measure the nebular emission due to free-free and bound-free scatterings caused by the ionization of the IGM, but this has also not been accomplished with current instruments.

One last option is to measure $\beta$, the UV power-law slope of the high-z galaxies’ continuum. Comparing this measurement to models can yield both $f_{esc}$ and $\eta_Q$, determined in large part by the amount of dust in the models. HST measurements of $\beta<-3$ are tantalizing evidence of of dust-free, young-starburst galaxies with Populatation III stars, but this interpretation is controversial.

A definitive history of reionization will have to wait for future instruments. An ideal survey would measure the Lyman $\alpha$ emission from galaxies throughout cosmic time. A turnover in this parameter at high z would mark the end of reionziation, beyond which the neutral IGM absorbs the galactic emission. The JWST or the upcoming class of 30-m ground based telescopes are required to do detailed spectroscopy of these high-z galaxies to investigate their stellar populations and the details of their reddening due to dust.

## Beyond the IR

It must also be noted that the epoch of reionization can be probed by large-scale 21 cm surveys or 21 cm interferometry looking for individual HII bubbles, as Alyssa will discuss in class (see HI page). Furthermore, distant GRBs can provide signposts to the first galaxies and can illuminate the intervening IGM.

1. […] Nathan described, the IGM transitioned from an HI dominated phase to an HII dominated phase at . Here I will go into […]

2. […] Observations of the Lyman-α forest in distant quasars has demonstrated to us that at some point after the Big Bang, the hydrogen in the universe transitioned from being neutral to ionized. In other words, there existed a phase change during the epoch of reionization. […]