Galaxy Formation and Reionization

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Galaxy formation and reionisation
Eduard Salvador Solé∗†
Institut de Ciències del Cosmos. Universitat de Barcelona (UB-IEEC), E-08028 Barcelona,
Spain
E-mail: e.salvador@ub.edu
Alberto Manrique and David Canales
Institut de Ciències del Cosmos. Universitat de Barcelona (UB-IEEC), E-08028 Barcelona,
Spain
E-mail: a.manrique@ub.edu
I review the present knowledge of two fundamental processes in cosmology: galaxy formation and
reionisation. After a brief description of the observations informing on reionisation, I then focus
on the theoretical modelling of galaxy formation and the evolution of the intergalactic medium.
I show that all the information we currently have on cosmic evolution at high-zcombined with
the preceding one on reionisation allows us to severely constrain the reionisation process. Special
attention is paid to the possible implications on that scheme of some recent unexpected observa-
tions.
Frontier Research in Astrophysics - III (FRAPWS2018)
28 May - 2 June 2018
Mondello (Palermo), Italy
∗Speaker.
†Funding for this work was provided by the Spanish MINECO under projects AYA2015-70498-C02-2-R (co-funded
with FEDER funds) and MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘Maríade Maeztu’), and the Catalan DEC
grant 2014SGR86.
c
Copyright owned by the author(s) under the terms of the Creative Commons
Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/

Galaxy formation and reionisation Eduard Salvador Solé
1. INTRODUCTION
Galaxy formation and reionisation are two intertwined fundamental issues in modern cosmol-
ogy. Indeed, it is nowadays believed that the reionisation of the cosmic gas outside galaxies after
it became essentially neutral at a redshift of z∼1100 is the result of the ionising emission from
luminous sources, which also reheated it and enriched it with metals and left as remnants the seeds
of supermassive black holes (SMBHs) and reheated it. Conversely, the evolution of the intergalac-
tic medium (IGM) also plaid a crucial role in galaxy formation, as the temperature, metallicity and
ionisation state of the IGM determined at a great extent the possibility that it were trapped by haloes
of different masses, cooled within them and fed galaxy growth. However, that general scheme is
still to be confirmed and the details of the process to be determined.
In this contribution I give a brief review of the observational information we currently have
on reionisation and explain the big progress expected to be achieved on that line in the near future.
On the other hand I describe the connection between reionisation and galaxy formation from a
theoretical viewpoint and show how the information we also have on the global cosmic evolution
since very high-z, combined with the information on reionisation, can be used to severely constrain
the epoch of reionisation (EoR), i.e. the way galaxies formed and evolved and their effects on the
IGM, in particular on reionisation.
2. Observational basis of reionisation
As of today, all the information we have on reionisation is partial. It comes from the light of
distant sources and the CMB radiation. However, there is founded hope that we will soon be able
to directly probe the EoR by means of 21 cm line observations.
2.1 Distant luminous sources
Distant sources allow us to determine the ending redshift of reionisation. Indeed, the absence
of global absorption shortwards of the rest-frame Lyman-
α
(Ly
α
) emission line seen in the spectra
of quasars at z<3 made [60] realise that the hydrogen present in the nearby intergalactic medium
(IGM) was ionised (xHI <10−4) except for small intervening systems yielding discrete absorption
lines, the so-called Ly
α
forest. The Gunn-Peterson trough caused by neutral intergalactic hydrogen
was finally found by [5] and [42] in the spectra of quasars at z∼6, suggesting that value for the
redshift zion,Hof ionisation completion.
Several subsequent studies using: (a) the mean opacity of the Ly
α
forest [49]; (b) the size
of the proximity zone around quasars [170, 49, 10, 86, 93]; (c) the detection of damping wing
absorption by neutral IGM in quasar spectra [102, 103, 113]; (d) its non-detection in the spectra of
gamma ray bursts [159, 97]; (e) the abundance of Ly
α
emitters (LAEs) [90, 61, 55, 97, 101, 123,
80]; and (f) the covering fraction of dark pixels in the Ly
α
and Ly
β
forests [95] confirmed a value
of zion,Hof 6.0+0.3
−0.5.
The fact that the number of LAEs decreases very steeply beyond z=6 is particularly illustra-
tive. The number density of LAEs at z=7 seems indeed to be only 18-36 per cent of the density
at z=6.6 [75], there being no spectroscopically confirmed LAE at z>7 ([122], but see the end of
this talk). The fact that we still see LAEs at z>6 is well understood. Ly
α
photons are somewhat
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Galaxy formation and reionisation Eduard Salvador Solé
redshifted in origin due to the velocity of the emitting gas clouds and, more importantly, due to the
fact they are also redshifted when leaving the ionised bubbles around galaxies. As the higher z, the
smaller ionised bubbles, such an effect, which is notable at znear 6, becomes negligible at z∼7
where the volume filling factor of ionised regions, QHII(z), has greatly decreased.
2.2 The CMB radiation
Another partial information on reionisation arises from the analysis of the large-scale cos-
mic microwave background (CMB) anisotropies. Thomson scattering of free electrons by CMB
photons yields an absorption and polarisation of that radiation which remains imprinted in the
temperature power spectrum and the E-mode polarisation power spectrum, both on large angular
scales. Unfortunately, such imprints are integral effects sothat different reionisation histories yield
identical results. The usual way to leave that degeneracy is to assume instantaneous reionisation
and adjust the values of zion,Hand the optical depth,
τ
.
The 9-year data gathered from the Wilkinson Microwave Anisotropy Probe (WMAP9, [67]) led
to
τ
=0.089±0.014, while the three-years temperature Planck data combined with the polarisation
WMAP data yielded
τ
=0.078±0.014 [125], and the most recent data inferred from the own large-
scale polarisation anisotropies have further decreased it to
τ
=0.058±0.012 [126].
The corresponding values of zion,Hare 10.6±1.2, 9.9+1.8
−1.6and 8.8+0.9
−0.8. The marked difference
from the previous value of zion,H∼6 indicates that reionisation, far from being instantaneous, ought
to be extended, and possibly non-monotonous [173, 30, 32, 69, 62, 149, 115, 57, 53, 172, 11].
The small-scale temperature power spectrum can also inform on the duration ∆zof reionisa-
tion through the kinetic Sunyaev-Zel’dovich effect. However, this piece of information is greatly
disturbed by dust emission whose correction is hard to achieve.
Another integral quantity that constrains the EoR, similar to
τ
but more sensitive to low red-
shifts, is the weak comptonisation distortion of the CMB radiation spectrum. Although its mea-
sured upper limit of y<1.5×10−5[94] is a rather loose constraint, it has the advantage with
respect to
τ
of being inferred with no modelling.
2.3 The 21 cm line
The hyperfine 21 cm line is a powerful tool to directly probe the EoR (see [111] for a com-
prehensive review). Neutral hydrogen is seen in absorption or emission over the CMB continuum
depending on whether the spin temperature, TS, is lower or higher than the CMB temperature, re-
spectively. This line is optically thin, so by varying the frequency in the observer frame one can
have a tomography of the cosmic HIcontent over redshift. Specifically, the brightness temperature
of the 21 cm line at the redshift zdepends on the density of neutral hydrogen and the spin and CMB
temperatures at that zthrough the expression
δ
T(z)≈0.14K×xHI(z)Ωbh1+z
Ωm1/21−T
γ
(z)
TS(z)(2.1)
where xHI is the neutral hydrogen fraction, Ωmand Ωbare the matterand baryon density parameters
in the flat ΛUniverse and his the Hubble constant in units of 100 Km s−1Mpc−1. Therefore, as
T
γ
(z)is known fromthe current value of the CMB temperature, by measuring TS(z)we can estimate
xHI(z).
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Galaxy formation and reionisation Eduard Salvador Solé
TScan be obtained from the kinetic temperature TKof the gas. Indeed, at z>30 the gas
density is so large that collisions warrant TS=TK, with TKdecaying adiabatically since z∼150
(until then the gas was coupled to the CMB radiation through Compton scattering with residual
electrons). At lower z TStends to meet T
γ
. But, at a redshift of about 20, stars begin to form and
Ly
α
photons couple againTSto TK(the Wouthuysen-Field effect), which begins to rapidly increase
heated through X-rays mainly produced in supernovae and the Ly
α
photons themselves.
Therefore, the problem with this method is not only the difficulty to measure the cosmological
21 cm signal, which is 5 orders of magnitude smaller than the synchroton emission from the Galaxy,
but also that it relies on the accurate modelling of galaxy formation and the evolution of the IGM
temperature (see below).
Last week [18] reported the detection of a weak absorption line on the CMB continuum which
is believed to correspond to the wanted 21 cm line signal. However, the shape of that absorption
feature is quite unexpected. We will comback to this point at the end of the talk.
3. Theoretical insight
Among the various mechanisms that might cause reionisation (see e.g. [31]), the most sim-
ple and natural one is photo-ionisation by luminous sources, namely active galactic nuclei (AGN),
normal galaxies with ordinary Population II (Pop II) stars, and first generation metal-free Popula-
tion III (Pop III) stars. The X-ray background demonstrates that AGN emit typically one order of
magnitude less UV photons than needed at z∼6 [169, 29, 99]. This implies that either massive
SMBHs are too scarce [167], or their associated AGN are too obscured by dust [161], while more
abundant mini-quasars associated with stellar black holes would have too short duty cycles [2, 105].
Likewise, the star formation rate (SFR) densities derived from the rest-frame UV luminosity func-
tions (LFs) of normal bright galaxies [96, 88, 14, 15] show that these objects are insufficient to
ionise the IGM by z∼6. Therefore, ionisation should be achieved either as the result of a substan-
tial abundance of faint star-forming galaxies [136, 74, 17] or of the still undetected Pop III stars
[149, 144].
The situation is even more uncertain regarding HeII reionisation. The He II mean opacity in-
ferred from the Ly
α
forest suggests that the redshift of complete HeII reionisation, zion,He, should
be less than or approximately equal to 3 [135, 142, 43, 98, 6], and probably no smaller than 2 as the
AGN emission begins to decline at that redshift [29]. AGN are indeed the most plausible ionising
sources responsible of HeII reionisation as they emit more energetic photons than normal galaxies
and Pop III stars, the other sources of energetic photons, do not form at z<6.
Therefore, the full characterisation of the EoR from the CMB anisotropies or the 21 cm line
observations relies on the theoretical modelling of galaxy formation.
3.1 Galaxy formation
The modelling of galaxy formation has been a subject of intense work since the pioneer work
by [133], [145], [166], [21] and [165]. This has been carried out by means of hydrodynamic
simulations (e.g. [158, 156, 153, 114, 154, 140, 46, 41, 168, 121, 141, 117] as well as semi-analytic
models (SAMs) (e.g. [77, 26, 150, 76, 34, 66, 9, 104, 19, 110, 134, 52]).
3

Galaxy formation and reionisation Eduard Salvador Solé
SAMs are more practical and inform more easily on the typical properties of objects. They
have the bad reputation of describing the baryon physics by means of simple recipes with a very
large number of free parameters. But simulations, which are believed to be based on first principles
only and to provide more accurate and detailed information, involve the same recipes and parame-
ters as SAMs at subresolution scales. On the other hand, they are more CPU expensive and hard to
deal with.
A general problem with all those models is that they are not complete as they do not include
molecular cooling at the base of the first generation zero-metallicity Population III (Pop III ) stars,
which caused theinitial reheating and metal-enrichement of IGMand released the seeds ofSMBHs
that evolved into active galactic nuclei (AGN). What is worse, the feedback on IGM is not self-
consistently modelled, but it is dealt with in a rather arbitrary way through some parameters to be
adjusted.
3.1.1 Feedback on IGM
The impact of galaxy formation on the IGM began to be addressed in a series of papers study-
ing mechanical heating by activegalactic nuclei [19, 35], radiative heating through X-rays produced
in supernovae [166, 40, 28, 165, 83, 119] and ionisation from young stars [72, 132, 143, 108, 106,
47].
The IGM evolution is described by a couple of differential equations for its ionisation state
and temperature with some source functions provided by a galaxy model. It is in this latter part
where most approximations and simplifying assumptions are made, depending on the particular
approach followed, namely hydrodynamic simulations [129, 164, 116, 27, 173, 73, 120, 160, 4,
147], numerical and semi-numerical simulations [177, 50, 176, 148], pure analytic models [63,
157, 44, 54, 1, 78], and semi-analytic models [3, 47, 100, 52, 171], each of them with its pros and
cons.
Most of the previous works assume simple hydrogenic composition and a constant, uniform
temperature, equal to that of photoionised hydrogenic gas (∼104K). The first coupled equations
for the IGM ionisation state and temperature after reionisation taking into account the dependence
of the latter on the hydrogen and helium abundances and local density of the gas [107] were derived
by [70]. And [71] and [69] extended them to the EoR itself. [24] derived the equations taking into
account the full composite, inhomogeneous, and multiphase nature of IGM (i.e., singly and doubly
ionised regions embedded within a neutral background; [109]).
On the other hand, the source functions are calculated assuming an evolving universal halo
mass function (MF), while the halo MF is different in ionised and neutral regions because as the
mass of haloes able to trap gas and form stars depends on the temperature and ionisation state of
the IGM. [92] derived for the first time the equations governing the IGM evolution, taking into
account all these effects.
3.2 Coupled evolution of galaxies and IGM
But, as mentioned in the introduction, to model in a fully self-consistent way galaxy formation
and reionisation one must account for the coupled effects of one on each other.
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Galaxy formation and reionisation Eduard Salvador Solé
In the last few years a big effort has been done along this line in the hydrodynamic cosmo-
logical simulations of last generation, such as the so-called Horizon-AGN project [8], First Billion
Year project [37], the Technicolor Dawn project [51], and the SPHINX [138] project.
However, the goal has been only partially accomplished as none of these cosmological sim-
ulations is complete enough. For instance they include the parallel growth of SMBHs and AGN
feedback, but the seeds of SMBHs are put in an adhoc way and the same is true for the origin of
metals. Indeed, none of these simulations include molecular cooling and Pop III star formation and
feedback.
Another important limitation of all these models is, as mentioned, the large number of free
parameters they harbour. Such a freedom facilitates, of course, the recovery of the data one is
interested in, but at the cost of making the result less reliable. This is particularly true because these
models are usually used to explain very specific phenomena only, whereas the model capabilities
to recover other observables is not checked.
4. Observations on cosmic evolution
There is nowadays numerous observational data on the evolution of Universe since the Dark
Ages.
The most representative datasets of each kind (and their references) are the following:
(a) The cold gas mass density history [124, 128, 130, 84, 175, 22, 39].
(b) The stellar mass density history [131, 155, 58, 59, 81, 82, 112, 25].
(c) The SMBH mass density history (following [85], taking into account the universal SMBH
to spheroid mass ratio [79] times the spheroid to total stellar mass ratio [56]).
(d) The hot gas metallicity history [152, 137, 146, 45, 38].
(e) The cold gas metallicity history ([89, 151, 36, 174]).
(f) The stellar metallicity history ([64, 151]).
(g) The IGM metallicity history (based on estimates by [137, 146, 45]).
(h) The galaxy morphology history (specifically, the fraction of spheroid-dominated galaxies
with masses >1011 M⊙, [23, 20, 162, 127]).
(i) The galaxy size history (specifically, the median effective radii of spheroid-dominated
galaxies, [23, 163]).
(j) The SFR density history [131, 88, 16, 118, 33, 48, 68].
(k) The HI-ionising emissivity history (from galaxies [7], and from AGN [29])
(l) The IGM temperature history [87, 12, 13].
Moreover, we have a few differential properties at discrete redshifts:
(m) the galaxy stellar MFs (or UV LFs),
(n) the SMBH MFs (or AGN optical and X-ray LFs)
and SFR vs. galaxy stellar mass or galaxy star-forming main sequences.
All this information should be taken into account by any model of galaxy formation and IGM
evolution such as AMIGA pretending to be trusted.
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Galaxy formation and reionisation Eduard Salvador Solé
Figure 1: Best S (red lines) and D (green lines) solutions with single and double reionisation, respectively,
fitting all data available (black dots) on the evolution of global or averaged cosmic properties since the Dark
Ages. Solid lines stand for the contributions from galactic Pop II stars and SMBHs; short-dashed lines
include the contribution from stars in the diffuse intrahalo medium; and dotted lines include Pop III stars
and their black hole remnants. In panel (a), full dots mark the total gaseous (HIand H2) contribution, while
empty circles stand for H Ialone. In panel (k), the long-dashed lines and open circles refer to the contribution
from AGN, and in panel (l), solid, dashed, and dotted lines show the predictions for singly ionised, doubly
ionised, and neutral regions, respectively (the dotted lines are shifted a factor 500 upwards at zhigher than
the redshift of first or unique ionisation). No observational data are available for the intrahalo gas mass
density (x), IGM mass density (y), and metallicity of the matter fallen into SMBHs (z), whose predictions
are plotted here for completeness. Density parameters are scaled to the critical cosmic density ¯
ρ
0at z=0.
The remaining scaling factors are: r0=re(z=0),˙
ρ
0=1 M⊙yr−1Mpc−3,˙
N0=1051 photons s−1Mpc−3,
and T0=104K.
6

Galaxy formation and reionisation Eduard Salvador Solé
5. The AMIGA model
AMIGA (Analytical Model of IGM and GAlaxy evolution) [91] is the most complete, fully
consistent model of galaxy formation model built so far.
It includes all the theoretical developments in the monitoring of luminous sources and IGM
mentioned above as well as other technical improvements which make it particularly accurate.
Indeed, the properties of dark matter haloes and their baryon content are dealt with by interpolating
them in grids of masses and redshifts that are progressively built from trivial boundary conditions
as haloes merge and accrete. This procedure is less computer memory-demanding than the usual
method based on Monte-Carlo or N-body realisations of halo merger trees, and enables one to reach
redshifts as high as wanted and halo masses as low as needed while maintaining a good sampling
over the entire redshift and mass ranges. In this way one can integrate at every zthe feedback of
luminous sources for the halo MF (inionised and neutral regions separately) and accurately evolve
the IGM.
The number of free parameters in AMIGA is greatly reduced in comparison to other galaxy
formation models thanks to causally linking physical processes that are usually treated as indepen-
dent from each other. In fact, the 9 free parameters left are fully constrained through the fit to the
observational information on reionisation described in Section 2 and the information on the main
cosmic properties given in Section 4.
All the acceptable solutions found [139] are tightly grouped in two narrow sets, one for mod-
erately top-heavy Pop III star initial mass functions (IMFs) leading to single reionisation with
τ
=0.072+0.004
−0.005, and another one for top-heavier Pop III star IMFs leading to double reionisation
with
τ
=0.102+0.001
−0.001 (see Fig. 2). The first ionisation phase in the latter solutions is driven by
Pop III stars until z∼10, and after a short recombination period a second ionisation phase takes
place, driven by normal bright and faint galaxies. While in the solutions with single reionisation,
both kinds of sources compete in parallel.
Both kinds of solutions give excellent fits to all the 13 independent observed cosmic histories
(Fig. 1), the galaxy stellar MFs and the galaxy star-forming main sequences at different redshifts,
being the first time that a galaxy formation model fits all the information available on cosmic
evolution.
The CMB Thomson optical depth found in double reionisation, though consistent with the
observational estimates from the WMAP 9-year and Planck three-year data, is 3
σ
larger than the
most recent estimate from the Planck data. While the CMB optical depth found in single reioni-
sation is consistent with that estimate. Thus,
τ
favours the single reionisation scenario. However,
double reionisation cannot be rejected yet. Indeed, the uncertainty in
τ
is still big and, what is
more important, it has the following advantages. First, it can explain in a simple natural manner
the Ly
α
-emitting galaxies recently observed at z∼9 [178, 65], together with the gap in their dis-
tribution between z∼7 and ∼9. Second, the strange shape of the 21 cm line signal reported by
[18] could also be naturally explained. Indeed, Ly
α
photons are only present in a thin shell around
ionised bubbles, with an intermediate temperature between those in the ionised bubbles and in the
deep neutral background, so in equation (1) we should replace xHI(z)by the fraction of neutral
hydrogen in those shells, xlya(z), and TSby the corresponding temperature, Tlya. The fact that Tlya
should increase in a much more moderate way (if not keep essentially constant) and that xlya(z)
7

Galaxy formation and reionisation Eduard Salvador Solé
should rapidly vanish with the growth of ionised bubbles in double reionisation could explain the
poorly understood shape of that absorption feature.
Figure 2: Only acceptable solutions with single (left panel) and double (right panel) reionisation. In thick
lines models S and D giving the best solution of the respective types. In thin lines the solutions bracketing
the two sets. The error bars centred at z=2.5 and z=8.8 along QSII =1.0 give the estimated limits for the
redshifts of complete helium and hydrogen ionisations, respectively (see Sec. 2); the vertical dotted black
line marks the redshift z=7 where QHII is found to decrease with increasing z.
6. Conclusions
In the last decades a big progress has been achieved in the modelling and observational charac-
terisation of cosmic evolution since the Dark Ages. Thanks to these improvements it has nowadays
become possible to severely constrain the intertwined complex processes of galaxy formation and
reionisation.
Our ignorance on the Pop III star IMFstill leads to a small degeneracy in the allowed solutions
as two different solutions, one with single and the other with double reionisation, are still possible.
However, the rapidly growing observational data on the high-zUniverse, coming from the
CMB anisotropies and 21 cm line experiments as well as the observation of very distant LAEs
could soon leave that degeneracy.
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DISCUSSION
W. KUNT QUESTION: As you apparently believe in the existence of SMBHs, how do you ex-
plain that in the Kormendy and Bender plot in Nature 469, 374-379 (2011), they all lose mass
statistically?
E. SALVADOR-SOLE ANSWER: In the paper you mention it is shown that, if dark matter haloes
predicted BH masses independent of their baryon content, then galaxy clusters should harbour very
massive BHs that are not seen. However, the only observed correlation is that between the masses
of SMBHs and (classical) bulges, not between SMBHs and disks as required by that premise. This
means that bulges grow in parallel to SMBHs in galaxy mergers, but the growth of diks through
gas accretion from haloes does not imply any BH growth. This is what our model considers and
there is no problem about that.
G. AURIEMMA QUESTION: I have not seen in the list of free parameters the dark matter mass.
E. SALVADOR-SOLE ANSWER: The mass of dark matter particles is not needed in the model
as we do not consider dark matter annihilation. We just need to know it is cold as the CDM power
spectrum of density fluctuations determines the evolution of dark matter haloes.
G. M. BUCHER: What is the process that turns off the Population III stars after the initial burst in
the double reionisation scenario?
E. SALVADOR-SOLE ANSWER: Population III stars form in neutral regions with primordial
metallicity which are rapidly ionised. Metals are then ejected inside those ionised bubbles so that
after the first ionisation phase is completed at z=10 they are spread over the whole Universe.
Consequently, during the subsequent recombination period, even though new neutral regions form,
they are metal-rich so that Population III stars cannot form anymore.
D. PAOLETTI Comment: Current CMB experiments are sensitive to the optical depth, but future
experiments will be able to constrain specific models of reionisation with constraints like the dura-
tion of the EoR and possibly be sensitive to the shape of the ionisation fraction which may be an
interesting development for the model presented.
14