Table Of ContentRedshifted 21 cm Emission From the Pre-Reionization Era
II. H II Regions Around Individual Quasars
Katharina Kohler, Nickolay Y. Gnedin
CASA, University of Colorado, Boulder, CO 80309, USA; kohlerk,[email protected]
5
0
Jordi Miralda-Escud´e
0
2 Department of Astronomy, Ohio State University, Columbus, OH 43210; [email protected]
n and
a
J
0 Peter A. Shaver
1 ESO, Karl-Schwarzschild-Strasse 2, Garching, D-85748, Germany; [email protected]
2
v
6
8
ABSTRACT
0
1 We use cosmological simulations of reionization to predict the effect of large HII regions
0
around individual high-redshift quasars on the possible signal from the redshifted 21cm line of
5
0 neutralhydrogeninthepre-reionizationera. WeshowthattheseHIIregionsappearas“spectral
/ dips” in frequency space with equivalent widths in excess of 3mK MHz or depths in excess of
h
about1.5mK,andthattheyarebyfarthemostprominentcosmologicalsignalsintheredshifted
p
- HI distribution.
o Thesespectraldipsareexpectedtobepresentinalmosteverylineofsight. Ifthespectraldips
r
t of a large enough sample of HII regions are well resolved in frequency space, the distribution of
s
linedepthandequivalentwidthinfrequencywithaknownobservingbeamsizecanbeusedtoinfer
a
: theHIIregionsizedistributionandthemeandifferenceinneutralhydrogendensitybetweenthe
v
HII regions( which maycontainself-shielded neutralgasclumps) and the surroundingmedium,
i
X providing a powerful test for models of reionization.
r
a Subject headings: cosmology: theory - cosmology: large-scale structure of universe - diffuse radiation -
galaxies: formation - galaxies: intergalactic medium - radio lines: general
1. Introduction by discrete sources. The latter source of 21cm
fluctuations was discussed in the pioneering work
Theoreticalinterestinthe redshifted21cmline
of Scott & Rees (1990), Madau, Meiksin, & Rees
signalfromintergalactichydrogenbeforeanddur-
(1997), and Tozzi et al. (2000), but has received
ingthereionizationerahassurgedinrecentyears.
only limited attention recently (Wyithe & Loeb
Fluctuations in the 21cm signal can be generated
2004).
by variations in the density, spin temperature, or
However, ionized (HII) regions around high-
ionized fraction of the intergalactic gas. These
redshift quasarscan easily reachsizes comparable
could arise from primordial density fluctuations,
to the angular beams of future radio telescopes
from spatial variations of the radiation intensity
such as LOFAR and SKA. Thus, they could be
near the wavelength of the Ly-α hydrogen line
the most prominent features in the angular and
(which affects the spin temperature), from other
frequency distribution of the redshifted 21cm sig-
radiation that can heat the gas, or from HII re-
nal from the early universe, and the first features
gions created during the process of reionization
1
to be measured observationally. the gas is followed in every cell as determined by
In this paper we estimate the effects of these the local radiation intensity.
large features on the possible cosmological sig- Inthisspecificprojectweuseamulti-resolution
nal by using numerical simulations of reioniza- approachthatutilizesasmall-scalesimulationasa
tion. This becomes feasible now as simulations “sub-cell” model for larger-scalesimulations. The
of reionization reach the level of sophistication “sub-cell” model is implemented by using the so-
and accuracy sufficient to model quantitatively called “clumping factors”, which account for the
not only the small-scale details of reionization structure on scales too small to be resolved in a
(Gnedin 2004), but also very large regions (up to large-scale simulation. The complete description
ahorizonsize: Kohler,Gnedin,&Miralda-Escud´e ofourapproachandtheappropriatetestsarepre-
2004). The latter approach is used here, because sented in a separate paper (Kohler et al. 2004).
quasars are relatively rare at high redshift, and Using the clumping factor formalism allows us
sufficiently large computational volumes (several to increase the size of the simulation box to sev-
hundred Mpc in size) must be used to include a eralhundredcomovingMpc,whilesimultaneously
representative sample of quasars. accounting for the ionizing radiation transfer and
We concentrate solely on the redshifted 21cm recombination rate in a gaseous medium that is
signal in the frequency domain, because, as has highly inhomogeneous on small scales.
been shown before, foreground contamination is In our simulation of reionization, we add in-
a severe limiting factor in observing the cosmo- dividual quasars as discrete, luminous sources of
logical features in the angular domain on the sky ionizingradiationinadditiontotheemissionasso-
(Di Matteo et al. 2002; Oh & Mack 2004; Gnedin ciated with star-formation. The luminosity distri-
& Shaver 2004). Several recent papers have dis- bution of quasars added to the simulation is cho-
cussed elegant and sophisticated approaches to sen from the model of Schirber & Bullock (2003).
circumventing this contamination (Zaldarriaga, This model is consistent with all known observa-
Furlanetto & Hernquist2004;He etal.2004;San- tionaldataontheevolutionofthequasarluminos-
tos et al. 2004, Loeb & Zaldarriaga 2004), but ity function, including recent GOODS data (Cris-
these approaches would require bigger telescopes tianietal.2004). Theimpactofquasarsonreion-
than currently planned, so it is most likely that ization depends of course on the luminosity func-
the first detections will be made in the frequency tion at very high redshift, z = 6, before reioniza-
domain and attempts to de-contaminate the an- tionended,sowehavetoextrapolatetheSchirber
gular signal will require follow-on observations. & Bullock model to redhifts higher than observed
quasar redshifts, which introduces a substantial
2. Simulation uncertainty. Our goal, therefore, is to discuss a
rangeofpossibilities,asprecisepredictionsarenot
InordertomodelthespectralsignaturesofHII
possible. The extrapolated luminosity function of
regions in the early universe, we need to simulate
quasars introduced in the simulation is shown in
alargeenoughregionofspacethatincludesbright
Figure 1 for z = 10; the finite box size causes
quasars during the reionization era. Such quasars
the discreteness effects observed at high luminos-
aresparseathighredshift,sinceinthehierarchical
ity end. Our simulation box includes quasars up
structure formation paradigm they only form in to a luminosity of about 1012LSun at z = 10 (al-
extreme over-densities at early times.
though quasars this luminous are rare, and there-
The simulation code we use is a modified ver-
fore appear in only a few lines of sight).
sionofthe“Softened-LagrangianHydrodynamics”
In our simulation we include biasing of sources
codedescribedinGnedin(2004),whichfollowsthe
of ionizing and Ly-α radiation. Specifically, we
evolution of dark matter and gas. The code in-
assume that galaxies are biased with a bias factor
cludes a model for star formation in regions of
oftwo,while quasarsarebiasedwith abias factor
dense gas that can cool, and for the emission of
ofthree. In this workwe do notconsiderredshift-
ionizing radiation from stars. Radiative transfer
dependent bias factors.
is fully included using the method described in
The specific simulation used in this paper has
Gnedin &Abel (2001),andthe ionizationstate of
2
Gnedin & Shaver 2004). For the redshift range
that we consider in this paper (corresponding
to frequencies largely above the FM bands), the
atomic gas is heated above the CMB tempera-
ture and produces an emission signal. Therefore,
HII regions should produce dips in the spectrum
because they contain less neutral hydrogen than
their environment, so their emission is reduced
compared to the regions around them. We shall
generallyrefertotheseHIIregionfeaturesasdips.
Note that these dips look like absorption features
eventhoughtheyhavenothingtodowithabsorp-
tion.
The basic observable properties of the spectral
Fig. 1.—Ouradoptedquasarluminosity function
dipofanHIIregionareitswidthanddepth. The
atz =10,as extrapolatedfromSchirberandBul-
depthdependsontheionizationfraction,gasden-
lock(2003). Thedash-dottedline showsthe lumi-
sity, spin temperature, and also on the angular
nosity of a typical quasar which is expected to be
size of the HII region if this angular size is not
′
present in almost all 10 observational beams.
resolvedbythebeamoftheradiotelescopethatis
used (the angular size of a typical observable HII
1283 cells with an average comoving cell size of region is about 1.5−2arcmin). The width of the
2h−1Mpc. The box size of 256h−1Mpc allows us spectral dip in frequency space is determined by
the radial extent of the ionized region (assuming
to resolve individual HII regions around typical
quasars at z ∼ 8 − 10, although it is still too that peculiar velocities are small compared to the
Hubble expansion across the HII region).
smalltoincludethebrightesthigh-redshiftquasars
found in the Sloan Digital Sky Survey (Fan et In practice, the detected cosmological HII re-
al. 2003). But since we are interested in typical gions will probably be smaller than the angular
(rather than the rarest,most extreme)features in size of the radio beam. However, if the HII re-
the redshifted 21cm signal, this simulation is suf- gions are resolved in frequency, their frequency
ficient for our purpose. widthdeterminestheirsize. Thus,theaveragelin-
ear (and angular) size for a sufficiently large sam-
3. 21cm “Spectral Dips” due to Quasar ple of observed HII regions can be estimated (for
HII Regions a given cosmological model) from the frequency
data alone, and, taking into account the dilution
We now investigate the characteristics of HII by the known radio beamsize, the actual average
regions as they appear in the redshifted 21cm depth of the spectral dip can be inferred from the
spectra from neutral hydrogen. The intergalactic measured dip depth.
hydrogen can be observed in absorption or emis-
In this paper, however, we do not investigate
sion against the CMB, depending on whether the
such a measurement any further, because it will
spintemperatureislowerorhigherthantheCMB
mostlikely require a largenumber ofindependent
temperature. Althoughanabsorptionsignalisex-
lines of sight.
pectedwhentheearliestemissionofLy-αphotons
The average depth of a spectral dip is related
occurs (which couples the spin and kinetic tem-
to the difference in the amount of neutral hydro-
perature of hydrogen, bringing the spin tempera-
gen present (on average) inside and outside an
turebelowtheCMBtemperature;seeMadauetal.
HII region. The observational determination of
1997), the 21 cm signal in our simulation quickly
this quantity would introduce a new tool for test-
turns into emission, as X-rays, far-ultraviolet ra-
ing models of reionization. In the HII regions
diation, and weak shocks from structure forma-
the fraction of gas that is still atomic depends on
tion heat the atomic gas to a temperature higher
how much of the gas in collapsed, low-mass ha-
thantheCMB(e.g.,Chen&Miralda-Escud´e2004;
los remains self-shielded, and how much has been
3
ionized and evaporated from halos (e.g., Shapiro, tion of the horizon distance, so we simulate the
Iliev, & Raga 2004), a process that is important line of sight on a fixed past light-cone instead of
to determine the clumping factors of ionized gas. a fixedcosmictime, usingconsecutive outputfiles
Outside the identified HII regions, the fraction at different timesteps of the simulation. We also
of gas already ionized depends on the presence of accountforafiniteobservingbeamsizebyconvolv-
hard photons and low-luminosity sources produc- ing the 21cm signal over a plane perpendicular to
ing unresolved ionized regions. Determining the the line of sight with a Gaussian beam, with a
dip depth distribution will requirea largenumber physical radius that varies over the line of sight
of independent lines of sight, and the theoretical according to a fixed angular size of a radio beam
interpretation will be complex. In the rest of this Θb.
paper we focus on how spectral dips due to HII The starting redshift of our spectra is z = 13,
regions can be identified. which corresponds to a frequency of 101MHz.
In the absence of HII regions, the distribution Thisredshiftwaschosentoplacetheresultingfre-
of brightness temperature of the redshifted 21cm quency in the range of next-generation radio ob-
signal should be Gaussian, reflecting the imprints servatories. Weused450independentlinesofsight
ofcosmicdensity fluctuations,whicharelinearon to accumulate sufficient statistics.
the large scales that are most easily observable. After the synthetic spectrawerecreatedin this
The HII regions add additional features in the way, we analyzed the brightness temperature dis-
spectrum that are mainly caused by variations in tribution for signatures of HII regions. The pro-
neutral fraction. Gaussian regions of lower emis- cess we followed for this analysis consists of the
sion correspond to regions of lower density, but followingsteps. First, we fit the meansignalhTBi
HIIregionsusuallyhavehigherthanaverageden- with a fourth-degree polynomial in order to re-
sity and a dramatically lowered neutral fraction. move variations on a very wide frequency scale.
This canbe usedfor distinguishing Gaussianfluc- Thisprocess,similartothecontinuumfittingused
tuations fromthose causedby the ionizationfrom in the analysis of Ly-α forest spectra, is intended
quasarsinthe simulation,butinrealobservations as an approximation to the removal of the com-
we will have to rely on the intrinsic properties of bined galactic and extragalactic foregrounds and
spectraldips toseparateHIIregionsfromdensity the cosmological mean signal in an observation.
fluctuations. In the next two sections we will use Next, we calculate the fluctuating signal as:
our simulation to predict how such a separation
can be made from the observational data. ∆TB =TB−hTBi, (1)
4. Analysis of Simulated Lines of Sight to obtainafluctuating signalwith zeromeanthat
canbesearchedforHIIregiondips. Fortheanaly-
We now discuss how we use the output at con- siswedisregardallpartsofthespectruminwhich
secutive timesteps from the simulation described theemissionexceedsthemeansignal,whichcorre-
in §2 to create synthetic spectra of redshifted spond to regions of high gas density that are part
21cm emission. These spectra reflect the large- of linear Gaussian fluctuations. We are then left
scaledistributionofgasdensity,spintemperature, with a spectrum showing dips due to both Gaus-
and hydrogen neutral fraction. The spin temper- sian fluctuations (corresponding to regions of low
ature is computed self-consistently in the simu- gasdensity)andHIIregionsaroundbrightsources
lation including the effects of Ly-α pumping and (correspondingtoregionsofverylowneutralfrac-
collisions with electrons and neutral atoms (see tion compared to the averagemedium).
Gnedin & Shaver 2004 for details). The pixel size
in the spectra is set by the cell size of 2h−1Mpc, 5. Results
which corresponds to a frequency range of about
0.2MHz at z ∼9. InFigure2weshowanexampleofatypicalline
ofsightwiththe meansignalsubtracted. The top
The synthetic spectra are created by casting a
panel shows the brightness temperature fluctua-
random line of sight through the simulation box.
Oursimulatedlinesofsightspanasignificantfrac- tion∆TB versusν after subtractingthe meansig-
nal. AsignificantfluctuationduetoanHIIregion
4
Fig. 3.— The auto-correlation function of the
brightness temperature ∆TB as a function of
FWHM frequency width δν.
HII region around a typical high-redshift quasar
expands in the already pre-heated gas, in which
the spin temperature of the 21cm transitionis al-
ready much higher than the CMB temperature,
so the extra Ly-α radiation from the quasar does
not leadto an increasein the emission. We would
like to re-emphasize here that, since we are treat-
Fig. 2.—Toppanel: the fluctuationinthebright- ingthe radiativetransferinfull3D,wedoinclude
ness temperature ∆TB as a function of frequency the proximity effect of the increased Ly-α radia-
in a 10′ beam with a 0.5MHz bandwidth. Also tion aroundquasars,but this effect, as our results
shown are the 5σ sensitivity limits for a 1000hrs indicate, is not significant.
integration time (Shaver et al. 1999). Bottom TodistinguishHIIregionsfromunder-densere-
panel: the distribution of gas density (gray) and gions with low neutral hydrogen density, we now
hydrogen neutral fraction (black) along the same lookatthedistributionofdensityandneutralfrac-
line of sight. The HII region spectral feature can tion in the same frequency range in the data ob-
be seen at ν =144MHz. tained from the simulation.
The bottom panel in Figure 2 depicts the vari-
at ν = 144MHz is easily identifiable in the spec- ations in these two parameters. The neutral frac-
trum. Superimposed are the 5σ sensitivity limits tion shows a dip at ν = 144MHz, whereas the
for an integration time of 1000hrs and a band- density shows a definite increase. Consequently
width of 0.5MHz (we discuss our choice for the wecandeterminethatthisfluctuationresultsfrom
bandwidth below). a high density region containing more ionized gas
than the average. We expect to find quasars in
Itisimportanttonoteherethatourresultsdif-
high density regions since their population is bi-
fer to a smalldegreefromthe predictions of Tozzi
ased. Iftheradiationintensitywereapproximately
etal.(2000)andWyithe&Loeb(2004)inthatwe
uniform, we would expect to find lower densities
do not observean increasein the redshifted 21cm
of neutral gas in under-dense regions of the IGM,
emission just outside the HII region. This is due
becauseofthedecreasedrecombinationrate. Here
to the fact that the main source of Ly-α radia-
the high density and ionized fraction of the IGM
tion that couples the gas kinetic temperature and
allowustoconcludethatthespectraldipiscaused
thespintemperatureofthe21cmtransitioninour
by an HII region surrounding a bright quasar.
simulationisnormalgalaxies. Since,inoursimula-
tion,galaxiestypicallyformbeforethequasars,an The fluctuations in the brightness temperature
on large scales are expected to be Gaussian, re-
5
Fig. 4.— The histogram of ∆TB for the normal-
izedspectrumfromFigure2: noticethelongtailof
the non-Gaussian contribution from HII regions.
flectingthelarge-scalevariationsinthecosmicgas
density and neutral fraction. However, on suffi-
ciently smallscalesthe fluctuationsbecome corre-
lated. Thus, unless the beam size of a radio tele-
scope is small enough (less than about 1 arcmin)
toresolveindividualHIIregionsaroundhighred-
shift galaxies, one would expect the cosmologi-
calsignalto become smoothonscalescomparable Fig. 5.— Top panel: in black is shown the distri-
to the correlation length of high redshift galax- bution of equivalent widths and sizes of the spec-
ies. Figure 3 shows the auto-correlationlength of tral dips from 450 lines of sight. The gray data
the brightness temperature from the line of sight shows the same distribution for a pure Gaussian
showninFig.2Thus,decreasingthebandwidthof distribution. Bottompanel: Asimilarplotbutfor
observationtobelowabout0.5MHzwillnotresult equivalent width versus the depth of the spectral
in measuring new information in the signalunless dip distribution.
it also coincides with a decrease in the beam size
(this is also apparent from Fig. 11 of Gnedin &
fluctuations.
Shaver2004). Intherestofthispaper,weassume
afixedvalueof0.5MHzforthebandwidthforour We use a simple calculation of the equivalent
fiducial beam size of 10′. width of each dip as a way to measure the dip
depth. We integrate the area below the mean
In addition to investigating individual spec-
signal for each dip (i.e. a connected region with
tra as shown above, we can use the variations
of brightness temperature around the average to ∆TB < 0), and compile a distribution for all the
dips of 450 different spectra. This distribution is
look at the distribution of spectral dips statisti-
showninFigure5byplottingtheequivalentwidth
cally. Figure4showsahistogramofthedifference
versusthedipwidthinfrequencyspace(measured
in brightness temperature of the spectrum in Fig-
as FWHM). As a comparison, we also show the
ure 2. One can see the tail of the distribution
same distribution for artificial lines of sight that
on the negative ∆TB side that correspondto dips
contain no HII regions, so that any dips are en-
in the spectrum due to quasar HII regions. The
tirelyduetoGaussianvariationsincosmicdensity.
peak centered around ∆TB = 0 is mainly due to
theGaussianfluctuations,butthelongtailonthe Itisclearthatthelargestequivalentwidthsand
negative∆TB reaching∆TB =−4.5mKshowsthe depths correspondtoHIIregionsaroundquasars,
significant contribution from regions that are due since the Gaussian density variations do not gen-
to ionized regions and not from Gaussian density erate such large dips. The radial sizes, as shown
6
by ∆ν, of both samples are comparable,since the
Gaussian density fluctuations also yield the wide
dips seen in the spectra. However, the Gaussian
fluctuationsaremuchshallower,ascanbeseenby
the smaller values in the equivalent width. There
is also a range of smaller equivalent widths that
is not reached with purely Gaussian fluctuations.
This could be due to faint quasars in the simula-
tioncausingthe smallfeatures. Judgingfromthis
graph, all spectral dips with equivalent width in
excess of 3mKMHz or depth in excess of 1.5mK
are caused by individual HII regions.
We can also look at cumulative distributions
of various parameters characterizing these spec-
tral dips, which are shown in Figures 6, to de-
termine which are due to Gaussian fluctuations
comparedtotheonesduetoHIIregions. Thefig-
ure shows distributions for the simulated fluctua-
tionsinblackandcontrastsitwiththedistribution
for pure Gaussian fluctuations in gray. From Fig-
ure 6a it is again clear that all spectral dips with
equivalentwidths inexcessofabout3mKMHz or
depths inexcessof about1.5mK arecomingfrom
high-redshift HII regions. The widths of the dips
in frequency space, however, cannot be used to
separate HII regions from linear Gaussian fluctu-
ations. From these graphs we can infer that there
isaboutaoneinthreechancetodetectanHIIre-
gionwithequivalent width inexcess of3mKMHz
ineachline ofsight, butnarrowerdeepdips (with
depth in excess of 1.5mK) are present in almost
any line of sight.
The results shown in Figures 6 were obtained
for a bandwidth of 0.5MHz, but as long as the
bandwidthislessthanabout1MHz,spectraldips
fromHIIregionsareresolved(ascanbeseenfrom
Fig.5a),andthedistributionsofequivalentwidths
and depths remain the same.
6. Discussion
We have shown that by far the easiest to ob-
serve features of the cosmological signal of red-
Fig. 6.— Top: The cumulative distribution of
shifted 21cm emission from neutral hydrogen
spectral dips per line of sight as the function of
in the pre-reionization era are the spectral dips
thedipwidth∆ν (measuredasFWFM-top), the
due to individual HII regions from high-redshifts
equivalentwidth(middle),andthedepth(bottom)
quasars. The largest of these features can be eas-
for the simulated spectra (black) and for purely
ily distinguished from Gaussian fluctuations due
Gaussian fluctuations (gray).
to large-scalestructure: for example, we find that
allspectraldipswithequivalentwidthinexcessof
7
3mKMHz or depth in excess of 1.5mK come ex- gas most likely is locked inside Lyman-limit sys-
clusively from quasar HII regions (for a 0.5MHz tems, an important constraint can be put on the
bandwidth). abundance of low mass objects.
Thesedipsarenotrare-forouradoptedplausi- In conclusion, the spectral features predicted
ble (albeit uncertain) extrapolation of the quasar in this paper - the spectral dips due to HII re-
luminosity function, detectable dips are present gions around individual high-redshifts quasars -
in almost every line of sight. This conclusion will be the most prominent signals in the red-
may sound counterintuitive to the common wis- shifted 21cm line of neutral hydrogen from the
dom that “high redshift quasars are rare”, but pre-reionizationera. Their spectralsharpnesswill
we need to emphasize that the quasars that cre- easily distinguish them from the smoothly vary-
atedetectableHIIregionsaremuchlessluminous ingcontinuumspectraoftheforegroundemissions,
(and much more numerous) than, say, SLOAN andtheirstrengthshouldmakethemdetectablein
′
quasars. Besides, a 10 beam (for example) go- reasonableintegrationtimes with the new genera-
ing from z = 6 to z = 12 (the onset of the FM tion of low frequency radio telescopes.
radioband)containsasignificantvolumeofabout
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