21cm Forest with the SKA

0.24 MB·English

by  Benedetta Ciardi

21cm Forest with the SKA
5
1
0
2
BenedettaCiardi

n MaxPlanckInstituteforAstrophysics,Garching,Germany
a
E-mail: ciardi at mpa-garching.mpg.de
J

9
SusumuInoue
1
InstituteforCosmicRayResearch,UniversityofTokyo,Tokyo,Japan

] E-mail: sinoue at icrr.u-tokyo.ac.jp
O
C KatherineJ.Mack
. UniversityofMelbourne,Melbourne,Australia
h
p E-mail: kmack at unimelb.edu.au
-
o YidongXu
r
t NationalAstronomicalObservatories,ChineseAcademyofSciences,Beijing,China
s
a E-mail: xuyd at nao.cas.cn
[

GianniBernardi
1 ∗
v SKASA,CapeTown,SouthAfrica
5 RhodesUniversity,Grahamstown,SouthAfrica
2
E-mail: giannibernardi at ska.ac.za
4
4
0 An alternativeto boththe tomographytechniqueandthe power spectrumapproachis to search
.
1 forthe21cmforest,thatisthe21cmabsorptionfeaturesagainsthigh-zradioloudsourcescaused
0
by the interveningcold neutralintergalactic medum (IGM) and collapsed structures. Although
5
1 the existence of high-z radio loud sources has not been confirmed yet, SKA-low would be the
:
v instrumentofchoicetofindsuchsourcesastheyareexpectedtohavespectrasteeperthantheir
i
X lower-zcounterparts.Sincethestrongestabsorptionfeaturesarisefromsmallscalestructures(few
r tens of physicalkpc, or even lower), the 21cm forestcan probethe HI density powerspectrum
a
on small scales not amenable to measurements by any other means. Also, it can be a unique
probeoftheheatingprocessandthethermalhistoryoftheearlyuniverse,asthesignalisstrongly
dependentontheIGMtemperature.HereweshowwhatSKA1-lowcoulddointermsofdetecting
the21cmforestintheredshiftrangez 7.5 15.
∼ −
AdvancingAstrophysicswiththeSquareKilometreArray
June8-13,2014
GiardiniNaxos,Italy
Speaker.
∗
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
21cmForestwiththeSKA GianniBernardi
1. Introduction
Analternativetoboththetomographytechniqueandthepowerspectrumapproachistosearch
for the 21cm forest, that is the 21cm absorption features against high-z radio loud sources caused
by the intervening cold neutral IGM and collapsed structures (e.g. Carilli, Gnedin & Owen2002;
Furlanetto &Loeb2002; Furlanetto 2006; Carilli etal. 2007; Xuetal. 2009; Xu,Ferrara&Chen
2011;Mack&Wyithe2012;Ciardietal. 2013;Ewall-Wiceetal. 2014). Infactthe21cmforestis
morethanacomplementtotomographyorpowerspectrumanalysis. Sincethestrongestabsorption
featuresarisefromsmallscalestructures,the21cmforestcanprobetheHIdensitypowerspectrum
onsmallscalesnotamenabletomeasurementsbyanyothermeans(e.g. Shimabukuroetal. 2014).
Also, itcanbeaunique probe oftheheating process andthethermal history oftheearlyuniverse,
asthesignalisstrongly dependent ontheIGMtemperature.
Thephotons emitted by aradio loud source at redshift z with frequencies n >n , willbe
s 21cm
t
removedfromthesourcespectrumwithaprobability1 e 21cm,absorbedbytheneutralhydrogen
−
−
present along the line of sight (LOS) at redshift z=n /n (1+z ) 1. The optical depth t
21cm s 21cm
−
canbewrittenas(e.g. Madau,Meiksin&Rees1997;Furlanetto, Oh&Briggs2006):
3 h c3A x n
t (z) = p 21cm HI H , (1.1)
21cm 32p k n 2 T(1+z)(dv /dr )
B 21cm s
k k
where n is the H number density, x is the mean neutral hydrogen fraction, T is the gas spin
H HI s
temperature (which quantifies the relative population of the two levels of the 2S transition),
1/2
A =2.85 10 15 s 1 is the Einstein coefficient of the transition and dv /dr is the gradient
21cm − −
of the proper×velocity along the LOS (in km s 1), which takes into accountkalsokthe contribution
−
of thegas peculiar velocity. Theother symbols appearing in theequation above have thestandard
meaningadopted intheliterature.
Analogously to the case of the Ly-a forest, this could result in an average suppression of
thesourceflux(produced bydiffuseneutralhydrogen), aswellasinaseriesofisolatedabsorption
lines(producedbyoverdenseclumpsofneutralhydrogen),withthestrongestabsorptionassociated
withhighdensity,neutralandcoldpatchesofgas. Thissuggeststhattheabsorptionfeaturesdueto
collapsed structures withnoorverysmallstarformation (tomaximizethe amountofHIavailable
for absorption), such as minihalos or dwarf galaxies (Furlanetto & Loeb 2002; Meiksin 2011;
Xu, Ferrara & Chen 2011) would be easier to detect than those due to the diffuse neutral IGM.
However,thisdoesstrongly dependonthefeedback effectsactingonsuchobjects. Becauseofthe
large uncertainties inthenatureandintensity ofhigh-zfeedback effects(forareviewseeCiardi&
Ferrara2005anditsupdated versionarXiv:astro-ph/0409018), itisnotstraightforward toestimate
therelativeimportance oftheabsorption signalsfromthediffuseIGMandfromcollapsed objects.
While gas which has been (even only partially) ionized has a temperature of 104 K, gas
∼
whichhasnotbeenreachedbyionizingphotonshasatemperaturewhichcanbeevenlowerthatof
theCMB.ThisneutralgascanbeheatedbyLy-a orX-rayphotons,thusreducingtheopticaldepth
to21cm. WhileLy-a heating isnotextremely efficient,heating duetoX-rayphotons couldeasily
suppress theotherwisepresent absorption features (e.g. Mack&Wyithe2012;Ciardietal. 2013).
Thisseemstosuggestthatwithobservationsofthe21cmforestitwouldbepossibletodiscriminate
betweendifferentIGMreheating histories, inparticular ifahighenergycomponentintheionising
spectrum werepresent(Ewall-Wiceetal. 2013).
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21cmForestwiththeSKA GianniBernardi
2. Observed spectra
InthisSectionwedescribetheprocessusedtosimulateanobserved spectrum. Thesimulated
absorption spectrum, S ,iscalculated from afull3D radiative transfer simulation ofIGMreion-
abs
izationwhichresolvesscalesof 1kHz(corresponding to 50kpccomoving;Ciardietal. 2012;
∼ ∼
Ciardi et al. 2013). In the simulation used here, the contribution to ionization and heating from
x-raysand/orLy-a photonsisnotincluded(althoughseeCiardietal. 2013forexamplesofspectra
whichincludesucheffects),i.e. thegaswhichisnotreachedbyUVionizingphotonsremainscold.
The instrumental effects are estimated using the pipeline of the LOFAR telescope. More
specifically, theequation givingtheobserved visibilities is:
Vn (u)=Ns(cid:229)ourcesIn (s)e−2p iu·s+ns, (2.1)
i
where u=(u,v,w) are the coordinates of a given baseline at a certain time t, In is the observed
sourceintensity, s=(l,m,n)isavectorrepresenting thedirectioncosinesforagivensourcedirec-
tionandn represents additivenoise. Thenoiseisgivenbytheradiometerequation:
s
1 SEFD
n = , (2.2)
s h √2t D n
s int
where h is the system efficiency, D n is the bandwidth andt is the integration time. Because of
s int
our experience with the LOFAR telescope, we will make predictions based on its characteristics,
andwewillthenscalethenoisetomatchtheoneexpectedfromSKA.Wethusassumethath =0.5
s
andN =48. Thesystemequivalent fluxdensity isgivenby:
st
2k T
B sys
SEFD= , (2.3)
Ndiph a Aeff
wherek isBoltzmann’sconstant,A =min(l 2,1.5626)istheeffectiveareaofeachdipoleinthe
B eff 3
denseandsparsearrayregimesrespectively,N isthenumberofdipolesperstation(24tilestimes
dip
16 dipoles per tile for a LOFARcore station) and h a is the dipole efficiency which weassume to
be1. ThesystemnoiseT hastwocontributions: (i)fromtheelectronicsand(ii)fromthesky. We
sys
assumethattheskyhasaspectralindexof-2.55,obtainingT =[140+60(n /150MHz) 2.55]K.
sys −
ThecompleteFourierplanesamplingcanbedonebyevaluatingtheaboveequationforeverysetof
baselinecoordinates. ThepredictedvisibilitiesarethengriddedandtransformedviainverseFourier
transforms in order to obtain the dirty images. For the purpose of the 21 cm forest, fine spectral
resolution ( 1kHz, see later for further discussion) is needed, which means that the spectra need
∼
to be predicted for a large number of channels ( 10000). After assembling the full image cube,
∼
the LOS spectrum is extracted. In principle, the effect of the Point Spread Function (PSF) side
lobes running through the source of interest can be taken into account by including more sources
at different positions, with or without absorption features. Here, we have ignored the effect of
side lobe noise. In fact, as the SKA will have a very dense uv coverage and the expected 21cm
absorption lines will be narrower than a few tens of kHz, we expect the side lobe noise to play a
marginal role.
Figure 1 shows the 21cm absorption spectrum due to the diffuse IGM along a random LOS
for a bright radio source at z=10 (i.e. n 129 MHz). For an easy comparison to existing work
∼
3
21cmForestwiththeSKA GianniBernardi
Figure1:Upperpanels:Spectrumofaradiosourcepositionedatz=10(n 129MHz),withapower-law
∼
index a =1.05 and a flux density J =50 mJy (lefthand panels) and 10 mJy (righthandpanel). The red
dottedlines referto theinstrinsic spectrumofthe radiosource, S ; the bluedashedlines tothe simulated
in
spectrum for21cm absorption,S (in a universewhereneutralregionsremaincold); and the black solid
abs
linestothespectrumfor21cmabsorptionasitwouldbeseenwithanobservationtimet =1000handa
int
frequencyresolutionD n =10kHz. ThefirstpaneltotheleftcorrespondstoacasewiththeLOFARnoise,
whiletheothertwopanelshave1/10thoftheLOFARnoise,roughlyexpectedforSKA1-low.Lowerpanels:
Theratios /s correspondingtotheupperpanels.
abs obs
onthe21cm forest(e.g. Carilli, Gnedin &Owen2002; Mack&Wyithe 2012; Ciardietal. 2013),
the intrinsic radio source spectrum, S , is assumed to be similar to Cygnus A, with a power-
in
law with index a =1.05 and a flux density J =50 mJy and 10 mJy. The simulated absorption
spectrum, S , iscalculated from the simulations mentioned above. The observed spectrum, S ,
abs obs
iscalculatedassuminganobservationtimet =1000hwiththeLOFARandSKA1-lowtelescopes
int
and abandwidth D n =10kHz. A clear absorption signal isobserved. Thisis moreevident in the
lower panels of Figure 1, which show the quantity s /s , where s =S S and i=abs, obs.
abs obs i i in
−
As already mentioned above, the inclusion of Ly-a or x-ray heating could suppress or reduce the
absoprtion features, withthe extent of the effect being highly dependent on the source model (see
e.g. Mack&Wyithe2012;Ciardietal. 2013).
Very strong absorption features could be easily detected also at lower redshift, when most of
the IGM is in a highly ionization state, if we were lucky enough to intercept high density cold
pockets ofgas(witht >0.1;thesecellsarefoundin 0.1%oftheLOSinthesimulation), as
21cm
∼
showninFigure2.
Movingtowardshigherredshift,whenmostofthegasintheIGMisstillneutralandrelatively
cold, would offer the chance of detecting a stronger average absorption (rather than the single
absorption featuresobserved atlowerredshift). Ifaradiosourcewithcharacteristics similartothe
ones described above were found, SKA1-low would easily detect the global absorption as shown
inFigure3,although itwouldnotbestraightforward todistinguish whetherthesuppression ofthe
4
21cmForestwiththeSKA GianniBernardi
Figure2:Upperpanels:Spectrumofaradiosourcepositionedatz=7.6(n 165MHz),withapower-law
∼
index a =1.05 and a flux density J =50 mJy (lefthand panels) and 10 mJy (righthandpanel). The red
dottedlines referto theinstrinsic spectrumofthe radiosource, S ; the bluedashedlines tothe simulated
in
spectrum for21cm absorption,S (in a universewhereneutralregionsremaincold); and the black solid
abs
linestothespectrumfor21cmabsorptionasitwouldbeseenwithanobservationtimet =1000handa
int
frequencyresolutionD n =5kHz. Thefirstpaneltotheleftcorrespondstoa casewith theLOFARnoise,
whiletheothertwopanelshave1/10thoftheLOFARnoise,roughlyexpectedforSKA1-low.Lowerpanels:
Theratios /s correspondingtotheupperpanels.
abs obs
sourcefluxwereduetotheintervining neutralIGMoranintrinsically lowerflux.
3. Challenges
Themostchallenging aspectofthedetection ofa21cmforestremainstheexistence ofhigh-z
radio loud sources. Although a QSO has been detected at z=7.085 (Mortlock et al. 2011), it is
radio quiet (Momjian et al. 2014), and the existence of even higher redshift quasars is uncertain.
Toobservetheabsorptionfeaturesinthespectrum,thishastobeobservedwithacertainprecision,
whichdependsonthebrightnessofthequasarandthesensitivityoftheinstruments. Theminimum
detectable fluxdensityofaninterferometer canbewrittenas:
2k T S
D S = B sys , (3.1)
min A√D n t N
int
where A is the collecting area of the array and S/N is the signal-to-noise ratio. As one may not
be able to distinguish whether the flux decrement were due to the diffuse IGM or an intrinsically
lower flux, we will probably only detect the additional absorptions with respect to the absorption
by the IGM. Therefore, the minimum flux density of the background source required to observe
theabsorption linesis:
S/N 0.01 5kHz 1/2 1000m2K 1 1000hr 1/2
−
S = 10.3mJy .(3.2)
min (cid:18) 5 (cid:19)(cid:18)e tIGM e t (cid:19)(cid:18) D n (cid:19) (cid:18) A/T (cid:19)(cid:18) t (cid:19)
− − sys int
−
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21cmForestwiththeSKA GianniBernardi
Figure3: Upperpanels: Spectrumofaradiosourcepositionedatz=14(n 95MHz),withapower-law
∼
index a =1.05 and a flux density J =50 mJy (lefthand panels) and 10 mJy (righthandpanel). The red
dottedlines referto theinstrinsic spectrumofthe radiosource, S ; the bluedashedlines tothe simulated
in
spectrum for21cm absorption,S (in a universewhereneutralregionsremaincold); and the black solid
abs
linestothespectrumfor21cmabsorptionasitwouldbeseenwithanobservationtimet =1000handa
int
frequencyresolutionD n =20kHz. ThefirstpaneltotheleftcorrespondstoacasewiththeLOFARnoise,
whiletheothertwopanelshave1/10thoftheLOFARnoise,roughlyexpectedforSKA1-low.Lowerpanels:
Theratios /s correspondingtotheupperpanels.
abs obs
The SKA1-low will have A/T 1000m2K 1, and we expect A/T 4000m2K 1 for SKA2-
sys − sys −
∼ ∼
low.
Extrapolating the observed number density of radio sources at z=4 (Jarvis et al. 2001) to
higher redshift and lowerluminosity, one can calculate the number ofquasars withfluxdensity at
theobservedfrequencyn =1420.4/(1+z)MHz largerthanthelowerlimitdescribedabove,for
obs
aflatevolutionmodelandasteepevolutionmodelrespectively(Xuetal. 2009). Usingtheplanned
SKAsensitivities, thepredicted numbersofqualifiedradiosourcesareplottedinFig.4.
Thepredictednumberofradiosourceswhichcanbeusedfor21cmforeststudiesinthewhole
skyper unitredshift atz=10varies intherange 8 102 2 104. Thisexpected number, which
× − ×
is based on observations at redshift lower than reionization, is very uncertain. The exact number
depends on the model adopted for the luminosity function of such sources and the instrumental
characteristics (e.g. Carilli, Gnedin & Owen 2002; Xu et al. 2009), making such a detection an
extremelychallengingtask. Asareference,theestimatedquasarnumberperunitredshiftatz=10
forthe3-tieredsurveyisreported inTable1.
If a sufficiently bright radio loud quasar were found beyond the redshift of reionization, then
the absorption lines generated from early non-linear structures could be easily detected, as the
spectral resolution of the SKA will not be a problem. Assuming the minimum halo mass hosting
cold neutral gas to be 106M , about one absorption line in every 8.4kHz is expected at redshift
⊙
z 10. The absorption line density is lower for lower redshift and higher minimum mass. On
∼
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21cmForestwiththeSKA GianniBernardi

105 Flat evolution Steep evolution 105
104 104
z
d
N/
d103 103
102 SKA1−low: A/Tsys = 1000 m2/K SKA1−low: A/Tsys = 1000 m2/K 102
SKA2−low: A/T = 4000 m2/K SKA2−low: A/T = 4000 m2/K
sys sys

6 8 10 12 14 6 8 10 12 14
z z
t t
Figure4:Thenumberofquasarsinthewholeskythatcanbeusedtodetectsignalswithe− IGM e− 0.01
− ≥
perredshiftinterval.ThesensitivityoftheradioarrayistakentobeA/T =1000m2K 1(blacksolidlines)
sys −
and4000m2K 1 (bluedashed). Theintegrationtimeisassumedtobe1000hours. Leftpanel: thenumber
−
of qualified quasarsin the flat evolutionmodel. Rightpanel: the numberof qualifiedquasarsin the steep
evolutionmodel.
dN/dz Model W [sqd] t [h] A/T [m2K 1]
int sys −
11 Flat 100 1000 1000
27 Flat 1000 100 1000
68 Flat 10000 10 1000
57 Flat 100 1000 4000
142 Flat 1000 100 4000
358 Flat 10000 10 4000
2 Steep 100 1000 1000
5 Steep 1000 100 1000
12 Steep 10000 10 1000
10 Steep 100 1000 4000
25 Steep 1000 100 4000
63 Steep 10000 10 4000
Table1: Estimatedquasarnumberatz=10forthe3-tieredsurvey. Thecolumnsreferto: numberperunit
redshift,sourcemodel,surveyarea,observationtime,A/T .
sys
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21cmForestwiththeSKA GianniBernardi
the other hand, the line width from non-linear structures ranges mostly from 1kHz to 5kHz.
∼ ∼
Given that the SKA1-low will have a spectral resolution of 1kHz, the line counting is feasible as
long as sufficiently bright radio sources are available at high redshift. Especially, if one stacks
together several lines to get an average profile, it will hopefully reveal the physical status of the
earlynon-linear structures.
Analternativepossibilityistheradioafterglowsofcertaintypesofgamma-raybursts(GRBs).
GRBshavealreadybeenobserveduptoz 8 9,anditisplausiblethattheyoccuruptotheearliest
∼ −
epochsofstarformationintheuniverseatz 20orhigher. Inaddition, theyhaveasimplepower-
∼
law spectrum at low frequencies, making the signal extraction easy. However, if such GRBs are
similartothoseseenatlowerredshifts, theirradioafterglows arenotexpectedtobebrightenough
at the relevant observed frequencies n . 100 MHz due to strong synchrotron self-absorption
obs
(Ioka & Meszaros 2005; Inoue, Omukai & Ciardi 2007). On the other hand, it has been recently
proposed that GRBs arising from Population (Pop) III stars forming in metal-free or very metal
poorenvironmentsmaybemuchmoreenergeticcomparedtoordinaryGRBs,leadingtoblastwaves
expanding to much larger radii, and consequently much brighter low-frequency radio afterglows,
exceedingtensofmJy(Toma,Sakamoto&Mészáros2011). Thisoccursovertimescalesofupto
∼
1000yr,makingthemvirtuallysteadyradiosources,differentlyfrommorestandard,lowerredshift
GRBswhich,ontheotherhand,offerrelativelyshortintegrationtimesandalimitedspectrallength
between the location oftheGRBand theendofreionization (e.g. Xuetal. 2011). InFigure 5we
show anexampleofabsorption spectra inhigh-zGRBs,from bothPopIIIandPopIIstars (Ciardi
etal.,inprep).
IftherateofPopIIIGRBswithsufficientlybright radioemission is0.1yr 1 orroughly 10 4
− −
of all GRBs, one may expect 100 such sources all sky at a given time. A practical question
∼
that remains is how we can observationally identify such sources. One possibility of using GRB
afterglows asthebackground radiosourceisthebroad-band observation, measuring themeanflux
decrement ineachbandwithoutresolving individual absorption lines(Xuetal. 2011).
4. Discussionand Summary
Asexplained above, absorption features due to small collapsed objects can be much stronger
than those due tothe diffuse neutral IGM.Sincetheir cross-sections aresmall, thebestconditions
fordetectingthemwouldbewhenLy-a couplingpushesthespintemperatureintheirlowerdensity
outskirtstothegastemperaturebeforetheseregionshavebeenaffectedbyanyheating(seeFig.22
in Meiksin 2011), conditions expected above z 10. However, even after heating has started to
∼
suppress the 21cm absorption signal, someweak features due tocollapsed structures mayremain.
Interestingly, even when it may not be possible to detect these weak features individually, the
presence of absorption may be detected statistically. Weak absorption would produce an increase
in the variance of brightness fluctuations, as an addition to the telescope noise, resulting in an
apparently noisier spectrum blue-ward ofthe21cm transition (seeFig. 29inMeiksin 2011;Fig. 8
in Mack &Wyithe 2012). Thepossibility to have astatistical detection of the 21cm forest (rather
thanthedetectionofsingleabsorptionfeatures),isintriguingasthesignatureoftheforestwouldbe
observed inthe21cm powerspectrum (seealsoEwall-Wiceetal. 2013). Byintegrating thesignal
frommanyhighredshiftsourceswithinthefieldofview,wouldreducethesensitivityrequirements
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21cmForestwiththeSKA GianniBernardi
Figure5: Upperpanels: SpectrumofaGRBpositionedatz=10(n 129MHz),withapower-lawindex
∼
a =0.5andafluxdensityJ=30mJy(GRBfromPopIIIstars; lefthandpanel)and0.1mJy(GRBfrom
PopIIstars;righthandpanel).Thereddottedlinesrefertotheinstrinsicspectrumofthesource,S ;theblue
in
dashedlinestothesimulatedspectrumfor21cmabsorption,S (inauniversewhereneutralregionsremain
abs
cold);andtheblacksolidlinestothespectrumfor21cmabsorptionasitwouldbeseenwithanobservation
time t =1000 h and a frequency resolution D n =10 kHz. The panel to the left (right) corresponds to
int
a case with 1/10th (1/100th) of the LOFAR noise, roughly expected for SKA1-low (SKA2-low). Lower
panels: Theratios /s correspondingtotheupperpanels.
abs obs
of the instrument. On the other hand, the main problem of the paucity of high-z radio sources
wouldpersist.
Theattempt todetect the 21cm forest has the potential to provide unprecedented information
about the large-scale evolution of the intergalactic medium as well as the growth of small-scale
structures. Different information can be gleaned depending on the nature of the observation. An
attempt to detect the presence of the 21cm forest via a statistical analysis of the power spectrum
(Ewall-Wice et al. 2013) will allow us to put constraints on the presence of high-redshift radio-
loud sources at high wavenumbers (k& 0.5 Mpc 1), and to study the IGM thermal history at low
−
wavenumbers (k. 0.1Mpc 1). Assuming high-redshift radio-loud sources are identified, and we
−
are able to observe them directly in targeted observations, detailed study of the source spectra
can reveal the mean thermal properties of the IGM via the flux decrement (Furlanetto 2006) or
variance in the flux (Carilli et al. 2004; Mack & Wyithe 2012). If individual absorption features
areidentifiedinthespectrum, thiscouldallowustoputconstraints ontheclumpingfactoratearly
times(Xu,Ferrarra&Chen2011)andtomapstructurealongthelineofsight(IGMand/orthefirst
collapsed structures andmini-halos), thussignificantly extendingourunderstanding oftheprocess
ofreionization andthehierarchical growthofstructure intheUniverse.
Finally,wewouldliketocommentonthefactthatasobservations ofthe21cmforestrequire
very high frequency resolution, they are demanding both in terms of data storage and processing.
However, when a bright continuum radio source is identified after an all-sky survey or deep EoR
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21cmForestwiththeSKA GianniBernardi
observations, itispossibletosignificantlyaverageintimeafterphasinguptothesource. Themax-
imum amount of data compression willbe dictated by the need toidentify and subtract bright, far
away sources that maygenerate sidelobe noise in the measurement of the 21 cm forest. However,
ifbrightsourcesaremeasuredapriorifromaskysurveytheycanbesubtractedfromthehightime
resolution visibilities and, afterwards, data can be easily compressed by an order of magnitude or
more.
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