SZ effect from radio-galaxy lobes: astrophysical and cosmological relevance

0.33 MB·English

by  S. Colafrancesco

Mon.Not.R.Astron.Soc.000,1–8(2008) Printed4February2008 (MNLATEXstylefilev2.2)
SZ effect from radio-galaxy lobes: astrophysical and
cosmological relevance
S. Colafrancesco1, 2, 3 ⋆
8 1ASI Science Data Center, ASDCc/o ESRIN, Via G. Galilei 00044 Frascati, Italy
0 2Agenzia Spaziale Italiana, Unit`a Osservazione dell’Universo, Viale Liegi 26 00198 Roma, Italy
0 3INAF - Osservatorio Astronomico di Roma, Via Frascati 33, Monteporzio 00040, Italy
2

n
a Accepted 2008January14.Received2008January14;inoriginalform2007February19
J

9
2 ABSTRACT
We derive the SZ effect arising in radio-galaxy lobes that are filled with high-energy,

]
non-thermal electrons. We provide here quantitative estimates for SZ effect expected
h
p from the radio galaxy lobes by normalizing it to the Inverse-Comptonlight, observed
- in the X-ray band, as produced by the extrapolation to low energies of the radio
o emitting electron spectrum in these radio lobes. We compute the spectral and spa-
r
tial characteristics of the SZ effect associated to the radio lobes of two distant radio
t
s galaxies (3C294 and 3C432) recently observed by Chandra, and we further discuss
a
its detectability with the next generation microwave and sub-mm experiments with
[
arcsec and ∼ µK sensitivity. We finally highlight the potential use of the SZE from

1 radio-galaxylobes in the astrophysical and cosmologicalcontext.
v
5 Key words: Active galactic nuclei – SZ: cosmology – theory.
3
5
4
.
1 1 INTRODUCTION theyarecurrentlyavailabletoproduceinverse-ComptonX-
0
ray emission and the relativistic SZ effect which we want
8 The Sunyaev-Zel’dovich effect (hereafter SZE, Sunyaev &
todiscusshere,beyondthelow-frequencysynchrotronradio
0 Zel’dovich 1972, 1980) is a powerful probe of the physical
emission.
: conditionsofelectronicplasmasinastrophysicalandcosmo-
v Inthiscontext,Erlundetal.(2006)foundthattheextended
i logical context (see Birkinshaw 1999 for a review). A SZE X-rayemissionobservedbyChandraalongthelobesofthree
X canbeproducedbythermal(hotand/orwarm)electronsin
powerful, high-redshift radio galaxies 3C 432, 3C 294 and
r theatmospheresofgalaxiesandgalaxyclusters(Birkinshaw
a 3C191 islikely duetoInverseCompton scattering(ICS)of
1999, Itoh et al. 1998, Colafrancesco et al. 2003), by non-
Cosmic Microwave Background (CMB) photons by the rel-
thermal (and relativistic) electrons in clusters and in the
ativistic electrons confined in the lobes. This is consistent
cavities produced by AGN radio lobes (Ensslin & Kaiser
with previous findings of X-ray emission from the lobes of
2000, Colafrancesco etal.2003,Colafrancesco 2005) andby
FR-IIradio galaxies (like 3C223 and 3C284, see Croston et
thesecondary electrons producedbyDarkMatter annihila-
al. 2004) attributed tothe same ICS of CMB photons.
tion in cosmic structures (Colafrancesco 2004), beyond the
Several studies have been already performed on inverse-
kinematic SZErelated tothe bulk motion of such plasmas.
Compton scattering in thelobes of radio galaxies and lobe-
ASZEfromthelobesofradiogalaxiesisalsoexpected(En-
dominatedquasarsatlowredshift(seee.g.Hardcastleetal.
sslin & Kaiser 2000, Colafrancesco et al. 2003, Blundell et
2002;Comastri etal.2003; Crostonetal.2004;Bondietal.
al. 2006, Colafrancesco 2005, 2007) but it has not been de-
2004;Kataoka&Stawarz2005;Crostonetal.2005;Hardcas-
tectedyet.Nonetheless,several indirectlimits canbesetto
tle & Croston 2005). These studies haveshown that the X-
the SZE from radio-galaxy lobes using both the available
rayemissionfromthelobesofradiogalaxiesistwo-sidedand
radio and X-rayinformation of these structures.
isnotdominatedbythejetinverse-ComptonX-rayemission,
In fact, detailed studies of radio-galaxy lobes (e.g.,
ashappensinsteadinpowerful,core-dominatedquasars(see,
Brunetti et al. 2002, Harris & Krawczynski 2002, Kataoka
e.g.,theprototypicalcaseofPKS0637-752, Tavecchioetal.
etal.2003,Crostonetal.2005,Blundelletal.2006endref-
2000).Onlyifrelativisticbeamingeffectsareimportant,the
erences therein) have shown that these extendedstructures
jetswill dominatethesynchrotronand/orinverse-Compton
containelectronsthathavepassedthroughtheinnerjetsand
emissiononkpcscales.Onthecontrary,itisclearthatrela-
the hotspots and are diffusing on larger-scale lobes where
tivisticbeamingisneverimportantinextendedradiolobes.
DetailedstudiesoftheICSX-rayemissionprovidecon-
⋆ E-mail:[email protected](SC) straints to the energetics of the electron population in the
2 S. Colafrancesco
lobes. Specifically, a lower limit on the electron energy in
thelobe,which isoforderofafewtimes1059 erg,hasbeen
derived for relativistic electrons that have an energy cutoff
γ ∼103 (see,e.g.,Erlundetal.2006),whereE =γm c2
min e
forrelativisticelectrons.Suchavalueofthelobeenergyhas
to be considered, however, as a lower limit since the total
energyestimatedependsontheshapeandontheextension
of theelectron spectrum (see eqs.1 and 2 below) and might
increase by even a large factor for lower values of γ and
min
steep electron spectra.
Under the assumption that the X-ray emission from
radio-galaxy lobes is due to ICS of CMB photons, a simple
energy argument yields a value of the minimum electron
energy E ≈ 0.35GeV(E /keV)1/2 that corresponds to
min X
γ ≈ 484 in order to be detected by Chandra in the
min
energy range 0.5−3.0 keV.
There are also various arguments indicating that realistic Figure 1. The simplified geometry of the IC emission in the
values of γmin are likely in the range ∼ 1−102 (see e.g. lobes of3C432 and 3C294. TheX-rayimageofthe sources have
Hardcastle et al. 2002; Comastri et al. 2003; Croston et al. been taken from Erlund et al. (2006). The two lobes have an
2004; Bondi et al. 2004; Kataoka & Stawarz 2005; Croston extension of Llobe ≈130 kpc and a transverse size of ≈30−40
et al. 2005; Hardcastle & Croston 2005). In this respect, kpc.ThecentralAGNsandthekpc-scaleloberegionareindicated
direct constraints on the value of γ of the order of byshadedcirclesandarenotconsideredinthisanalysis.
min
γ ∼ afew ·102 − 103 can be derived in radio galaxy
min
hotspots (see, e.g., Hardcastle 2001). Since we expect that
there is adiabatic expansion of the relativistic plasma out
SZE as a simplified geometry shown in Fig.1. In fact, the
of the hotspots, the value of γ in the radio galaxy
min specificcasesof theradio-galaxies 3C432 and3C294 canbe
lobes should then be substantially lower than the previous
representedbyacentralnon-thermalAGNpoint-likesource
estimate,andverylikely<102 (see,e.g.,alsothediscussion
(we consider for simplicity that the kpc-scale jet is within
in Blundell et al. 2006).
the same central AGN source) plus two symmetric lobes.
Thelinearsizeoftheobservedlobesofthesesourcesis∼130
Assuming that a unique electron spectrum is responsi-
kpc(forboth3C294 and3C432) andtheirtransversesizeis
blefortheradio(i.e.synchrotron)andX-ray(i.e.IC)emis-
in the range ∼30 to ∼40 kpc.
sionfeaturesofthelobes,thesameelectronpopulationthat
The photon spectral index derived from the extended
produces X-raysby ICS inevitably produces also an associ- ICS X-ray emission is Γ ∼ 1.57+0.27 (for 3C432) and Γ ∼
ated SZE which has a specific spectral shape that depends −0.36
2.08+0.11 (for 3C294). For a power-law electron spectrum
on the shape and on the energy extention of the relative −0.08
electronic spectrum. Such SZE emission is also expected to n (γ)=n γ−α (1)
e,rel e0
beco-spatial with the relative ICS X-ray emission.
Wepresentherepredictionsfortherelativistic,non-thermal the index α = 2Γ−1 takes values α = 2.14 (range 1.42−
SZE produced by the electrons diffusing within powerful 2.68, for 3C432) and α = 3.16 (range 3−3.38, for 3C294),
radio-galaxy lobes. A relevant aspect that motivated our respectively.
study is that more reliable estimates of the lobe SZE are The energy density of the electronic population in the lobe
obtainedbynormalizingtheenergyoftheelectronicpopula- is
tionresidinginthelobestotheavailableX-rayobservations γmax
of twospecificsources, 3C432 (at z=1.785) and3C294 (at E = dγne,rel(γ)γmec2. (2)
Z
z = 1.779). We study the amplitude and the spatial dis- γmin
tribution of the SZE from the lobes of these sources and For a value γ = 103, γ = 105 and Γ = 1.7 (i.e.,
min max
provide estimates of detectability with the next generation α= 2.4), Erlund et al. (2006) found a total energy, E =
tot
SZEinstrumentswitharcsecandµKsensitivity(likeALMA dV E integratedoverthevolumeV oftheradiolobe,
lobe lobe
and/or SPT). Wefinally highlight thepotential astrophysi- RofEtot≈3.7·1059 erg(for 3C432) andEtot≈5.9·1059 erg
calandcosmological relevanceofcombiningSZEandX-ray (for 3C294). The energy density estimate however changes
observations of radio-galaxy lobes. For a direct comparison for different choices of γ and α: while the spectral slope
min
of our results with the X-ray observations of Erlund et al. αcan bestimated from X-raydata(see,.e.g., theresultsof
(k2m00s6−)1wMepucs−e1,thΩe0s=am1eacnodsmΩoΛlo=gic0a.7l3m. odel with H0 = 71 aEnrdlunitdisetaactl.u2a0ll0y6a),ftrheee ppaarraammeetteerrγinmitnheisrnanotgeco∼ns1tr−ain1e0d2
(see discussion above).
The previous parameters allow to calculate realistic esti-
2 IC EMISSION FROM RADIO-GALAXY matesofboththeX-rayICSemissionfromtheradio-galaxy
LOBES lobeandofthespectralandspatialfeaturesoftheassociated
SZE.
For the purposes of this paper we describe the system of Inverse Compton (IC) scatterings of relativistic elec-
the powerful radio-galaxy lobes for which we calculate the trons on target cosmic microwave background (CMB) pho-
The SZ effect from radio-galaxy lobes 3
tons give rise to a spectrum of photons stretching from the ThegeneralizedexpressionfortheSZEwhichisvalidinthe
microwave up to the gamma-ray band.The IC power Thomson limit (γhν ≪ m c2 in the electron rest frame)
e
foragenericelectronpopulationintherelativisticlimitand
P (E ,E)=cE dǫn(ǫ)σ(E ,ǫ,E). (3) includesalsotheeffectsofmultiplescatteringsandthecom-
IC γ γ γ
Z
binationwithotherelectronpopulationshasbeenderivedby
is obtained by folding the differential number density of Colafrancesco et al. (2003) and we will refer to this paper
target photons n(ǫ) with the IC scattering cross section fortechnicaldetails.Accordingtotheseresults,thespectral
σ(E ,ǫ,E) given by theKlein-Nishina formula: distortion oftheCMB spectrumobservablein thedirection
γ
of theradio-galaxy lobe is
3σ
σ(E ,ǫ,E)= T G(q,Γ ) , (4)
γ 4ǫγ2 e (k T )3
∆I (x)=2 B CMB y g˜(x) , (12)
where σ is the Thomson cross section and lobe (hc)2 lobe
T
(Γ q)2(1−q) with x≡hν/kBTCMB, where the Comptonization parame-
G(q,Γe)≡(cid:20)2qlnq+(1+2q)(1−q)+ 2e(1+Γeq) (cid:21) (5) terylobe is
σ
with y = T P dℓ , (13)
lobe mec2 Z e
Γ =4ǫγ/(m c2) ; q=E / Γ γm c2−E . (6)
e e γ e e γ in terms of the pressure P contributed by the electronic
e
(cid:2) (cid:0) (cid:1)(cid:3)
HereǫistheenergyofthetargetphotonsandE theenergy population. The spectral function g˜(x) of theSZE is
γ
owthfietthhloetchuaelp-etsmhceaistestqievurietildyibporfihuoImCtonpsp.heoFctotolrdnuismnogfotefhnetehrIegCyeplEeocγwtroeorbntisan,innesqe:,.r(e3l), g˜(x)= mhεeeci2 (cid:26)τ1e (cid:20)Z−+∞∞i0(xe−s)P(s)ds−i0(x)(cid:21)(cid:27) (14)
in terms of the photon redistribution function P(s) and of
jIC(Eγ,r)=Z dEne,rel(E)PIC(Eγ,E) (7) i0(x)=I0(x)/[2(kBTCMB)3/(hc)2]=x3/(ex−1), where
∞
from which theintegrated flux density spectrum obtains: hε i≡ σT P dℓ= dpf (p)1pv(p)m c (15)
e τ Z e Z e 3 e
j (E ,r) 0
F (E )= dV IC γ , (8)
IC γ Z lobe 4πD2 is the average energy of the electron plasma (see Co-
lafrancesco et al. 2003). The optical depth of the electron
or theIC brightness along theline of sight (los)
population within the(cylindrical) lobe is
S (E )= dℓj (E ,r) . (9)
IC γ IC γ τ (p )=σ dℓn (p ) (16)
Z e 1 T Z e,rel 1
Here D is the luminosity distance to the lobe source. In and takes thevalue
Eq. (3) and Eq. (7) the limits of integration over ǫ and E
are set from the kinematics of the IC scattering which re- τ (p )≈4.1×10−8 ne,rel(p1) rlobe (17)
stricts q in therange 1/(4γ2)6q61. e 1 (cid:20)10−6cm−3(cid:21)(cid:18)10kpc(cid:19)
The IC emissivity of a radio lobe (whose geometry is along thelos to the centerof the lobe elongation axis.
sketched in Fig.1) in the energy range ∆Eγ from Eγ,1 to For low values of τe, the following expression of ∆Ilobe(x),
Eγ,2 is given by valid at first order in τe, holds:
3 (k T )4 8π ∆E −(α−1)/2 (k T )3
j = Acσ B CMB I(t)n γ ,(10) ∆I (x)=2 B CMB τ j (x)−j (x) , (18)
IC 4 T (hc)3 α+1 e0(cid:18) A (cid:19) lobe (hc)2 e(cid:20) 1 0 (cid:21)
where where j (x) = dsi (xe−s)P (s) and j (x) = i (x). The
1 0 1 0 0
I(t)= dtt3(et−1) (11) photon redistr′ibRution function P1(s) = dpfe(p)Ps(s;p)
Z with s = ln(ν /ν), in terms of the CMB pRhoton frequency
increase factor ν′/ν = 4γ2− 1, dependson the momentum
1w0it−h6tk≡eVh.νT/hkeBITCCMemBisasnivditEyγd=epAen(Eds/GbaesVic)a2llwyiothnAth=el2o.w1e3r· (wphincohrmaraelifizleldingtothmeerca)d3idoi-sgtarilba3xuytiolonb,ef.e(p) of the electrons
limitofintegrationEγ,1forα>2,ontheCMBtemperature Wedescribeheretherelativistic electron plasmawithin the
TCMB and on theelectron density normalization ne0. lobe with a single power-law momentum spectrum
f (p;p ,p ,α)=A(p ,p ,α)p−α ; p 6p6p (19)
e,rel 1 2 1 2 1 2
3 THE SZ EFFECT IN RADIO-GALAXY where the normalization A(p ,p ,α) = (α−1) , with
LOBES 1 2 p1−α−p1−α
1 2
α = 2.14 and 3.16 for the cases of 3C432 and 3C294, re-
The SZE seen along the los to a radio-galaxy lobe is pro- spectively.
duced by the ICS of CMB photons by the relativistic elec- In the calculation of the SZE from the lobes, the relevant
tronsconfinedintotheradio-galaxylobes.Assuch,theSZE momentum is the minimum momentum p of the electron
1
is – in this case – of a complete non-thermal nature, since distribution(whichisonlymarginally constrained byX-ray
the electron spectrum in the lobe can be represented by a observations) while the specific value of p ≫ p is irrele-
2 1
power-law distribution n ∼γ−α (see eq.1). vant for power-law indices α > 2, which are indicated by
e,rel
4 S. Colafrancesco
the electron spectra observed in radio galaxy lobes we con-
siderhere.Infact,forα>2andp ≫p ,thenormalization
2 1
A of theelectron spectrum A→ (α−1).
p1−α
1
The value of p sets the value of the electron density n
1 e,rel
as well as the value of the other relevant quantities which
depend on it, namely the optical depth τ , the pressure P
e e
and the energy density E of the non-thermal population.
e
The pressure P , for the case of an electron distribution as
e
in eq.(19), writes as
∞
1
P = n dpf (p) pv(p)m c (20)
e e,relZ e 3 e
0
= ne,relmec2(α−1) B α−2,3−α p1
6[p1−α]pp12 h 1+1p2 (cid:16) 2 2 (cid:17)ip2
(see,e.g.,Ensslin&Kaiser2000,Colafrancesco etal.2003),
where B (a,b) = xta−1(1−t)b−1dt. The energy density
x 0
for the same electrRon population writes as
∞ 1/2
E = n dpf (p) 1+p2 −1 m c2 (21)
e e,rel e e
Z (cid:20)(cid:18) (cid:19) (cid:21)
0
n m c2 1 α−2 3−α Figure 2. The CMB temperature change ∆T due to the SZE
= [ep,1re−lα]ppe12 (cid:20)2B1+1p2 (cid:16) 2 , 2 (cid:17) (22) f(rinomGHthze).loTbheessopfe3cCtr4a3l2shisapsehoowfn∆aTsiassfuhnowctniofnorofditffheerefrnetqvuaelnuceys
+p1−α (1+p2)1/2−1 (cid:21)p1 Eofmthine=mi0n.i1m1uGmeVen(ebrgluyeo),fEthmeienle=ctr0o.0n1s:GEemVin(c=ya0n.)49anGdeVEm(rined=),
(cid:0) (cid:1) p2 0.001 GeV (green). The level of brightness temperature due to
CMBprimaryanisotropy(dashedyellow)andtothesynchrotron
andforarelativisticpopulation ofelectronsE =3·P .For
e e
emissionoftheradio-galaxylobe(dottedmagenta)areshownfor
an electron population with a double power-law (or more
comparison.ThelevelofCMBbrightnesstemperatureduetothe
complex) spectrum, analogous results can be obtained (see
synchrotronemissioninthelobehasbeencomputedintheouter
Colafrancesco et al. 2003 for details).
partof the radiolobewhere ithas a brightness of 1mJy/beam.
Thelobesoftheradiogalaxieshereconsideredareassumed, Inner,higherradiobrightnessregionsproduceaCMBbrightness
for simplicity, to be cylindrical with a radius rlobe =20kpc. temperaturescaledupaccordingtotheirrelativeintensity.
Wealsoassumethattheelectronspectrumgivenbyeq.(19)
does not depend on the position within the lobe. The non-
thermal electron spectrum is normalized to reproduce the
valuesn and p which reproduce thepressure P (p ).
total energy E = dV E of the electronic component e,rel 1 e 1
tot lobe e
Weshow in Figs.2 and 3 theCMB temperature change
in the lobe as derivRed from the Chandra X-ray observa-
tions, after assuming (following Erlund et al. 2006) that: ∆T (ex−1)2 ∆I
i) γ = 103; and ii) the values of α derived from the IC = (23)
min (cid:18) T (cid:19) x4ex (cid:18) I0 (cid:19)
X-ray emission spectra observed for each source here con- lobe lobe
sidered. induced by the SZE in the case of the lobes of 3C432 and
ThetotalenergyestimatesgivenbyErlundetal.(2006)cor- 3C294, respectively. We stress that the lobe SZE is nega-
respond,hence,toarelativisticelectrondensityn (p )≈ tiveinsignatallmicrowavefrequencies,uptothecrossover
e,rel 1
2.77×10−9cm−3 for a value p = 9.6×102 and a slope frequency, i.e. the frequency x (P ) at which the SZE from
1 0 e
α = 2.14 for the case of 3C432, and to n (p ) ≈ 7.5× the electron population with pressure P is zero (see Co-
e,rel 1 e
10−10cm−3 for the same value p = 9.6×102 and a slope lafrancesco et al. 2003, Colafrancesco 2005). Its amplitude
1
α=3.16 for the case of 3C294. increasesfordecreasingvaluesofp ,whichconsistentlyyield
1
Given the value of E , the electron density n de- increasingvaluesofn ,andisspatiallylocatedonlyinthe
tot e,rel e,rel
creases/increases for increasing/decreasing values of p , ac- lobe regions (as also theIC X-ray emission).
1
cording to eqs.(20) and (21). Because the energy E (p = The crossover frequency, x (P ), of the SZE increases
tot 1 0 e
9.6·102) for each source has been obtained from theChan- with increasing values of p (i.e. E ) and, hence, of the
1 min
draobservationwithavalueofE =2keV(seeErlund lobe pressure/energy (see Figs 2 and 3). Thus, its deter-
X,min
etal.2006),correspondingtoaminimumenergyintheelec- mination can provide a unique probe of the overall pres-
tron spectrum of E =0.35GeV(E /keV)1/2 ≈0.49 sure/energy density of the electrons in thelobe and, hence,
min X,min
GeV,itshouldbedefinitelyconsideredasalowerlimittothe ofE for agiven electron spectrum (seeColafrancesco et
min
actual energy/pressure within the lobe. As a consequence, al. 2003). Figs. 4 and 5 show the dependence of the am-
theSZEnormalizedtothisenergyvalueisalsoalowerlimit plitudeof ∆T (evaluated at ν =200 GHz) associated to
lobe
to the actual SZE produced by the non-thermal electron thelobesof3C432and3C294asafunctionofthelowercut-
distribution within the lobe. Thus, given the observed lobe off E of the electron spectrum. Steeper power-law elec-
min
pressure P and the electron spectrum slope α, the relative tronspectraproducelargerSZEamplitudesatlowvaluesof
e
SZEtakesdifferentamplitudesandspectralfeaturesforthe E (for a fixedfrequency) because theyyield larger total
min
The SZ effect from radio-galaxy lobes 5
Figure 3.Sameas Fig.2butforthecaseof3C294. Thelevel of Figure 4. The value of ∆T(ν = 200GHz) predicted for 3C432
CMBbrightnesstemperatureduetothesynchrotronradioemis- (redcurve)asafunctionofEmin.Noiselevelson5arcsecbeam
sioninthelobehasbeencomputedintheouterpartoftheradio produced by primary CMB anisotropies (yellow line) and syn-
lobewhereithasabrightnessof2mJy/beam.Inner,higherradio chrotronradioemissionextrapolatedto200GHz(usingthelow-
brightnessregionsproduceaCMBbrightnesstemperaturescaled frequency spectral slopefor the source) fromthe lobes of 3C432
upaccordingtotheirrelativeintensity. with brightness levels of 1 mJy/beam and 12 mJy/beam (thick
magentalines)areshown.TheALMAsensitivityfor1monthand
1yrexposurewitha5arcsecbeamarealsoshownforcomparison.
energy/pressure and optical depth for the electronic popu-
lationandhencealargeramountofCMBphotonscattering
off thenon-thermalelectrons residing in thelobes.
4 BIAS AND CONFUSION
Possible sources of confusion and contamination for theob-
servation of the non-thermal SZE in radio-galaxy lobes are
the high-frequency tail of the synchrotron radio emission
from the lobes and CMB primary anisotropies on angular
scales comparable with theradio lobe size.
Iftheenergyspectraof3C294 and3C432 extenddown
to ∼ 0.003 GeV, or even lower energies, the expected SZE
at200GHzfromthelobesofthesesourcesare∼0.2µKfor
3C432and∼30µKfor3C294(seeFigs.4and5).Theseval-
ues correspond to diffuse fluxes of ∼ 0.16 µJy (for 3C432)
and ∼ 24.3 µJy (for 3C294), respectively, observable with
ALMA. To compare these values of the diffuse flux with
thoseemergingfromthelobesof3C432and3C294,wecon-
sideredherevariouslevelsofradioemissionfromtheselobes
(asreportedinFigs.2and6ofErlundetal.2006)andweex-
trapolated theircontributionto200GHz,i.e.thefrequency
region where the contribution of the synchrotron spectra is Figure 5. The value of ∆T(ν = 200GHz) predicted for 3C294
minimum (see Figs.2 and 3). (bluecurve)asafunctionofEmin.Noiselevelson5arcsecbeam
The level of synchrotron contamination depends in fact on produced by primary CMB anisotropies (yellow line) and syn-
the brightness level of the radio lobes and it is more en- chrotronradioemissionextrapolatedto200GHz(usingthelow-
frequency spectral slopefor the source) fromthe lobes of 3C294
hanced in the central part of the lobes rather than in their
with brightness levels of 2, 20 and 200 mJy/beam (thick cyan
external sides.
lines) are shown. The ALMA sensitivity for 1 month and 1 yr
For3C294wefoundthatthehighestbrightnesslevelof
exposurewitha5arcsecbeamarealsoshownforcomparison.
600mJy/beamat1.425GHz,foundintheinnerpartofthe
lobes,withanenergyspectralslopeofα=2.14(correspond-
ing to a synchrotron radio slope of α = (α−1)/2= 1.08)
r
6 S. Colafrancesco
producesabrightnessof≈2.88mJy/beamat200GHz.This extended lobes which are likely the sites of IC X-ray emis-
yields a CMB temperature brightness of ≈ 11.5 µK in a 5 sion.
arcsec beam. Such high level of contamination renders ex- In the previous estimates, we have assumed that the
tremely difficult todetect theSZEproducedin thelobes of same electron spectrum producingtheX-rayIC emission is
3C294 unless Emin reaches very low values ∼< 1 MeV (see also holding for the more energetic electrons producing ra-
Fig.5). diosynchrotronemission,andwehavefurthercalculatedthe
However,theabsoluteamplitudeofthenon-thermalSZEis contribution of the synchrotron emission by extrapolating
higher than the synchrotron brightness in the outer parts suchaspectrumfromlow(∼1.4−1.5GHz)radiofrequencies
ofthelobe,wheretheradiobrightnessdropsdowntolevels up to microwave (∼ 200 GHz) frequencies. Such a power-
of ≈ 2 mJy/beam (see Fig.5). It is clear that such obser- law extrapolation to 200 GHz likely maximizes the level of
vational evidence implies (as already noticed by Hardcas- synchrotron contamination to theSZE signal in thecase in
tle & Croston 2005) that either the magnetic field strength whichthereis,instead,abreakintheradiolobespectrumat
or the electron spectrum cannot remain constant through- intermediate(∼10−100GHz)frequencies.Preliminary ex-
out theradio-galaxy lobes. The case in which the magnetic ploration at high frequencies (see e.g. Looney & Hardcastle
field strength decreases throughout the lobe maximizes the 2000; Hardcastle &Looney 2001) indicatesthat radiolobes
chance of detection of the associated SZE. However, also canstillemitat100GHz(inthesourcerestframe,whichis
modelsinwhichboththemagneticfieldissomewhatweaker not really comparable to the 300 GHz source frame for the
and the electron spectrum is more depleted of high-energy z ∼ 2 radio galaxies considered here). However, it can be
electrons as a function of the distance from theinner jet (a argumented - on general grounds - that, in the absence of
favoured model for the lobes of Pictor A, see Hardcastle & anefficientandcontinuousparticle(re-)accelerationmecha-
Croston 2005) tend to favour the detectability of the non- nism acting in the lobes, synchrotron and inverse-Compton
thermalSZEintheouterloberegionsbecausesuchSZEef- losses will rapidly deplete particles capable of radiating at
fectismainlysensitivetothelow-energypartoftheelectron thesehighfrequencies.Forequipartitionfieldstrengthsof∼
spectrumwhichislikelynotvaryingmuchwiththedistance afewµG,thebreakfrequencyduetolossprocessesislikely
fromtheinnerjet.Therefore,undertheassumptionthatthe found below ∼ 300 GHz after ∼< 2 Myr from the electron
electron spectrum does not depend on the position within injection event (see discussion by Leahy 1991). Therefore,
thelobeand themagneticfield strengthdecreases through- forelectronsolderthanthisage,theextrapolationfromlow
outthelobe,theouterpartsoftheradiolobesofthissource radiofrequenciesupto∼200GHzwillcertainlyoverpredict
are the optimal regions to detect the non-thermal SZE and the level of synchrotron emission and of its contamination
therefore to set constraints to the valueof E and to the to theSZEsignal.
min
overall energetics of thelobe. Spatially resolved spectroscopic observations of radio lobes
For 3C432, the highest brightness level of 144 at microwave frequencies (70−350 GHz) will be definitely
mJy/beam at 1.54 GHz, found in the central part of the able to set constraints on the existence and frequency lo-
radio lobes, with an energy spectral slope of α=1.53 (cor- cation of the possible break of the radio synchrotron emis-
respondingtoasynchrotronradioslopeofα =(α−1)/2= sion and, hence, on models of the particle re-acceleration
r
0.57) produces a brightness of ≈ 9 mJy/beam at 200 GHz. in these cosmic environments. In the context of this explo-
This yields a CMB temperature brightness of ≈ 36 µK in rativestudyaimed todetect thenon-thermalSZEfrom the
a 5 arcsec beam. Such high level of contamination renders radiolobes,itisinstructivetonoticethatitispossibletoset
impossibletodetecttheSZEproducedinthelobesof3C432 some constraints on the slope and on the frequency of the
even for values of Emin ∼< 1 MeV (see Fig.4). The absolute synchrotronbreakfrom therequirementtohavelittle orno
amplitudeofthenon-thermalSZEintheradiolobesofthis contaminationoftheSZEsignalbyradioemission from the
source are always lower than the synchrotron brightness in lobe. Assuming, for simplicity, that the synchrotron radio
theouterpartsofthelobe(evenintheoptimalcaseinwhich spectrum is given by a double power-law, F = F0(ν/ν0)αr
the magnetic field strength decreases throughout the lobe), up to the break frequency ν∗ and by a steeper spectrum
exceptthanattheouterboundariesoftheradiolobes,where F = F∗(ν/ν∗)β at ν > ν∗, it is possible to show that the
theradiobrightnessdropsdowntolevelsof≈1mJy/beam, slope β required in order to have a negligible contamina-
providingaCMBtemperaturebrightnessof∼0.25µK(see tionofthelobesynchrotronemissiontotheSZEdiffuseflux
Fig.4). It would be, nonetheless, rather arduous to detect FSZE at frequency ν is
this feeble signal due to both the low signal-to-noise ratio
log(F /F )−α log(ν/ν )
and to thelong (∼1 year) exposure required for ALMA. β>α + 0 SZE r 0 , (24)
r (cid:20) log(ν/ν∗) (cid:21)
Thedifferentbehaviourofthecontaminationofthetwo
sources depends mainly on the different synchrotron spec- which cen be estimated in terms of measurable quantities
trahereassumed,whichrenderflatsynchrotronspectraex- F0,FSZE,αr,ν0 and ν∗.
trapolated at microwave wavelengths more contaminating Nonetheless, it is clear that there will still likely be emis-
for the SZE measurements than steep synchrotron spectra sion from regions with ongoing particle acceleration (like,
radio lobes. For the same reason, the lobes of 3C294, for e.g.,theinnerjetsandthehotspotsofradiogalaxies)which
whichasteeperelectron spectrumisindicatedbytheICX- mightevensubstantiallycontaminatetheSZEsignal.These
raydata,producealargeramountofSZEsignalforthecase regions are, however,spatially localized in thecentral parts
of low values of E because most of the Comptonization of the extended lobes and certainly not contaminating the
min
of the CMB radiation is produced by low-energy electrons. outer regions of the lobes of a typical radio galaxy like
It seems, therefore, that steep-spectra radio lobes are the 3C294, i.e. the regions where there is the maximum proba-
best cases to detect the non-thermal SZE expected in the bility to detect thenon-thermalSZE signal.
The SZ effect from radio-galaxy lobes 7
Finally,itshouldbenoticedthat–beyondthesubstan- Blundell et al. 2006) should be reconsidered: lower values
tialcontaminationlevelofthehigh-frequencytailofthesyn- of γ consistent with the total pressure/energy estimate
min
chrotron emission from the radio lobes – a multi-frequency inlobes,aslikelyprovidedbySZEobservations,wouldindi-
analysis of both the synchrotron and SZE signals (which catehighervaluesofB intheradiolobes.Estimatesofthe
eq
havequitedifferentspectrainthemicrowaveband,seeFigs. overall B-field in the lobe by co-spatial IC X-ray and radio
2 and 3) could greatly help in subtracting the synchrotron synchrotron emission, F /F ≈ u /u ∝ B2,
radio IC,Xray B CMB
signalfromtheSZEmapsofradiolobes,eveninthecaseof stronglydependontheassumptionthatthevastmajorityof
strongly contaminated sources like3C432. X-rayemission is provided by ICS of CMB photons(a sim-
Theothersourceofcontamination,i.e.,thermsvalueof ilar assumption is usually done for estimates of wide-scale
theprimaryCMBanisotropy(predictedintheviableΛCDM B-fieldingalaxyclusters,seediscussionbyColafrancesco et
cosmological model) on a 5 arcsec angular scale is of the al. 2005). Partial contamination of the lobe X-ray emission
order of ∼0.01 µK and it is therefore a marginal contribu- byotheremissionprocesseswould,therefore,lowerthevalue
tion (at most) to the SZE from the radio lobes in the two of F and in turn increase the estimate of theoverall
IC,Xray
sources here considered. In addition, contamination from B-field in thelobe.
CMB anisotropies to the SZE from the radio lobes would In this context, it is interesting to notice that a better es-
appear as a constant level bias in Figs.3 and 2. Therefore, timate of the overall B-field in the lobe through this tech-
a multifrequency analysis at microwave frequencies could nique could be obtained by using the ratio F /F ≈
radio SZE
clearly separate the CMB anisotropy contamination (hav- u /u , where the SZE signal is a much safer messen-
B CMB
ing a flat spectrum in the ∆T −ν plot) from the SZE ger of the CMB energy density which is reprocessed by all
CMB
(havinga specific non-flat spectrum in the same plot). the possible Compton scatterings induced by the full elec-
We conclude that detection of the SZE from high-z radio tron population in the radio-galaxy lobes. In addition, the
lobes is possible with the next generation high-sensitivity, spatially resolved study of the SZE and of the synchrotron
high-resolution experiments (like ALMA) if the electron emissioninthelobesofradio-galaxieslike3C294couldpro-
spectrum extends down to sufficiently low energies. Upper vide interesting indication on the radial behaviour of the
limitstothelobeSZEwillprovidealowenergylimitonthe magnetic field in these radio lobes.
electron spectrum which is by far more constraining than A corollary of the previous considerations is that SZE sig-
the limit set by the available X-ray observations. Similar nalsarecrucialtoconstrainthelobepressureandenergetics,
observationscanalsobemadeinnearbyradio-galaxieswith atleast oftheleptoniccomponent,andtomaptheleptonic
theSPTinstrumentthathasamoremoderate(∼20arcsec pressurefromtheinnerloberegionsouttolobeboundaries.
- 1 arcmin resolution) but similar (∼µK) sensitivity. The study of the pressure evolution in radio lobes can
also provide crucial indications on the transition from ra-
dio lobe environments to the atmospheres of giant cavities
observedingalaxyclusteratmospheres(see,e.g.,McNamara
5 ASTROPHYSICAL AND COSMOLOGICAL
& Nulsen 2007 for a review), which seem naturally related
PERSPECTIVE
to the penetration of radio-galaxy jets/lobes into theintra-
The spatial observation of theSZE from radio-galaxy lobes clustermedium(see,e.g.,theextremecaseofthegiantcav-
has relevant astrophysical and cosmological implications. itiesintheclusterMS0735.6+7421). Previousstudiesofthe
Westressthattheconstraintsonγ obtainablefrom spatialandspectralfeaturesoftheSZEingiantintracluster
min
SZE observations are much more reliable than those ob- cavities(Colafrancesco 2005) willbenaturallyconnectedto
tained from X-ray IC emission, because the SZE depends the developments of this preliminary study of the SZE for
on the total pressure/energy density (that depends on the radio-galaxy lobes. The development of experimental tech-
trueγ )oftheelectronicpopulationalongthelosthrough nology in microwave polarization will hopefully provide the
min
the lobe, while the IC X-ray emission can only provide an possibility to detect SZE polarization signals from radio-
estimate of the electron energetics, and hence of γ , in galaxy lobes and allow the possibility to build a full 3-D
min
the high-energy part of the electron spectrum, namely at tomography of radio lobes.
energies larger than E ≈ 0.35GeV(E /keV)1/2, where Wefinallystressthat,underthehypothesisthattheX-
min X
E isthelower energy threshold of theX-raydetector (see ray emission and the SZE from the radio-galaxy lobes are
X
discussion in Sect.1 above). The conclusions of Blundell et producedbythesamespatially-diffuseelectronicpopulation
al. (2006) on the discovery of a low energy cutoff in pow- andbythesamemechanism(i.e.ICSofCMBphotons),the
erful giant radio galaxies should, therefore, be rephrased in X-ray and the SZE brightness have to be co-spatial. If the
the previous framework. These authors found, indeed, only SZE along the los to the lobe is not found to be coinci-
that value of E ∼ 103 consistent with the lower energy dent with the relative IC X-ray emission, then the nature
min
threshold (∼ 1 keV) of their X-ray analysis of the radio- of the lobe should be different from that of a diffuse lep-
galaxy 4C39.24 (the previous value is of the same order of tonicplasma,anditsX-rayemission shouldbeproducedby
thatfoundbyErlundetal.2006,beinginfactobtainedwith a different mechanism.
the same X-ray instrument). SZE observations of the lobes To conclude this discussion, we outline here a few cos-
ofthissourceshouldprovidemuchmorereliableestimatesof mological implications of the SZE detectable from radio-
γ andhenceoftherelativevalueofγ inthecompact galaxy lobes. If the SZE and the IC X-ray flux of the lobes
min min
radio galaxy hotspots, where the energetic electrons have are produced by thesame electronic population, theratio
been likely originated.
Anestaiccfioenlsde,quBeenqce∝,aγlsm−oδinthweistchaliδng=fo(r2tαhre−eq1u)i/p(a3rt+itiαonr)m(asege- (F∆ITC,)lloobbee = 34rlobDeL2lobe(cid:20)g˜(x)(exx4−ex1)2(cid:21)mAec2ck1B
8 S. Colafrancesco
(hc)3 1 α+1 γ−(α−1) but also potentially important with the advent of the next
× min (25)
(kBTCMB)3I(t)α−1(∆Eγ)−(α−21) technology.
A Most of the non-thermal SZE signal is predicted to
between the SZE temperature decrement (∆T) and the be detectable in the outer regions of the radio-galaxy
lobe
X-ray IC flux F integrated in the energy band ∆E lobes,wheretheradiosynchrotroncontaminationdimsout.
IC,lobe γ
(seeeqs.12,13,23,8and10)providesanestimateofT Therefore, SZE detectability is likely possible with instru-
CMB
at the radio-galaxy redshift in terms of measurable quan- mentswitharcsecspatialresolutionandµKsensitivity(like
tities and fundamental constants. In other words, the ra- ALMA) in distant sources, and with a somewhat lower res-
tio (∆T)lobe providesan operative way to test theevolution olution instruments(like SPT) in nearby radio galaxies.
FIC,lobe
of the CMB temperature with redshift. For a specific lobe All the arguments presented in this paper show that the
source like 3C294, eq.(25) provides thescaling studyoftheSZEfromradio-galaxylobesarehighlycomple-
mentarytothestudyoftheirICX-rayemissionandarealso
∆T(100GHz) ≈ 0.72 µK (0.E01mGienV)−(α−1) crucial for theirastrophysical and cosmological relevance.
LIC(2−10keV) (cid:18)1044ergs−1(cid:19) ( Emin )−2.16
0.01GeV
1
×[2−(α−1)/2−10−(α−1)/2]. (26) ACKNOWLEDGMENTS
S.C. acknowledges fruitful suggestions made by the Referee
ofthispaper,M.J.Hardcastle,whichhaveledtoasubstan-
6 CONCLUDING REMARKS
tial improvement of thepresentation of the results.
We have shown in this paper that detailed predictions for
theSZEfromradio-galaxylobescanbeobtainedtakingad-
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