Non-thermal Sunyaev-Zeldovich signal from radio galaxy cocoons
MMNRAS , 1–12 (2020) Preprint 9 September 2020 Compiled using MNRAS L A TEX style file v3.0
Non-thermal Sunyaev-Zeldovich signal from radio galaxycocoons
Sandeep Kumar Acharya, (cid:63) Subhabrata Majumdar, † Biman B. Nath ‡ Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India Raman Research Institute, Sadashiva Nagar, Bangalore 560080, India
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Energetic electrons in the cocoons of radio galaxies make them potential sources fornot only radio and X-rays but also Sunyaev-Zeldovich (SZ) distortions in the cosmicmicrowave background (CMB) radiation. Previous works have discussed the energeticsof radio galaxy cocoons, but assuming thermal SZ effect, coming from the non-thermalelectron population. We use an improved evolutionary model for radio galaxy cocoonsto estimate the observed parameters such as the radio luminosities and intensity ofSZ-distortions at the redshifts of observation. We, further, quantify the the effects ofvarious relevant physical parameters of the radio galaxies, such as the jet power, thetime scale over which the jet is active, the evolutionary time scale for the cocoon, etc onthe observed parameters. For current SZ observations towards galaxy clusters, we findthat the non-thermal SZ distortions from radio cocoons embedded in galaxy clusterscan be non-negligible compared to the amount of thermal SZ distortion from the intra-cluster medium and, hence, can not be neglected. We show that small and young (andpreferably residing in a cluster environment) radio galaxies offer better prospects forthe detection of the non-thermal SZ signal from these sources. We further discuss thelimits on different physical parameters for some sources for which SZ effect has beeneither detected or upper limits are available. The evolutionary models enable us toobtain limits, previously unavailable, on the low energy cut-off of electron spectrum( p min ∼ – ) in order to explain the recent non-thermal SZ detection (Malu et al.2017). Finally, we discuss how future CMB experiments, which would cover higherfrequency bands ( >
400 GHz), may provide clear signatures for non-thermal SZ effect.
Key words:
Radio galaxy – CMB spectral distortions – Cosmology
Studying the distortion of the cosmic microwave backgroundradiation (CMB) through the Sunyaev-Zel’dovich effect (SZeffect) (Zeldovich & Sunyaev 1969) has become a main-stay of modern cosmology. The inverse Compton scatter-ing of the CMB photons by energetic electrons has openedup a new window of probing the warm and hot gaseous re-gions of the universe (Birkinshaw 1999; Aghanim et al. 2008;Mroczkowski et al. 2019). Being complementary to the tra-ditional X-ray observation of these ionized regions, SZ effectnot only enables a robust determination of their physicalproperties, but also makes it possible to study them at highredshift, and consequently, study their evolution. The inten-sity of distortion of CMB does not dilute with increasing (cid:63) [email protected] † [email protected] ‡ [email protected] redshift resulting from the fact that the energy density ofscattered CMB photons and the intensity of CMB photonshave same functional dependance on redshift.Besides energetic thermal electrons in hot gas, non-thermal relativistic gas can also produce SZ signal, whosedistinct spectral signature makes it an interesting probe ofreservoirs of such gas in the universe (Enßlin & Kaiser 2000;Majumdar 2001). One source of energetic particles can beradio galaxy cocoons where relativistic particles are suppliedby the radio jet (Scheuer 1974; Begelman & Cioffi 1989; Nath1995), which was first predicted by Felten & Rees (1969)soon after the discovery of CMB. The pressure from theenergetic particles can push out the surrounding gas withthe size of the cocoon growing to megaparsec length scales(Baldwin 1982; Kaiser et al. 1997). Recent detection of X-ray emission from radio lobes has been explained through in-verse Compton scattering of CMB photons by non-thermalrelativistic electrons that are responsible for the radio emis-sion (Croston et al. 2005; Erlund et al. 2008; Fabian et al. © a r X i v : . [ a s t r o - ph . H E ] S e p Acharya, Majumdar & Nath y -distortion (Zeldovich & Sunyaev1969). In previous works,Yamada et al. (1999) & Majumdar(2001) had estimated the global y − distortion caused by ra-dio galaxies to be ≈≥ − , using a simple model of radio co-coon evolution and cosmological population of radio galaxiesconstructed from the Press-Schechter mass function.In this paper, we first present an improved model forthe evolution of radio cocoons in order to predict the non-thermal SZ signal from radio galaxy cocoons which can betargets for upcoming SZ observations. We use the galaxyevolution model of Kaiser et al. (1997) (KDA1997 hereafter)with suitable modification for jet stopping as in Nath (2010)(N2010 hereafter). We explicitly keep track of the evolu-tion of the relativistic particles. We then calculate the non-thermal SZ spectrum from these population of relativisticparticles. Using the procedure detailed in this work, futureobservations of non-thermal SZ effect can be used to put con-straints on the underlying physical model of radio galaxies,for example, that on the jet luminosity and lifetime, as alsoon the nature of relativistic population of electrons drivenout by the radio jet, for example, the lowest energy thresholdof the electron spectrum. The rest of the paper is arrangedas follows: In Sec 2 we lay down our model for the radiogalaxy cocoons, followed by physics related to SZ distor-tions from non-thermal relativistic population of electronsin Sec 3. These are combined to estimate the non-thermalSZ from radio cocoons in Sec 4. Next, Sec 5 & 6 discussthe degeneracies in model parameters and the prospects offuture detection of non-thermal SZ effect. We discuss ourresults in 7 and, finally, conclude in 8. For calculating theangular diameter distance in converting angular to physicalsize we use H = 67 kms − Mpc − , Ω M = 0.32, Ω Λ = . (Aghanim et al. 2018). We start by assuming that the jet of the radio galaxy, whichhas a luminosity Q j , injects relativistic particles through-out the jet lifetime t j ( ≈ – yr), after which it ceases tobe active. The injected energy causes a cocoon around the
100 1000 R a d i o po w e r ( W H z - S r - ) size of cocoon (kpc) Figure 1.
Comparison of radio power, at 150 MHz, ob-tained in this work (in thick lines) with the corresponding val-ues in KDA1997 (thin lines) for the three cases as given inKDA1997 (their Fig. 1). The parameters for the blue (dot-dashed), red (dashed) and black (solid) lines correspond to [ Q j (ergs − ), z ] = [( , ), ( , . ) & ( , . )] respectivelywhere Q j is the jet luminosity and z is the observed redshiftof radio galaxy.The spectral index of electron energy is taken tobe α = . . jet to expand against the surrounding medium. We describethe density profile of the surrounding gas with a power law, ρ ( r ) = ρ ( ra ) − β g with β g =2 (Wang & Kaiser 2008). Thisdensity profile can be written as, ρ ( r ) = Λ r − , with Λ = gcm − (Fukazawa et al. 2004; Jetha et al. 2007). The cocoonnon-thermal electron energy distribution is assumed to be apower law with, n ( γ i , t i ) = n γ − α i d γ i , where γ i is the Lorentzfactor of electrons at time of injection t i , and α is the spec-tral index. We assume the minimum γ min = and the max-imum, γ max = . The evolution of the radio cocoons canbe described by (Reynolds & Begelman 1997), Q j ( t ) = Γ c − ( V c . p c + Γ c p c . V c ) , dL j dt = (cid:18) p c ρ (cid:19) / , (1)where Q j ( t ) is the jet luminosity which is non-zero when jetis on ( t < t j , where t j is the jet lifetime) and zero for t > t j , Γ c = , V c is the volume of the cocoon, p c is the pressure inthe cocoon, L j is the fiducial size of the cocoon and ρ is thedensity of surrounding gas. We assume the axial ratio of thecylinder shaped cocoon to be R = , the average observedratio (Leahy & Williams 1984). The volume of the cocoonis then given by, V c = π R L j . (2)The magnetic and particle energy densities in the cocoonare given by, U B ( t ) = Ap c ( t )( Γ c − )( + A ) , U e ( t ) = p c ( t )( Γ c − )( + A ) , (3)where A = ( + α )/ (Kaiser & Alexander 1997). For a com-parison with result of KDA1997, we first consider the casewhen jet is on all the time. We then proceed to compute theradio flux at 150 MHz as a function of time or size of thecocoon. Assuming that for synchrotron radiation, an elec-tron emits only at the frequency ν = γ ν L , where ν L is the MNRAS000
Comparison of radio power, at 150 MHz, ob-tained in this work (in thick lines) with the corresponding val-ues in KDA1997 (thin lines) for the three cases as given inKDA1997 (their Fig. 1). The parameters for the blue (dot-dashed), red (dashed) and black (solid) lines correspond to [ Q j (ergs − ), z ] = [( , ), ( , . ) & ( , . )] respectivelywhere Q j is the jet luminosity and z is the observed redshiftof radio galaxy.The spectral index of electron energy is taken tobe α = . . jet to expand against the surrounding medium. We describethe density profile of the surrounding gas with a power law, ρ ( r ) = ρ ( ra ) − β g with β g =2 (Wang & Kaiser 2008). Thisdensity profile can be written as, ρ ( r ) = Λ r − , with Λ = gcm − (Fukazawa et al. 2004; Jetha et al. 2007). The cocoonnon-thermal electron energy distribution is assumed to be apower law with, n ( γ i , t i ) = n γ − α i d γ i , where γ i is the Lorentzfactor of electrons at time of injection t i , and α is the spec-tral index. We assume the minimum γ min = and the max-imum, γ max = . The evolution of the radio cocoons canbe described by (Reynolds & Begelman 1997), Q j ( t ) = Γ c − ( V c . p c + Γ c p c . V c ) , dL j dt = (cid:18) p c ρ (cid:19) / , (1)where Q j ( t ) is the jet luminosity which is non-zero when jetis on ( t < t j , where t j is the jet lifetime) and zero for t > t j , Γ c = , V c is the volume of the cocoon, p c is the pressure inthe cocoon, L j is the fiducial size of the cocoon and ρ is thedensity of surrounding gas. We assume the axial ratio of thecylinder shaped cocoon to be R = , the average observedratio (Leahy & Williams 1984). The volume of the cocoonis then given by, V c = π R L j . (2)The magnetic and particle energy densities in the cocoonare given by, U B ( t ) = Ap c ( t )( Γ c − )( + A ) , U e ( t ) = p c ( t )( Γ c − )( + A ) , (3)where A = ( + α )/ (Kaiser & Alexander 1997). For a com-parison with result of KDA1997, we first consider the casewhen jet is on all the time. We then proceed to compute theradio flux at 150 MHz as a function of time or size of thecocoon. Assuming that for synchrotron radiation, an elec-tron emits only at the frequency ν = γ ν L , where ν L is the MNRAS000 , 1–12 (2020) on-thermal SZ from radio cocoons x p min = Table 1.
Value of g NT ( x ) as in Fig. 2 at the frequency band ofSimons Observatory (Ade et al. 2019). Larmor frequency, we calculate the number density of elec-trons with Lorentz factor γ which will emit at 150MHz as a function of time t . We then find the value of γ i which were injected at time t i < t and which would havecooled to γ at time t. The equation for evolution ofelectron Lorentz factor γ is given by, d γ dt = −
13 1 V c dV c dt − σ T m e c γ ( U B + U C ) , (4)where σ T is Thomson cross-section, m e is the mass of elec-tron, c is the speed of light, U B , U C are the magnetic energydensity and CMB energy density, respectively. The normal-isation of particle spectrum n at time t i is given by (Kaiseret al. 1997; Nath 2010), n ( t i ) = U e ( t i ) m e c ∫ γ max γ min ( γ i − ) γ − α i d γ i . (5)The number density of electrons with γ = γ , at time t due to expansion of cocoon, is given by, n ( γ ) = n γ − α i γ (cid:18) p c ( t i ) p c ( t ) (cid:19) − , (6)where V c dV c dt = L j dL j dt and cocoons are assumed to evolveself-similarly (as warranted by the assumption of a constantaxial ratio). Any volume segment of the cocoon at time t can be related to pressure at time t i as, δ V ( t ) = ( Γ c − ) Q j p c ( t i ) ( R ) ( − Γ c )/ Γ c (cid:18) p c ( t ) p c ( t i ) (cid:19) / Γ c δ t i , (7)where δ t i is the time interval over which electrons were in-jected. Then, the power emitted at t at 150 MHz is given by, P ν = ∫ t π σ T cU B γ ν n ( γ ) δ V , (8)where the integral is done over electron injection time t i . Forjet shutdown at time t j , the upper limit of integral shouldbe min( t , t j ) (Nath 2010).In Fig. 1, we have compared our results with the resultof KDA1997 with the jet on for all the time for three dif-ferent cases. The differences between the solid (this work)and dashed (KDA1997) lines are due to the fact that wehave used equation 1 instead of using a power-law solution( L j ∝ t / − β ) at all times. A higher jet luminosity increasesthe radio power due to a larger number of energetic particles.This, also, increases the size of the cocoon due to an increasein pressure owing to these particles. The initial expansion ofthe cocoon is dominated by the pressure of the energeticparticles and the synchrotron and inverse Compton coolingcan be ignored. However, once the pressure drops due to -6 -5 -4 -3 -2 -1 | g N T ( x ) | Dimensionless frequency (x)frequency (GHz) p min =123510 Figure 2.
Absolute value of spectral function g NT ( x ) for powerlaw distribution of electrons number density ( f e ( p ) ∝ p − α ) with α = . The lowest energy cutoff is denoted by p min and the highestenergy cutoff is chosen to be p max ∼ . Note, p = (cid:112) ( γ − ) . expansion of the cocoon, the inverse Compton cooling be-comes important. At higher redshifts, cooling by CMB pho-tons become increasingly efficient as CMB energy densityis proportional to ( + z ) . This can be seen in the leftwardshift in the break of slope of the curve at ∼ γ MHz dueto efficient cooling.
It is well known that energetic electrons can boost the CMBphotons to higher energy through inverse Compton scatter-ing creating a distortion in the CMB blackbody spectrum.If the energy distribution of the electrons is non-relativisticand thermal, then the distortion has universal y -distortionshape (Zeldovich & Sunyaev 1969). For relativistic electrons,with a Lorentz factor γ , a photon with energy (cid:15) gets boostedto γ (cid:15) . In this case, the spectral distortion shape will be afunction of the electron energy distribution. The intensity ofthe CMB spectrum per frequency is given by, I ν ( x ) = ( k B T CMB ) ( hc ) x e x − = I I ( x ) , (9)where I ( x ) = x e x − , I ( x ) is the dimensionless intensity, x is thedimensional frequency which is given by x = E γ k B T CMB ,where E γ is the energy of photon, k B is the Boltzmann constant, T CMB is the CMB temperature, and other symbols have usualmeanings. The intensity of distorted CMB spectrum is inde-pendent of redshift for a given population of electrons. TheCMB distortion in the optically thin limit can be written as(Zeldovich & Sunyaev 1969; Birkinshaw 1999), ∆ I ( x ) = ( j ( x ) − i ( x )) τ, (10)where j ( x ) is the spectral intensity of photons at frequency x after being upscattered while i ( x ) is the intensity of photonsat frequency x before upscattering, τ = σ T ∫ n e dl where n e isthe electron number density and dl is the line of sight widthof this electron population. i ( x ) is non-zero only for . < MNRAS , 1–12 (2020)
Acharya, Majumdar & Nath x < because only these photons are getting upscattered.Eq. 10 can be recast to include a y -parameter as ∆ I ( x ) = yg ( x ) , where y = σ T m e c ∫ n e k B ∼ T e dl with k B ∼ T e = P e n e . In orderto distinguish non-thermal spectral distortion shape from y -type distortion (the well known thermal SZ effect), we willrefer to non-thermal distortion amplitude as y NT , such that, ∆ I NT ( x ) = y NT g NT ( x ) , (11)where g NT ( x ) is the spectral distortion function resultingfrom scattering of the CMB in a non-thermal population ofclusters. The pressure for a distribution of relativistic elec-trons is given by (Enßlin & Kaiser 2000), P e = n e ∫ dp f e ( p ) p v ( p ) m e c , (12)where f e ( p ) is the normalized electron spectrum i.e. ∫ f e ( p ) dp = with electron energy p = (cid:112) ( γ − ) , v = β c ,where γ is the Lorentz factor and β is the boost factor ofenergetic electrons.The number of CMB photons which getupscattered from energy x (cid:48) to x is given by, N ( x (cid:48) − > x ) = P ( t , p ) × ( k B T CMB ) ( hc ) x (cid:48) dx (cid:48) e x (cid:48) − , (13)where P ( t , p ) is the kernel of the inverse Compton scatteringwhich captures the kinematics of photon scattering with theelectrons with electron energy p , t = xx (cid:48) . The number of CMBphotons within energy x (cid:48) and x (cid:48) + dx (cid:48) is ( k B T CMB ) ( hc ) x (cid:48) dx (cid:48) e x (cid:48) − and ∫ dtP ( t , p ) = , which conserves the number of photons. Theformula for P ( t , p ) is given by (Enßlin & Kaiser 2000), P ( t ; p ) = − |( − t )| p t [ + ( + p + p ) t + t ] + ( + t ) p (cid:34) + p + p (cid:112) + p − + p p ( p − | ln t |) (cid:35) , (14)The spectral intensity of upscattered photons per frequency,in frequency bin x and x + ∆ x , is given by, j ( x ) = ∫ ∫ f e ( p ) dpP ( t , p ) x (cid:48) dx (cid:48) e x (cid:48) − x ∆ x . (15)Similar expression can be obtained for i ( x ) .In Fig. 2, we plot the absolute value of spectral function g NT ( x ) for power law distribution ( f e ( p ) ∝ p − α ) with powerlaw index α =3.0. The minimum electron energy in the powerlaw distribution is denoted by p min . The value of g NT ( x ) atspecific frequencies corresponding to frequency band of theupcoming Simons Observatory (Ade et al. 2019) is given inTable 1. It is clear from the previous discussion that we need to calcu-late the number density of relativistic electrons as a functionof the energy in order to calculate the non-thermal SZ spec-trum for individual radio cocoons. To proceed, we use thesame strategy as used to calculate the number density ofelectrons which emit at 150 MHz. We divide the range in γ from 1 to in 400 log spaced bins. Then, we use Eq. 4 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 N u m b e r d e n s it y ( c m - ) redshift γ =2 γ =5 γ =20 Figure 3.
Number density of electrons inside a radio cocoon forjets starting at different redshifts ( z = , ) for Q j = ergs − and t j = yr. For each starting redshift, we show the results forthree different energy distributions given for γ = 2 (black solidlines), 5 (red dashed lines) and 20 (blue dot-dashed lines). Seetext for details regarding the abrupt fall of the γ =20 curves. and 6 for the whole range of electron energy (or γ ) at eachinstant of time to calculate the number density n ( γ ) d γ atthat instant of time.In Fig. 3, we plot the number density of electrons withthree different instantaneous energy with jets starting at dif-ferent redshifts. The lowest energy electrons dominate thetotal number of relativistic particles. The cooling of elec-trons via inverse Compton is proportional to γ U C . There-fore, at higher redshifts electrons cool much more efficientlyvia CMB photons. This can be clearly seen for γ = curvefor a jet starting at redshift , , as the electron number pre-cipitously drops after reaching z = , z = . respectively.The efficiency of cooling of electrons is a strong function ofredshift ( ∝ ( + z ) ). Therefore, the number density of elec-trons with the relatively higher γ = 20 falls immediatelyafter jet the is shut off at higher redshift (e.g. for jet start-ing at z =3) while for jet starting at z =1, there are energeticelectrons left even after the jet is shut off.In Fig. 4, we plot the radio power as a function of size ofcocoons with different jet starting redshifts and jet luminosi-ties keeping t j = yr. For a constant jet luminosity, radiopower is independent of the initial redshift. Since we haveassumed that the surrounding medium of cocoon has densityprofiles that is independent of redshift. The fall gets sharperwith increasing redshift due to efficient cooling of the elec-trons at higher redshifts. After the jet stops, as there are nomore energetic electrons that emit at 150 MHz, the powerfalls sharply. With increasing jet luminosity, the radio powerincreases as expected which is shown in Fig. 4. In Fig. 5, weshow y NT as a function of cocoon size and jet luminosity.The expression for y NT is given by y NT = σ T m e c p c × L j , (16)where the symbols carry their usual meanings. The timetaken for light to travel across the length of a cocoon issmall compared to the light travel time to reach us. There-fore, the SZ observation of a radio cocoon gives a snapshotof the cocoon during its evolution at the observed redshift.With increase in cocoon size, the pressure inside the cocoon MNRAS000
Number density of electrons inside a radio cocoon forjets starting at different redshifts ( z = , ) for Q j = ergs − and t j = yr. For each starting redshift, we show the results forthree different energy distributions given for γ = 2 (black solidlines), 5 (red dashed lines) and 20 (blue dot-dashed lines). Seetext for details regarding the abrupt fall of the γ =20 curves. and 6 for the whole range of electron energy (or γ ) at eachinstant of time to calculate the number density n ( γ ) d γ atthat instant of time.In Fig. 3, we plot the number density of electrons withthree different instantaneous energy with jets starting at dif-ferent redshifts. The lowest energy electrons dominate thetotal number of relativistic particles. The cooling of elec-trons via inverse Compton is proportional to γ U C . There-fore, at higher redshifts electrons cool much more efficientlyvia CMB photons. This can be clearly seen for γ = curvefor a jet starting at redshift , , as the electron number pre-cipitously drops after reaching z = , z = . respectively.The efficiency of cooling of electrons is a strong function ofredshift ( ∝ ( + z ) ). Therefore, the number density of elec-trons with the relatively higher γ = 20 falls immediatelyafter jet the is shut off at higher redshift (e.g. for jet start-ing at z =3) while for jet starting at z =1, there are energeticelectrons left even after the jet is shut off.In Fig. 4, we plot the radio power as a function of size ofcocoons with different jet starting redshifts and jet luminosi-ties keeping t j = yr. For a constant jet luminosity, radiopower is independent of the initial redshift. Since we haveassumed that the surrounding medium of cocoon has densityprofiles that is independent of redshift. The fall gets sharperwith increasing redshift due to efficient cooling of the elec-trons at higher redshifts. After the jet stops, as there are nomore energetic electrons that emit at 150 MHz, the powerfalls sharply. With increasing jet luminosity, the radio powerincreases as expected which is shown in Fig. 4. In Fig. 5, weshow y NT as a function of cocoon size and jet luminosity.The expression for y NT is given by y NT = σ T m e c p c × L j , (16)where the symbols carry their usual meanings. The timetaken for light to travel across the length of a cocoon issmall compared to the light travel time to reach us. There-fore, the SZ observation of a radio cocoon gives a snapshotof the cocoon during its evolution at the observed redshift.With increase in cocoon size, the pressure inside the cocoon MNRAS000 , 1–12 (2020) on-thermal SZ from radio cocoons
100 1000 R a d i o po w e r ( W H z - S r - ) size of cocoon (kpc) Q j =10 ergs -1 ,z=0.5z=1.0Q j =10 ergs -1 ,z=0.5z=1.0 Figure 4.
Radio power as a function of the size of cocoon fora combination of jet luminosities Q j and starting redshifts. Theupper two red lines are for higher Q j = ergs − and lowertwo black lines are for a lower Q j = ergs − , with solid linescorresponding to z st = . and dashed lines for z st = . The jetlifetime is t j = yr. falls and, therefore, y NT decreases. With increase in jet lu-minosity, pressure and y NT increases. The curves show thatin order to achieve y NT ≥ − , either the cocoons have tobe young (i.e. smaller in size) and the jet has to be active.In other words, it would be difficult to detect non-thermalSZ effect from ‘dead’ radio galaxies, because their distor-tion would be y NT ≤ − . Also, giant radio galaxies withMpc size are not favourable. For a jet luminosity of erg s − or higher, radio galaxies with size ≤ kpc arefavourable for non-thermal SZ detection. We note that thecocoon size depends on the ambient density and would besmaller for a radio galaxy residing in a cluster environment(see also N2010), and may provide with good targets fornon-thermal SZ detection. From Fig. 5, it is interesting tonote that a small young radio cocoon of L j ∼ − kpcand Q j = ergs − can have an y NT equal in amplitude tothermal SZ from hot ICM of a galaxy cluster. Then takinginto account the spectral distortion shape (see Fig. 9), theCMB distortion by a radio cocoon inside a cluster can be asignificant part of the SZ distortion from the cluster ICM.Neglecting any y NT woould result in a source of systematicbias for the SZ measurements towards a cluster. In this section, we study the degeneracy between parametersof our radio cocoon model. Previous discussion shows thatthe non-thermal SZ effect depends on the jet luminosity,the starting redshift, and the observed redshift. We scan theparameter space in jet luminosity ( Q j ) and starting redshiftof jet ( z st ) which will expand to a particular size at a givenredshift z . The parameter ( z st ) can be translated to the timeinterval ( ∆ t ) after jet opening until the observed redshift. Weconsider two sources for illustrative purpose: 3C 274.1 andB2 1358+30C (Colafrancesco et al. (2013) , their Table 1),observed at z = . and 0.206 respectively. The size of theirmajor axis are 460 kpc and 1400 kpc respectively. We require -8 -7 -6 -5 -4 -3
100 1000 y N T size of cocoon (kpc) Q j =10 ergs -1 ergs -1 ergs -1 Figure 5.
The non-thermal CMB distortion amplitude, y NT ,from cocoons as a function of their size for different jet luminosi-ties Q j . In each case, the jet starting redshift is z st = . and thejet is evolved upto z = . . The jet lifetime is t j = yr. that cocoon starting at z st > z with some Q j will grow to size( L j ) ± kpc and ± kpc by z = . and 0.206respectively. We assume initial size of cocoon to be 10 kpcwhich is the size of a galaxy. The degeneracy between thejet luminosity and elapsed time after jet opening formation,for two different jet lifetimes, which satisfies the constraintof getting the observed cocoon size at z is shown in Fig. 6.The luminosity is chosen to vary between ergs − and ergs − (Hardcastle & Croston 2020). The inferred jetluminosities from observed radio galaxies upto now seemto be below ergs − . Note that for shorter jet lifetime,luminosity has to be larger so that pressure inside the cocoonis high enough to make it expand to a particular size. For ∆ t less than yr, the total energy content in the cocoonis Q j ∆ t irrespective of jet lifetime being or yr and,therefore, the curves with the two different lifetimes merge.Next, we plot the degeneracies between the estimated y NT and the radio power at 150 MHz in Fig. 7 for the life-times yr and yr. We take the same two sources de-picted in Fig. 6. We also plot the scenario in which the radiococoon of size 1400 kpc is observed at z =0.6 instead z =0.206and show how it is almost degenerate with the other radiococoon of size 1400 kpc, but at z =0.206. We have assumed α = for the rest of the calculations as the detected radiogalaxies used in this work have observed spectral index ∼ .Compared to α = . , this results in a reduction of the radiopower by more than an order of magnitude as electron pop-ulation dies off steeply. For the range of luminosities chosen,the radio power drops drastically before the size of cocoonreaches ∼ t j = yr as the jet dies off. Ra-dio power is directly correlated with y NT as the synchrotronand SZ signal comes from same population of high energyelectrons. Higher y NT corresponds to higher Q j , and conse-quently, higher radio power, as more number of high energyparticles are emitted by the jet.It is interesting to note that although the pressure insidea cocoon changes as the cocoon expands, for a particularcocoon size at any instant, both the radio power and y NT are independent of the redshift. This may be understoodfrom Eq. 1. Given a particular size, since we assume thedensity of the surrounding medium to be independent of MNRAS , 1–12 (2020)
Acharya, Majumdar & Nath J e t l u m i no s it y ( e r g s - ) Time after jet opening (yr)
Figure 6.
Modelling the jet luminosity as a function of jet start-ing redshifts (or equivalently time elapsed) for two sources se-lected from Table 2. The evolution of the cocoons are constrainedto match with observations, i.e, to reach a given observed size ata particular redshift of observation. The upper two lines are forthe source B2 1358+30C with a cocoon size of 1400 kpc with at z = 0.206 and the lower two lines are for the source 3C 274.1 witha cocoon size of 460 kpc at z = 0.422. For each source, the solidand dashed lines are for jet lifetimes of t j = &10 yr. The greencross shows that a combination of Q j ∼ ergs − , t j = yrand time evolved of ∼ yr would model the radio cocoon 3C274.1. redshift, the pressure inside the cocoon and, therefore y NT ,is independent for all redshifts. Radio power is the same oncethe jet lifetime is held constant and the injected particlesby the jet becomes constant for all cases. For a fixed radiopower, y NT increases with decreasing cocoon size as pressureincreases with decreasing volume. For yr < ∆ t < yr, thejet with lower lifetime stops supplying particles, which thenleads to reduction in emitted radio power for the jet with t j = yr compared to one with t j = yr. The size of thecocoon also makes a difference. For a given jet luminosity,the cocoon can expand to 460 kpc relatively easily comparedto 1400 kpc for t j = yr while the jet is still on. Therefore,a cocoon of size 460 kpc has significant radio power for bothlifetimes, t j = and yr. In contrast, for a 1400 kpc sizedcocoon, there is practically no radio power for the lowerlifetime of t j = yr . We conclude that selecting cocoonsof high radio power and small size (which is more likelyin cluster environment, as discussed earlier) would pay offtowards detection of non-thermal SZ signal.It is interesting to consider the recent detection of non-thermal SZ signal from a radio galaxy by Malu et al. (2017)assuming it to be near the bullet cluster at z ≈ . . Withthis assumption, the distance of the hotspot from the ra-dio galaxy core is estimated to be ≈ Mpc. The radiopower at . GHz is × W, over a GHz bandwidth(S. Malu, 2020, private communication). Considering theobserved bandwidth, this implies radio power of × W Hz − . Considering the angular area of the lobe to be (cid:48) × (cid:48) ≈ . × − sr, and assuming the minor axis to behalf the hotspot distance, as in our model, the radio powerturns out to be × W Hz − sr − . Then, with a spectralindex of − (corresponding to α = ), this implies a powerat MHz ≈ . × W Hz − sr − . This level of radiopower is shown with 15 percent measurement uncertainty with a grey horizontal band in Fig. 8. In this figure, we alsoshow the radio power as a function of y NT for different jetlifetimes t j . The jet luminosity is varied between − ergs − . In their paper, Malu et al. (2017) reported an ob-served non-thermal SZ distortion with y = × − . Notethat in our calculation, the jet luminosity has to be slightlyhigher than ergs − to explain the observed radio powerfor a 1 Mpc cocoon. The radio power for a 1 Mpc cocoonwhich can be achieved by jet luminosity ergs − is shownas the black cross in Fig. 8. The required jet luminosity toexplain the radio power turns out to be ∼ × ergs − .Alternatively, the radio galaxy may be a foreground object,in which case its size is smaller, and a smaller jet luminosityis needed to explain this observation. In order to determinethe requirements of energetics, we fix the jet luminosity at Q j = ergs − and vary the size of cocoon. We find thatfor a cocoon with size 200 kpc, the radio power can be ex-plained by Q j = ergs − (shown with the magenta crossin the same figure) . This foreground object has to be, then,located at z = . to have the observed angular size in thesky. We would like to point out that Malu et al. (2017) as-sumed non-relativistic distortion in obtaining their value of y = × − . However, one actually measures ∆ I ν whichcan be written as, ∆ I ν ( x ) = yg T ( x ) ( Malu et . al . ( )) = y NT g NT ( x ) ( this work ) , (17)where y and g T ( x ) is the non-relativistic y -distortion andthe spectrum respectively, and similarly y NT and g NT ( x ) for non-thermal distortions. Therefore, there is a degeneracybetween y NT and g NT ( x ) (or p min ) for a given ∆ I ν ( x ) . Thisis true for the measurement of ∆ I ν ( x ) at a single frequencywhich was the case for the reported detection at 18 GHz.The magnitude of g NT ( x ) is lower than g T ( x ) for all x (seeFig. 6 of (Enßlin & Kaiser 2000)) and this difference dependssensitively on the value of p min . At x = . (correspondingto frequency 18 GHz), the value of g T = . while g NT = . and 0.03 for p min = and 2 respectively (as seen in Fig. 2).Therefore, for p min = and 2, y NT is higher than y = × − by a factor of 2.5 and 10 respectively, and can easily reach y NT = × − for p min = .The degeneracy between y NT and p min was alreadynoted in Malu et al. (2017) (their Fig. 2). They obtain anupper limit on p min between 5 to 10 using X-ray constraints.Note, that their y -value is for non-relativistic SZ where theelectron spectrum ( p min ) does not enter. Moreover, withouta radio cocoon evolution model, they could not relate y -valueto the size of the cocoon. In contrast, our approach of usinga detailed radio cocoon evolution model leads us to predict avalue of y NT for a given cocoon size and radio power. Fromour model, y NT for 1 Mpc object turns out to be − × − (corresponding to jet luminosity of ∼ × ergs − ). Thisvalue of y NT is consistent with the the value of p min = .Even if we mistake the source to be a foreground object ofsize 200 kpc, the obtained value of y NT from our evolution-ary model is ∼ × − which is consistent with p min = .The increase in y NT for 200 kpc cocoon as compared to 1Mpc size cocoon necessarily leads to increase in p min (ordecrease in value of g NT ( x ) at x = . ) such that ∆ I ν ( x ) isunchanged as in Eq. 17. Note, that irrespective of the degen-eracy between y NT and p min , an arbitrary increase in y NT MNRAS000
Modelling the jet luminosity as a function of jet start-ing redshifts (or equivalently time elapsed) for two sources se-lected from Table 2. The evolution of the cocoons are constrainedto match with observations, i.e, to reach a given observed size ata particular redshift of observation. The upper two lines are forthe source B2 1358+30C with a cocoon size of 1400 kpc with at z = 0.206 and the lower two lines are for the source 3C 274.1 witha cocoon size of 460 kpc at z = 0.422. For each source, the solidand dashed lines are for jet lifetimes of t j = &10 yr. The greencross shows that a combination of Q j ∼ ergs − , t j = yrand time evolved of ∼ yr would model the radio cocoon 3C274.1. redshift, the pressure inside the cocoon and, therefore y NT ,is independent for all redshifts. Radio power is the same oncethe jet lifetime is held constant and the injected particlesby the jet becomes constant for all cases. For a fixed radiopower, y NT increases with decreasing cocoon size as pressureincreases with decreasing volume. For yr < ∆ t < yr, thejet with lower lifetime stops supplying particles, which thenleads to reduction in emitted radio power for the jet with t j = yr compared to one with t j = yr. The size of thecocoon also makes a difference. For a given jet luminosity,the cocoon can expand to 460 kpc relatively easily comparedto 1400 kpc for t j = yr while the jet is still on. Therefore,a cocoon of size 460 kpc has significant radio power for bothlifetimes, t j = and yr. In contrast, for a 1400 kpc sizedcocoon, there is practically no radio power for the lowerlifetime of t j = yr . We conclude that selecting cocoonsof high radio power and small size (which is more likelyin cluster environment, as discussed earlier) would pay offtowards detection of non-thermal SZ signal.It is interesting to consider the recent detection of non-thermal SZ signal from a radio galaxy by Malu et al. (2017)assuming it to be near the bullet cluster at z ≈ . . Withthis assumption, the distance of the hotspot from the ra-dio galaxy core is estimated to be ≈ Mpc. The radiopower at . GHz is × W, over a GHz bandwidth(S. Malu, 2020, private communication). Considering theobserved bandwidth, this implies radio power of × W Hz − . Considering the angular area of the lobe to be (cid:48) × (cid:48) ≈ . × − sr, and assuming the minor axis to behalf the hotspot distance, as in our model, the radio powerturns out to be × W Hz − sr − . Then, with a spectralindex of − (corresponding to α = ), this implies a powerat MHz ≈ . × W Hz − sr − . This level of radiopower is shown with 15 percent measurement uncertainty with a grey horizontal band in Fig. 8. In this figure, we alsoshow the radio power as a function of y NT for different jetlifetimes t j . The jet luminosity is varied between − ergs − . In their paper, Malu et al. (2017) reported an ob-served non-thermal SZ distortion with y = × − . Notethat in our calculation, the jet luminosity has to be slightlyhigher than ergs − to explain the observed radio powerfor a 1 Mpc cocoon. The radio power for a 1 Mpc cocoonwhich can be achieved by jet luminosity ergs − is shownas the black cross in Fig. 8. The required jet luminosity toexplain the radio power turns out to be ∼ × ergs − .Alternatively, the radio galaxy may be a foreground object,in which case its size is smaller, and a smaller jet luminosityis needed to explain this observation. In order to determinethe requirements of energetics, we fix the jet luminosity at Q j = ergs − and vary the size of cocoon. We find thatfor a cocoon with size 200 kpc, the radio power can be ex-plained by Q j = ergs − (shown with the magenta crossin the same figure) . This foreground object has to be, then,located at z = . to have the observed angular size in thesky. We would like to point out that Malu et al. (2017) as-sumed non-relativistic distortion in obtaining their value of y = × − . However, one actually measures ∆ I ν whichcan be written as, ∆ I ν ( x ) = yg T ( x ) ( Malu et . al . ( )) = y NT g NT ( x ) ( this work ) , (17)where y and g T ( x ) is the non-relativistic y -distortion andthe spectrum respectively, and similarly y NT and g NT ( x ) for non-thermal distortions. Therefore, there is a degeneracybetween y NT and g NT ( x ) (or p min ) for a given ∆ I ν ( x ) . Thisis true for the measurement of ∆ I ν ( x ) at a single frequencywhich was the case for the reported detection at 18 GHz.The magnitude of g NT ( x ) is lower than g T ( x ) for all x (seeFig. 6 of (Enßlin & Kaiser 2000)) and this difference dependssensitively on the value of p min . At x = . (correspondingto frequency 18 GHz), the value of g T = . while g NT = . and 0.03 for p min = and 2 respectively (as seen in Fig. 2).Therefore, for p min = and 2, y NT is higher than y = × − by a factor of 2.5 and 10 respectively, and can easily reach y NT = × − for p min = .The degeneracy between y NT and p min was alreadynoted in Malu et al. (2017) (their Fig. 2). They obtain anupper limit on p min between 5 to 10 using X-ray constraints.Note, that their y -value is for non-relativistic SZ where theelectron spectrum ( p min ) does not enter. Moreover, withouta radio cocoon evolution model, they could not relate y -valueto the size of the cocoon. In contrast, our approach of usinga detailed radio cocoon evolution model leads us to predict avalue of y NT for a given cocoon size and radio power. Fromour model, y NT for 1 Mpc object turns out to be − × − (corresponding to jet luminosity of ∼ × ergs − ). Thisvalue of y NT is consistent with the the value of p min = .Even if we mistake the source to be a foreground object ofsize 200 kpc, the obtained value of y NT from our evolution-ary model is ∼ × − which is consistent with p min = .The increase in y NT for 200 kpc cocoon as compared to 1Mpc size cocoon necessarily leads to increase in p min (ordecrease in value of g NT ( x ) at x = . ) such that ∆ I ν ( x ) isunchanged as in Eq. 17. Note, that irrespective of the degen-eracy between y NT and p min , an arbitrary increase in y NT MNRAS000 , 1–12 (2020) on-thermal SZ from radio cocoons -6 -5 -4 R a d i o po w e r ( W m - S r - H z - ) y NT Figure 7. y NT vs radio power at 150 MHz for two sources se-lected from Table 2. The evolution of the cocoons are constrainedto match with observations, i.e, to reach a given observed size ata particular redshift of observation. The dashed lines are for thesource 3C 274.1 having cocoon size of 460 kpc at z = . , withthe black thick dashed line for jet lifetime t j = yr and thinred dashed line for t j = yr. The other source, B2 1358+30C,having size of 1400 kpc at z = . , is shown with the red solidline. Note, that B2 1358+30C would have been almost degener-ate in y NT -radio power plane with a source of size 1400 kpc at z = . & t j = yr, shown with the blue dot-dashed line. in our radio cocoon evolutionary model would result in thesize of the cocoon to be unrealistically small. Therefore, theobserved radio power and cocoon size (assuming the cocoonto be at z ∼ . ) is consistent with y NT = − × − whichrequires p min ∼ . This is the first estimate of the lowerenergy cutoff of non-thermal electron population in radiogalaxy cocoon using SZ effect.If we have measurements of the CMB distortions at mul-tiple frequencies, we can directly measure the value of p min from the shape of distortion and break the degeneracy be-tween y NT and g NT ( x ) . The viability of such measurementswith upcoming CMB experiments is discussed in Sec. 6. We compare our non-thermal SZ calculation with the radiogalaxies listed in Colafrancesco et al. (2013). The authorsassumed a static electron distribution where the electronnumber density is given by, N e ( p , r ) = k g e ( r ) A ( p , p , α ) p − α , (18)The value of k is fixed to be 2.6 cm − and the average valueof observed α =3 which is obtained from fitting data to radioand X-ray observations. The electron number density is as-sumed to be constant, so that g e ( r ) = . A is a normalizingconstant such that ∫ p p Ap − α = . p is fixed to be 1. Thiscan be converted to cutoff in γ as γ = (cid:113) ( + p ) . The sizeof galaxy is assumed to be ellipsoidal with major and minoraxis as given in Table 1. The line of sight is assumed to bethe major axis. From these informations one can calculatethe optical depth for CMB photons.In Table 2, we list the sources, their size, radio powerat 150 GHz which were considered in Colafrancesco et al.(2013). We then predict the y NT , an estimate of t j and flux -6 -5 -4 R a d i o po w e r ( W m - S r - H z - ) y NT t j =5 × yrt j =10 yrt j =5 × yr Figure 8.
Similar to Fig. 7, y NT vs radio power at 150 MHz forradio cocoons constrained to have size L j = Mpc at z obs = . (to model the source observed by Malu et al. (2017)) for differ-ent jet lifetimes. The jet luminosity is varied between − ergs − . The grey horizontal band shows the radio power observedby Malu et al. (2017). The black cross corresponds to the radioluminosity and y NT which can be achieved for a 1 Mpc cocoonwith a Q j of ergs − . In contrast, for the cocoon being closerto us (i.e., having a lower z , see text for details) such that thesize is 200 kpc, but with the same Q j , the corresponding point isshown by the magenta cross which touches the grey band. for Simons Observatory at two frequencies, which are al-lowed by our model and satisfy the size and radio flux asgiven. The beam and instrument noise for Simons Observa-tory are listed in Table 1 of Ade et al. (2019). We use thebest case scenario with specifications for LAT ( f sky = . )with FWHM as the beam. The expected noise are 6.3 and37 µ K-arcmin for the two frequencies in Table 2. The t j val-ues listed in Table 2 should be considered as an lower limitof jet lifetime that satisfies the constraints. We see that formost of the sources, the required jet luminosity needs to behigher than erg s − . Therefore, we have allowed thejet luminosity to vary between and erg s − . For agiven radio galaxy size, there is a three-way degeneracy be-tween the jet luminosity, the lifetime of jet and the startingredshift of jet ( z st ) or the time-interval between jet startingredshift and observed redshift ( ∆ t ) (Fig. 6). For a given jetlifetime and size, we can increase ∆ t by reducing jet luminos-ity or vice versa. Therefore, a bound on jet luminosity givesa bound on ∆ t . The radio power from a galaxy drops sharplyonce jet is off i.e. we should not observe radio flux if ∆ t > t j .This criteria and prior condition on jet luminosity gives alower bound on t j . However, radio observation does not givean upper bound on t j since the radio cocoons becomes invis-ible in radio as it grows too big and faint . In contrast, theradio galaxy should be observable in SZ even after jet goesoff. Therefore, SZ observations can put an upper bound onjet lifetimes of these radio galaxies. In this section, we study the feasibility of detecting non-thermal SZ with future CMB experiments. The distortion in
MNRAS , 1–12 (2020)
Acharya, Majumdar & Nath source z angular size size Flux y NT t j flux ( µ K-arcmin) flux ( µ K-arcmin)arcsec (major axis) kpc mJy yr (150 GHz) (280 GHz)CGCG 186-048 0.063 388 485 1 × − ×
399 (63 σ ) 6.1 (1.6 σ )B2 1158+35 0.55 70 462 1.3 × − ×
130 (21 σ ) 20 (0.5 σ )3C 270 0.0075 577 93 113 × −
441 (70 σ ) 68 (1.8 σ )87GB 121815.5+.. 0.2 924 3141 0.43 × − σ ) 174 (4.7 σ )3C 274.1 0.422 89 508 30 × − ×
630 (100 σ ) 174 (2.6 σ )4C +69.15 0.106 822 1646 26 × − × σ ) 1378 (37 σ )3C 292 0.71 64 473 16 × − ×
434 (69 σ ) 67 (1.8 σ )B2 1358+30C 0.206 408 1421 0.28 × −
441 (70 σ ) 68 (1.8 σ )3C 294 1.779 29 253 2 × −
45 (7 σ ) 7 (0.2 σ )PKS 1514+00 0.052 519 543 480 × − × σ ) 2746 (74 σ )GB1 1519+512 0.37 312 1646 22 × − σ ) 595 (16 σ )3C 326 0.0895 684 1177 22 − σ ) 954 (26 σ )7C 1602+3739 0.814 100 778 0.33 − ×
132 (21 σ ) 20 (0.5 σ )MRK 1498 0.0547 583 639 15 × − × σ ) 1386 (37 σ )B3 1636+418 0.867 57 452 16 − ×
43 (6.8 σ ) 7 (0.2 σ )Hercules A 0.154 200 551 253 × − × σ ) 734 (20 σ )B3 1701+423 0.476 120 735 1.1 − ×
191 (30 σ ) 29 (0.8 σ )4C 34.47 0.206 92 320 9.5 × − ×
337 (53 σ ) 52 (1.5 σ )87GB 183438.3+.. 0.5194 69 443 3.9 × − ×
190 (30 σ ) 29 (0.8 σ )4C +74.26 0.104 773 1522 94 × − × σ ) 3655 (99 σ )RG01 (Malu et al. 2017) 0.3 240 1100 × −
534 (85 σ ) 82.2 (2.2 σ ) Table 2.
We list the redshifts of the sources, size (major axis), radio flux at 150 GHz given in Table 1 and 2 of (Colafrancesco et al.2013). We predict the corresponding y NT , t j and flux for the source with Simons Observatory (Ade et al. 2019) or CMB-S4 (Abazajianet al. 2019) type experiment to match the observation of size and radio power, allowed by our model for radio galaxy. We have used thebest case noise limit (LAT, f sky = . ) of Simons Observatory to derive the significance of the detection. For non-thermal spectrum, wechoose p min = . We have abbreviated a couple of source names to make space. Please note that for radio galaxy RG01, the flux is givenat 5.5 GHz. We also assume the source to be at z =0.3 (at the location of bullet cluster). If the source is a foreground object, then thephysical properties of the galaxy will be different (see text). intensity I ν of CMB at a frequency ν and towards a localizedconcentration of hot electrons can be written as, ∆ I ν = ∆ I y + ∆ I µ + ∆ I kSZ + ∆ I rSZ + ∆ I NT , (19)where ∆ I y is the typically dominant non-relativistic y dis-tortion, ∆ I µ is the µ distortion, ∆ I kSZ is the temperatureshift of the CMB black body due to kSZ effect (Sunyaev& Zeldovich 1980), ∆ I rSZ is the relativistic SZ signal froma massive galaxy cluster and ∆ I NT is the non-thermal SZdistortion. The expression for ∆ I y , ∆ I µ and ∆ I kSZ are givenby (Zeldovich & Sunyaev 1969; Sunyaev & Zeldovich 1970;Illarionov & Siuniaev 1975), ∆ I y = y ν c x e x ( e x − ) (cid:20) x e x + x − − (cid:21) (20) ∆ I µ = µ ν c e x ( e x − ) (cid:104) x . − (cid:105) (21) ∆ I kSZ = ∆ T ν c e x ( e x − ) (22)The y -distortion can have contribution from both pre-recombination universe as well as post-recombination uni-verse while µ -distortion can only be created at redshiftsgreater than × . The SZ spectrum from electrons withenergy (cid:38) keV is obtained by including Klein-Nishina correc-tions for Compton scattering which can be calculated per-turbatively as an expansion in T e m e (Itoh et al. 1998; Challi-nor & Lasenby 1998; Sazonov & Sunyaev 1998; Dolgov et al.2001). For example, The temperature of massive galaxy clus-ter with mass times solar mass can be ∼ y ∼ − . -1-0.5 0 0.5 1 1.5 2 2.5 200 400 600 800 1000 ∆ I ( × - ) W m - S r - H z - frequency (GHz) y-distortionrSZ (5 keV) µ distortion+ve ∆ T-ve ∆ TNon-thermal
Figure 9.
The frequency dependence of various possible distor-tions from CMB black body including the non-thermal SZ distor-tion (green solid line). The amplitude of distortion is chosen tobe − for each type. Moreover, for the non-thermal spectrum,we choose p min = . The vertical dashed grey lines correspond tocurrent and upcoming CMB observational frequencies. The unique spectral shapes of the different SZ distor-tions can be used to separate them, hence isolating the non-thermal SZ from other dominant CMB fluctuations, at rel-evant angular scales. In Fig. 9, we plot the intensity of dif-ferent distortions as discussed above. The spectral shapesof these distortions are different from each other. Therefore,with a multifrequency study, we can distinguish non-thermaldistortion from other forms of distortions. To check if non-thermal distortion can be mimicked by combination of other
MNRAS000
MNRAS000 , 1–12 (2020) on-thermal SZ from radio cocoons -0.5-0.4-0.3-0.2-0.1 0 0.1 20 40 60 80 100 120 140 160 180 200 ∆ I ( × - ) W m - S r - H z - frequency (GHz) Non-thermalBest fit (Unconstrained)
Figure 10.
The intensity of non-thermal distortions at the cur-rent operational frequencies for ACT, 98 and 150 GHz (shownwith open circles), having the amplitude y NT = − . The bestfit to non-thermal distortion using a linear combination of y , µ , kSZ and rSZ distortions is shown by the solid red line, whichperfectly passes through the observed points. distortions, we find the best fit to non-thermal distortionshape from a linear combination of y , µ , kSZ and rSZ dis-tortions i.e. we want to write ∆ I NT as, ∆ I NT = y ∆ I y + µ ∆ I µ + ∆ T ∆ I kSZ + y rSZ ∆ I rSZ , (23)where y , µ, ∆ T and y rSZ are the best fit parameters. Thebasic idea is that if the non-thermal distortions cannot bewritten as a linear combination of other forms of distortionsi.e. if there is a non-zero residual after the best fit has beenremoved from total distortion, then we can detect the non-thermal part of the total distortion as the residuals of totaldistortion signal.In Fig. 10, we plot the best fit to non-thermal distor-tions as a combination of other distortions. The two pointsare the intensity of non-thermal distortions at 98 GHz and150 GHz which are the current operating frequency of At-acama Cosmology Telescope (ACT) (Aiola et al. 2020). Ascan be expected, two points can be fit with 4 parametersvery well. This discussion also holds true for SPTpol (SouthPole Telescope) (Austermann et al. 2012) with two frequen-cies at 90 and 150 GHz and SPT-3G (Benson et al. 2014)with three frequencies at 90, 150 and 220 GHz. Therefore,we cannot distinguish non-thermal distortions from otherdistortions with current observations.In Fig. 11, we plot the best fit with six frequency chan-nels of Simons Observatory which will start observation innear future. For the unconstrained best fit, the best fit pa-rameter of y , y rSZ , µ and ∆ T can have positive and nega-tive sign. With these unconstrained parameters, we have avery good fit to non-thermal distortion. Note that even inthe absence of a galaxy cluster, the y and µ -type distortioncan be created in pre-recombination universe from acous-tic damping, baryon cooling or injection of electromagneticenergy from decay or annihilation of unstable particles etc.(Chluba & Sunyaev 2012; Khatri et al. 2012; Chluba et al.2012). While acoustic damping and injection of energy cangive rise to positive y or µ -type distortion, baryon coolinggives rise to negative µ distortion of the order − − − .In post recombination universe, the hotter electrons in the -0.4-0.2 0 0.2 0.4 50 100 150 200 250 300 350 400 ∆ I ( × - ) W m - S r - H z - frequency (GHz) Non-thermalBest fit (Unconstrained)y>0,y rSZ >0 ∆ T=0,y>0,y rSZ >0 Figure 11.
Same as Fig. 10, but for a larger number of frequenciesat 27, 39, 93, 145, 225 and 280 GHz as proposed for the upcomingSimons Observatory. The unconstrained fit as in Fig. 10 is shownby red-solid line whereas constraints on the amplitude of thermalSZ results in the blue dashed line and an additional constraint ofno kinematic SZ gives the green dot-dashed line. structures boost CMB photons to higher energy. Therefore,it is reasonable to assume that y and y rSZ should be positivewhile the kSZ temperature shift can be positive and negativeas this distortion is produced by moving electrons. With theconstraints that y and y rSZ >
0, we can still manage to havea very good fit to non-thermal spectrum in the frequencyrange 20-300 GHz. Note that, a negative kSZ temperatureshift can mimic non-thermal SZ spectrum by shifting thenull point to higher frequencies. As can be seen from Fig.9, the shape of a negative kSZ is roughly similar to non-thermal distortion for frequency (cid:46)
300 GHz. Once, we ig-nore kSZ with the positivity condition on y and y rSZ , weare able to distinguish non-thermal SZ signal as there arenon-zero residual at some frequencies (Fig. 13). For an or-der of magnitude estimate of temperature shift due to kSZ ,we consider the source Hercules A from Table 2 with highest y NT parameter ( y NT = × − ). The optical depth of thissource turns out to be ∼ − . With v / c ∼ − , we see thatthe distortion due to kSZ are of the order vc τ ∼ − − − .Therefore, we can safely ignore the kSZ temperature shiftand consequently will be able to differentiate non-thermalSZ from other distortions, for this source.For a completely unambiguous detection without anyassumption on the y , µ , k SZ and rSZ distortions, it is clearfrom the above discussion that the location of the null pointof the total distortion may not be a reliable signature of non-thermal SZ from future CMB experiments. However, as canbe seen from Fig. 9, the intensity of y , µ , kSZ and rSZ dis-tortions after 400 GHz starts to decrease in magnitude andapproach zero while for non-thermal SZ, the spectrum is rel-atively flat. Therefore, high frequency channels ( > )would be able to differentiate non-thermal distortion fromothers. We design a hypothetical experiment with all thefrequency band of Simons Observatory and add three morefrequency channel at 350 GHz, 500 GHz and 600 GHz. Inthis setup, we are able to distinguish non-thermal distor-tion from others without putting any constraints on best fitparameters of y , µ , temperature shift due to kSZ and rSZdistortions as can be clearly seen in Fig. 12 and Fig. 13. MNRAS , 1–12 (2020) Acharya, Majumdar & Nath -0.4-0.2 0 0.2 0.4 100 200 300 400 500 600 700 ∆ I ( × - ) W m - S r - H z - frequency (GHz) Non-thermalBest fit (Unconstrained)
Figure 12.
Same as Fig. 10, but for a hypothetical experimentwith the six frequencies of Simons observatory and additionalfrequency bands at 350 GHz, 500 GHz and 600 GHz. A linearcombination of y , µ , kSZ and rSZ distortions can no more passthrough all the observed points. -0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 0 100 200 300 400 500 600 700 800 R e s i du a l ( × - ) W m - S r - H z - frequency (GHz) Unconstrained (Simons observatory)y>0,y rSZ >0 ∆ T=0,y>0,y rSZ >0Unconstrained (Hypothetical)
Figure 13.
Residual after subtracting best fit linear combinationof y , µ , kSZ and rSZ distortions from non-thermal distortionscorresponding to Figs. 11 & 12. Some of the sources listed in Table 2 can be very goodcandidates for Simons Observatory or CMB-S4 experimentsdue to high signal to noise ratio at 150 and 280 GHz fre-quency bands. However, for unambiguous detection, we willneed higher frequency bands. Experiments like Probe of In-flation and Cosmic Origins (PICO) (Hanany et al. 2019)with many more frequency bands with noise ∼ O(1) µ K-arcmin upto 500 GHz will be extremely useful for such de-tections.
For the sake of simplicity, we have assumed a constantvalue of the ambient density in our radio galaxy evolution-ary model. Realistically, the density increases with redshift,since it should scale with the critical density, thus imply-ing smaller sized of radio cocoons and higher radio power atlarger redshifts, but also with rapid decline in radio poweronce the jet switches off. The net non-thermal SZ signal will be larger. Note, that for particular radio galaxies consideredin this work (refer to Table 2), the estimates of radio powerand y NT will not differ significantly from those presentedhere.The SZ effect from galaxy clusters can be used as clustermass proxy in SZ surveys which aims at using cluster num-ber counts and their spatial correlations to constrain cosmo-logical parameters. However, this is crucially dependent onestablishing an unbiased SZ distortion - cluster mass scaling.The thermal SZ effect y -distortion is the dominant distortionfor large clusters ( y ∼ − − − for clusters of virial mass ∼× M (cid:12) − M (cid:12) ). The non-thermal SZ signal from radiococoons inside the clusters can easily be a significant frac-tion of the thermal SZ from the cluster gas and cannot notbe ignored. In the absence of observations at many differentfrequencies, one needs to model the non-thermal SZ (as inTable 2) and subtract it out from the total SZ distortion soas to have an unbiased estimate of the SZ from the clus-ter gas. However, if there are many observable frequencies,then the separation of the different components can be doneby utilising their unique spectral shapes as demonstrated inthe previous section. Additionally, neglecting SZ distortionsfrom radio cocoons (inside clusters) would be bias the es-timate of the Hubble Constant H using a combination ofSZ and XRay observations towards galaxy clusters. It is in-teresting to note that subtracting a contribution from radiococoons lowers the estimate of the net SZ distortion fromthe cluster gas, and pushes the the value of H up, in theright direction.Other than radio cocoons residing within clusters, ra-dio galaxies having cocoons are ubiquitous in our Universe.In the previous sections, we have calculated the magnitudeof distortion of the CMB spectrum from individual radiogalaxy cocoons. As a next step, we can consider an en-semble of radio cocoons populating the universe and cal-culate the global averaged CMB distortions. A first calcu-lation of the average y -distortion has been done in Yamadaet al. (1999) and Majumdar (2001) assuming that the ra-dio cocoons reside inside the dark matter halos with one-percent halo occupational efficiency. The jet luminosity wasassumed to be equal to the Eddington luminosity of cen-tral black hole of mass M BH with M BH = . M halo . More-over, Majumdar (2001) calculated the angular power spec-trum, C (cid:96) , of CMB distortions from unresolved radio galaxycocoons. However, these initial efforts assumed the distor-tion to be non-relativistic y -distortion and concluded thata cosmological distribution of cocoons with t j = yr to beseverely constrained due to the COBE CMB spectral dis-tortion limit (Fixsen et al. 1996). Our calculations suggestthat in a Λ CDM universe with the current cosmological pa-rameters, the global averaged < y > ∼ − for t j = yr.Several improvements are in order to make progress - forexample, the assumed jet luminosity of their model may betoo high compared to the jet luminosity inferred from in-dividual radio galaxies (Hardcastle & Croston 2020). Also,the efficiency factor will not be a constant but a function ofdark matter halo mass. Our preliminary work on calculatingthe two point correlation functions of SZ fluctuations implythat the contribution from radio galaxies can be ∼
10 per-cent of contribution from galaxy clusters. We will presentthe results for < y > and C (cid:96) for a cosmological distributionof radio cocoons in a followup work. MNRAS000
10 per-cent of contribution from galaxy clusters. We will presentthe results for < y > and C (cid:96) for a cosmological distributionof radio cocoons in a followup work. MNRAS000 , 1–12 (2020) on-thermal SZ from radio cocoons We perform a detailed quantitative study of the non-thermalhot electrons in radio galaxy cocoons, both during the life-time of the radio jets and after the jets stop, as a po-tential source of non-thermal SZ distortion to CMB blackbody spectrum. Since the energetic particles inside the co-coons cool via both synchrotron radiation and inverse Comp-ton scattering, there is a correlation between emitted radiopower and expected intensity of CMB distortion at any in-stant. Combining radio galaxy evolution models of Kaiseret al. (1997) with suitable modification for jet stopping asin Nath (2010), we are able to estimate the physical proper-ties of the radio cocoons at any instant of time.We predict the value of y NT , given the observed size andradio power of a cocoon, from our evolutionary model by tak-ing into account the cooling of electrons of all energy. Thisis in contrast to previous works, for example Colafrancescoet al. (2013), in which the authors inferred the value of num-ber density of electrons from radio and X-ray observations.Radio and X-ray observation constrain the spectrum of elec-trons at γ > . The authors extrapolate the spectrum ofelectrons to lower energy electrons which are responsible forthe SZ signal. We do no such extrapolation. Further, we usethe non-thermal spectrum of these relativistic particles tocalculate the distortion on the CMB for a given size andradio power of the radio galaxy cocoons. A summary of ourpredictions for 21 radio cocoons is tabulated in Table 2. Thekey points of this work are summarized below : • Although the pressure inside a cocoon changes as thecocoon expands, for a particular cocoon size at any instant,both the radio power and y NT is independent of redshift.This is a consequence of assuming the density of the sur-rounding medium to be independent of the redshift. As longas jet is turned on, radio power is just a function of the jetluminosity and not the jet lifetime i.e. the radio power fromtwo sources with t j = and yr are the same when bothsources are relatively young. • The injected electrons, when the jet is on, cool effi-ciently via inverse Compton scattering especially at higherredshifts. After the jet shuts off, there is no more supplyof energetic electrons. Therefore, as soon as the jet turnsoff, there is a steep fall of radio power as the energetic elec-trons which are responsible for radio emission have all cooleddown. • For a fixed radio power, y NT increases with decreasingcocoon size as pressure is larger for smaller volume (whichleads to the expansion of the cocoon). The prospect of de-tecting non-thermal SZ from cocoons increases if the cocoonsare young (or smaller in size) and/or jet the is active. • A direct consequence of the above points is that radiogalaxy cocoons residing in cluster environments would bebetter potential targets for non-thermal SZ detection. Sim-ilarly, dead field radio galaxies, with large cocoon sizes, arenot favourable sources for non-thermal SZ detection. • The analysis presented in this paper can successfullymodel the recent first detection of non-thermal SZ effectfrom the radio galaxy RG01(Malu et al. 2017) . This gives usthe confidence in predicting the non-thermal SZ distortionfor a further sample of 20 radio galaxy sources (in Table2) which can be targeted by upcoming ground based SZsearches. • For a given intensity of distortion on the CMB, there isa degeneracy between y NT and g NT ( x ) . In contrast to pre-vious studies, we can predict y NT from our galaxy evolutionmodel which can then constrain the value of spectral func-tion g NT ( x ) . • Radio and SZ detection of radio cocoons can help de-termine the physical properties of energetic electrons insidethe cocoons. For the non-thermal SZ detection from RG01,we are able to constrain the value of p min (the lowest energythreshold of the electron spectrum) using SZ effect for thevery first time. We find p min ∼ − is needed to explain theobservations. • We demonstrate that future CMB experiments, withhigher frequency bands ( (cid:38)
300 GHz), are needed for dif-ferentiating non-thermal SZ from radio cocoons from otherSZ distortions (for example, kSZ distortions from clusters ofgalaxies). In this respect CMB S4 (Abazajian et al. 2016),PICO (Hanany et al. 2019), CMB Bharat (CMB BharatConsortium 2018) would be most promising.
ACKNOWLEDGEMENTS
We acknowledge the use of computational facilities of De-partment of Theoretical Physics at Tata Institute of Fun-damental Research, Mumbai. We acknowledge support ofthe Department of Atomic Energy, Government of India,under project no. 12-R&D-TFR-5.02-0200. SKA is grate-ful for financial support from the Royal Society and Prof.Jens Chluba for the invitation to University of Manchester,during which a part of this work was done. BN wishes tothank Siddharth Malu for useful discussions. SM wishes touse this opportunity to recollect the very fond memory ofhis first meeting with late Sergio Colafrancesco when SMwas an PhD student on his first trip outside his country andSergio had driven his car to Roma Termini station to pickup SM so that young an Indian student does not get lost inthe chaos of a new city.
REFERENCES
Abazajian K. N., et al., 2016, arXiv e-prints, p. arXiv:1610.02743Abazajian K., et al., 2019, arXiv e-prints, p. arXiv:1907.04473Ade P., et al., 2019, JCAP, 2019, 056Aghanim N., Majumdar S., Silk J., 2008, Reports on Progress inPhysics, 71, 066902Aghanim N., et al., 2018, preprint, ( arXiv:1807.06209 )Aiola S., et al., 2020, arXiv e-prints, p. arXiv:2007.07288Austermann J. E., et al., 2012, in Millimeter, Submillimeter, andFar-Infrared Detectors and Instrumentation for AstronomyVI. p. 84521E ( arXiv:1210.4970 ), doi:10.1117/12.927286Baldwin J. E., 1982, in Heeschen D. S., Wade C. M., eds, IAUSymposium Vol. 97, Extragalactic Radio Sources. pp 21–24Begelman M. C., Cioffi D. F., 1989, ApJL, 345, L21Benson B. A., et al., 2014, in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII.p. 91531P ( arXiv:1407.2973 , 1–12 (2020) Acharya, Majumdar & Nath
Colafrancesco S., Marchegiani P., 2011, A&A, 535, A108Colafrancesco S., Marchegiani P., de Bernardis P., Masi S., 2013,A&A, 550, A92Croston J. H., Hardcastle M. J., Harris D. E., Belsole E., Birkin-shaw M., Worrall D. M., 2005, ApJ, 626, 733Dolgov A. D., Hansen S. H., Pastor S., Semikoz D. V., 2001, ApJ,554, 74Enßlin T. A., Kaiser C. R., 2000, A&A, 360, 417Erler J., Basu K., Chluba J., Bertoldi F., 2018, MNRAS, 476,3360Erlund M. C., Fabian A. C., Blundell K. M., 2008, MNRAS, 386,1774Fabian A. C., Chapman S., Casey C. M., Bauer F., BlundellK. M., 2009, MNRAS, 395, L67Felten J. E., Rees M. J., 1969, Nature, 221, 924Fixsen D. J., Cheng E. S., Gales J. M., Mather J. C., Shafer R. A.,Wright E. L., 1996, ApJ, 473, 576Fukazawa Y., Makishima K., Ohashi T., 2004, PASJ, 56, 965Hanany S., et al., 2019, arXiv e-prints, p. arXiv:1902.10541Hardcastle M. J., Croston J. H., 2020, arXiv e-prints, p.arXiv:2003.06137Illarionov A. F., Siuniaev R. A., 1975, Soviet Astronomy, 18, 413Isobe N., Tashiro M. S., Gandhi P., Hayato A., Nagai H., HadaK., Seta H., Matsuta K., 2009, ApJ, 706, 454Itoh N., Kohyama Y., Nozawa S., 1998, ApJ, 502, 7Jetha N. N., Ponman T. J., Hardcastle M. J., Croston J. H., 2007,MNRAS, 376, 193Johnson O., Almaini O., Best P. N., Dunlop J., 2007, MNRAS,376, 151Kaiser C. R., Alexander P., 1997, MNRAS, 286, 215Kaiser C. R., Dennett-Thorpe J., Alexander P., 1997, MNRAS,292, 723Khatri R., Sunyaev R. A., Chluba J., 2012, A&A, 543, A136Leahy J. P., Williams A. G., 1984, MNRAS, 210, 929Majumdar S., 2001, PhD thesis (Indian Institute of Science, Ban-galore)Malu S., Datta A., Colafrancesco S., Marchegiani P., Subrah-manyan R., Narasimha D., Wieringa M. H., 2017, ScientificReports, 7, 16918Mroczkowski T., et al., 2019, Space Sci. Rev., 215, 17Nath B. B., 1995, MNRAS, 274, 208Nath B. B., 2010, MNRAS, 407, 1998Reynolds C. S., Begelman M. C., 1997, ApJL, 487, L135Sazonov S. Y., Sunyaev R. A., 1998, ApJ, 508, 1Scheuer P. A. G., 1974, MNRAS, 166, 513Sunyaev R. A., Zeldovich Y. B., 1970, ApSS, 7, 20Sunyaev R. A., Zeldovich I. B., 1980, MNRAS, 190, 413Wang Y., Kaiser C. R., 2008, MNRAS, 388, 677Yamada M., Sugiyama N., Silk J., 1999, ApJ, 522, 66Zeldovich Y. B., Sunyaev R. A., 1969, ApSS, 4, 301This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000