Sunyaev-Zel'dovich Signal from Quasar Hosts: Implications for Detection of Quasar Feedback
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SUNYAEV-ZEL’DOVICH SIGNAL FROM QUASAR HOSTS: IMPLICATIONS FOR DETECTION OF QUASARFEEDBACK D HRUBA D UTTA C HOWDHURY , , S UCHETANA C HATTERJEE Department of Physics, Presidency University, Kolkata, 700073, India, Department of Astronomy, Yale University, New Haven, CT 06511.
Draft version November 13, 2018
ABSTRACTSeveral analytic and numerical studies have indicated that the interstellar medium of a quasar host galaxyheated by feedback can contribute to a substantial secondary signal in the cosmic microwave background(CMB) through the thermal Sunyaev-Zel’dovich (SZ) effect. Recently, many groups have tried to detect thissignal by cross-correlating CMB maps with quasar catalogs. Using a self-similar model for the gas in theintra-cluster medium and a realistic halo occupation distribution (HOD) prescription for quasars we estimatethe level of SZ signal from gravitational heating of quasar hosts. The bias in the host halo signal estimationdue to unconstrained high mass HOD tail and yet unknown redshift dependence of the quasar HOD restricts usfrom drawing any robust conclusions at low redshift ( z < .
5) from our analysis. However, at higher redshifts( z > . INTRODUCTIONThe measurement of the temperature fluctuations in the cos-mic microwave background (CMB) maps at large and smallangular scales have proven to be one of the most powerfulprobes of cosmology (e.g., Spergel et al. 2003, 2007; Re-ichardt et al. 2009; Dunkley et al. 2011; Das et al. 2011b,a; Se-hgal et al. 2011; Sherwin et al. 2011; Hlozek et al. 2012; Re-ichardt et al. 2012; Sievers et al. 2013; Calabrese et al. 2013;Story et al. 2013; Planck Collaboration et al. 2014a,b,c,d;Das et al. 2014; Hou et al. 2014; Planck Collaboration et al.2015a,b,c,d; George et al. 2015).The detection of the secondary fluctuations from astrophys-ical sources via cross-correlation techniques with other wave-bands have been the primary focus of many microwave exper-iments (e.g., Diego et al. 2003; Hirata et al. 2004; Afshordiet al. 2004; Cheng et al. 2004; Padmanabhan et al. 2005; Hoet al. 2008; Chatterjee et al. 2010; Feng et al. 2012; Kov´acset al. 2013; Giannantonio et al. 2014; Munshi et al. 2014;Cabass et al. 2015; Bianchini et al. 2015; Ferraro et al. 2015;Ruan et al. 2015; Greco et al. 2015; Crichton et al. 2016;Spacek et al. 2016; Zieser & Merkel 2016; Verdier et al. 2016;Soergel et al. 2016). The Sunyaev-Zeldovich effect (SZ; Sun-yaev & Zeldovich 1970, 1972), arising from inverse Comptonscattering of CMB photons happens to be the dominant sec-ondary signal at angular scales of an arcminute. The SZ effectcreates a spectral distortion in the CMB and serves as a probefor accumulations of hot gas in the Universe (see Carlstromet al. 2002 and references therein).The major SZ signal comes from galaxy clusters which arereservoirs of keV energy electrons (e.g., Birkinshaw et al.1978; Joy et al. 2001; Hincks et al. 2010; Staniszewskiet al. 2009; Planck Collaboration et al. 2015e). However,apart from the cluster signal several small scale astrophysicalsources produce measurable SZ distortions in the CMB (e.g.,McQuinn et al. 2005; Iliev et al. 2007; White et al. 2002; Ma-jumdar et al. 2001; Aghanim et al. 2000; de Zotti et al. 2004;Rosa-Gonz´alez et al. 2004; Massardi et al. 2008; Babich & [email protected]@presiuniv.ac.in
Loeb 2007; Oh et al. 2003; Aghanim et al. 2008; Reichardtet al. 2012; Archidiacono et al. 2012; van de Voort et al. 2016).The SZ signal from these sources provides a new observa-tional tool to study the role of baryonic physics on structureformation.A generic astrophysical signal that is related to the SZ dis-tortion from hot gas surrounding an active galactic nucleus(AGN) has been studied by several authors using analytic andnumerical tools (e.g., Natarajan & Sigurdsson 1999; Aghanimet al. 1999; Yamada et al. 1999; Lapi et al. 2003; Platania et al.2002; Roychowdhury et al. 2005; Chatterjee & Kosowsky2007; Scannapieco et al. 2008; Chatterjee et al. 2008; Zanniet al. 2005; Sijacki et al. 2007). The first attempt to detect thissignal was carried out by Chatterjee et al. (2010) who useda technique of stacking quasars from the Sloan Digital SkySurvey (SDSS; Schneider et al. 2010) onto the CMB temper-ature maps from the Wilkinson Microwave Anisotropy Probe(WMAP; Bennett et al. 2003).Chatterjee et al. (2010) reported a tentative detection of thesignal within the noise sensitivity and the angular resolutionof WMAP. Recently, several other teams have tried to detectthis signal using the Planck Surveyor Satellite (R15 hereafterRuan et al. 2015; Verdier et al. 2016, V16 hereafter), theAtacama Cosmology Telescope (ACT; Crichton et al. 2016,C16 hereafter) and the South Pole Telescope (SPT; Spaceket al. 2016). Spacek et al. (2016) co-added the SPT (e.g.,Staniszewski et al. 2009) SZ maps around quiescent ellipti-cal galaxies and showed that the observed mean integratedCompton Y parameter is greater than that is expected fromsimple models without feedback.R15 prepared two different stacks of Planck SZ maps andcross-correlated them with the SDSS quasar catalog. The twostacks corresponded to two different redshift intervals ( z > . z < . a r X i v : . [ a s t r o - ph . C O ] M a r Dutta Chowdhury & Chatterjee F IG . 1.— Comparison of R15 (magenta circle) and V16 (orange square)observations for (cid:104) ˜ Y (cid:105) with predictions for the host halo signal consideringonly gravitational heating of the halo gas from KS and PC13 Y − M relations.Quasars are populated in dark matter halos according to the HOD modelsof Richardson et al. (2012) and Shen et al. (2013). The low redshift signalof R15 is consistent within error limits with the host halo signal predictedusing R12 quasar HOD. Using S13 quasar HOD we get a marginally lowervalue for the host halo signal than what is observed. The high redshift signalsof both R15 and V16 are in excess than the host halo contribution predictedfrom our model. C16 analysed a sample of radio quiet SDSS quasars withredshifts spanning from 0 . − .
5. By stacking Herschel (Lutzet al. 2011) and ACT (Hincks et al. 2010) data, they derivedthe spectral energy distribution of quasars in millimeter andfar infrared wavebands. Assuming a quasar host halo massdistribution of ( − ) × h − M (cid:12) C16 find that after cor-recting for dust emission, the observed signal is in excess overthat expected from gravitational heating of virialized halo gasalone, favoring a quasar SZ contribution.V16 analysed Planck SZ maps cross correlated with SDSSquasars in the redshift range 0 . < z <
5. For their radio quietquasar sample they detected thermal SZ emission at 2 . < z < z < . z > .
5, V16find that the observed signal may or may not be explainablewith gravitational heating alone depending on uncertainties inthe systematics of the Y-M calibration.In this paper, we theoretically examine the validity of thedetection of SZ effect from quasar feedback in R15, C16 andV16 using a Halo Occupation Distribution (HOD) based ap-proach. We propose that the interpretation of the observed sig-nals is largely dependent on the precise characterization of themass distribution of quasar hosts, with possible biases arisingfrom poor constraints available on the high mass HOD tail andthe largely unexplored redshift dependence of the HOD. Forexample, using a HOD model of quasars, Cen & Safarzadeh(2015) show that the signal in R15 can be explained by SZeffect arising from the virialized halo gas alone. We apply adifferent HOD model proposed by Chatterjee et al. 2012 (C12hereafter) to characterize the SZ contribution from the virial-ized gas in the quasar host halos and use it to interpret thefindings of the cross-correlation signals.Our paper is organized as follows. In §2 we briefly describeour model for quantifying the host halo SZ signal. The resultsof our analysis are presented in §3. We discuss the implica-tions of our results and summarize the main conclusions in §4. Throughout the paper we assume a spatially flat, Λ CDMcosmology (Planck Collaboration et al. 2015a): Ω m = . Ω Λ = . Ω b = . n s = . σ = .
82, and h = . THEORETICAL MODELThe thermal SZ temperature distortion at a frequency ν isgiven by (Sunyaev & Zeldovich 1970, 1972) ∆ TT = [ x coth ( x / ) − ] y , (1)where T is the mean CMB temperature (2.73 K) and x = h ν / T . The temperature distortion is parametrized by the di-mensionless Compton y -parameter which is proportional tothe line-of-sight integral of the electron pressure ( P e ). Thetotal SZ distortion ( Y ) from a halo can be obtained by inte-grating the line of sight signal over the solid angle subtendedby the halo at the position of the observer.The thermal energy of the electron gas can be calculated as E e = (cid:90) R vir P e dV (2)For protons and electrons in thermal equilibrium, the total en-ergy of the ICM gas is given by E tot = (cid:18) + µ e (cid:19) E e , (3)where µ e is the mean particle weight per electron which weassume as 1.17. To estimate Y and E tot from the virialized gasof quasar host halos in absence of feedback, we use two dif-ferent methods, namely the analytic prescription of Komatsu& Seljak (2001) (KS hereafter) and the observed Y − M relation of Planck Collaboration et al. 2013 (PC13 hereafter).The main ingredients of the KS model are as follows: Thedark matter density in a halo is described by the self similarNFW profile (Navarro et al. 1995). The ICM gas is assumedto be in hydrostatic equilibrium, with gas pressure gradientbalancing the gravitational attraction of the dark matter. Inaddition, the gas is assumed to have a polytropic equation ofstate and gas density is assumed to follow dark matter at halooutskirts. The model does not take gas cooling and star for-mation into account. For further details on the model we referthe reader to KS.PC13 measured the SZ signal from host halos of locallybrightest galaxies in the SDSS DR7 catalog as a function oftheir stellar masses. By assigning halo masses to these galax-ies according to the semi-analytic galaxy formation simula-tion of Guo et al. (2011), they found a simple power lawscaling between Y and M extending over a wide rangeof halo masses from rich clusters down to atleast M = . × h − M (cid:12) . The observed relation after rescaling Y from each source to a common angular diameter distance of500 Mpc is given by˜ Y = Y M (cid:18) M . × M (cid:12) (cid:19) α (4)The power law exponent α is fixed at 5 / Y M is found to be ( . ± . ) × − arcmin .We assume the validity of this relation for halo masses below M = . × h − M (cid:12) as well. For further details on thismodel, we refer the reader to PC13.Z signal from Quasar Hosts 3 F IG . 2.— Comparison of R15 (magenta circle) observations for (cid:104) ˜ Y (cid:105) at me-dian redshift z = .
96 with predictions for the host halo signal consideringonly gravitational heating of the virialized gas from KS and PC13 Y − M re-lations. Quasars are populated in dark matter halos according to the HODmodels of Richardson et al. (2012) and Shen et al. (2013) but the mass ofquasar hosts is restricted below M = h − M (cid:12) . The estimated signalsare now lower in magnitude than the observed signal at low redshift indicat-ing that host halo signal modeling at low redshift is sensitive to the high massHOD tail.F IG . 3.— Comparison of C16 observations (magenta circle) for the meantotal thermal energy with estimates for the mean total thermal energy of thehost halo gas due to gravitational heating alone from KS and PC13 Y-M re-lations. Quasars are populated in dark matter halos according to the quasarHOD models of R12 and S13. While the host halo signal predicted using S13HOD is consistent with the observations, that predicted using R12 HOD isabove the observed value. R15 integrate the Compton- y from each source over a pro-jected radius of 3 . h − M pc . On the other hand, PC13measurements constrain Y in a spherical volume of radius R . Given these differences, R15 note that their observed˜ Y = .
52 ˜ Y . Similarly C16 note that given the ACT beamsize, their observed ˜ Y = . Y .To model the average Y in a stack of SZ maps cross-correlated with several quasars, we need to model the hosthalo distribution of SDSS quasars. To model the distributionof quasar numbers in dark matter halos we follow the HODformalism (e.g., Berlind & Weinberg 2002; Zheng et al. 2005,2007; Chatterjee et al. 2012). The HOD defines the condi-tional probability that a halo of mass M at redshift z hosts N quasars. We use the 5-parameter HOD model proposed byC12 which is motivated from a study of low luminosity AGNin cosmological hydrodynamic simulations. This particular HOD model has been successfully used to describe the clus-tering properties of z = M min , σ log M , M , α , M cut ) is given as (cid:104) N ( M ) (cid:105) = (cid:20) + erf (cid:18) log M − log M min σ logM (cid:19)(cid:21) + (cid:18) MM (cid:19) α exp (cid:18) − M cut M (cid:19) . (5)The average ˜ Y (integrated over a range of halo masses andredshifts) is then given as (cid:104) ˜ Y (cid:105) = (cid:82) z max z min (cid:82) M max M min ˜ Y ( M , z ) (cid:104) N ( M ) (cid:105) dndM dM dVdz dz (cid:82) z max z min (cid:82) M max M min (cid:104) N ( M ) (cid:105) dndM dM dVdz dz , (6)where dV is the comoving volume between redshift z to z + dz and dndM is the comoving density of dark matter halos per unithalo mass for which we adopt the Sheth & Tormen (1999)mass function. Similarly, the average host halo thermal en-ergy (cid:104) E tot (cid:105) can be calculated.We adopt the best-fit HOD parameters from R12 whichwere obtained by fitting the 2-point correlation functionof quasars in the SDSS DR7 catalog at 0 . < z < . .
4. The best fit valuesare log M min ( h − M (cid:12) ) = . + . − . , σ logM = . + . − . ,log M ( h − M (cid:12) ) = . + . − . , log M cut ( h − M (cid:12) ) = . + . − . and α = . + . − . . R12 interpret their derived HOD to berepresentative of the true HOD of quasars at the median red-shift of their clustering sample. However, in our model forthe average host halo signal we assume the HOD to be red-shift independent and use the R12 parameters for all redshiftsin the range 0 . < z <
4. This can possibly lead to bias in ourcalculations and we discuss this issue in §4.We also calculate the average host halo signal at all red-shifts using the best-fit parameters from Shen et al. (2013)(S13 hereafter). S13 used the C12 HOD model for fitting the2-point cross-correlation function of quasars with galaxies inSDSS DR7 catalog at 0 . < z < . . M min , σ log M , M (cid:48) , α , M ) as log M min ( h − M (cid:12) ) = . + . − . , σ logM = . + . − . ,log M (cid:48) ( h − M (cid:12) ) = . + . − . , log M ( h − M (cid:12) ) = . + . − . and α = . + . − . . We however note that due to the narrowredshift range of the S13 sample, R12 HOD will do a com-paratively better job in predicting the host halo signal at highredshifts ( z >
1) than S13 HOD. RESULTSIn Fig. 1 we present our results for (cid:104) ˜ Y (cid:105) calculated usingboth PC13 and KS models corresponding to R15 and V16quasar samples. For comparison with the low redshift stackof R15, the limits for the redshift integral in Eq. 6 are takenas z min = . z max = .
5. Similarly, for comparison withthe high redshift stacks of R15 and V16, the limits are takenas z min = . z max = . z min = . z max = . Y − M relation and HOD parameters. For KS model,they represent uncertainties in the HOD parameters only. Wefind that in case of R15 measurements (magenta circle), ob-served (cid:104) ˜ Y (cid:105) at low redshift ( z < .
5) is consistent with the sig-nal we can expect from the virialized gas in quasar host ha-los using both PC13 (blue square) and KS (brown asterisk)models with the R12 host halo distribution ( M varies from10 h − M (cid:12) to 10 h − M (cid:12) ). Although the best-fit esti-mates are higher than the observed signal, they overlap withinthe 1 σ error limits.For the high redshift stack of R15 ( z > .
5) however, theseestimates are about an order of magnitude lower than the ob-served signal. The absence of massive halos at high redshifttogether with a redshift independent HOD gives rise to a de-crease in the host halo signal. If the S13 HOD parametrizationis used ( M varying from 10 h − M (cid:12) to 10 h − M (cid:12) ), wefind that the estimated host halo signal for the low redshiftstack of R15 (cyan cross for PC13 and black dot for KS) ismarginally less than the observed signal. For the high redshiftstack these estimates are roughly about 2 orders of magnitudelower than the observed signal.In the R15 study, all pixels within the angular extent ofknown clusters are masked. The tSZ maps used in this anal-ysis are derived from Planck Collaboration et al. (2011) earlySZ cluster catalog. The least massive clusters in this cataloghave masses of the order of M = . × h − M (cid:12) whichtranslates to M ∼ h − M (cid:12) using M / M =1.6 (Duffyet al. 2008). In Fig. 2, we show how applying this mass-cutaffects the host halo signal modeling for the low redshift stackof R15. Using R12 HOD with host halo masses varying from M = h − M (cid:12) to M = h − M (cid:12) , we find that theobserved signal at low redshift is at least 3 times higher thanthe estimate using PC13 model and at least 2 times higher thanthe estimate using KS model. Using the S13 HOD with hosthalo masses varying from 10 h − M (cid:12) to 10 h − M (cid:12) leadsto an even lower prediction for the host halo signal. At higherredshifts on the other hand excluding/including the high massHOD tail makes almost no statistical difference in the signalmodeling. This is expected because of the small number ofmassive ( M > h − M (cid:12) ) halos at high redshift.In their study, R15 neglect the contribution from host halogas in their high redshift sample, assuming it to be entirelydominated by feedback. For their low redshift stack, R15 es-timate the contribution from host halo virialized gas by find-ing the mean ˜ Y at z = . z = .
96. They find it to bearound 2 to 3 times smaller with the 5 and 6 parameter modelsrespectively than the observed signal. From our analysis, wewould like to note that the interpretation of the observed sig-nal at low redshift depends on the HOD model used and alsoon the range of host halo masses considered which would bedependent on the quasar selection function. For the high red-shift stack of R15 on the other-hand, there is clear evidenceof enhanced signal. Our maximum host halo signal estimateusing PC13/KS model with R12 HOD is about an order ofmagnitude lower than the observed signal. This leaves roomfor the excess signal being attributed to heating of the ICM byquasar feedback. R15 also draw a similar conclusion for theirhigh redshift stack, however they do not calculate the levelof host halo signal that could be present and assume it to beentirely feedback dominated.Contrary to the R15 results, V16 report that they find no ev- idence for tSZ signal from quasars below z < .
5. They arguethat the enhanced signal detected by R15 is due to improperdust subtraction. However, above z = .
5, V16 do detect tSZsignal from quasars marked by the orange square in Fig. 1.This is obtained by stacking Planck SZ maps cross-correlatedwith SDSS quasars in the redshift range 2 . < z < .
0. Planckmeasures Y , which has been converted to ˜ Y using the con-version factor from R15 for the sake of comparison. V16 findthe host halo contribution for this sample of quasars by firstobtaining a lower mass bound such that the total number ofquasars at 2 . < z < . . × h − M (cid:12) .This is then used to predict the average host halo signal usingthe Y − M relation from Arnaud et al. 2010.The Arnaud et al. (2010) relation is calibrated from XMMobservations of galaxy clusters and therefore has a mass biasparameter, b which accounts for any bias between the esti-mated mass and the true halo mass due to deviation from hy-drostatic equilibrium. Planck cluster counts suggest a highvalue of b and taking b = .
4, V16 find the that host halocontribution accounts for about 40% of the observed signal.However, V16 implicitly assume (cid:104) N ( M ) (cid:105) = . (cid:104) Y (cid:105) . If b is takento be zero, then their estimate for the host halo signal is just1 σ below the observed signal.In our model, maximum host halo signal is obtained fromusing the R12 HOD. With PC13 model for the ICM, we esti-mate the host halo signal to be at most ∼
11 % of the observedsignal. Using KS model the estimate is at most ∼
16 %. Whilewe find much more excess signal than what can be expectedfrom gravitational heating of gas alone, our results should alsobe interpreted with caution because of the extrapolation ofR12 HOD parameters to 2 . < z <
4. R12 did do a cross-correlation study for z ∼ . . + . − . × h − M (cid:12) ,suggesting an increase in mean mass with redshift. Howevertheir results are tentative due to poor statistics. We note thatthere is a tension between the results of V16 and R12 at lowredshifts. We suggest that the poorly constrained contributionof the high mass HOD tail in the clustering studies of R12 andS13 and also the assumption of a redshift independent HODact as caveats in our theoretical modeling, which in turn re-mains inconclusive about the true amplitude of the halo gassignal at low redshifts.In Fig. 3, we compare (cid:104) E tot (cid:105) obtained by C16 (pink circle)with the theoretical estimates from KS and PC13 models us-ing R12 and S13 HODs. The limits for the redshift integralin Eq. 6 are taken as z min = . z max = .
5. We find thatusing the R12 host halo distribution , our estimate for the hosthalo signal (blue square for PC13 and brown asterisk for KS)is greater than the observed signal. Using the S13 HOD (cyancross for PC13 and black dot for KS), our estimate is consis-tent with the observed signal within error-limits, leaving noroom for excess heating due to feedback. By assuming hosthalo masses of quasars to vary to ( − ) × h − M (cid:12) , C16noted that gravitational heating could account for only 30%Z signal from Quasar Hosts 5of the observed signal. However, modeling the average hosthalo signal using the R12 HOD at the median redshift of theirsample ( z = . DISCUSSIONSeveral observational evidences and theoretical modelssuggest that there exists a strong link between galaxy evo-lution and the growth of super massive black holes (SMBH)at galaxy centers (e.g., Merritt & Ferrarese 2001; Tremaineet al. 2002; Graham et al. 2011). The key ingredient to thislink has been attributed to feedback from the central blackhole (e.g., Shankar et al. 2004; Hopkins et al. 2006; Lapi et al.2006; Hopkins et al. 2008; Di Matteo et al. 2008; Booth &Schaye 2009; Ciotti & Ostriker 2007). Different observationalprobes, such as the SZ effect, have been proposed in the lit-erature to systematically study the effect of feedback on thegas in the ICM (see references in Chatterjee et al. 2015). Thenoise sensitivity and the angular resolution of current and pro-posed CMB experiments are just in the limit of detecting theSZ signal from quasar feedback.However, a key issue related to this detection involves dis-entangling the signal from the SZ effect arising from the viri-alized gas in the host dark matter halos of AGN. In recentwork the effect has been mostly studied with bright quasarsdue to their abundance in large surveys. We observe thatwhile estimating the SZ contribution from quasar hosts, moststudies assume the host halos of quasars to lie in the range of ≈ M (cid:12) , which happens to be the peak in the mass distri-bution of quasar hosts (see R12). In this study, we emphasizethe importance of understanding the implication of the fullhost halo mass distribution of quasars in characterizing theSZ signal from the virialized gas. Recent measurements ofquasar HOD allows us to account for this correction.An important component to this approach lies in model-ing the redshift dependence of the quasar HOD which is yetto be understood in numerical simulations (or semi-analyticwork). For low-luminosity AGN, C12 (HOD model used inthis work) report a redshift dependence of the HOD parame-ters but the results are tentative due to lack of statistics. Wealso note that while fitting the 2PCF of z ≈ z > .5), there is evidence for enhanced signal thatcannot be explained with gravitational heating alone. FutureAGN surveys will enhance the statistical power of 2PCF mea-surements providing tighter constraints on quasar/AGN HOD.That would allow us to estimate the SZ signal from quasarhosts with better precision. The pre-requisite for interpretingthose results links to a superior theoretical understanding ofthe HOD itself (e.g., accurate redshift evolution). We thus em-phasize the need for both theoretical and observational studiesof the HOD for better understanding of the relationship be-tween quasars and their host dark matter halos. Our analysison the need for precise determination of the HOD is not onlyimportant for determination of quasar SZ signal but is essen-tial for using quasars as probes of the high redshift Universe.ACKNOWLEDGMENTSThe authors thank the anonymous referee for many usefulcomments that helped in improvement of the paper and YueShen for sharing some of his data products that helped in theHOD comparison. DDC thanks Kanan Kumar Datta for hissupport, Saumyadip Samui for his help with some aspects ofthe analysis and acknowledges the Department of Science andTechnology, Govt. of India for financial support through theINSPIRE scholarship. DDC also acknowledges useful discus-sions with Daisuke Nagai and Kaustav Mitra that helped ininterpreting some results in the paper. SC acknowledges par-tial support from the University Grants Commission throughthe start-up grant and Presidency University Kolkata throughthe FRPDF grant. SC is grateful to the Inter University Cen- Dutta Chowdhury & Chatterjeeter for Astronomy and Astrophysics (IUCAA) for providing infra-structural and financial support along with local hospi-tality through the IUCAA-associateship program.