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Max-Moerbeck, W.; Hovatta, T.; Richards, J.L.; King, O.G.; Pearson, T.J.; Readhead, A.C.S.;Reeves, R.; Shepherd, M.C.; Stevenson, M.A.; Angelakis, E.; Fuhrmann, L.; Grainge, K.J.B.;Pavlidou, V.; Romani, R.W.; Zensus, J.A.Time correlation between the radio and gamma-ray activity in blazars and the production siteof the gamma-ray emission

Published in:Monthly Notices of the Royal Astronomical Society

DOI:10.1093/mnras/stu1749

Published: 01/01/2014

Document VersionPublisher's PDF, also known as Version of record

Please cite the original version:Max-Moerbeck, W., Hovatta, T., Richards, J. L., King, O. G., Pearson, T. J., Readhead, A. C. S., Reeves, R.,Shepherd, M. C., Stevenson, M. A., Angelakis, E., Fuhrmann, L., Grainge, K. J. B., Pavlidou, V., Romani, R. W.,& Zensus, J. A. (2014). Time correlation between the radio and gamma-ray activity in blazars and the productionsite of the gamma-ray emission. Monthly Notices of the Royal Astronomical Society, 445(1), 428-436.https://doi.org/10.1093/mnras/stu1749

MNRAS 445, 428–436 (2014) doi:10.1093/mnras/stu1749

Time correlation between the radio and gamma-ray activity in blazarsand the production site of the gamma-ray emission

W. Max-Moerbeck,1,2‹ T. Hovatta,1,3 J. L. Richards,4 O. G. King,1 T. J. Pearson,1

A. C. S. Readhead,1 R. Reeves,1,5 M. C. Shepherd,1 M. A. Stevenson,1 E. Angelakis,6

L. Fuhrmann,6 K. J. B. Grainge,7 V. Pavlidou,1,6,8 R. W. Romani9 and J. A. Zensus6

1Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA2National Radio Astronomy Observatory (NRAO), PO Box 0, Socorro, NM 87801, USA3Aalto University Metsahovi Radio Observatory, Metsahovintie 114, FI-02540 Kylmala, Finland4Department of Physics, Purdue University, West Lafayette, IN 47907, USA5Departamento de Astronomıa, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile6Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany7Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, M13 9PL, UK8Department of Physics, University of Crete/Foundation for Research and Technology-Hellas, Heraklion GR-71003, Greece9W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physicsand SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA

Accepted 2014 August 26. Received 2014 August 21; in original form 2014 June 20

ABSTRACTIn order to determine the location of the gamma-ray emission site in blazars, we investigatethe time-domain relationship between their radio and gamma-ray emission. Light curves forthe brightest detected blazars from the first 3 yr of the mission of the Fermi Gamma-ray SpaceTelescope are cross-correlated with 4 yr of 15 GHz observations from the Owens Valley RadioObservatory 40 m monitoring programme. The large sample and long light-curve durationenable us to carry out a statistically robust analysis of the significance of the cross-correlations,which is investigated using Monte Carlo simulations including the uneven sampling and noiseproperties of the light curves. Modelling the light curves as red noise processes with power-law power spectral densities, we find that only one of 41 sources with high-quality data inboth bands shows correlations with significance larger than 3σ (AO 0235+164), with onlytwo more larger than even 2.25σ (PKS 1502+106 and B2 2308+34). Additionally, we findcorrelated variability in Mrk 421 when including a strong flare that occurred in 2012 July–September. These results demonstrate very clearly the difficulty of measuring statisticallyrobust multiwavelength correlations and the care needed when comparing light curves evenwhen many years of data are used. This should be a caution. In all four sources, the radiovariations lag the gamma-ray variations, suggesting that the gamma-ray emission originatesupstream of the radio emission. Continuous simultaneous monitoring over a longer timeperiod is required to obtain high significance levels in cross-correlations between gamma-rayand radio variability in most blazars.

Key words: galaxies: active – BL Lacertae objects: general – quasars: general – gamma rays:galaxies – radio continuum: galaxies.

1 IN T RO D U C T I O N

Blazars are active galactic nuclei (AGN) with jets closely aligned tothe line of sight (e.g. Blandford & Konigl 1979). They are the mostnumerous class of sources detected in the GeV band by the Large

� E-mail: wmax@nrao.edu

Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope(Ackermann et al. 2011b). Blazars have double-peaked broad-bandspectral energy distributions and show strong variability from radioto gamma-rays (e.g. von Montigny et al. 1995). It is accepted thatthe low-energy emission is produced by synchrotron radiation fromelectrons within the jet, while the high-energy gamma-ray emissionis produced by inverse-Compton scattering of a soft photon fieldby the same electrons (e.g. Jones, O’dell & Stein 1974; Dermer

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Radio and gamma-ray variability in blazars 429

& Schlickeiser 1993; Sikora, Begelman & Rees 1994; Błazejowskiet al. 2000) or by hadronic processes (e.g. Mannheim & Biermann1992). That a common mechanism regulates the luminosity at highand low energies is demonstrated by the correlation between themean radio flux density and mean gamma-ray flux (Kovalev et al.2009; Mahony et al. 2010; Nieppola et al. 2011). Ackermann et al.(2011a) and Pavlidou et al. (2012) showed that this correlation isnot an effect of distance modulation of the fluxes.

The location of the gamma-ray emission site in blazars is not yetknown. Gamma-rays may be produced, for example, in the radio-emitting regions (e.g. Jorstad et al. 2001), or much closer to the cen-tral engine (e.g. Blandford & Levinson 1995). Radio observationswith milliarcsecond resolution have resolved the radio-emitting re-gions and measured outflow velocities, but at high energies theangular resolution is insufficient and we must infer the size andlocation of the emission regions from flux variations. If gamma-rayand radio emission are triggered by shocks propagating along a rel-ativistic jet, the time delay between flares in the two bands dependson their separation. Several studies have found time-lagged corre-lation between these two energy bands, but without a large samplewith well-sampled light curves it is difficult to assess the signif-icance of the correlations (e.g. Marscher et al. 2008; Abdo et al.2010a; Agudo et al. 2011a,b). In a statistical study of 183 brightFermi-detected sources, Pushkarev, Kovalev & Lister (2010) foundthat, on average, radio flares occur later than gamma-ray flares.A more recent investigation using multiple radio frequencies andlonger light curves (Fuhrmann et al. 2014) also found correlatedradio and gamma-ray variability with a frequency-dependent radiolag.

In comparing multiwavelength light curves of individual blazarsover short time periods, claims are often made for correlations butthe actual significance is rarely computed. To remedy this situationand search for the existence of significant correlations and theirphysical origin, we have undertaken a long-term radio monitoringcampaign of a large number of blazars. We apply robust statisticalmethods to estimate the significance of correlations and find thatmost of the blazars in our sample only show correlations below2.25σ . Only three out of 41 objects show correlations above a 2.25σ

level where we expect to find one random uncorrelated source toappear, with only one above the 3σ level of significance. Thus, it isclear that establishing a statistically significant cross-correlation ismore difficult than is generally assumed. We also provide a tentativeinterpretation for the origin of the time lag and the location of thegamma-ray emission site.

2 O BSERVATIONS

Through our Owens Valley Radio Observatory (OVRO) 40 m pro-gramme, twice per week we observe all sources in the CandidateGamma Ray Blazar Survey (Healey et al. 2008) and the blazarsdetected in the Fermi-LAT AGN catalogues (Abdo et al. 2010b;Ackermann et al. 2011b) north of declination −20◦ at 15 GHz. Thissample has a total of 1593 sources, of which 685 have gamma-raydetections, with 454 and 634 in the first and second Fermi-LATAGN catalogues, respectively.

Radio observations from 2008 January 1 to 2012 February 26are included in this study. The radio flux density measurementshave a thermal noise floor of ∼5 mJy with an additional 2 percent contribution from pointing errors. The flux density scale isdetermined from regular observations of 3C 286 assuming the Baarset al. (1977) value of 3.44 Jy at 15.0 GHz, giving a 5 per cent overallscale accuracy. A detailed discussion of the observing strategy and

calibration procedures can be found in Richards et al. (2011). Theradio light curves have different characteristics, with a mean andstandard deviation for length 1178 ± 441 d, number of data points195 ± 88, and average sampling 6.4 ± 1.4 d. The light curves of thecases discussed in this paper are shown in Fig. 1. The monitoringprogramme is ongoing and all the light curves are made public onthe programme website.1

The LAT is a pair-conversion gamma-ray telescope, sensitiveto photon energies from about 20 MeV up to >300 GeV, thatobserves the whole sky once every three hours (Atwood et al.2009). Fermi-LAT light curves with 7 d time bins from 2008 Au-gust 4 through 2011 August 12 were produced for 86 sourcesdetected in at least 75 per cent of monthly time bins (Nolanet al. 2012). We use an unbinned likelihood analysis, with sourcespectral models and positions from Ackermann et al. (2011b).We froze the sources spectral parameters (including the target)and let only the flux vary in sources within 10◦ of the target.We use Fermi-LAT ScienceTools-v9r23p1 with P7_V6 sourceevent selection and instrument response functions, diffuse modelsgal_2yearp7v6_v0.fits and iso_p7v6source.txt, only pho-tons with zenith angle <100◦ and other standard data cuts and filters(e.g. Abdo et al. 2011).2 We use a region of interest of 10◦ radiusand a source region of 15◦ radius. Photon integral fluxes from 100MeV to 200 GeV are reported when the test statistic3 TS ≥ 4, and2σ upper limits when TS < 4 (∼30 per cent of the data).

3 T I M E L AG S A N D T H E I R SI G N I F I C A N C E

The radio light curves are sampled unevenly due to weather andother problems. The gamma-ray light curves are weekly averages,but some measurements are upper limits (∼30 per cent of the data)that are ignored in this analysis. We tested the possible effect ofignoring upper limits by using the best flux estimate independent ofTS and the upper limit itself as a flux, obtaining comparable resultsin all cases, thus showing that it is safe to ignore upper limits forthis sample of bright sources. The cross-correlation is measured us-ing the discrete cross-correlation function (DCF; Edelson & Krolik1988), with local normalization (Welsh 1999), also known as localcross-correlation function (LCCF). We find that the LCCF resultsin a greater detection efficiency for known correlations injected insimulated data. We estimate the cross-correlation significance withMonte Carlo simulations that assume a simple power-law powerspectral density model for the light curves (PSD ∝ 1/fβ ), motivatedby previous work (e.g. Hufnagel & Bregman 1992; Edelson et al.1995; Uttley et al. 2003; Arevalo et al. 2008; Chatterjee et al. 2008;Abdo et al. 2010c). We simulate a large number of independent,uncorrelated light-curve pairs that replicate the sampling, measure-ment error distribution, and statistical properties of the observations,using the method of Timmer & Koenig (1995). From the distribu-tion of cross-correlations at each time lag, we estimate the chanceprobability of obtaining a given correlation value. The method isdescribed in detail by Max-Moerbeck et al. (2014).

For 13 sources where a PSD fit is possible in both bands, weuse the best-fitting power-law index values; for the others, we use

1 http://astro.caltech.edu/ovroblazars/2 Science Tools, LAT data, and diffuse emission models are available fromthe Fermi Science Support Center, http://fermi.gsfc.nasa.gov/ssc3 The test statistic is a measure of detection significance, defined as TS=2�log (likelihood) between models with and without the source (Mattoxet al. 1996).

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Figure 1. Light curves (left) and cross-correlation (right) for sources with significant cross-correlation. Contours indicate the cross-correlations significances(red dotted line: 1σ ; orange dash–dotted line: 2σ ; green dashed line: 3σ ). The most significant peak for AO 0235+164 is at −150 ± 8 d with 99.99 per centsignificance, for PKS 1502+106 it is at −40 ± 13 d with 98.09 per cent significance for the best-fitting PSD model and 97.54 per cent for the lower limit, andfor B2 2308+34 it is at −120 ± 14 d with 99.99 per cent significance for the best-fitting PSD model and 99.33 per cent for the lower limit. The significancelower limit for PKS 1502+106 is above the 97.56 per cent threshold within the error (see Table 1).

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Radio and gamma-ray variability in blazars 431

population-average values as described below. We characterize thePSDs using a modified implementation of Uttley, McHardy & Pa-padakis (2002) that uses sampling window functions to reduce red-noise leakage. The effects of uneven sampling are incorporated bycomparing the observed PSD to those derived from simulated lightcurves. We compute the PSD from the data and obtain a mean PSDwith scatter from simulated light curves for several values of thepower-law index. The best fit is found by comparing the PSD fromthe data with the simulated ones using a χ2 test. We find goodconstraints for the radio PSD power-law index for 43 sources (Ta-ble 1). The distribution of indices is clustered around 2.3, with atypical error of 0.4, and is consistent with a single value equal tothe sample mean of 2.3 ± 0.1. We adopt a value of β radio = 2.3 forsources with no fitted radio PSD. In the gamma-ray band, the PSDpower-law index is constrained for 29 sources. The distribution haspeaks at about 0.5 and 1.6. The peak at 1.6 is consistent with resultsfor the brightest sources from Abdo et al. (2010c) (1.4 ± 0.1 forflat spectrum radio quasars (FSRQs) and 1.7 ± 0.3 for BL Lacs)but steeper than that found in Ackermann et al. (2011b) (about 1.15for the average PSD of the brightest blazars). For sources with nogamma-ray PSD fit, we assume βγ = 1.6 which gives conservativeestimates of the cross-correlation significance.

4 R E S U LT S O F T H E C RO S S - C O R R E L AT I O NS I G N I F I C A N C E

We estimated the cross-correlation between the radio and gamma-ray light curves and its significance for 41 of the 86 sources. 23are excluded for being non-variable at the 3σ level (a χ2 test of thenull hypothesis of constant flux shows that the observed variationsare consistent with observational noise). We also exclude ‘noisy’light curves where more than 1/3 of the variance comes from ob-servational noise. We also exclude light curves consistent with alinear trend in the overlapping section; for such sources, longerlight curves are needed to probe the relevant time-scales. These tworestrictions eliminate 22 more objects.

To include the effects of red-noise leakage and aliasing, we sim-ulate 10 yr light-curves with a 1 d time resolution. The cross-correlation is estimated for independent bins of 10 d. In each case,we simulate 20 000 independent light-curve pairs using the appro-priate PSD (Section 3 and Table 1). To eliminate spurious corre-lations, we restrict the time-lag search interval to ±0.5 times thelength of the shortest light curve. For each source, the position andsignificance of the most significant cross-correlation peak are givenin Table 1. The peak position uncertainty is estimated by ‘flux ran-domization’ and ‘random subset selection’ (Peterson et al. 1998).The error on the significance is determined using a bootstrap method(Max-Moerbeck et al. 2014). We set the significance threshold at97.56 per cent (2.25σ ), at which we expect to have one object witha chance high correlation.

At this threshold, three of our 41 sources show interesting levelsof correlation: AO 0235+164, τ = −150 ± 8 d with 99.99 per centsignificance (the only case with significance ≥3σ ); PKS 1502+106,τ = −40 ± 13 d with 97.54 per cent significance;4 and B2 2308+34,τ = −120 ± 14 d with 99.33 per cent significance. The resultsare presented in Fig. 1, where a negative lag indicates that radiovariations occur after gamma-ray variations.

4 This is consistent with the threshold of 97.56 per cent when the 0.13 percent uncertainty is considered as shown in Table 1.

Significant correlated variability has been reported by Agudoet al. (2011b) for AO 0235+164, with a delay of about −30 d usingradio data up to MJD 55000. With our longer light curves, we finda significant correlation at a delay of −150 d, although the cross-correlation peak is broad and there is a second peak of comparableamplitude and significance at −30 d. This adds a large uncertaintywhen considered in the estimation of the location of the gamma-rayemission site because our current data cannot discriminate betweenthese two peaks. No significant cross-correlations have been previ-ously reported for PKS 1502+106 or B2 2304+34.

5 TH E C A S E O F MR K 4 2 1

A major radio flare was observed from Mrk 421 on 2012 September21, when its 15 GHz flux density reached 1.11 ± 0.03 Jy, approx-imately 2.5 times its previous median value (Hovatta et al. 2012).On 2012 July 16, the source was detected at its highest level todate by Fermi-LAT. Its integrated photon flux for E > 100 MeVwas (1.4 ± 0.2) × 10−6 ph cm−2 s−1, a factor of 8 greater thanthe average in the second Fermi-LAT catalogue (D’Ammando &Orienti 2012).

Mrk 421 does not show significant correlated variability whenanalysed as part of the uniform sample described in Section 2.Furthermore, neither the radio nor the gamma-ray PSD can be fittedso the population averages were used as described in Section 3.To include the radio and gamma-ray flares, we extended the lightcurves beyond the period used for the uniform sample (Section 2).We repeated the analysis using these extended light curves and found0.6 < β radio < 2.0, with best-fitting value 1.8, and 1.6 < βγ < 2.1,with best-fitting value 1.6. The cross-correlation peak at −40 ± 9 dhas a significance between 96.16 and 99.99 per cent dependingon the PSD model. The significance obtained using the best-fittingPSD models is 98.96 per cent (Fig. 2). This result should be treatedwith caution: extending the data set after noticing the flare is ‘aposteriori’ statistics, and as such cannot be used to make inferencesabout the rate at which significant correlations are found in thegeneral blazar population.

6 IN T E R P R E TAT I O N O F T H E T I M E D E L AY S

The duration of the correlated events is typically a few hundreddays, and a detailed model is needed to understand the relation-ship between the lags and the location of the emission regions.Here, we ignore the flare duration and tentatively interpret the de-lays using a model in which a moving emission region, confinedto the jet, produces the radio and gamma-ray activity. This regionmoves outwards at the bulk jet speed βc (Fig. 3), and correspondsto the moving disturbances observed with very long baseline in-terferometry (VLBI). The gamma-ray flare becomes observable atdistance dγ from the central engine, after crossing the surface of unitgamma-ray opacity (gamma-sphere; Blandford & Levinson 1995).Likewise, the radio flare becomes observable upon crossing the sur-face of unit radio opacity (‘radio core’), at distance dcore from thecentral engine (Blandford & Konigl 1979).

The time lag between these wavebands provides an estimate of theinterval between the emergence of gamma-ray and radio radiation.The distance travelled by the emission region between the peaks ingamma-ray and radio emission is

d = D βc �t

(1 + z), (1)

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432 W. Max-Moerbeck et al.

Tabl

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gnifi

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sults

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nt)

(c)

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cent

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4C+0

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0135

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099

2.3

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490.

82ng

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2J0

112.

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LL

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265

2.0

1.4

2.4

0.9

0.0

1.8

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0.24

59.6

336

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50.

480.

84–

4C31

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J011

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189

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90.

6992

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174

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±16

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81.0

975

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90.

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FSR

QL

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281.

74tg

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4.8+

2005

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3862

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1+01

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0917

+44

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4441

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162

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05–

MG

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0124

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Radio and gamma-ray variability in blazars 433

Tabl

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813

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5980

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0.77

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0.65

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211

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530

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817

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434 W. Max-Moerbeck et al.

Figure 2. Light curves (left) and cross-correlation (right) for Mrk 421. The most significant peak is at −40 ± 9 d with 98.96 per cent significance. Coloursand line styles as in Fig. 1.

Figure 3. Model for the interpretation of time lags. The central engine launches a jet in which disturbances propagate at speed βc. A moving disturbance(shaded area) is depicted at two times: tγ at which gamma-ray emission peaks and tR for the peak of radio emission when crossing the radio core.

where is the bulk Lorentz factor, D is the Doppler factor, �tis the time lag, and z is the redshift (Pushkarev et al. 2010). Theapparent jet speed, βapp, is determined from VLBI monitoring andthe Doppler factor is estimated from the radio variability time-scale(Hovatta et al. 2009). Doppler factors from this method have atypical 27 per cent scatter for individual flares in a given source,which we adopt as the uncertainty in D. From D and βapp, we obtain and the jet viewing angle θ (e.g. Hovatta et al. 2009). βapp and Dare not measured simultaneously with our observations; we assumethem constant in our calculations.

We estimate dγ = dcore − d, where dcore is determined from VLBImeasurements of the angular diameter of the radio core, θ core. This,plus the intrinsic opening angle, αint, and redshift, gives

dcore ∼ (θcore/2)dA

tan(αint/2), (2)

where dA is the angular diameter distance, obtained assuming a� cold dark matter cosmology with H0 = 70 km s−1 Mpc−1, m = 0.27, and � = 0.73 (Komatsu et al. 2011). Equation (2)is only valid for a conical jet with vertex at the central engine. How-ever, there is observational evidence for collimation in the M87jet, which we use as a prototype for the collimation properties ofother sources where no such information is available. Asada &Nakamura (2012) model the jet profile as zjet ∝ ra, where r is theradius of the jet cross-section at distance zjet from the central engine,

and found a = 1.73 ± 0.05 for zjet � 2.5 × 105 rs, where rs is theSchwarzschild radius, and a = 0.96 ± 0.1 at distances outside thecollimation zone. Assuming that the radio core is in the collimationzone and setting r and dr/dzjet equal for both models

dcore(coll) = 1

adcore(cone). (3)

This model reduces our estimate of dcore by a factor of 1.73. Wethus obtain lower and upper limits on dcore using these alternatives.

Detailed distance estimates are provided below forAO 0235+164, the highest significance case, and Mrk 421which has the sharpest cross-correlation peak. For PKS 1502+106,only the final result is given as a reference, and for B2 2308+34,there are no published VLBI results which makes it impossible toprovide a constraint. A summary of the results for AO 0235+164is given in Table 2.

6.1 Estimation of d

For AO 0235+164, we have D = 24 (Hovatta et al. 2009) but no βapp

since its jet is unresolved in 15 GHz VLBI (Lister et al. 2009). Weassume that the source is seen at the critical angle, θ cr = θ = 2.◦4. Weobtain d = 37.3 ± 22.8 pc for τ = −150 ± 8 d, the most significanttime lag, and d = 7.5 ± 5.3 pc for the peak at τ = −30 ± 9 d.For comparison, if we use θ = θ cr/2, we obtain d = 20 ± 15 pc

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Radio and gamma-ray variability in blazars 435

Table 2. Results of the distance estimates for the different jet components in the most significant case.a

Source d dcore(coll) dcore(cone) dγ (coll) dγ (cone)(pc) (pc) (pc) (pc) (pc)

AO 0235+164, τ = −150 ± 8 d 37 ± 23 � 23 ± 6 � 40 ± 11 � −14 ± 24b � 3 ± 25AO 0235+164, τ = −30 ± 9 d 8 ± 5 � 23 ± 6 � 40 ± 11 � 15 ± 8 � 32 ± 12

aColumns – d: distance travelled by the emission region between the peaks in gamma-ray and radioemission. dcore(coll/cone): distance between radio core and central engine with and without collimation.dγ (coll/cone): location of the peak of the gamma-ray emission with respect to the central engine.bThe negative value is an artefact produced by the large measurement errors.

(3.9 ± 3.2 pc) for the peak at −150 d (−30 d). If θ = 0, we obtaind = 18 ± 12 pc (3.7 ± 2.6 pc).

For Mrk 421, we use a preliminary variability Doppler factor forthe recent flare of D = 4 (Richards et al. 2013). βapp is uncertain,with jet components consistent with being stationary (Lico et al.2012). Assuming θ ∼ 4◦ (Lico et al. 2012 estimate 2◦–5◦), then ∼ 2.2 and d ∼ 0.2 pc. It is difficult to estimate uncertaintiesbecause of the limited knowledge of the jet properties.

6.2 Estimation of dcore

The core angular size (full width at half-maximum) has been mea-sured for AO 0235+164 (θ core = 0.21 ± 0.06 mas; Lister et al.2009). Here, we have averaged multiple epochs, with uncertaintiesestimated from their scatter. For Mrk 421, we use θ core = 0.16 mas(Kovalev et al. 2005), assuming an error of 0.05 mas, the angularresolution of the observations.

For the intrinsic opening angle, we use αint � 2.◦4 forAO 0235+164, which is the critical angle upper limit from Sec-tion 6.1, consistent with what is used by Agudo et al. (2011b). ForMrk 421, we adopt αint = 2.◦4, the mean value for BL Lacs fromPushkarev et al. (2009).

The estimates of dcore for a conical jet are � 40 ± 11 pc forAO 0235+164 and about 2.4 pc for Mrk 421. For a collimated jet,we obtain dcore � 23 ± 6 pc for AO 0235+164, and about 1.4 pcfor Mrk 421.

Similar estimates can be made for PKS 1502+106, resulting indγ of 22 ± 15 pc for a conical jet and 12 ± 9 pc for the collimatedjet case.

7 C O N C L U S I O N S

Out of 41 sources for which a detailed correlation analysis is pos-sible, three show correlations with larger than 2.25σ significance,with only one of those larger than 3σ . In all cases, radio variationslag behind gamma-ray variations, suggesting that the gamma-rayemission originates upstream of the radio emission. We use a sim-ple model to tentatively estimate the distance from the black holeat which the gamma-ray emission is produced. Due to correlationpeak breadth and uncertain jet parameters, these estimates havelarge uncertainties. In particular, AO 0235+164 shows two peaksin its cross-correlation with comparable amplitude and equivalentsignificance, leading to a highly uncertain location for the gamma-ray emission site.

These results show that correlations between radio and gamma-ray light curves of blazars are only found in a minority of the sourcesover a 4 yr period. This could indicate a complex multiwavelengthconnection not detectable with the tools and data we use. A bet-ter understanding of this connection requires continuation of theOVRO and Fermi monitoring and will benefit from the addition of

polarization and other wavebands and methods that provide addi-tional information.

AC K N OW L E D G E M E N T S

We thank Russ Keeney for his support at OVRO. The OVRO pro-gramme is supported in part by NASA grants NNX08AW31G andNNX11A043G and NSF grants AST-0808050 and AST-1109911.TH was supported by the Jenny and Antti Wihuri foundation andAcademy of Finland project number 267324. Support from MPIfRfor upgrading the OVRO 40 m telescope receiver is acknowledged.WM thanks Jeffrey Scargle, James Chiang, Stefan Larsson, and Ios-sif Papadakis for discussions. The National Radio Astronomy Ob-servatory is a facility of the National Science Foundation operatedunder cooperative agreement by Associated Universities, Inc. TheFermi-LAT Collaboration acknowledges support from a number ofagencies and institutes for both development and the operation ofthe LAT as well as scientific data analysis. These include NASA andDOE in the United States, CEA/Irfu and IN2P3/CNRS in France,ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K.A. Wallenberg Foundation, the Swedish Research Council, and theNational Space Board in Sweden. Additional support from INAF inItaly and CNES in France for science analysis during the operationsphase is also gratefully acknowledged. We thank the anonymousreferee for constructive comments that greatly improved the pre-sentation of some sections of this paper.

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