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Active galactic nuclei (AGN) emitting relativistic jets aligned along the line of sight, known as blazars1, dominate the extragalactic γ-ray sky7. Observations of fast variability of the γ-ray flux2,3 indicate that sites of the γ-ray emission are probably situated not far away from their supermassive black hole ‘central engine’. However, the interaction of γ-rays with the dense soft background photons8 produced by the jet9 or by the accretion flow10,11, and subsequently scattered in the broad line region12,13, should prevent the escape of γ-rays from the central engine. A possible solution to this problem is to assume that the γ-rays come from a larger, parsec-scale region, where the density of the soft photon backgrounds is low enough to allow escape of the high-energy photons4,5,6. In such a scenario, the fast variability of the γ-ray flux is unrelated to the central black hole and has to be attributed to other physical phenomena—for example, to the presence of small inhomogeneities inside theparsec-scale jet14,15,16.

Central engines of AGN of size RBH ≃ 3 × 1014(MBH/109M⊙) cm (MBH is the mass of the black hole) are not directly resolvable by telescopes. Nevertheless, observations in the visible band do manage to extract information on the central engines of gravitationally lensed AGN, using the effect of microlensing17,18,19,20,21. This effect is due to stars in the intervening galaxy that act as a natural ‘magnifying glass’, selectively magnifying the flux from sub-structures with sizes smaller than the size of the Einstein ring RE∗ ≃ 4 × 1016(M∗/M⊙)1/2 cm (M∗ is the mass of the lensing star).

Here we report detection of the microlensing of the blazar PKS 1830-211. We further use this detection to measure the size of the X- and γ-ray emitting parts of its jet. PKS 1830-211 is a known gravitationally lensed AGN (ref. 22) at redshift zS ≃ 2.5 (ref. 23), lensed by a face-on spiral galaxy at redshift zL ≃ 0.89 (ref. 24) and, possibly, by another galaxy at redshift zL2 ≃ 0.19 (ref. 25). The source image consists of an Einstein ring of radius θE ≃ 0.5′′, on which two images of the source separated by an angular distance θ ≃ 2θE are superimposed. The ring and the two images are not resolvable by the γ-ray and X-ray telescopes used in our analysis. For this reason both images and the ring contribute to the observed γ- and X-ray fluxes.

The contributions of each of the two images to the overall source flux could be distinguished based on the variability properties of the signal26,27. The gravitational time delay of the source is measured from the observations in the radio band, (ref. 28). As the gravitational time delay is an achromatic phenomenon, a γ-ray flare of the primary source is expected to produce a double-peak signal in the telescope, with two subsequent flaring episodes of the two images separated by the interval τradio. The ratio of the peak fluxes of the two flares is equal to the magnification ratio μradio = 1.52 ± 0.05, also known from the radio observations28.

PKS 1830-211 has exhibited several pronounced flares during the six-year observation period by the Large Area Telescope (LAT) on board of the Fermi satellite. The source flux during the flares varied by almost an order of magnitude on timescales of 1–100 d (Fig. 1) in the energy band 0.1–500 GeV. We have searched for the gravitational time delay in the γ-ray signal using structure function and wavelet analysis techniques (see Supplementary Information for details). Both techniques have identified two characteristic timescales, and recurrent in all flaring episodes. A recent paper27, which appeared during the referring process of this paper, has also identified the timescale of 76 days. The timescale of 19 d, comparable to τγ, noticed in ref. 27, was considered to be not significant. Our analysis is based on six years of data (compared to a three-year period in ref. 27) and higher-quality Pass 7 event selection (compared to Pass 6 in ref. 27) with a lower energy threshold. Repeating the wavelet timing analysis of ref. 27 with our data set, we detect the timescale τγ with significance 5.2σ (see Supplementary Information for details).

Figure 1: Fermi/LAT light curves of PKS 1830-211 over the flaring episodes, produced with adaptive time binning.
figure 1

The error bars are 68% confidence intervals computed using the likelihood analysis (see Supplementary Information for details). The data points marked with red represent the time bins with significance of detection less than 3σ. The quiescent flux of the source, determined over the time period MJD 56,300–56,700 (between the third and fourth flaring episodes) using only the data points with significant detection, is indicated by the horizontal dashed line. The characteristic timescales identified from the structure function analysis— ≈ 21 d and ≈ 76 d—are marked with red and green horizontal bands.

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τγ can be identified with the gravitational time delay measured in the radio band. An alternative possibility of identification of the time delay with τrep is inconsistent with the radio data28 at more than 5σ level (see Supplementary Information for details). Detection of the gravitational time delay allows a measurement of the magnification factor ratio μγ = 3.1 ± 0.5, averaged over all detected flares. This value of μγ is not consistent with μradio. Moreover, μγ seems to be variable in the range μγ ∼ 2–7 from flare to flare (with a chance probability of 0.7%, see Supplementary Information).

The difference in the magnification factor ratios between radio and γ-ray emission, as well as from flare to flare, can be consistently explained as an effect of the gravitational microlensing17,18,19,20,21. Microlensing does not affect μradio because the radio emission comes from the parsec-scale jet—that is, from a source which is much larger than RE∗. Instead, the microlensing affects only the flux of the γ-ray source, if its size is comparable or smaller than RE∗.

The maximum magnification of the source flux due to microlensing occurs during the caustic crossing events. It is determined by the ratio of the size of the γ-ray source, Rγ, and RE∗, μγ ≤ μradio(RE∗/Rγ)1/2 (ref. 29). The observed values in the range μγ ∼ 2–7 can be achieved if the γ-ray source is extremely compact, Rγ ≲ 0.1RE∗ ∼ 2 × 1015(M∗/M⊙)1/2 cm. This qualitative result is confirmed by numerical simulation of the caustic crossing events (see Supplementary Information for details).

The strong magnification events are transient, because the source, the lensing galaxy and the microlensing centres in the galaxy are moving with respect to each other. The relative velocity of the source with respect to the lens is composed of the contributions from the motions of all objects involved. The velocity of the Sun with respect to the cosmic microwave background reference frame is vobs ≃ 300 km s−1 in the direction at an angle ≃ 106° with respect to the direction towards PKS 1830-211 (ref. 30). Assuming that velocities of the lens, vL, and the source, vS, are of the same order, one finds vrel ∼ 103 km s−1. The relative velocity determines the timescale of the strong magnification, tcc = Rγ/vrel ≃ 0.3(Rγ/1015 cm) yr. The detected changes of μγ occur already on the timescale of the flare repetition time τrep (see Supplementary Information), implying that tcc ≲ τrep. This limits the source size to be Rγ ≲ tccvrel ≃ 6 × 1014(tcc/0.2 yr) cm. In the particular case of blazars, the source could be a blob in the jet moving with projected velocity vs ∼ c. If this is the case, the constraint from the caustic crossing timescale becomes much weaker than the constraint imposed by the maximal magnification ratio.

The mass of the lensing galaxy can be estimated from the observed size of the Einstein ring RE, gal = θEDL ≃ 4 kpc. This gives Mgal ∼ 1011M⊙ within RE, gal—that is, a galaxy similar to the Milky Way. The surface density of stars in the galaxy is only about Σgal ∼ 1M⊙/π(RE∗)2, assuming that the galactic mass within RE is dominated by the luminous matter component. The microlensing events follow each other on the timescale yr. We argue that the caustic crossing events are responsible for the observational appearance of the strong flares of PKS 1830-211. Indeed, large, up to an order of magnitude, increases of the source flux during the flares are mostly caused by the large magnification factor in one of the images. The observed difference in the magnification factors μγ between the separate sub-flares of a single flaring episode (for example, μγ changes from 6.5 ± 1.5 to 2.4 ± 0.5 during the brightest flaring episode) confirms this assumption.

To verify the conclusion on the influence of microlensing on the source variability and on the small source size Rγ, we have performed simulations of microlensing caustics maps produced taking into account the surface mass density of the lensing galaxy (see Supplementary Information for details). We find that at least one magnification event with μγ ∼ 2–7 is expected for a very compact source with extension Rγ ≈ (1–10) × 1015 cm, consistent with our estimate based on the caustic crossing timescale τcc, as well as the simplified analytical estimate, given above.

The intrinsic source variability is characterized by the timescale τrep ≈ 76 d, which could be associated with the repetition rate of the sub-flares in each flaring (or caustic crossing) episode. The multiples of τrep also correspond to the intervals between the flaring episodes (see Supplementary Information for the detailed information). There are, in total, seven sub-flares in the four flaring episodes detected within the light curve of the source. Splitting the entire observation time span into ∼25 d bins, corresponding to the duration of the sub-flares, one finds that the chance coincidence probability for the sub-flares to fall into time bins spaced by multiples of the 76 d interval is less than 1%.

Although the exact origin of the repetition timescale τrep can not be firmly established, its possible interpretation is that it is associated with the quasi-periodicity of the signal. Tentatively associating τrep with the period of rotation over a Keplerian orbit, one finds that the size of the orbit is Rγ ≃ 2 × 1015(τrep/76 d)2/3(MBH/109M⊙)1/3 cm.

Another complementary estimate of the emission region size can be derived from the minimal variability timescale of the γ-ray emission. The time dependence of the particularly fast variable episode around MJD 55484.5 is fitted well with an exponential rise/decay profile, with the e-folding rise/decay timescales being trise = 0.49 ± 0.15 d and tdecay = 1.2 ± 0.2 d (see Supplementary Information for details). The rise timescale corresponds to the light-crossing time of the region of the size Rγ < ctrise/(1 + zS) ≃ 1015 cm. This constraint should be corrected by the bulk Doppler factor of the jet if the emission is produced in the relativistic jet aligned along the line of sight. A summary of all constraints on the γ-ray source size derived from the intrinsic variability and microlensing timescales is given in Fig. 2.

Figure 2: Summary of constraints on the size of the γ-ray emission zone of PKS 1830-211, compared to its characteristic distance scale.
figure 2

The range of the source sizes constrained by the detection of microlensing is based on our simulation of the caustic patterns, described in Supplementary Information. Constraints based on the flare repetition timescale τrep and flare rise time trise are less direct and are thus indicated with the dashed arrows. The constraint based on the trise was computed under the assumption of a stationary source and does not include the correction for the uncertain Doppler factor of the jet. The colour coding along the coordinate axis represents the putative location of the γ-ray emission region (red) and the typical sizes of the accretion flow (pink), broad line region (light pink) and jet (light blue).

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Contrary to the γ-ray light curve, the X-ray light curve of the source does not reveal the signatures of the gravitational microlensing (see Fig. 2 of the Supplementary Information). The X-ray flux measured by SWIFT/XRT during the MJD 55550–55600 interval is consistent within ∼10% with the previous measurements of the flux, spanning over almost a decade. The same is true for the hard X-ray flux monitored by INTEGRAL and SWIFT/BAT. Thus, the possibility of strong magnification by a factor μX ≃ μγ due to microlensing in the X-ray band is ruled out. This imposes a constraint on the (hard)X-ray source size of RX ≳ RE∗ ≃ 4 × 1016 cm.

PKS 1830-211 is one of the most powerful known blazars, with a luminosity L ∼ 3 × 1048μ−1Γ−2 erg s−1, where μ ∼ 10 is the overall magnification factor and Γ ∼ 10 is the bulk Lorentz factor of the jet (both uncertain). Such a luminosity corresponds to the Eddington luminosity LEdd ≃ 1047(MBH/109M⊙) erg s−1 of a black hole of mass MBH ∼ 108–109M⊙ and size 2RBH ≃ 1014–1015 cm. The size of the AGN ‘central engine’ in PKS 1830-211 is comparable to the projected γ-ray source size derived above. The deprojected size of the γ-ray emitting part of the jet could be ∼Γ times larger. Still, the γ-ray emission is produced in a very compact source, at most ∼10–100 times larger than the black hole size.

Our analysis constrains the size, but not directly the location of the γ-ray emission region. However, typical linear scales of structures in the AGN jet with opening angle Θjet grow as RΘjet with the distance R from the black hole. This indicates that the γ-ray emission region should be situated in the vicinity of the black hole, rather than in the parsec-scale jet. The possibility that small sub-structures in the parsec-scale jet dominate the γ-ray signal is also disfavoured by the data (see Supplementary Information for details).

Detection of the extremely compact size of the γ-ray source poses a conventional problem for the escape of γ-rays. The essence of the problem is that γ-rays with energy Eγ larger than Ethr = 2(mec2)2/(ε(1 + zS)2) ∼ 4 × 107(ε/1 keV)−1 eV produce e+e− pairs in collisions with the soft background photons of energy ε. The low-energy photons, contributing to the pair production opacity of the source, could either originate from the accretion flow onto the black hole or be a part of the overall emission from the AGN jet. In the latter case, the pair production threshold has to be corrected by taking into account that the collision angle α ∼ Γ−1, so that Ethr ≃ 108Γ2(ε/1 keV)−1 eV.

The constraint RX ≳ RE∗ ≃ 4 × 1016 cm on the size of the X-ray emission region implies the optical depth with respect to pair production is τ ≲ 3. Thus, γ-rays with energies Eγ ∼ 10 GeV are able to escape from the source (see Supplementary Information for the detailed calculation).

The accretion flow onto the black hole mainly produces radiation in the visible and ultraviolet band (forming the so-called ‘big blue bump’ in the source spectrum). The energy of the visible–ultraviolet photons, 1–30 eV, is too low to affect the source flux in the observed range of γ-ray energies, E ≤ 30 GeV. Similar conclusions can be reached for the synchrotron photons, spanning the even lower energy range 10−5 eV ≤ ε ≤ 1 eV. Thus, the condition that the source should be at most moderately opaque with respect to the γγ pair production does not contradict the measurement of the compact size of the γ-ray emission region of PKS 1830-211.

The measurement of the extremely compact size of the γ-ray source in PKS 1830-211, reported here, removes the long-standing uncertainty of the location of the AGN γ-ray emitting zone (see Fig. 2). GeV band γ-ray emission is produced at the base of the jet, at a distance no greater than 10–100 times the Schwarzschild radius of the supermassive black hole powering the emission. The γ-ray emission dominates the energy output of the formation/collimation region of the jet. This implies that the particle acceleration process is an essential element of the (uncertain) physical mechanism at play in the generation of jets by supermassive black holes.