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Measuring star formation in galaxies containing powerful AGN has long been a problem, because the radiation from the AGN outshines that from star formation in almost all wavebands. Of all parts of the electromagnetic spectrum, the far-infrared to millimetre waveband offers the best opportunity to measure star formation in galaxies hosting AGN because, in contrast to strongly star-forming galaxies, AGN emit comparatively little radiation at these wavelengths10. The combination of deep X-ray and submillimetre observations therefore offers the best prospects for studying the association of star formation and accretion during the 1 < z < 3 epoch (2–6 billion years after the Big Bang) when star formation and black hole growth in massive galaxies were at their most vigorous (z is redshift).

The X-ray catalogue of the Chandra Deep Field North (hereafter CDF-N) derives from a series of observations made with the Chandra X-ray observatory with a total of 2 × 106 s exposure time11. We restrict the sample to those sources detected in the most penetrating (2–8 keV) band to minimize the influence of obscuration on our results, and we further limit the sample to those sources (64%) for which spectroscopic redshifts are available in the literature12,13. Luminosities in the 2–8 keV band were calculated assuming that AGN X-ray spectra are power laws of the form14 Sν ∝ ν−0.9 where ν is frequency and Sν is flux density; the luminosities are not corrected for absorption intrinsic to the AGN or their host galaxies. In order to restrict the X-ray sample to AGN, we have discarded any sources with 2–8 keV luminosity LX < 1042 erg s−1. Submillimetre observations (by the SPIRE15 instrument on the Herschel Space Observatory) of the CDF-N were carried out in October 2009 as part of the HerMES programme16. Maps and source catalogues at wavelengths of 250, 350 and 500 µm were constructed17. At the depth of the SPIRE maps, the dominant source of uncertainty in the maps is confusion noise due to the high sky density of sources. For cross-matching with the Chandra source catalogue11 we chose the 250 µm catalogue, which has the most precise positions, and we used only sources with 250 µm flux densities greater than 18 mJy, which corresponds to a signal-to-noise ratio greater than 3 when the effects of confusion are included17. X-ray sources were matched to 250 µm sources within 6 arcsec, corresponding to approximately 95% confidence in the 250 µm positions. The detection statistics are given in Table 1. The expected level of spurious associations between X-ray and 250 µm sources was calculated from the sky density of 250 µm sources in annular regions of radius 10–30 arcsec around the X-ray source positions, and is reported in Table 1.

Table 1 250 µm detection statistics in various regions of parameter space
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The distribution of CDF-N AGN in the redshift–X-ray luminosity (z–LX) plane is shown in Fig. 1, and reveals a striking trend of 250 µm detectability with X-ray luminosity: of the 24 AGN detected at 250 µm, none of them have LX > 1044 erg s−1. The redshift range between 1 and 3 is of most interest, because it corresponds to the epoch in which powerful AGN accreted most of their black hole mass and present-day massive galaxies formed most of their stars. Within this redshift range, Fig. 1 shows that 11 out of 44 AGN () with 1043 erg s−1 < LX < 1044 erg s−1 are detected at 250 µm, while none of the 21 objects with LX > 1044 erg s−1 are detected. The difference in detection rates has a significance of >99%, according to a single-tail Fisher’s exact test. We have considered the effects that incompleteness in the spectroscopic redshifts, or absorption of the X-ray flux by gas and dust, might have on our results. We find that the systematic non-detection of the powerful AGN is robust against both effects, although X-ray absorption does appear to be a common property of the AGN detected at 250 µm. We have also verified the low 250 µm detection rate of AGN with LX > 1044 erg s−1 using the Extended Chandra Deep Field South field, finding that of 49 such sources with 1 < z < 3, only 1 is detected at 250 µm.

Figure 1: Redshifts ( z ) and 2–8 keV X-ray luminosities ( L X ) of AGN in the CDF-N.
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The luminosities have been corrected to the rest frame assuming a spectrum Sν ∝ ν−0.9 and are not corrected for intrinsic absorption. The blue dashed rectangles delimit the luminosity decades above and below 1044 erg s−1 in the 1 < z < 3 redshift range. Error bars, 68% confidence limits.

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Infrared spectral energy distributions for the 250-µm-detected AGN were constructed by combining the SPIRE photometry with 3.6–160 µm photometry from the Spitzer Space Telescope. X-ray and infrared properties of the 11 250-µm-detected AGN with 1 < z < 3 and LX in the range 1043–1044 erg s−1 are given in Table 2. In most cases, the AGN contributes less than 10% to the infrared luminosity. The best-fit infrared luminosities lie between 4 × 1011 and 1013 times solar luminosity (), implying star formation rates between 50 and 1,750 solar masses () per year18.

Table 2 Properties of SPIRE-detected AGN
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We performed a stacking analysis for the 1 < z < 3 AGN to probe below the confusion limit of the SPIRE images. We split the sample into five bins of LX from 1043 to 1045 erg s−1 and determined the average star formation rates of AGN in each bin. The results are shown in Fig. 2. In the redshift range 1 < z < 3, the mean star formation rate in AGN with LX of 1043–1044 erg s−1 is per year, compared to a mean star formation rate for AGN with LX > 1044 erg s−1 of per year. These averages are independent of the SPIRE 250 µm detection limit because they are obtained from a stack of all sources within a given range of LX, whether detected at 250 µm or not.

Figure 2: Average star formation rates, 〈SFR〉, derived from averaged far-infrared luminosities of 1 <  z  < 3 AGN, as a function of LX.
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We converted the 250, 350 and 500 µm flux densities for each source into an equivalent 8–1,000 µm luminosity by fitting a grey-body curve, with a temperature of 30 K in the rest-frame of the source, an emissivity index of β = 1.6, and a power-law extension to the Wien side29 and multiplying by , where DL is the luminosity distance. Fluctuations in the map sometimes scatter the fluxes of undetected sources to negative values, which translate to negative luminosities when multiplied by . Such negative solutions for individual AGN were allowed so as not to produce an artificial positive bias in the averages. The luminosities were averaged in five bins in LX, which were chosen to include a similar number of AGN in each bin. The average luminosities were then converted to star formation rates18. AGN which are individually detected at 250 µm are included in the averages shown in bold black, but have been excluded from the averages which are shown in grey, to show the contribution that these sources make to the average star formation rates. The grey points have been offset horizontally from the bold black points for clarity. Error bars correspond to 68% confidence limits and were determined by bootstrap resampling, with a 7% systematic error added in quadrature to account for the calibration error on SPIRE photometry.

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At redshifts of 1–3, the X-ray luminosity of 1044 erg s−1, which divides the regions of 250 µm detection and non-detection in Fig. 1, corresponds approximately to the knee in the luminosity function of AGN19. The steep shape of the luminosity function at LX > 1044 erg s−1 implies that this part of the luminosity function is dominated by objects which are at the peak of their accretion rates. Our observations therefore imply that the most prodigious episodes of star formation are common in the host galaxies of 1 < z < 3 AGN, but avoid powerful AGN in which accretion is at its peak.

This systematic non-coincidence of the peak periods of star formation and accretion implies a direct interaction between the two processes, and provides a powerful discriminator for the form of AGN feedback which is responsible for terminating star formation in the host galaxy. Two families of feedback models have been proposed, widely referred to as ‘quasar mode’ and ‘radio mode’20. In quasar-mode feedback, a luminous AGN generates a powerful wind which terminates star formation by driving the interstellar medium from the surrounding host galaxy. In radio-mode feedback, star formation is suppressed because collimated jets of relativistic particles emitted by a radiatively inefficient AGN prevent gas in the surrounding hot halo from cooling, thereby starving the galaxy of cool gas from which to form stars.

Radio-mode feedback is commonly invoked in semi-analytical models to limit galaxy masses and luminosities20,21. In these models, black holes grow through luminous accretion episodes and black hole mergers. The correlation between black hole mass and bulge mass comes from assuming that a fixed fraction of the gas is accreted by the nucleus during each star forming episode that results from a galaxy merger or disc instability, and hence star formation and accretion rate should be correlated over the full range of luminosity. Our observations are therefore inconsistent with models in which AGN influence their host galaxies only through radio-mode feedback20,21. In contrast, models of galaxy formation in which quasar-mode feedback is responsible for terminating the star formation7,8,9,22, and which have received some observational support recently23,24, predict that the AGN luminosity peaks later than the star formation rate, and thus are consistent with our observations. These models also predict that residual star formation, at the level of a few tens of per cent of the peak, will continue during the period in which the AGN luminosity is at its maximum, consistent with our stacked results; our results show that, on average, AGN with LX > 1044 erg s−1 are still forming stars at approximately per year. Our observations do not discriminate between models invoking major mergers8 or accretion of gas into a massive halo22 as the trigger for the intense star formation. After the interstellar medium has been driven out by the luminous AGN and the AGN itself becomes starved of fuel, radio-mode feedback is the most credible agent by which further star formation is inhibited.