Exploring the X-ray-radio connection for AGN via measurements of the multi-dimensional luminosity function

TL;DR

This study tackles how AGN emit in X-ray and radio by constructing a multi-dimensional luminosity function (XRLF) that jointly describes space densities across $L_{\mathrm{X}}$ and $L_{\mathrm{R}}$ over $0<z<6$ using 1538 X-ray+radio-detected sources from COSMOS and Boötes. It demonstrates that the apparent correlation between X-ray and radio luminosities in heterogeneous samples is primarily a selection effect, and that a broad, continuous XRLF exists without a simple one-to-one mapping between the two bands. To quantify this, the authors extend the $\Sigma V_{ ext{max}}^{-1}$ approach (PandC) to account for joint X-ray and radio sensitivities, deriving $\phi_{\mathrm{XR}}$ and conditional LFs $\phi_{\mathrm{X}}(L_{\mathrm{X}}|L_{\mathrm{R}})$ and $\phi_{\mathrm{R}}(L_{\mathrm{R}}|L_{\mathrm{X}})$, then compare with single-band LFs and existing models. They also examine an AGN-dominated subset to measure how the fraction of X-ray- and radio-detected AGN varies with luminosity, finding that at the highest luminosities the joint detections approach unity, indicating that the most powerful accretion events are more likely to launch jets, even if the two emission regions operate on different timescales. Overall, the XRLF provides a direct, nuanced view of AGN demographics across cosmic time and highlights the need for multi-wavelength, joint-coverage analyses to understand accretion and jet production in AGN.

Abstract

We present new methods to quantify the AGN population in terms of a multi-dimensional luminosity function that describes the space density of sources as a function of both X-ray and radio luminosity. We compile a sample of 1538 radio and X-ray detected extragalactic sources from the Boötes and COSMOS fields. First, we investigate the X-ray-radio luminosity correlation in the sample and find that an apparent correlation is introduced due to the sensitivity limits of the surveys; when considering individual redshift bins we find a wide range of radio luminosities associated with a given X-ray luminosity, and vice versa, indicating little direct connection between the emission processes. We then measure the X-ray luminosity function, radio luminosity function and multi-dimensional X-ray-radio luminosity function across redshift ($0<z<6$). We apply luminosity thresholds in X-ray and radio to restrict our sample to those in the AGN-dominated regime and explore how the fraction of radio-selected AGN within the overall X-ray sample varies with increasing X-ray luminosity (and vice versa). We find that towards the highest X-ray and radio luminosities the fraction of sources with both an X-ray and radio detection increases towards 100%, indicating that at the highest luminosities we are more likely to obtain a detection in both bands, though the source will not necessarily be bright in both bands. Thus, the most luminous accretion events are more likely to be associated with the production of a jet, despite the distinct physical structures that produce the emission and likely persist over very different timescales.

Figures (13)

• Figure 1: Redshift distribution of the Boötes and COSMOS survey samples used in this work, separated into radio and X-ray. They are a combination of spectroscopic (where available) and photometric redshifts. Of the sources with $z>0$, 6362/18,880 radio detected sources, 3878/7491 X-ray detected sources and 941/1538 detected X-ray+radio sources have spectroscopic redshifts.
• Figure 2: Radio luminosity (1.4 GHz) vs X-ray luminosity (2--10 keV) for the combined Boötes and COSMOS sample, where a detection in both radio and X-ray is required to be displayed. Circles represent sources detected in the COSMOS field and squares represent those in the Boötes field. Blue represents those that their X-ray is due to an AGN ('X AGN'), whilst magenta represents those whose radio and X-ray emission is due to an AGN ('XR AGN'). Yellow represents those where both the X-ray and radio emission is due to star-formation processes ('XR SFG'). There appears to be a good correlation between the two luminosities, albeit with a large scatter, especially towards higher $L_{\rm1.4~GHz}$. Over plotted are lines representing relations from dAmato2022 and Panessa2015, as well as a black dashed line representing the divide between radio-loud and radio-quiet populations based on the radio loudness parameter, $R_{\rm X}$ = log($\frac{L_{\rm R}}{L_{\rm X}}$) Terashima2003Lambrides2020. Caution is, however, advised with using these relations; see Figure \ref{['LxvsLr_zbins']} for more information.
• Figure 3: Radio luminosity (1.4 GHz) vs X-ray luminosity (2--10 keV) for the combined Boötes and COSMOS sample, separated into redshift bins. Shaded regions represent the flux limits of the X-ray (blue) and radio (red) surveys converted to luminosity space from the beginning to the end of the redshift bins. Our results show the lack of a direct, underlying correlation between the X-ray and radio luminosities of AGN. These results show that the positive correlation, seen in Figure \ref{['LxvsLr']}, is primarily introduced due to the flux limits of the surveys used to identify them. As such, correlations between X-ray and radio luminosities presented in prior literature should be treated with caution.
• Figure 4: Examples of the XLF (left) separated into different ranges of detected radio luminosities and RLF (right) separated into different ranges of detected X-ray luminosities for the combined Boötes and COSMOS sample for 0.5 $<$ z $<$ 1. We illustrate the difference between using the standard Page & Carrera method ($\rm\phi_{2-10~keV}$ and $\rm\phi_{1.4~GHz}$) that only accounts for limits in the corresponding waveband ('+' and 'x' symbols in left and right panels, respectively) and using our updated method ($\rm\phi_{\mathrm{XR}}$), where the detection limits of both X-ray and radio have been taken into account (coloured diamonds in both panels). In the left panel we plot XLF models from Ueda2014 (purple line) and Aird2015 (dashed grey and solid grey lines representing soft X-rays and hard X-rays, respectively) and in the right panel we plot the RLF model from Novak2018 (dashed lines), separated into AGN (red), star-forming (blue) and combined (black). All models are plotted at $z=0.75$. The updated method has a greater impact on the lower luminosity bins that are more prone to incompleteness for either wavelength.
• Figure 5: X-ray radio luminosity function (XRLF), where the density of sources has been calculated per X-ray and radio luminosity bin. The different coloured bins represent the areas of the LF where either SF or AGN are expected to dominate in the radio and/or X-ray bands (see legend for details). It should be noted that in some redshift ranges we also show 'Radio AGN, X-ray SF' in yellow, which can be seen in Appendix \ref{['sec:XRLF']}. The lines on the $\phi_{\mathrm{XR}}$ vs $\log L_{\rm 2 \text{--} 10~keV}$ axis are the XLF models from Ueda2014Aird2015 and the lines on the $\phi_{\mathrm{XR}}$ vs $\log L_{\rm 1.4~GHz}$ axis is the RLF model from Novak2018, separated into AGN and star-forming sources. All models are plotted at $z=0.75$. The shaded regions on the $\log L_{\rm 1.4~GHz}$ vs $\log L_{\rm 2 \text{--} 10~keV}$ axis represent the flux limits of the X-ray (blue) and radio (red) surveys converted to luminosity space from the beginning to the end of the redshift bins. See Appendix \ref{['sec:XRLF']} for equivalent 3D representations of the XRLF at different redshifts.