Open Access
Issue
A&A
Volume 678, October 2023
Article Number L4
Number of page(s) 8
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202347495
Published online 12 October 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

Active galactic nuclei (AGN) can be subdivided into two main groups, radio-quiet (RQ) and radio-loud (RL) AGN, depending on their radio-loudness Rν1 (Kellermann et al. 1989). The threshold value between the two groups is typically R5 GHz ∼ 10. The two groups are also characterised by a different radio to X-ray luminosity ratio (Terashima & Wilson 2003), where LR/LX ∼ 10−2 for RL AGN, and LR/LX ∼ 10−5 in RQ AGN (Laor & Behar 2008). In the case of RL AGN, the origin of their radio emission is relatively well understood and is a direct signature of synchrotron emission from large-scale and powerful jets. On the contrary, the physical origin of the radio emission in RQ AGN is still unclear. It is suspected to be a mix of emission of different origins. The most favored ones are the following: nuclear star-forming regions, weak and small-scale jets, and/or an opaque (optically thick) unresolved source in the close environment of the accretion disk around the supermassive black hole, referred to as the corona (see Panessa et al. 2019, for a recent review). The presence of the latter is sustained by the observation of flat and inverted radio spectra at ∼100 GHz frequencies, which are characteristic of synchrotron self-absorption emission, which exceeds the low-frequency spectral slope (Doi et al. 2011; Park et al. 2013; Behar et al. 2015, 2018; Inoue & Doi 2018), the so called mm-wave excess. This excess luminosity can extend with a flat slope up to 230 GHz (Kawamuro et al. 2022), and shows a tight Lmm/LX ∼ 10−4 correlation with the X-ray luminosity (Behar et al. 2015, 2018; Kawamuro et al. 2022).

Recent observations with the Very Long Baseline Array (VLBA), reaching a resolution of a few milli-arcseconds corresponding in some cases to a few parsecs, also suggest that the radio emission of low Eddington ratio RQ AGN (LAGN/LEdd ≲ 0.3) predominately originates from an unresolved and extremely compact region (Alhosani et al. 2022). A larger VLBA sample shows that most RQ AGN have a flat-slope compact core that coincides with the Gaia position, and whose luminosity tightly correlates with the X-ray luminosity (Chen et al. 2023). Currently, it is not possible to go below the parsec scale with imaging, and one has to turn to variability timescales to constrain the source size based on light travel time arguments. This is the purpose of this Letter, presenting for the first time intraday (hour timescale) variability of simultaneous mm (NOEMA) and X-ray (NuSTAR) observations of an AGN (MCG+08-11-11).

Simple estimates do indeed show that the size of an opaque self-absorbed synchrotron source decreases strongly with frequency. The physical size R of a self-absorbed synchrotron source can indeed be estimated from its measured radio flux density Fν (in units of μJy) at the frequency ν (e.g., following Laor & Behar 2008):

(1)

(2)

where νGHz is the frequency in gigahertz, BG is the magnetic field strength (assumed to be uniform) in Gauss, and z is the redshift of the AGN, a proxy for its distance at low-z, assuming a Hubble constant equal to 70 km s−1 Mpc−1. Equation (2) was rescaled with respect to the gravitational radius Rg of a 107M supermassive black hole2. Since above 300 GHz the thermal dust emission starts to dominate (Barvainis et al. 1992), the best radio window to observe radio emission as close as possible to the central black hole (BH) is in the range ∼50–250 GHz.

Equation (1) shows that for sources dominated by self-absorbed synchrotron emission with a radio flux density at 100 GHz in the range of 1–10 mJy and redshift of 0.02 (which is the one of MCG+08-11-11), the size of the radio photosphere is on the order of 1014 − 1016 cm (∼1–100 h for the light crossing time). This corresponds to 102 − 104 gravitational radii for a supermassive black hole of 107M (see Fig. A.1 with the contour plot of the radio flux density Fν in the R − BG plane). These sizes are close to the estimated size of the X-ray emitting region in RQ AGN, the so-called hot corona, a plasma of hot electrons at a temperature of kT ∼ 100 keV estimated from hard X-ray spectra (e.g., Perola et al. 2002; Fabian et al. 2015, 2017; Tortosa et al. 2018; Akylas & Georgantopoulos 2021). Variability of the mm emission (on an approximate day timescale) already supports the small (< light day) size of (part of) the mm radio emitting region (e.g., Doi et al. 2011). The similar inter-day variability parameters detected at 100 GHz and in X-rays in the RQ AGN NGC 7469 adds even more to the evidence that the mm and X-ray emission may have the same physical origin, and that they could both be associated with the hot corona (Baldi et al. 2015; Behar et al. 2020). Actual inter-day temporal correlation between radio and X-ray light curves, however, is much harder to substantiate (Panessa et al. 2022; Chen et al. 2022), mostly due to radio photometric stability over weeks and months.

Here, we introduce a novel approach to catch intraday variability in RQ AGN simultaneously in X-ray and mm waves. Indeed, the dramatic X-ray variability on short timescales known to exist in RQ objects should definitely help to look for correlated variability and to properly test the physical connection between the two bands. In this Letter, we present the result of the simultaneous NOEMA/NuSTAR campaign on the RQ AGN MCG+08-11-11, with the main result of this Letter being the very first detection of fast intraday variability in, and a simultaneous increase between, the mm and X-ray bands.

2. Target selection and observation strategy

For this project, we selected bright X-ray AGN that are also bright (∼5–10 mJy) in the mm range, show short (∼1 h) timescale variability in X-rays, and are visible by NOEMA. Our two first targets were NGC 7469 and NGC 5506, which were observed in X-rays with XMM-Newton. Their unsuccessful campaigns are presented in the appendix, where we also show a similar failed attempt with the JVLA and Chandra for Ark 564.

The observations of MCG+08-11-11 (z = 0.02) benefited from this experience and are the subject of this Letter. MCG+08-11-11 is a well-known and bright X-ray RQ AGN with a supermassive black hole mass of MBH = (2.0 ± 0.5)×107M (e.g., Bentz & Katz (2015) and references therein). It is among the few RQ AGN that have been observed at mm wavelengths with the ATCA and CARMA telescope arrays (Behar et al. 2015, 2018). It is bright (∼5–10 mJy) at 95 GHz, it shows short (∼1 h) timescale variability in X-rays with variations of ∼20% in a few hours (e.g., Matsumoto et al. 2006), and it was visible by NuSTAR and NOEMA for more than 12 h at night at the beginning of the NOEMA winter period (December).

The log of the observations is reported in Table 1. The NOEMA/NuSTAR observations of MCG+08-11-11 lasted ∼13 h and were performed during the night of December 18–19, 2021. The details of the data reduction of both instruments are presented in Appendix B.

Table 1.

Log of the radio mm and X-ray observations of MCG+08-11-11 by NOEMA and NuSTAR.

3. Results

The light curves, normalised to their mean, of the NOEMA LSB flux density at ∼100 GHz and the NuSTAR 3–10 keV X-ray count rate of MCG+08-11-11 are reported in Fig. 1 in blue and red, respectively. The NOEMA and NuSTAR time bins are on the order of 20 min. The NuSTAR and NOEMA normalised light curves clearly increase during the observations (even taking the small residual variability found in the calibrator into account, see Appendix B.1.2), while the one of the NOEMA calibrator remains constant. This is confirmed by linear fits of each normalised dataset with best-fit values for the line slope equal to (4.2 ± 0.4)×10−3 h−1 and (1.2 ± 0.1)×10−2 h−1 for the NOEMA LSB and NuSTAR, respectively. Both slopes are positive and significantly different from zero. This confirms the variability of the source in the two bands. This is the first time that mm variability on hour timescales is observed in a RQ AGN.

thumbnail Fig. 1.

MCG+08-11-11 radio/X-ray variability. The black, blue, and red circles and dashed lines are the NOEMA calibrator, the NOEMA LSB, and 3–10 keV NuSTAR light curves normalised by their mean, respectively. The solid lines are the corresponding linear best fits (see Sect. 3).

Moreover, the fact that we detected the same variability behaviour (both mm and X-ray emission are increasing during the observation) is remarkable on such short timescales. We applied the classical Spearman’s rank correlation test on the mm and X-ray light curves. To do so, we needed to take the gaps in the NuSTAR and NOEMA light curves into account and we defined time zones where both instruments were observed simultaneously (see Fig. C.1). Then we computed the weighted mean of the mm and X-ray light curves in these time zones. These weighted mean fluxes are reported in Fig. 2. We found a Spearman correlation coefficient r = 0.64 and its corresponding p value of 0.02, indicating a rather strong correlation. The trueness of the causality between the two wavebands is admittedly questionable, however, given the short time interval on which the increasing trend is observed. We also searched for lags between the different light curves using the PYCCF3 PYTHON code (Peterson et al. 1998; Sun et al. 2018). However, this search was inconclusive with a flat cross-correlation function and a lag consistent with zero.

thumbnail Fig. 2.

Weighted mean NuSTAR count rates vs. NOEMA fluxes. The black solid line and gray shadowed area represent the best-fitting linear correlation and its 90% confidence bands computed using the bayesian linear fitting PYTHON package LINMIX4, respectively. The Spearman correlation coefficient r and its corresponding p value are indicated in the figure.

3.1. Variability estimates

To better quantify the variability of the light curves, and following Behar et al. (2020), we have reported in Table 2 the weighted mean 2–10 keV count rates (combining the two NuSTAR detectors), ⟨FX⟩, the weighted mean mm flux densities, ⟨Fmm⟩, with their errors (including 0.3% of the systematics, see Appendix B.1.2), and their respective standard deviation σFX and σFmm. We also computed the following fractional variability amplitudes:

(3)

Table 2.

Variability properties of X-ray (3–10 keV), mm (100 GHz), and NOEMA calibrator light curves.

where and are the mean of the squared flux errors. The error on the fractional variabilities, and , is given in Eq. (2) of Behar et al. (2020) and they have also been reported in Table 2. For comparison, we have also reported in this table the weighted mean flux density ⟨Fcalib⟩ with its error, the respective standard deviation σFcalib, and the fractional variability amplitude with its error for the NOEMA calibrator.

The value of shows that the NOEMA photometric accuracy is much better than 1% during this observation. In comparison, the fractional variability amplitude of the source at 100 GHz, , confirms intraday variability of a RQ AGN at a mm wavelength. A few NOEMA data points even suggest variability on an hour timescale. This corresponds, in terms of light travel time, to a size of tens of Rg for a 2 × 107M BH. This indicates that at least a few percent of the mm emission of the source is coming from such small regions. On the other hand, while the increasing trend all along the monitoring looks stronger in X-rays than in the mm, the 3–10 keV fractional variability amplitude of the source is of about 7%, due to the larger X-ray error bars.

3.2. Structure function

An interesting method to better quantify time variability when we have a rather small number of measurements (limiting the use of standard Fourier analysis) is via a structure function (SF) analysis (e.g., Simonetti et al. 1985; Hughes et al. 1992; Gliozzi et al. 2001). The shape and extrema of the SF can indeed reveal the range of timescales that contribute to the variations in the dataset (see, e.g., Paltani 1999). There are different definitions of the SF in the literature (e.g., Simonetti et al. 1985; Hughes et al. 1992; di Clemente et al. 1996; Vagnetti et al. 2011; Middei et al. 2017). We have chosen the following one (we have checked that the results do not depend on the SF expression qualitatively):

(4)

where F(t) and F(t + τ) are two measures of the flux, τ is the time lag between these two flux measurements, and ⟨⟩ means that an average was computed within an appropriate bin with a time lag around τ. The term is the quadratic contribution of the photometric noise to the observed variations. The computation of the errors of the SF is detailed in Appendix F.

The SFs of the NuSTAR and NOEMA light curves of MCG+08-11-11 are reported in Fig. 3. The SF of the light curve of the NOEMA calibrator is also reported at the top of that figure. The linear (in log space) best fit of the SFs are over-plotted with a black solid line and the corresponding slope is indicated in each plot. In the case of the NOEMA calibrator, the slope of the SF is consistent with zero, with an average variability fraction of less than 0.5% on the whole range of time lags explored. The slope is, however, significantly different from zero for the NuSTAR and NOEMA light curves. In the case of NuSTAR, the significance is just above 3σ (due to the large error bars), while it is > 10σ for NOEMA.

thumbnail Fig. 3.

Structure function for the NOEMA calibrator (top), the NOEMA (middle), and NuSTAR (bottom) observations of MCG+08-11-11. The solid line is the best linear log–log fit, and the corresponding slopes (with the corresponding errors) are indicated in each figure. The vertical dotted line in the middle plot indicates a local maximum around τ = 2 × 104 s. The dashed line corresponds to the cubic polynomial best fit (in log scale), which was used to plot the data/model ratio in Fig. 4.

More interestingly, we observed a local maximum of the NOEMA SF around τ ∼ 2 × 104 s (indicated by the vertical doted line in Fig. 3), suggesting a typical variability timescale of a similar order. To make this local maximum more apparent, we have reported with red points in Fig. 4 the ratio between the NOEMA SF and its cubic polynomial best fit (reported with the black dashed line in the middle plot of Fig. 3) obtained by ignoring the SF point in the time lag range of [7 × 103 − 2.5 × 104] s.

thumbnail Fig. 4.

Red points correspond to the residuals in term of sigma between the NOEMA SF data points and its cubic polynomial best fit reported in the middle plot of Fig. 3. The colored area corresponds to the 50% (orange), 90% (blue), and 99% (green) percentile of the distribution of the same ratios, but they were obtained with simulated data.

We tried different tests to check the pertinence of this timescale in the NOEMA data. We first performed a Fourier analysis anyway. We computed the power spectral density (PSD) of the NOEMA light curve. It is reported in Fig. D.1. The PSD statistics is quite poor at low frequency (which corresponds to the SF peak). This is expected since it is very close to the lowest possible frequency of the light curve. We did not detect any excess that would be the counterpart of the local maximum detected in the SF.

Estimating the significance of such a feature in a SF is not straightforward. We thus tried to reproduce such a local maximum via simulations. For that purpose, we generated 104 NOEMA light curves using the quadratic (in log scale) best fit of the PSD of the observed data (reported in blue in Fig. D.1). This quadratic best fit was used as the PSD input to the light curve simulator PYTHON package PYLCSIM5 (Campana 2017). With the phases having been generated randomly in the process, most of the simulated light curves did not behave like the observed one. Thus we selected the simulated light curves that are at less than 5σ from the observed one. For each of these selected simulated light curves, we produced the corresponding SF following the procedure applied to the real data. An example of a simulated light curve and the associated SF are plotted in Fig. E.1 with the observed ones for comparison. Then we computed the ratio between the simulated SF and its best-fit cubic polynomial. The orange, blue, and green areas reported in Fig. 4 correspond to the 50%, 90%, and 99% percentile of the distribution of these simulated ratios, respectively. The observed local maximum peaks above the 90% contour, meaning that a similar maximum is reproduced in less than 10% of the simulated SF. While this is by no means an estimate of the significance of the observed peak (longer observations would be necessary for that), our procedure shows that this is not a generic feature that can be reproduced easily.

Assuming then this peak is real, for the BH mass of MCG+08-11-11, its timescale corresponds to a light crossing time of 100–300 Rg. The value of the mm SF at this peak corresponds to an average variability fraction of about 2.5%. Assuming the mm emission is optically thick, the variation of the observed flux is then related to the variation of the surface of the emitting region, that is, to the squared of its typical size. An upper limit of this typical size can then be estimated assuming the emitting surface is homogeneous. Then a 100% variation of its flux would correspond to a total emitting surface that is a factor ∼6–7 larger in radius. This puts the upper limit of the mm emitting region typical size on the order of ∼1300 Rg. This is about the accretion disk to the broad line region scales, that is, significantly larger than the size of the hot corona as deduced by, for example, micro-lensing (e.g., Morgan et al. 2010; Chartas et al. 2016). Despite this difference in size, our results suggest that the two emitting regions are connected with each other, indicating that the mm radio emitting region could be an extension of the hot corona, similar to an outflow and weak jet (see the discussion in Panessa et al. 2019). Such outflow components are indeed expected as soon as a poloidal magnetic field component is present in the accretion flow (e.g., Beckwith et al. 2008).

In this respect, the upper limit in size translates, from Eq. (2), into an upper limit of the magnetic field of a few Gauss for the radio flux density of 18 mJy observed for MCG+08-11-11. This is an admittedly fairly loose constraint, but this magnetic field strength is on the order of the one expected at a distance of 1300 Rg for a magnetic field distribution that starts around a few Rg in equipartition with radiation at Eddington luminosity around a supermassive black hole of 107M (e.g., Rees 1984).

It is also worth noting that the mm SF starts to increase again after this local maximum, with a steeper slope, and with no evidence for flattening in agreement with longer (day) timescale variability observed in mm in several RQ AGN (e.g., Doi et al. 2011; Baldi et al. 2015; Behar et al. 2020). In comparison, the NuSTAR SF is rather flat down to the smallest time lags (τ < 103 s), without an apparent peculiar timescale, and with a variability fraction of about on the whole range of time lags explored.

4. Concluding remarks

In this Letter, we report the results of a strictly simultaneous NOEMA/NuSTAR observation > 10 h of the RQ AGN MCG+08-11-11. For the very first time, we observed intraday (few hours) variability of a few percent of the 100 GHz emission of a RQ AGN. Moreover, the mm and X-ray light curves showed a similar increasing trend throughout the observation. This fast variability in the mm band and the apparent correlation with the X-rays clearly suggest a strong physical link between the two emitting regions.

A SF analysis suggests a typical mm-wave variability of 2–3% on a timescale around 2 × 104 s, which translates into an upper limit of the size of the emitting regions ∼1300 Rg. These results indicate that the mm radio emitting region could be an extension of the hot corona, similar to an outflow and weak jet.

New mm–X-ray observations are needed to support or rule out different interpretations (e.g., lags between the mm and X-ray light curves). Along these lines, an XMM/NOEMA campaign on NGC 4051 is expected from November to December 2023.


1

Rν is generally defined as the ratio between the rest frame radio luminosity at a given frequency ν and the optical luminosity, usually in the B band.

2

Rg = 1.5 × 1012M7 cm with M7 = M/107M.

6

See http://heasarc.gsfc.nasa.gov/docs/NuSTAR/analysis/NuSTAR_swguide.pdf

7

https://docs.stingray.science/index.html

Acknowledgments

The strict simultaneity between NOEMA and NuSTAR or XMM was perfectly conducted thanks to the efforts of the Science Operation Committee of the different observatories. The results presented in this letter would not have been possible without their precious help! Thanks a lot to all the SOC people of both instruments! Part of this work has been done thanks to the financial supports from CNES and the French PNHE. The Technion group was supported in part by a Center of Excellence of the Israel Science Foundation (grant No. 1937/19). The scientific results reported in this article are based on observations with the XMM-Newton and NuSTAR satellites and NOEMA ground based telescopes. This work is based on observations carried out under project numbers S21BI and W21BU with the IRAM NOEMA Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).

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Appendix A: The R − BG plane

The contour plot of the radio flux density Fν in the R − BG plane is shown in Fig. A.1. It results from Eq. 1 and 2 assuming a redshift of 0.02 (which is the one of MCG+08-11-11) and for a frequency of 100 GHz (which corresponds to the frequency of our NOEMA observation). The scaling in terms of Rg is indicated by the right y scale of Fig. A.1.

thumbnail Fig. A.1.

Contour plot (blue) of the radio flux density Fν (in milliJansky) in the R − BG plane following the expression of R given in Eq. 1 for a frequency of 100 GHz and a source redshift z = 0.02. The red line is the corresponding NOEMA sensitivity for an integration time equal to the source size light travel time R/c. Above this line, the required exposure time to detect a flux density Fν is lower than R/c. It is larger below. The left y scale is in centimeter units while the right y scale being in Rg units for a supermassive black hole mass of 107 M.

Appendix B: Observation and data reduction

B.1. NOEMA

B.1.1. Observation

The weather conditions for the NOEMA observation were excellent, with less than 1mm of precipitable water vapor. The phase stability was excellent with less than 15° r.m.s. We used 3C454.3 for the bandpass calibration, and MWC349 for the flux calibration. The amplitude and phase calibrator was 0538+498, which is only 4 degrees away from MGC+08-11-11. Compared to standard NOEMA projects, we used a shortened calibration cycle of ∼13min to track instrumental and weather variations better.

The source was observed from 17.3h UT, December 18, 2021, to 06.5h UT, December 19, 2021, with a 1.2h gap when the source transited at a high local elevation and when it was impossible to track. Data were reduced using the standard NOEMA pipeline. At the time of observation, a slight non-closure problem was affecting NOEMA, so baseline-based amplitude calibration was used. Any residual amplitude gain error due to the distance between the calibrator and source was estimated to be < 1%.

The data were then exported in uv tables in small time chunks – separately for the lower sideband (LSB) and upper sideband (USB). Each uv table corresponding to one time step was then self-calibrated in phase, and a circular Gaussian was fitted to the data in the (u,v) plane. The fitted fluxes and associated errors were then used to produce a light curve.

B.1.2. Calibration

The NOEMA calibrator light curve, with a time bin of ∼10 minutes and normalised to its mean flux, is reported in black in Fig. 1. A linear fit gives a best-fit value for the slope of (1.1 ± 0.9)×10−4 hour−1, that is, almost consistent with zero (at 1 σ), which is as expected for a constant flux. The linear best fit is reported with a black solid line in Fig. 1. The result of a fit by a constant value (chi2/dof = 1604/70) indicates, however, that some variability is not captured in the error bars. This is expected since the errors were computed from the thermal noise of the antenna and they do not include their variations in gain. The standard deviation σFcalib of the calibrator light curve allowed us to estimate the systematic error related to this variation in gain. It is equal to 0.3% (see Tab. 2). It was thus included in the total error of the NOEMA light curve (quadratically added to the thermal noise error) of the source.

B.2. NuSTAR

We calibrated and clean raw NuSTAR (Harrison et al. 2013) data of MCG+08-11-11 using the NuSTAR Data Analysis Software (NuSTARDAS6 package v. 2.1.1). Level 2 cleaned data products were obtained with the standard nupipeline task while third level science products (spectra and light curves) were computed with the nuproducts pipeline and using the calibration database 20211202. A circular region with a radius of 50 arcsec centred on a blank area nearby the source was used to estimate the background. The extraction region for the source was selected using an iterative process that maximizes the signal-to-noise ratio (S/N) similarly to what is described in Piconcelli et al. (2004). While we are mainly interested in the variability aspects in this Letter, we took a quick look at the spectra. A simultaneous fit of the A and B module spectra in the 3-78 keV energy range with a cutoff power law + reflection component (WABS*(CUTOFFPL+XILLVER) in XSPEC) gives a reasonable fit with χ2/dof = 3647/3743 corresponding to a null hypothesis probability of ∼0.9. The best-fit parameters are a power-law photon index Γ = 1.56 ± 0.05, a cutoff energy Ec = 20 ± 2 keV, and a reflection parameter ≃0.4. A more detailed spectral analysis will be done in a following paper. The present fit enabled us to estimate the 2-10 keV luminosity (assuming z = 0.02) of L2 − 10keV = 4 × 1043 erg s−1, and the corresponding bolometric luminosity (applying a X-ray bolometric correction factor κX = 10 based on the empirical relation computed by Duras et al. 2020) of Lbol = 4 × 1044 erg s−1, that is, ∼15% of the Eddington luminosity for a BH of 2 × 107 M.

Appendix C: Good time interval for correlation analysis

The light curves of NOEMA and NuSTAR, with a time binning of 60 and 6 sec, respectively, are reported on the top and bottom of Fig. C.1. The gaps in the NuSTAR light curve correspond to the time when the satellite was not acquiring valid data due to, for example, Earth occultation or south atlantic anomaly (SAA) passages. The gap in the middle of the NOEMA observation is when the source transited at a high local elevation and was impossible to track.

thumbnail Fig. C.1.

Light curves of NOEMA (top, blue line) and NuSTAR (bottom, red line) with time bins of 60 and 6 sec., respectively. The 1.2h gap in the middle of the NOEMA light curve corresponds to the source transit at a high local elevation where it became impossible to track. The gaps in the NuSTAR light curve correspond to Earth occultation and SAA passages. The gray areas correspond to the time ranges where both NOEMA and NuSTAR data were acquired simultaneously. The black points in each panel correspond to the weighted mean of each light curve in these different time ranges, which are reported in Fig. 2

The gray area in Fig. C.1 corresponds to the time zones where both NOEMA and NuSTAR data were acquired. The black points correspond to the weighted mean of each light curve in the different time zones. These weighted mean values have been used for the Spearman’s rank correlation test discussed in Sect. 3.

Appendix D: Power spectral density

We computed the PSD of the NOEMA light curve using the astrophysical spectral-timing Python software package STINGRAY v1.1.2 7 (Huppenkothen et al. 2019b,a). We used the AVERAGEDPOWERSPECTRUM class adapted for light curves that are not sampled regularly such as the NOEMA one. The resulting PSD is plotted in Fig. D.1. It was normalized to the squared fractional r.m.s. of the light curve. The quadratic (in log space) best fit is reported in blue.

thumbnail Fig. D.1.

PSD of the NOEMA light curve (black line). The quadratic (in log space) best fit is reported in blue.

Appendix E: Simulated light curve and structure function

We have reported in Fig. E.1 an example of a simulated NOEMA light curve (top) and its corresponding SF (bottom). The simulation procedure is explained in Sect. 3.2.

thumbnail Fig. E.1.

Examples of simulated (blue lines) NOEMA light curve (top) and SF (bottom). The black points correspond to the observations.

Appendix F: Structure function errors

The errors on the SF were estimated by simulating ntrial light curves from the observed ones. For that purpose, we simulated light curves with the same number of data points as the observed ones, with each data point having been randomly distributed in a normal distribution centered on the observed flux and with a standard deviation equal to the observed photometric error. For each simulated light curve, we computed the corresponding SF, SFi(τ) (i between 1 and ntrial). Then we deduced the SF error at each τ from the standard deviation of the ntrial measurements. A number ntrial> 10 (we took 30) is generally sufficient to have a good error estimate of the SF for the range of τ covered by our observed light curves.

Appendix G: Previous tentatives

The unsuccessful campaigns on NGC 5506, NGC 7469, and Ark 564 are described below, and they were crucial for the development of this project. In addition to learning the best observing strategy for a successful campaign, we validated that with good weather conditions it was possible to reach a sensitivity of 12.5 μJy/beam at 100 GHz, allowing us to catch variability of a few percent for milliJansky sources.

G.1. NGC 5506

NGC 5506 (z = 0.006, MBH poorly known in between 106 − 108 M, e.g., Matt et al. 2015) was well detected by NOEMA at a few milliJansky. However, to fit with the XMM visibility window, the observation had to be conducted from June to August. The weather conditions were very bad at the NOEMA site, preventing any good estimate of the mm variability, while clear X-ray variability occured during the entire XMM pointing (see Fig. G.1). We have reported the light curve of the NOEMA calibrator in black in that figure. This observation demonstrates that to reach the conditions to detect weak (< 5-10 %) variability in the mm on hour timescale, the season from June to August has to be avoided.

thumbnail Fig. G.1.

NOEMA (blue, right scale) and XMM X-ray (red, left scale) light curves of NGC 5506 obtained during the first semester of 2021. The NOEMA light curves (at 100 GHz) have a time binning of 4 min. The XMM light curves have a time binning of 17 min. The calibrator light curve is plotted in black (right scale). The calibration accuracy needed to constrain the mm variability could not be reached during the entire observation for NGC 5506 due to bad weather conditions at the NOEMA site.

G.2. NGC 7469

NGC 7469 (z = 0.016, MBH = 106.9 M, e.g., Peterson et al. 2014; Bentz & Katz 2015) was also well detected by NOEMA at a few milliJansky. The weather was good at the NOEMA site. The NOEMA pointing lasted about 8 hours, as expected, while the XMM one, which covers the NOEMA observation entirely, was almost twice as long. However, the source stayed almost constant in X-ray during throughout NOEMA coverage, with its X-ray flux starting to significantly vary (after 8-9h UTC) when the lower source elevation and sunrise induced large amplitude gain variations at NOEMA (see Fig. G.2). These large amplitude gain variations produced variation in the light curve of the calibrator overplotted in black in that figure.

thumbnail Fig. G.2.

NOEMA (blue, right scale) and XMM X-ray (red, left scale) light curves of NGC 7469 obtained during the first semester of 2021. The NOEMA light curves (at 100 GHz) have a time binning of 7 min. The XMM light curves have a time binning of 17 min. The calibrator light curve is plotted in black (right scale). The calibration accuracy needed to constrain the mm variability could not be reached after 8-9h UTC.

G.3. Ark 564

Ark 564 (z = 0.024, MBH = 106.2 M, e.g., Zhang & Wang 2006) was chosen for a simultaneous X-ray radio campaign seeking intraday variability, due to its documented X-ray variability over hours, and its relatively low BH mass. Chandra/LETG observed Ark 564 in X-rays simultaneously with the JVLA at 45 GHz, for 3+3 hours (gap again due to high sky elevation) on December 20, 2019. At 45 GHz, each observing scan is 4 min on target and 1 min on the phase calibrator. The light curves are shown in Fig G.3. Unfortunately, no significant variability could be detected.

thumbnail Fig. G.3.

JVLA 45 GHz (blue, right scale) and Chandra X-ray (red, left scale) light curves of Ark 564 over 3+3 hrs with a gap due to high sky elevation. Data were binned to 15 min, about 12 min on target for JVLA. The phase calibrator is plotted in black (right scale). No significant variability was detected at 45 GHz, and there was only marginal variability in X-ray.

All Tables

Table 1.

Log of the radio mm and X-ray observations of MCG+08-11-11 by NOEMA and NuSTAR.

Table 2.

Variability properties of X-ray (3–10 keV), mm (100 GHz), and NOEMA calibrator light curves.

All Figures

thumbnail Fig. 1.

MCG+08-11-11 radio/X-ray variability. The black, blue, and red circles and dashed lines are the NOEMA calibrator, the NOEMA LSB, and 3–10 keV NuSTAR light curves normalised by their mean, respectively. The solid lines are the corresponding linear best fits (see Sect. 3).

In the text
thumbnail Fig. 2.

Weighted mean NuSTAR count rates vs. NOEMA fluxes. The black solid line and gray shadowed area represent the best-fitting linear correlation and its 90% confidence bands computed using the bayesian linear fitting PYTHON package LINMIX4, respectively. The Spearman correlation coefficient r and its corresponding p value are indicated in the figure.

In the text
thumbnail Fig. 3.

Structure function for the NOEMA calibrator (top), the NOEMA (middle), and NuSTAR (bottom) observations of MCG+08-11-11. The solid line is the best linear log–log fit, and the corresponding slopes (with the corresponding errors) are indicated in each figure. The vertical dotted line in the middle plot indicates a local maximum around τ = 2 × 104 s. The dashed line corresponds to the cubic polynomial best fit (in log scale), which was used to plot the data/model ratio in Fig. 4.

In the text
thumbnail Fig. 4.

Red points correspond to the residuals in term of sigma between the NOEMA SF data points and its cubic polynomial best fit reported in the middle plot of Fig. 3. The colored area corresponds to the 50% (orange), 90% (blue), and 99% (green) percentile of the distribution of the same ratios, but they were obtained with simulated data.

In the text
thumbnail Fig. A.1.

Contour plot (blue) of the radio flux density Fν (in milliJansky) in the R − BG plane following the expression of R given in Eq. 1 for a frequency of 100 GHz and a source redshift z = 0.02. The red line is the corresponding NOEMA sensitivity for an integration time equal to the source size light travel time R/c. Above this line, the required exposure time to detect a flux density Fν is lower than R/c. It is larger below. The left y scale is in centimeter units while the right y scale being in Rg units for a supermassive black hole mass of 107 M.

In the text
thumbnail Fig. C.1.

Light curves of NOEMA (top, blue line) and NuSTAR (bottom, red line) with time bins of 60 and 6 sec., respectively. The 1.2h gap in the middle of the NOEMA light curve corresponds to the source transit at a high local elevation where it became impossible to track. The gaps in the NuSTAR light curve correspond to Earth occultation and SAA passages. The gray areas correspond to the time ranges where both NOEMA and NuSTAR data were acquired simultaneously. The black points in each panel correspond to the weighted mean of each light curve in these different time ranges, which are reported in Fig. 2

In the text
thumbnail Fig. D.1.

PSD of the NOEMA light curve (black line). The quadratic (in log space) best fit is reported in blue.

In the text
thumbnail Fig. E.1.

Examples of simulated (blue lines) NOEMA light curve (top) and SF (bottom). The black points correspond to the observations.

In the text
thumbnail Fig. G.1.

NOEMA (blue, right scale) and XMM X-ray (red, left scale) light curves of NGC 5506 obtained during the first semester of 2021. The NOEMA light curves (at 100 GHz) have a time binning of 4 min. The XMM light curves have a time binning of 17 min. The calibrator light curve is plotted in black (right scale). The calibration accuracy needed to constrain the mm variability could not be reached during the entire observation for NGC 5506 due to bad weather conditions at the NOEMA site.

In the text
thumbnail Fig. G.2.

NOEMA (blue, right scale) and XMM X-ray (red, left scale) light curves of NGC 7469 obtained during the first semester of 2021. The NOEMA light curves (at 100 GHz) have a time binning of 7 min. The XMM light curves have a time binning of 17 min. The calibrator light curve is plotted in black (right scale). The calibration accuracy needed to constrain the mm variability could not be reached after 8-9h UTC.

In the text
thumbnail Fig. G.3.

JVLA 45 GHz (blue, right scale) and Chandra X-ray (red, left scale) light curves of Ark 564 over 3+3 hrs with a gap due to high sky elevation. Data were binned to 15 min, about 12 min on target for JVLA. The phase calibrator is plotted in black (right scale). No significant variability was detected at 45 GHz, and there was only marginal variability in X-ray.

In the text

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