Galaxy Mergers up to z < 2.5. II. AGN Incidence in Merging Galaxies at Separations of 3–15 kpc

Full details on the selection of galaxy mergers are described in Silva et al. (2018). Here, we only present the key aspects: Galaxy pairs were selected by applying the technique described in Lackner et al. (2014) to near-IR H160 postage stamps. These postage stamps were centered on 5717 galaxies with log(M_⋆/M_⊙) ≥ 10, m_AB < 24.5, and 0.3 < z < 2.5, which were obtained from the 3D-Hubble Space Telescope (HST) catalogs (Skelton et al. 2014; Momcheva et al. 2016). We selected galaxy pairs with nuclei separations between 3 and 15 kpc and with mass and flux ratios ≥1:4, to later select potential major mergers. We found that 28% of the selected galaxy pairs were unresolved in the 3D-HST catalogs (thus the total number of sources in the sample increased to 5907 ⁷ ). We extracted deblended photometry for these galaxies and derived photometric redshifts, colors, and stellar population properties.

We used the redshift values of the galaxies in pairs, provided by the 3D-HST catalogs and the deblended photometry (photometric, grism, and spectroscopic redshifts) to separate potential mergers of line-of-sight contaminants. We defined mergers as galaxies that are consistent with being at the same redshift within a 3σ uncertainty (when using either photometric or grism redshifts), or if the redshifts differ by less than 0.001 (if both have spectroscopic redshift). We found 130 major merging systems in which the merging galaxies have masses in the range $8.3\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 11.5$ (primary sample). Since star-forming clumps in galaxies usually have stellar masses $8\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 10$ (Guo et al. 2012), we constructed a more restrictive sample of major mergers (high-mass sample) in which both merging galaxies have stellar masses log(M_⋆/M_⊙) ≥ 10. ⁸ This high-mass sample contains 64 merging systems (128 galaxies). The sample of non-merging galaxies (i.e., galaxies not selected as mergers) with masses log(M_⋆/M_⊙) ≥ 10 consists of 5718 galaxies. In this work, we focus the study on the incidence of AGNs in mergers using the high-mass sample.

We used the rest-frame U − V and V − J colors (or UVJ colors) to separate merging galaxies into quiescent, unobscured star-forming, and dusty star-forming by using the criteria defined in Whitaker et al. (2015) and Martis et al. (2016). As found in Silva et al. (2018), for the 128 galaxies in the merger sample, 35.9% ± 5.3%, 21.9% ± 3.4%, and 42.2% ± 5.7% are quiescent, unobscured, and dusty star-forming galaxies, respectively. For non-mergers, the fractions are 30.5% ± 0.7%, 28.8% ± 0.7%, and 40.7% ± 0.8%, respectively.

We separated mergers into wet (both galaxies are star-forming, i.e., dusty or unobscured), mixed (one quiescent and one star-forming galaxy), and dry (both galaxies are quiescent) and found that 53.1% ± 6.4%, 21.9${\pm }_{3.4}^{4.9} \%$, and 25.0${\pm }_{3.7}^{5.2} \%$ of the major mergers correspond to wet, mixed, and dry mergers, respectively.

Star formation rates were obtained from a combination of rest-frame UV emission and mid-IR photometry obtained from Spitzer/MIPS imaging following Whitaker et al. (2012). When MIPS 24 μm data were not available or for detections with signal-to-noise ratio (S/N) < 3, the SFRs were obtained from the modeling of the spectral energy distributions (SEDs).

We found no difference in the star formation activity between merging and non-merging galaxies and only ${12}_{-3}^{+5} \%$ of the star-forming galaxies in mergers (6.5% ± 0.4% in non-mergers) are a starburst galaxy, i.e., a galaxy that lies 0.5 dex above the main-sequence fit of Whitaker et al. (2014). All of these starbursts are in wet mergers and are dusty star-forming galaxies. Note that some of the starburst galaxies in the sample of non-mergers are possibly mergers in the coalescence phase.

We use publicly available X-ray catalogs to cross-match the merger sample and non-merging galaxies with X-ray sources. We use the AEGIS-X Survey (The Chandra Deep Survey of the Extended Groth Strip; Laird et al. 2009), the Chandra COSMOS legacy Survey (Civano et al. 2016; Marchesi et al. 2016), the CDF-N (2 Ms Chandra Deep Field-North Survey; Xue et al. 2016) the CDF-S survey (7 Ms Chandra Deep Field-South Survey; Luo et al. 2017), the Chandra counterparts of CANDELS GOODS-S sources (Cappelluti et al. 2016), the X-UDS survey (The Chandra Legacy Survey of the UKIDSS Ultra Deep Survey Field; Kocevski et al. 2018), the Chandra COSMOS Survey (Elvis et al. 2009), and the ZFOURGE catalog of AGN candidates (Cowley et al. 2016).

We cross-match merging and non-merging galaxies with the closest X-ray source found in the catalogs. These sources have fluxes above the flux limit of the respective catalog from where they were extracted. The separation used for matching is equal to the point-spread function (PSF) of the observations performed to obtain the catalogs (in the range 15–50). When the catalogs indicate that the X-ray sources have an optical counterpart, we use a matching separation of 1'' with respect to the optical position.

Of the 64 merging systems, 14 (21.9${\pm }_{4.4}^{7.5}$%) are matched with an X-ray source. These mergers have galaxies with projected separations between 4.1 and 14.3 kpc (05–19), therefore we are not able to distinguish which of the merging galaxies is the source of X-ray emission. The X-ray matched sources have fluxes in the 0.5−7 keV band of f_x = 3.8 × 10⁻¹⁷–2.4 × 10⁻¹⁴ erg s⁻¹ cm⁻² and are at redshifts 0.68 < z < 2.13, corresponding to X-ray luminosities of L_x = 4.2 × 10⁴¹–3.9 × 10⁴⁴ erg s⁻¹. In the case of non-merging galaxies, 555 (9.7% ± 0.4%) are identified with an X-ray source. The sources have fluxes in the range f_x = 1.2 × 10⁻¹⁷–1.3 × 10⁻¹³ erg s⁻¹ cm⁻² and redshifts 0.31 < z < 2.49, corresponding to X-ray luminosities L_x = 1.4 × 10⁴⁰–5.7 × 10⁴⁴ erg s⁻¹.

The 3D-HST catalogs provide optical line measurements such as [O iii]λ5007 at 1.4 < z < 2.2 and Hβ at 1.5 < z < 2.3, which can be used to find potential AGNs. We select only galaxies in which the [O iii] and Hβ fluxes are available and have an S/N ≥ 3, as we will use the mass-excitation diagram of Juneau et al. (2014) to identify AGNs in Section 3.2. We find that six individual merging galaxies (in five systems) have both [O iii] and Hβ measurements. These galaxies are at 1.68 < z < 2.1 and have projected separations between 4.8 and 13.8 kpc. They have [O iii] fluxes in the range f_{[O iii]} = 3.8 × 10⁻¹⁷–5.6 × 10⁻¹⁶ erg s⁻¹ cm⁻², which correspond to luminosities L_{[O iii]} = 2.4 × 10⁴²–5.5 × 10⁴³ erg s⁻¹, and Hβ fluxes f_Hβ = 2.5 × 10⁻¹⁷–9.0 × 10⁻¹⁷ erg s⁻¹ cm⁻² and luminosities L_Hβ = 1.7 × 10⁴²–8.9 × 10⁴² erg s⁻¹. For non-mergers, 228 galaxies have both [O iii] and Hβ measurements and are at 1.4 < z < 2.3. The galaxies have [O iii] fluxes in the range f_{[O iii]} = 2.1 × 10⁻¹⁷–5.6 × 10⁻¹⁵ erg s⁻¹ cm⁻², which correspond to luminosities L_{[O iii]} = 1.1 × 10⁴²–3.7 × 10⁴⁴ erg s⁻¹, and have Hβ fluxes in the range f_Hβ = 1.1 × 10⁻¹⁷–3.0 × 10⁻¹⁵ erg s⁻¹ cm⁻² corresponding to a range in luminosities L_Hβ = 7.7 × 10⁴¹–2.4 × 10⁴⁴ erg s⁻¹.

Spitzer/IRAC 3.6, 4.5, 5.8, 8.0 μm fluxes for our sample of mergers and non-mergers are provided by the 3D-HST catalogs. The extraction of fluxes is described in detail in Skelton et al. (2014). Fluxes are obtained by measuring the mid-IR intensity using an aperture of 3'' on the Spitzer images. Contribution from neighboring blended sources in these images are obtained by using a high-resolution image. Fluxes are corrected to account for flux that falls outside the aperture due to the large PSF size of the Spitzer observations. Of the 128 galaxies in 64 merging systems, 102 galaxies have measured Spitzer/IRAC fluxes with S/N ≥ 3 in the four IRAC bands (44 systems have measurements in both merging galaxies). These mergers have galaxies with projected separations 3.7–14.3 kpc and are in the redshift range 0.5 < z < 2.4. In the case of non-mergers, 4493 galaxies have measured IRAC fluxes and are at 0.31 < z < 2.5.

We cross-match the merger sample and non-merging galaxies with radio sources in published radio catalogs. We use the AEGIS20 Survey (a radio survey of the Extended Groth Strip; Ivison et al. 2007), the Very Large Array (VLA)-COSMOS survey (Schinnerer et al. 2007), the VLA 1.4 GHz survey of the Extended Chandra Deep Field-South (Miller et al. 2008), VLA 1.4 GHz observations of GOODS-North field (Morrison et al. 2010), and the ZFOURGE catalog of AGN candidates (Cowley et al. 2016).

Since the resolution of the radio observations at 1.4 GHz ranges from 17 to 38, we match merging and non-merging galaxies with the closest radio source at a separation that depends on the beam size. Of the 64 merging systems, 5 (7.8${\pm }_{2.1}^{5.3}$%) are matched with a radio source. These systems are at redshift 0.70 ≤ z ≤ 2.11 and have galaxies with projected separations 6.9−12.2 kpc (083–15), therefore we are not able to identify which of the merging galaxies is the source of radio emission. The matched radio sources have fluxes in the range f_{1.4 GHz} = 0.03−0.26 mJy, which correspond to luminosities L_{1.4 GHz} = 4.1 × 10³⁹–8.4 × 10⁴⁰ erg s⁻¹, and the separation between the merging and the radio sources ranges 014−154. In the case of non-merging galaxies, 237 (4.1% ± 0.3%) are identified with a radio source. The radio sources have fluxes in the range f_{1.4 GHz} = 0.02−16.9 mJy, redshifts 0.32 ≤ z ≤ 2.49, luminosities L_{1.4 GHz} = 2.9 × 10³⁸–2.8 × 10⁴² erg s⁻¹, and separations between the galaxy and the radio source between 004 and 370.

To select X-ray AGNs, we use the technique described in Szokoly et al. (2004) and Cowley et al. (2016). This technique applies restrictions on the X-ray luminosity and the hardness ratio HR, which is defined as the normalized difference of counts in the soft and hard X-ray bands $\left(\tfrac{\mathrm{hard}-\mathrm{soft}}{\mathrm{hard}+\mathrm{soft}}\right)$. X-ray AGNs are selected using:

$$\begin{eqnarray}{L}_{x}\geqslant {10}^{41}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\ \&\ \mathrm{HR}\gt -0.2\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}{L}_{x}\geqslant {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\ \&\ \mathrm{HR}\leqslant -0.2\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{L}_{x}\geqslant {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\ \mathrm{if}\ \mathrm{HR}=\mathrm{none}.\end{eqnarray} \tag{ 3 }$$

The X-ray luminosity is obtained from

$$\begin{eqnarray}&&{L}_{x}[\mathrm{erg}\,{{\rm{s}}}^{-1}]=4\pi {d}_{l}^{2}{\left(1+z\right)}^{{\rm{\Gamma }}-2}{f}_{x},\end{eqnarray} \tag{ 4 }$$

where f_x is the measured X-ray flux in erg s⁻¹ cm⁻², d_l is the luminosity distance in cm, and Γ is the photon index of the X-ray spectrum. We use Γ = 1.4, a typical value of the photon index found in galaxies (Cowley et al. 2016). For the redshift z, we use the redshift values of the matched merging systems and non-merging galaxies. Based on this selection, we find that 10 of the 14 merging systems with matched X-ray sources are X-ray AGNs. All of these systems have HR measurements (in the range −0.34 < HR < 0.39), are at redshifts 0.68 < z < 2.13, and have fluxes f_x = 7.9 × 10⁻¹⁷–2.4 × 10⁻¹⁴ erg s⁻¹ cm⁻² and luminosities L_x = 1.1 × 10⁴²–3.9 × 10⁴⁴ erg s⁻¹. In the case of non-mergers, we find that 455 of the 555 X-ray matched sources are AGNs. These AGNs are in the redshift range 0.34 < z < 2.49, and have fluxes f_x = 1.9 × 10⁻¹⁷–1.3 × 10⁻¹³ erg s⁻¹ cm⁻² and luminosities L_x = 1.0 × 10⁴¹–5.7 × 10⁴⁴ erg s⁻¹.

We use the method described in Juneau et al. (2014) to find AGNs using both the [O iii] and Hβ optical lines. For galaxies with masses log(M_⋆/M_⊙) ≥ 10, AGNs are selected as galaxies in which

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{f}_{[{\rm{O}}{\rm\small{III}}]}}{{f}_{{\rm{H}}\beta }}\right) & \gt & 410.24-109.33\mathrm{log}\left[\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right]\\ & & +9.7{\mathrm{log}}^{2}\left[\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right]-0.28{\mathrm{log}}^{3}\left[\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right],\end{array}\end{eqnarray} \tag{ 5 }$$

where f_{[O iii]}/f_Hβ is the ratio of the [O iii] and Hβ line fluxes and M_⋆ is the stellar mass of the galaxies. This restriction selects galaxies containing AGNs with a probability between 60% and 85%. Based on this selection, we find that four of the six galaxies in mergers with optical lines are optically selected AGNs. These galaxies are at 1.68 < z < 2.1 and are in mergers with separations 4.9–13.8 kpc. Two AGNs are found in one system, i.e., it is a dual AGN system (two AGNs separated by a closed projected separation; e.g., Gross et al. 2019; Rubinur et al. 2019; Solanes et al. 2019). In the case of non-mergers, 180 of the 228 galaxies with [O iii] and H_β measurements are AGNs and are in the redshift range 1.4 < z < 2.3.

We use the fluxes f_{3.6 μm}, f_{4.5 μm}, f_{5.8 μm}, and f_{8.0 μm} in the four IRAC bands to identify mid-IR selected AGNs using the description indicated in Donley et al. (2012). Mid-IR AGNs are those that follow these five conditions (valid for z < 2.7):

• 1.  
  f_{4.5 μm} > f_{3.6 μm}, f_{5.8 μm} > f_{4.5 μm}, and f_{8.0 μm} > f_{5.8 μm}.
• 2.  
  ${\mathrm{log}}_{10}\left(\tfrac{{f}_{5.8\mu {\rm{m}}}}{{f}_{3.6\mu {\rm{m}}}}\right)\geqslant 0.08$
• 3.  
  ${\mathrm{log}}_{10}\left(\tfrac{{f}_{8.0\mu {\rm{m}}}}{{f}_{4.5\mu {\rm{m}}}}\right)\geqslant 0.15$
• 4.  
  ${\mathrm{log}}_{10}\left(\tfrac{{f}_{8.0\mu {\rm{m}}}}{{f}_{4.5\mu {\rm{m}}}}\right)\geqslant \left[1.21\times {\mathrm{log}}_{10}\left(\tfrac{{f}_{5.8\mu {\rm{m}}}}{{f}_{3.6\mu {\rm{m}}}}\right)\right]-0.27$
• 5.  
  ${\mathrm{log}}_{10}\left(\tfrac{{f}_{8.0\mu {\rm{m}}}}{{f}_{4.5\mu {\rm{m}}}}\right)\leqslant \left[1.21\times {\mathrm{log}}_{10}\left(\tfrac{{f}_{5.8\mu {\rm{m}}}}{{f}_{3.6\mu {\rm{m}}}}\right)\right]+0.27.$

Of the 102 galaxies with measured IRAC fluxes, we find that two galaxies are mid-IR selected AGNs. The galaxies have projected separations of 7.4 and 12.2 kpc and redshifts z = 1.9 and 2.11. For non-mergers, 81 of the 4493 galaxies with measured mid-IR fluxes are AGNs and are in the redshift range 0.44 < z < 2.49.

Radio AGNs are identified as those sources that have an excess of the star formation rate in the radio compared to the star formation rates obtained in the Infrared and UV wavelengths. When this Radio-AGN activity index is above 3 (SFR_Radio/SFR_UV+IR > 3), galaxies are classified as radio AGNs (Rees et al. 2016). The UV and IR star formation rates correspond to the unobscured and obscured star formation activity in the galaxies, respectively. The use of the SFR_UV+IR and not only the SFR_IR in the radio-AGN activity index avoids the misclassification as a radio-AGN of radio, low-dust, star-forming galaxies, which can produce an excess in the SFR_Radio if they are compared only with the obscured star formation.

The ten galaxies in the five merging systems with matched radio sources have SFRs obtained from the combination of rest-frame UV emission and mid-IR photometry obtained from Spitzer/MIPS imaging. For the 237 non-merging galaxies with matched radio sources, 217 have SFRs from UV+IR and 20 from modeling their SEDs.

The SFR_Radio is measured from the rest-frame radio luminosity L_Radio using the description indicated in Cowley et al. (2016):

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{Radio}}[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=3.18\times {10}^{-22}({L}_{\mathrm{Radio}}/{\rm{W}}\,{\mathrm{Hz}}^{-1}).\end{eqnarray} \tag{ 6 }$$

The rest-frame radio luminosity is given by

$$\begin{eqnarray}&&{L}_{\mathrm{Radio}}[{\rm{W}}\ {\mathrm{Hz}}^{-1}]=4\pi {d}_{l}^{2}{\left(1+z\right)}^{-(\alpha +1)}{f}_{\mathrm{Radio}},\end{eqnarray} \tag{ 7 }$$

where d_l is the luminosity distance in cm, f_Radio is the measured radio flux in W m⁻² Hz⁻¹, and α is the radio spectral index. In this work, we use the standard α = − 0.7 value. ⁹ The redshift z is obtained from redshift values of the matched mergers and non-merging galaxies.

We measure the radio-AGN activity index in non-mergers by measuring the ratio of the SFR_Radio of the matched radio source over the measured SFR value (SFR_UV+IR or SFR_SED). In the case of mergers, since we do not know which of the merging galaxies is the radio-AGN source, we assume that the galaxy with the highest SFR_UV+IR is the radio source. Therefore, the radio-AGN activity index in mergers is a lower limit.

We find that four of the five radio-matched merging systems are radio-AGNs. These AGNs have radio luminosities L_{1.4 GHz} = 4.1 × 10³⁹–8.4 × 10⁴⁰ erg s⁻¹, are in systems in which the merging galaxies have projected separations 6.9–10.7 kpc (083–15), and are at redshifts 0.70 < z < 2.11. For non-mergers, 81 of the 237 matched galaxies are radio-AGNs. The AGNs have luminosities L_{1.4 GHz} = 3.3 × 10³⁸–2.8 × 10⁴² erg s⁻¹ and are in the redshift range 0.32 < z < 2.48.

We combined the results of the previous AGN selections to analyze how many merging systems and non-merging galaxies have single or multiple AGN types. Of the 64 merging systems, 58 systems (105 galaxies) have either a matched X-ray source, IRAC colors in the four bands, [O iii] and Hβ optical lines, and/or a matched radio source. We find that ten and four systems are identified with an X-ray and a radio AGN, respectively, and four and two individual merging galaxies (in three and two merging systems) are optical- and mid-IR-selected AGNs, respectively. There are 13 systems identified with only one AGN type, while three systems are identified with multiple AGN types. In the case of non-mergers, 4625 galaxies have measurements to find potential AGNs. We find that 703 galaxies are identified as AGNs with 455, 180, 81, and 81 identified as X-ray, optical, mid-IR, and radio AGN, respectively. Of these 703 AGNs, 626 galaxies are identified with one AGN type and 77 with multiple AGN types. Figure 1 presents Venn diagrams indicating the combination of the results of the matched sources and AGN galaxies selected in the different wavelength ranges. ¹⁰

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4.1.1. Non-mergers

The total AGN fraction for non-mergers can be obtained from f_AGN = N_AGN/N_T, which is the ratio of the number of galaxies that are AGNs (N_AGN = 703) and the number of galaxies with measurements to find potential AGNs (N_T = 4625, Section 3.5). In this case, the total AGN fraction in non-mergers is f_AGN = 15.2% ± 0.6%. Uncertainties are obtained from 10,000 Monte Carlo realizations, where for each matched source, we draw a flux from the measured fluxes (f_x , f_{[O iii]}, f_Hβ , f_{3.6 μm}, f_{4.5 μm}, f_{5.8 μm}, f_{8.0 μm}, f_{1.4 GHz}) and perturb them with the errors of the flux measurements. For each realization, we calculate how many galaxies meet the criteria to be classified as AGNs and calculate the AGN fraction. The uncertainty is calculated from the standard deviation of the resulting fractions and then added in quadratures with 1σ errors obtained from Poisson statistics (Gehrels 1986). Due to the varying sensitivity of the Chandra observations, the denominator in the fraction needs to be corrected to account for the effective number of galaxies for which an X-ray-selected AGN could have been detected, as in Silverman et al. (2011).

The corrected AGN fraction is obtained from:

$$\begin{eqnarray}\begin{array}{rcl}{f}_{\mathrm{AGN} \mbox{-} {\rm{c}}} & = & {f}_{\mathrm{nonXR}}+{f}_{\mathrm{XR}}\\ & = & \displaystyle \frac{{N}_{\mathrm{AGN} \mbox{-} \mathrm{nonXR}}}{{N}_{{\rm{T}}}}+\displaystyle \sum _{i=1}^{{N}_{\mathrm{AGN} \mbox{-} \mathrm{XR}}}\displaystyle \frac{1}{{N}_{\mathrm{eff}-i}+{N}_{\mathrm{nonXR}}}.\end{array}\end{eqnarray} \tag{ 8 }$$

The fraction f_nonXR ¹¹ corresponds to the ratio of the number of AGNs not selected in X-ray at all (N_AGN-nonXR = 248) and the total number of galaxies with measurements to find potential AGNs (N_T = 4625). The fraction f_XR is the AGN fraction for X-ray-selected AGNs (even if they were identified as AGNs in other wavelengths). In this case, for each X-ray-selected AGN (with a total of N_AGN-XR = 455 galaxies), we measure the number of effective galaxies in which we could have detected an X-ray AGN (N_eff-i ) and then add the number of galaxies with measurements to find potential AGNs in optical, mid-IR, and radio only (N_nonXR = 4070). To calculate N_eff-i , we produce the luminosity sensitivity function (LSF; Birchall et al. 2020), which is the distribution of the fraction of galaxies where an AGN could have been detected above a given X-ray luminosity. To obtain this function, we use all the sources in our sample (mergers and non-mergers) that are spatially matched with an X-ray source (575 galaxies). For each of these matched galaxies, we assign a flux limit that corresponds to the flux limit of the survey where the galaxy was extracted. Using the redshifts of the matched galaxies in our sample, the flux limit is converted into a luminosity limit. The cumulative histogram as a function of the luminosity limits of these sources is normalized by the size of the sample of matched galaxies (Figure 2).

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For each X-ray-selected AGN with a luminosity L_x−i , we use the LSF to measure the effective number of galaxies where the Chandra observations were sufficiently sensitive to detect an AGN of this luminosity. This effective number is given by N_eff−i = LSF_i × N_XR, where N_XR is the number of non-merging galaxies with measurements to find potential X-ray-selected AGNs (N_XR = 555) and LSF_i is the value of the luminosity sensitivity function at a luminosity L_lim = L_x−i . For instance, for an X-ray-selected AGN with $\mathrm{log}({L}_{x}[\mathrm{erg}\,{{\rm{s}}}^{-1}])\geqslant 43.5$, the effective number of galaxies is N_eff−i = 1.0 × 555 = 555, while for an AGN with luminosity $\mathrm{log}({L}_{x}[\mathrm{erg}\,{{\rm{s}}}^{-1}])$ = 41.5, the effective number is N_eff−i = 0.61 × 555 = 338.5. After measuring N_eff−i for all the X-ray-selected AGNs, we sum them up and find a total corrected AGN fraction of f_AGN‐c = 15.4% ± 0.6% (black filled circle in Figure 3). This fraction is not significantly different from the non-corrected AGN fraction f_AGN = 15.2% ± 0.6%.

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4.1.2. Mergers

4.1.3. Comparison AGN Fraction between Mergers and Non-mergers

We find a similar AGN fraction in merging (16.4${\pm }_{3.1}^{5.0}$%) and non-merging galaxies (15.4% ± 0.6%) when assuming that the source of the unresolved AGNs (X-ray or radio) is only one of the merging galaxies in a system. Since the [O iii] luminosity itself is an indicator of AGN activity at high luminosities, we compare the normalized distribution of the [O iii] luminosity between mergers and non-mergers (Figure 4). An excess in this distribution would suggest higher AGN activity. We select all merging and non-merging galaxies with [O iii] measurements and S/N ≥ 3, even if they do not have Hβ measurements as used in the data selection presented in Section 2.3. We find 13 and 730 merging and non-merging galaxies with [O iii] measurements, respectively. We perform a Kolmogorov–Smirnov (K-S) test between the distributions of the merging and non-merging samples, to quantify whether the two samples are consistent with coming from the same parent population. We find a P-value (probability of the plausibility of the null hypothesis) of P = 0.32, therefore the two populations are indistinguishable at more than 3σ (since P > 0.003 ¹² ), in agreement with the lack of AGN excess in mergers found using the multiwavelength AGN selection.

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In the following results, we use the assumption that only one of the merging galaxies is the X-ray or the radio-selected AGN.

As indicated in Section 2.1, we separate galaxies into star-forming (dusty or unobscured) and quiescent using the rest-frame UVJ colors of the galaxies. Using this classification, we divide mergers into wet (two star-forming), mixed (one star-forming and one quiescent), and dry (two quiescent). The downward and upward triangles in Figure 3 present the AGN fraction for quiescent (f_Q) and star-forming galaxies (f_SF), respectively. For non-mergers, the fractions are obtained from the ratio of number of AGNs (N_A) over the total number of galaxies (N_t) with measurements to find potential AGNs of their respectively galaxy type (${f}_{{\rm{Q}}}={N}_{{{\rm{A}}}_{{\rm{Q}}}}/{N}_{{{\rm{t}}}_{Q}}$ and ${f}_{\mathrm{SF}}={N}_{{{\rm{A}}}_{\mathrm{SF}}}/{N}_{{{\rm{t}}}_{\mathrm{SF}}}$). The AGN fractions in non-mergers are f_Q = 11.4% ± 0.9% and f_SF = 16.8% ± 0.7%. ¹³ For mergers, the AGN fraction for the different galaxy types is not straightforward. The complication arises in the case of a mixed merger identified with a non-resolved X-ray or radio AGN and with no other resolved AGN selected in optical or mid-IR. In wet and dry mergers, since both merging galaxies are of the same type, the emitter in an unresolved AGN will be either a star-forming or a quiescent galaxy, respectively. The AGN fraction for star-forming and quiescent merging galaxies will be measured in two ways: (1) the AGNs in mixed mergers arise from the star-forming galaxies (dashed purple triangles in Figure 3), which gives an AGN fractions of f_Q = 5.9${\pm }_{1.9}^{7.8}$% and f_SF = $21.1{\pm }_{4.2}^{7.0}$%; (2) the AGNs arise from the quiescent galaxies (dotted purple triangles in Figure 3), resulting in AGN fractions of f_Q = 11.8${\pm }_{3.4}^{9.3}$% and f_SF = 18.3${\pm }_{3.8}^{6.6}$%. In summary, we find that, in non-mergers, the AGN fraction in star-forming galaxies is higher than in quiescent galaxies. The same trend is found in mergers, which is more significant when assuming that the unresolved AGN arises from the star-forming galaxy in a mix merger.

The square symbols in Figure 3 present the AGN fractions found for starbursts, i.e., galaxies that lie 0.5 dex above the main-sequence fit obtained by Whitaker et al. (2014). For non-mergers, the fraction is obtained from the ratio of the number of starbursts that are AGNs over the total number of starburst galaxies with measurements to find AGNs (f_SB = ${N}_{{{\rm{A}}}_{\mathrm{SB}}}/{N}_{{{\rm{t}}}_{\mathrm{SB}}}$). We find an AGN fraction in starbursting non-merging galaxies of f_SB = 31.4% ± 3.6%. For mergers, we find an AGN fraction in starbursting merging galaxies of f_SB = 44.4${\pm }_{12.9}^{35.1}$% (dashed purple square). However, this value is an upper limit, since we assume that, for non-resolved AGNs, the starburst is also the AGN galaxy. ¹⁴ If not, this value drops to f_SB = 33.3${\pm }_{10.2}^{32.4}$% ¹⁵ (dotted purple square). In any case, the AGN fraction in starbursts in mergers and non-mergers is higher than the total AGN fraction of the general population.

Figure 5 shows the fraction of AGNs in mergers depending of the merger type. We find AGN fractions of 4.3${\pm }_{1.3}^{10.0} \%$, 20.0${\pm }_{5.8}^{15.8} \%$, and 19.3${\pm }_{4.1}^{7.3}$% for dry, mixed, and wet mergers, respectively. This results might suggest that the presence of a star-forming galaxy in a merging system increases the incidence of AGNs, although the excess in the fraction in wet and mixed mergers compared to dry mergers is not significant given the associated error bars.

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Figure 6, left shows the fraction of AGNs in mergers (purple circles) and in non-mergers (black squares) as a function of redshift. The dotted line is the median of the three fraction values obtained for mergers. We find that the total AGN fraction in non-mergers increases with redshift, while for mergers it is almost constant at z ≲ 1.5 and increases at higher redshifts. We also include the evolution with redshift of the AGN fraction assuming that the unresolved AGNs are dual (blue circles in Figure 6).

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Figure 6, right shows the fraction of AGNs in mergers as a function of the projected separation of the merging galaxies. The black square shows the total AGN fraction for non-merging galaxies. The AGN fractions in all bins of projected separation are marginally larger than the fractions for non-mergers—but not significantly so, due to the large error bars. Note that we are missing the coalescence phase, when the highest black hole accretion activity is expected (e.g., Springel et al. 2005; Hopkins et al. 2008; Debuhr et al. 2011). Some of the starburst galaxies in the non-merger sample are possibly mergers at the coalescence phase. For instance, Cibinel et al. (2019) investigate the fraction of close pairs and morphologically identified mergers on and above the star-forming main sequence at 0.2 < z < 2.0. They found that starburst galaxies are mostly dominated (more than 70%) by mergers in their late stages. If, for simplicity, we assume that all the starburst in the non-merging sample are mergers at coalescence ¹⁶ (78 of the 248 matched starbursting non-merging galaxies are AGN), then the fraction of AGNs at the coalescence phase (i.e., projected separation is zero) is 31.4% ± 3.6% (purple star in Figure 6) and we can see a clear increment in the AGN fraction at projected separations below 10 kpc. With this assumption, the total fraction of AGNs in mergers increases from $16.4{\pm }_{3.1}^{5.0} \%$ to 26.9% ± 2.8%, while the fraction in non-mergers changes from 15.4% ± 0.6% to 14.3% ± 0.6%. Therefore, the fraction of AGNs in non-mergers remains almost the same as originally measured, while in mergers it increases significantly. However, contrary to the merger origin of starbursts, there are also findings indicating that high-redshift starbursts could be the result of galaxies with high levels of cold gas content (Scoville et al. 2016; Oteo et al. 2017) rather than mergers at coalescence. It is out the scope of this paper to identify which of these starbursts are actually the result of a merger event.

To analyze whether the black hole accretion rate (BHAR) is related to the star formation rate and/or the stellar mass in the galaxies, we use only X-ray and optically selected AGNs. With the X-ray and [O iii] luminosities of these AGNs, we can estimate their bolometric luminosity L_bol and the BHAR from L_bol = $\epsilon \dot{m}{c}^{-2}$, where is the matter-to-radiation efficiency conversion, $\dot{m}$ is the black hole accretion rate, and c is the speed of light. Of the 703 non-merging galaxies with AGNs, 596 are X-ray and/or optically selected AGNs (we use 447 and 149 galaxies with X-ray and optical emission, respectively). For mergers, 12 systems are X-ray-selected AGNs while two merging galaxies are AGNs selected from their [O iii]+Hβ emission. When a merging system or a merging galaxy is selected as an optical- and X-ray-selected AGN, we will use the X-ray emission to measure the bolometric luminosity, because the [O iii] emission is uncorrected by dust attenuation. To perform this correction, a measurement of the Balmer decrement Hα/Hβ is necessary. However, these lines are not available simultaneously for our sources. Bolometric luminosities can be estimated assuming

$$\begin{eqnarray}&&{L}_{\mathrm{bol}}=22.4\,{L}_{{\rm{X}}},\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{L}_{\mathrm{bol}}=3500\,{L}_{[{\rm{O}}{\rm\small{III}}]},\end{eqnarray} \tag{ 10 }$$

where L_X and L_{[O iii]} are the X-ray and [O iii] luminosities, respectively. In X-ray, the bolometric luminosity is obtained by assuming a conversion factor k_bol = 22.4, which is the median value obtained for local AGNs with L_x = 10⁴¹–10⁴⁵ erg s⁻¹ (Vasudevan & Fabian 2007). When X-ray emission is not available, we obtain bolometric luminosities from the [O iii] line assuming the conversion factor of 3500 given in Heckman et al. (2004). This value is obtained for sources non-corrected by dust extinction. Assuming an efficiency of 10% (Marconi et al. 2004), the black hole accretion rate is given by

$$\begin{eqnarray}&&\mathrm{BHAR}[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=0.15\,\displaystyle \frac{{L}_{\mathrm{bol}}}{{10}^{45}},\end{eqnarray} \tag{ 11 }$$

where the bolometric luminosity L_bol is in erg s⁻¹ (Alexander & Hickox 2012). For mergers, we find bolometric luminosities in the range 2.4 × 10⁴³–7.4 × 10⁴⁶ erg s⁻¹ and BHARs of 3.6 × 10⁻³–11.1 M_⊙ yr⁻¹ (median of 0.07 M_⊙ yr⁻¹). For non-mergers, bolometric luminosities are 2.2 × 10⁴²–1.3 × 10⁴⁸ erg s⁻¹ and BHARs are in the range 3.4 × 10⁻⁴–194 M_⊙ yr⁻¹ (median of 0.04 M_⊙ yr⁻¹). For star-forming galaxies, we also measure the BHAR in starbursts and main-sequence galaxies (Table 1) to analyze whether starbursting galaxies have higher black hole accretion rates. We find that starbursting merging galaxies have higher accretion into their black holes compared to non-mergers (starbursts and main sequence) and main-sequence merging galaxies, although precaution has to be taken with this result, due to the poor statistics of starbursts. Figure 7 presents the position of merging and non-merging galaxies in the main-sequence diagram of star-forming galaxies. Galaxies are color-coded by the intensity of the BHARs. The diagram shows that the accretion rate into black holes increases with redshift.

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We investigate the evolution of the relative growth rate of a galaxy and its central black hole at different cosmic times in mergers and non-mergers by measuring the ratio BHAR/SFR as a function of redshift. Figure 8 presents the median values of this ratio for mergers and non-mergers in the redshift range 0.3 < z < 2.5. For non-mergers, we show the median of the ratio in different redshift bins and find an increment with redshift—although not a significant one, given the high dispersion (black squares in Figure 8). The median of the BHAR/SFR ratios in the whole redshift range for non-mergers is 1.9 × 10⁻³ (dashed black line in Figure 8). Since the BHARs obtained from [O iii] luminosities are uncorrected by dust attenuation, we also analyze the ratio by using only the galaxies with BHARs obtained from X-ray emission. The median of the ratio in this case shows no evolution with redshift (orange triangles in Figure 8), similar to the lack of evolution shown in Silverman et al. (2009) for a sample of z ≲ 1 AGNs. However, we find a total median value for the ratio in non-mergers of 8.0 × 10⁻⁴ (dashed–dotted orange line in Figure 8), while Silverman et al. (2009) find 1.9 × 10⁻². This difference might be possible due to the different star formation rate indicators used in the measurements. Silverman et al. (2009) use the [O ii] line, which is known to be a tracer of current star formation activity, while in this work, we use star formation rates obtained from UV+IR, which trace long-term star formation. Because the X-ray AGNs are not resolved in 10 merging systems, we estimate the BHAR/SFR making two assumptions: the merging galaxy with the lowest and then with the highest star formation rate in a system is the AGN source. Differences in the measured values are listed in Table 1. When assuming that the merging galaxy with the highest SFR is the AGN source, we find a median for the BHAR/SFR ratio similar to that in non-mergers (2.4 × 10⁻³ and 1.9 × 10⁻³ for mergers and non-mergers, respectively). These values are similar to the values of the local relation M_BH/M_bulge = 1.5 × 10⁻³ and the value predicted from the simulations of Silk (2013).

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Figure 9 presents the relation between the BHAR and the star formation rate and stellar mass for mergers and non-mergers. We perform linear fits of the type $\mathrm{log}(\mathrm{BHAR})=\alpha \mathrm{log}(x)+\beta$, where x is log(M_⋆) or log(SFR). The slopes in the BHAR versus stellar mass diagram are α = 0.38, −0.23, and 0.45 for mergers/non-mergers with BHARs obtained from the X-ray and/or [O iii] emission (BHAR_{XR+[O III]}) and non-mergers with BHARs from X-ray emission only (BHAR_XR), respectively. The slopes in the BHAR versus star formation rate diagram are α = 0.4, 0.17, 0.19 for mergers/non-mergers with BHAR_{XR+[O III]} and non-mergers with BHAR_XR, respectively. We find no correlation between the BHAR and the SFR and the stellar mass in non-mergers. In mergers, it seems that a correlation exists, but precaution has to be taken with this result, due to the poor statistics and the unresolved emission of the X-ray AGNs. In the Appendix, Figures 10 and 11 show more relations between the black hole accretion rate with the stellar mass and star formation rate.