The role of radio mode AGN feedback on galaxy evolution is still under debate. In this study we utilize a combination of radio continuum observations and optical integral field spectroscopic IFS data to explore the impact of radio AGN on the evolution of their host galaxies at both global and subgalactic scales. We construct a comprehensive radioIFS sample comprising 5578 galaxies with redshift z lt 0.15 by crossmatching the LOFAR TwoMetre Sky Survey LoTSS with the MaNGA survey. We revisit the tight linear radio continuum  star formation relation and quantify its intrinsic scatter then use the relation to classify 616 radioexcess AGN with excessive radio luminosities over that expected from their star formation rate. Massive radio AGN host galaxies are predominantly quiescent systems but the quenching level shows no correlation with the jet luminosity. The mass assembly histories derived from the stellar population synthesis model fitting agree with the cosmological simulations incorporating radiomode AGN feedback models. We observe that radio AGN hosts grow faster than a control sample of galaxies matched in stellar mass and the quenching age  5 Gyr is at larger lookback times than the typical radio jet age lt 1 Gyr. By stacking the spectra in different radial bins and comparing results for radio AGN hosts and their controls we find emission line excess features in the nuclear region of radio AGN hosts. This indicates that radio AGN are ionizing the surrounding interstellar medium in the vicinity of the nucleus. We also find that ongoing star formation in the outer regions of the galaxy is weaker if a radio jet is detected. Our findings support the scenario that the observed presentday radio AGN activity is not responsible for the past quenching of their hosts but may help the host galaxies maintain quiescence through ionizing and heating the surrounding gas.
['Astrophysics - Astrophysics of Galaxies']
The Host Galaxies of Radio AGN New Views from Combining LoTSS and MaNGA Observations
{'The Host Galaxies of Radio AGN: New Views from Combining LoTSS and MaNGA Observations': 'Gaoxiang Jin ( 金 高 翔 ) 1 , Guinevere Kau ff mann 1 , Philip N. Best 2 , Shravya Shenoy 3 , and Katarzyna Małek 4  \n- 1 Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany e-mail: gxjin@mpa-garching.mpg.de\n- 2 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK\n- 3 Centre for Astrophysics Research, University of Hertfordshire, Hatfield, AL10 9AB, UK\n- 4 National Centre for Nuclear Research, Pasteura 7, PL-02093 Warsaw, Poland  \nReceived ???; accepted ???', 'ABSTRACT': 'The role of radio mode active galactic nuclei (AGN) feedback on galaxy evolution is still under debate. In this study, we utilize a combination of radio continuum observations and optical integral field spectroscopic (IFS) data to explore the impact of radio AGN on the evolution of their host galaxies at both global and sub-galactic scales. We construct a comprehensive radio-IFS sample comprising 5578 galaxies with redshift z < 0 . 15 by cross-matching the LOFAR Two-Metre Sky Survey (LoTSS) with the Mapping Nearby Galaxies at APO (MaNGA) survey. We revisit the tight linear radio continuum - star formation relation and quantify its intrinsic scatter, then use the relation to classify 616 radio-excess AGN with excessive radio luminosities over that expected from their star formation rate. Massive radio AGN host galaxies are predominantly quiescent systems, but the quenching level shows no correlation with the jet luminosity. The mass assembly histories derived from the stellar population synthesis model fitting agree with the cosmological simulations incorporating radio-mode AGN feedback models. We observe that radio AGN hosts grow faster than a control sample of galaxies matched in stellar mass, and the quenching age ( ∼ 5 Gyr) is at larger lookback times than the typical radio jet age ( < 1 Gyr). By stacking the spectra in di ff erent radial bins and comparing results for radio AGN hosts and their controls, we find emission line excess features in the nuclear region of radio AGN hosts. This indicates that radio AGN are ionizing the surrounding interstellar medium in the vicinity of the nucleus. We also find that ongoing star formation in the outer regions of the galaxy is weaker if a radio jet is detected. Our findings support the scenario that the observed present-day radio AGN activity is not responsible for the past quenching of their hosts, but may help the host galaxies maintain quiescence through ionizing and heating the surrounding gas.  \nKey words. galaxies: evolution - galaxies: active - radio continuum: galaxies', '1. Introduction': "Much e ff ort over the past decade, both in observations and simulations, has been devoted to the co-evolution of galaxies and their central supermassive black holes (SMBHs). One of the first pieces of evidence leading to this investigation was the tight correlation between the masses of SMBHs and the stellar velocity dispersion of their host galaxies and bulges (e.g., Magorrian et al. 1998). Additional indirect evidence supporting the co-evolution scenario is the observation that the cosmic growth history of SMBHs and the galaxy population is quite similar (e.g., Silverman et al. 2008). They both peak at redshift z ∼ 2 and decline rapidly after z ∼ 1 (see Madau & Dickinson 2014, for a review). These observational results indicate that there are physical processes linking the growth of the SMBHs and their host galaxies, even though their sizes di ff er by orders of magnitude (pc versus kpc). However, the SMBH-galaxy co-evolution picture is still not fully understood in detail.  \nAccreting SMBHs are known as active galactic nuclei (AGN), and they are often very luminous with emission across the full spectral energy distribution (SED) (see Padovani et al. 2017, for a review). These features are believed to arise from energy produced by matter that is accreting onto the central SMBH. This matter may reside in an accretion disk and give rise to very strong broadened emission lines from photo-ionized gas (BLR,  \ne.g., Baldwin 1997), a warm dusty torus contributing to near-tomid infrared continuum (e.g., Barvainis 1987), outer photoionized gas emitting high excitation narrow lines (NLR, e.g., Baldwin et al. 1981), and a corona surrounding the accretion disk that contributes more radiation in X-rays (e.g., Sun & Malkan 1989). There may also be radio jets created by relativistic charged particles (e.g. Begelman et al. 1984).  \nThe term AGN feedback describes the impact of AGN on the evolution of their host galaxies. A negative feedback scenario is widely favoured, in which the energy from accreting material can heat or eject the gas in the host galaxies, and then prevent star formation globally (e.g., Fabian 2012, and references therein). For most numerical and semi-analytic simulations, negative AGN feedback is crucial in massive halos to prevent galaxies from growing too massive (e.g., Di Matteo et al. 2005; Croton et al. 2006). On the other hand, the observed AGN-starburst connection in Type II Seyfert galaxies and infrared AGN indicate that positive AGN feedback may also exist (e.g., Heckman et al. 2004). The outflows and shocks from AGN may also create dense gas regions and boost star formation (e.g., Salomé et al. 2015; Schutte & Reines 2022). Alternatively, the correlation between AGN activity and star formation may arise because star formation and SMBH accretion share a common gas supply (e.g., Dai et al. 2018; Li et al. 2024). Recent theoretical models  \nsuggest that the dominant feedback mode transitions from positive to negative as redshift decreases (e.g., Silk et al. 2024).  \nIn this paper, we focus on the AGN with radio jet features, known as radio AGN. For this population, kinetic (or jet, radio) mode is considered as the main feedback mechanism. These AGN mainly output mechanical energy through powerful radio jets, heat the surrounding gas, and produce weak emission lines in the interstellar medium of the host galaxy (e.g., Heckman & Best 2014). Radio AGN are more likely to be found in massive elliptical galaxies (Best et al. 2005a), and in group or cluster environments (Croston et al. 2019) than AGN that emit most of their energy in the optical or UV. They usually have low black hole accretion rates and are lack of dusty torus near the black hole (Heckman & Best 2014). In galaxy-scale simulations, various AGN jet models have been found, in principle, to be capable of quenching a galaxy and preventing gas from cooling at the centers of dark matter halos (e.g., Dubois et al. 2010; Yang & Reynolds 2016). However, the challenge remains to connect the critical free parameters in these simulations to observational data.  \nRadio AGN themselves have diverse observational properties. They are historically divided into Fanaro ff & Riley (FR, Fanaro ff & Riley 1974) types by radio morphology, where in general FR I, FR II, and FR0 (Garofalo & Singh 2019) represent 'edge-brightened', 'edge-darkened', and compact jets, respectively. Recent works suggested that the excitation properties may be more fundamentally connected to the SMBH accretion rate than the morphology (e.g., Best & Heckman 2012). Radio AGN with strong optical emission lines (e.g., [O iii ] λ 5008) are classified as high-excitation radio galaxies (HERGs) with ongoing star formation activity in their hosts. The other population without strong emission lines are called low-excitation radio galaxies (LERGs).  \nThe radio flux of normal star-forming galaxies with no AGN is dominated by the synchrotron continuum emitting from relativistic particles moving through magnetic fields. These particles are mainly accelerated by supernova (Biermann 1976) and SMBH accretion. The incidence of supernovae is related to the birth rate of short-lived, high-mass stars ( M > 8 M ⊙ ), which is thought to be the origin of the tight correlation between star formation rate (SFR) and radio luminosity (hereafter radio-SFR relation). The radio-SFR relation was first observed through the constant ratios of radio and far-infrared luminosity in SFGs (e.g., de Jong et al. 1985; Condon et al. 1991), and has also been confirmed by diverse tracers of SFR (e.g., Wang et al. 2016; Brown et al. 2017; Gürkan et al. 2018; Smith et al. 2021; Heesen et al. 2022; Best et al. 2023; Das et al. 2024, Shenoy et al. in prep). Most radio AGN classification methods are based on the excessive total radio luminosities compared to the star formation properties. Thus, the excess of radio luminosity compared to the star formation rate is used to derive the luminosity of the radio AGN jet. There are also other approaches to classification using infrared colors and spectral indices (e.g., Sabater et al. 2019, and reference therein), but these methods cannot quantitatively decompose the radio contribution from star formation and AGN jets.  \nOur current knowledge about the population of radio AGN is based on several all-sky radio continuum surveys at 1.4 GHz, such as the NRAO Very Large Array Sky Survey (NVSS, Condon et al. 1998) and the Faint Images of the Radio Sky at TwentyCentimeters (FIRST, Becker et al. 1995). In the low-redshift universe ( z < 1), the sensitivity of these surveys probes radio AGN with luminosities greater than L 1 . 4GHz ∼ 10 23 WHz -1 .  \nThe new generation of radio telescopes and instruments, such as the LOw-Frequency ARray (LOFAR, van Haarlem et al. 2013), the Australian Square Kilometre Array Pathfinder (ASKAP, Hotan et al. 2021), MeerKAT (Jonas & MeerKAT Team 2016), etc., are now able to discover much fainter radio AGN. The LOFAR Two Meter Sky Survey (LoTSS, Shimwell et al. 2017) is one of the deepest ongoing radio continuum largesky surveys, which aims to observe the whole northern sky at frequencies 120-168 MHz. Compared to NVSS and FIRST at 1.4 GHz, LoTSS observes at lower frequencies, which are more sensitive to old, di ff use synchrotron emission and less a ff ected by the dust continuum thermal emission (e.g., Penney et al. 2020). For a extragalactic source with a typical radio spectra index, it is also about one order deeper than NVSS and FIRST, and sensitive enough to detect faint radio sources which are mainly star-forming galaxies (SFGs) at low redshifts (Williams et al. 2019; Hardcastle et al. 2023).  \nTo study the properties of radio AGN host galaxies, we need observations at wavelengths where emission from the stellar component and interstellar medium (ISM) become dominant. The optical integral field unit (IFU) technology is particularly useful to study star formation and stellar populations of galaxies. Spatially resolved galaxy properties, which are not measurable in single-fiber spectroscopic surveys, are now available from IFU observations. Within the sky coverage of LoTSS, Mapping nearby Galaxies at Apache Point Observatory (MaNGA, Bundy et al. 2015) is the largest optical IFU survey that has been completed. MaNGA includes spatially resolved spectroscopic observations of about ten thousand galaxies, from which we can build a statistically significant sample of radio AGN host galaxies. The data available for MaNGA galaxies also include classifications of morphology and environment, and we can thus investigate whether these parameters a ff ect radio AGN properties.  \nThe combination of LoTSS and MaNGA allows us to investigate radio AGN feedback on sub-galactic scales, particularly for faint radio AGN. The latest public data release, LoTSS-DR2, and the half MaNGA sample (DR16), were used by Mulcahey et al. (2022) to build a sample of 307 radio AGN and to compare the star formation, ionization maps, and age gradients of radio AGN hosts with control galaxies without radio AGN. It was found that radio AGN are generally quiescent, but are not more quenched than their controls. The authors concluded that radio AGN help host galaxies maintain quiescence but are not responsible for switching o ff star formation completely. Using a similar sample, Zheng et al. (2023) studies the stellar kinematics of radio AGN host galaxies. They found that the low angular momentum is important for galaxies to host luminous radio AGN.  \nIn this paper, we will update the sample using the final MaNGA data release (Abdurro'uf et al. 2022), which includes ∼ 6000 galaxies falling within the LoTSS-DR2 sky footprint. This roughly doubles the size of the radio AGN sample compared to Mulcahey et al. (2022). Firstly, we aim to utilize this currently largest IFU-radio sample to provide an improved derivation of the radio continuum - SFR relation and its intrinsic scatter. Because MaNGA provides full-coverage H α maps with dust attenuation information from the Balmer decrement, we can overcome the limitation of single fiber observations that only offer nuclear spectroscopic information for low-redshift galaxies. This also allows the radio continuum - SFR relation can be better constrained. Based on this relation, the excess radio luminosity compared to the prediction from its star formation rate is a physical and reliable criterion to classify radio-excess AGN (hereafter referred to as RDAGN). This relation to also be used to decom-  \ne the star formation and AGN contributions to the total radio flux, i.e., to calculate the jet luminosities (or upper limits).  \nWith this RDAGN host galaxy sample in hand, we then aim to study star formation in the RDAGN hosts and to investigate how the radio jets a ff ect the sub-galactic properties of their hosts. MaNGA provides maps of the optical spectra (3600 - 10300 Å) out to 1.5 × e ff ective radius Re . The emission and absorption lines can be used to analyze the properties of the ionized interstellar medium (ISM) and resolved stellar populations within the host galaxy. We also use results derived from the full spectrum fitting method (Wilkinson et al. 2017) to analyze the star formation histories (SFH) in di ff erent regions of the host galaxies.  \nThe structure of this paper is as follows. In Section 2, we introduce the LoTSS-MaNGA parent sample cross-matching and the calculation of physical parameters. In Section 3, we build the radio continuum - SFR relation and use it to build RDAGN and control samples. In Section 4, we examine the global star formation in RDAGN hosts. Additionally, we analyze the spatially resolved mass assembly history and emission line features of these hosts in di ff erent radial bins. We discuss the main results and the implication of our study as well as the future outlook in Section 5. Section 6 contains an overall summary of our main results.  \nThroughout this paper, we convert all radio luminosity and related relations to rest-frame 144MHz assuming a power spectra index α = -0.7 (Condon et al. 2002): L ν 1 / L ν 2 = ( ν 1 /ν 2) -0 . 7 . We adopt a flat cosmology with H 0 = 70 km s -1 Mpc -1 , Ω m = 0 . 3, and ΩΛ = 0 . 7. All stellar masses and starformation rates are based on the Chabrier initial mass function (Chabrier 2003). When comparing literature results based on di ff erent IMFs, we follow Madau & Dickinson (2014) and set the factor (for stellar masses and star formation rates) as Salpeter : Kroupa : Chabrier = 1 : 0.67 : 0.63.", '2.1. MaNGA': "MaNGA is part of the Sloan Digital Sky Survey IV (SDSS-IV, Bundy et al. 2015), and is the largest completed IFU survey. The final data products are released in SDSS DR17 (Abdurro'uf et al. 2022), which consist of ∼ 10 000 unique galaxies with good quality IFU coverage out to at least 1.5 times the r -band e ff ective radius ( Re ). MaNGA galaxies are selected from the NASA-Sloan Atlas catalog 1 (NSA, Blanton et al. 2011; Wake et al. 2017), and thus have measurements of many physical parameters based on the UV-optical photometric data, such as absolute magnitude, e ff ective radius, position angle, etc. We adopt the global stellar mass from the NSA catalog to avoid having to correct for the fact that the MaNGA IFU sizes vary. The stellar masses are based on the stellar population synthesis model fitted from FUV to z band photometry (Blanton & Roweis 2007). The redshift distribution of the sample is 0-0.15 and peaks at z ∼ 0 . 03, while the stellar mass distribution is designed to have a flat distribution between 10 9 -10 11 M ⊙ (Wake et al. 2017). The IFU cubes have r -band FWHM of ∼ 2.5 arcsec and cover 3600 - 10300 Å with a spectral resolution of R ∼ 2000 (Smee et al. 2013). We note that the MaNGA sample will under-sample at the faint end ( r -band absolute magnitude larger than -19, Ste ff en et al. 2023), but this does not a ff ect the main results in this paper since our radio AGN sample are dominated by massive galaxies (see Section 4.1).  \nAll the spatially resolved optical spectra used in this paper are obtained from the MaNGA Data Analysis Pipeline ( DAP , Westfall et al. 2019; Belfiore et al. 2019). Emission line, absorption line, and kinematic measurements in this paper are taken either directly from DAP-MAPS images or fitted from the DAP-LOGCUBE spectra.  \nThe global star formation rates are calculated from the attenuation- and AGN-corrected H α luminosity using the relation suggested by Kennicutt & Evans (2012): SFR (M ⊙ yr -1 ) = L H α SF (erg s -1 ) × 10 -41 . 30 . For dust attenuation, we use the Balmer decrement assuming the Case B recombination (Osterbrock 1989) and the reddening curve from Calzetti et al. (2000): L H α = L H α, obs × [(H α/ H β )obs / 2 . 86] 2 . 6 . The AGN contribution to L H α is estimated by a re-projected optical diagnostic diagram proposed in Ji & Yan (2020), which uses the line ratios [N ii ] / H α , [S ii ] / H α , and [O iii ] / H β . The empirical relation can be found in equation 6 of Jin et al. (2021). This step does not a ff ect the star forming galaxy sample used in Section 3.1. For RDAGN sample, the AGN contribution correction changes about -0.2 dex (median value) on the SFRs, while their SFRs are about -2.3 dex below the star formation main sequence, thus this correction does not a ff ect the discussions in Section 4.1 about the global quenching of RDAGN host galaxies.  \nWe build the spatially resolved star formation histories based on the non-parametric, full spectra fitting results from the Firefly-VAC (Goddard et al. 2017; Neumann et al. 2022). The stellar population models (Maraston et al. 2020) used for fitting are from the MaNGA Stellar library of Milky Way stellar spectra ( MaStar , Yan et al. 2019). These models are also used in the DAP and have matched spectral resolution with the galaxy spectra since they are observed by the same instrument. The age grids of MaStar models used in fitting can help us build the mass assembly history of a given spatially resolved region with a precision of at least 1 Gyr.", '2.2. LoTSS': 'The LOFAR Two Meter Sky Survey (LoTSS) is an ongoing deep wide area radio wavelength imaging survey (Shimwell et al. 2017). It aims to observe the whole northern sky at frequencies 120-168 MHz. The expected root-mean-square (RMS) sensitivity and spatial resolution are ∼ 100 µ Jy (at favorable declinations) and 6 arcsec, respectively. The latest data release, LoTSS-DR2 (Shimwell et al. 2022), covers a 5634 square degrees sky area. We refer the readers to Shimwell et al. (2022) for details about the data reduction. In summary, LoTSS-DR2 provides well-calibrated 6 arcsec resolution mosaic images. Additionally, it includes a catalog of approximately 5 million radio sources created by the Gaussian-fitting-based radio source extraction code PyBDSF (Mohan & Ra ff erty 2015).  \nIn this paper, we use the source positions, flux density and spatial size from a value-added catalog with optical host galaxy identification information (hereafter LoTSS-VAC, Hardcastle et al. 2023). The host galaxy identification is based on a likelihood-ratio cross-match method described in Williams et al. (2019), as well as visual classifications from the citizen science project, Radio Galaxy Zoo: LOFAR 2 . The total flux density and morphological parameters have been examined, and where necessary corrected, in the host identification steps. This correction is necessary for deep radio observations in the MaNGA redshift range, because many radio galaxies have large sizes or di ff use emissions, creating large radio-optical o ff sets which will a ff ect  \nz  \nFig. 1. Radio luminosity and upper limits of LoTSS-MaNGA sample versus their redshift. Blue dots show radio luminosities with errors for the LoTSS detections. Red arrows represent the upper limits of the radio luminosity for LoTSS non-detected galaxies. Solid line, dashed, and dash-dotted lines represent the 90% completeness sensitivity limits of LoTSS (Shimwell et al. 2022), FIRST (Becker et al. 1995), and NVSS (Condon et al. 1998), respectively.  \n<!-- image -->  \nthe traditional cross-matching method based on source separations. Furthermore, the erroneous segregation of a single radio galaxy into multiple components will result in the radio flux density being significantly underestimated. For the LoTSS-MaNGA matched sample used in this paper, the LoTSS-VAC recovers 44 radio galaxies missed in the raw PyBDSF catalog and corrects the flux density of 157 galaxies, which means that the raw catalog would have lost ∼ 8% accuracy.', '2.3. LoTSS-MaNGA parent sample': "Our analysis sample includes all z > 0 . 01 MaNGA galaxies (to ensure a large enough IFU field of view) with LoTSS observations. Galaxies outside the LoTSS sky coverage or in the badquality sky areas are excluded based on the mosaic images, leaving us with 5687 MaNGA galaxies covered by LoTSS DR2. We match the MaNGA galaxy positions with the galaxy positions in LoTSS-VAC (i.e., the positions for the identified host galaxy, not the radio positions) within a radius of 9 arcsec (1.5 × beamsize and smaller than MaNGA IFU). This process results in 2655 detections (47%) with radio flux density and size measurements. We also visually check all the radio and optical images to exclude 109 (2%) galaxies with severe background source blending or having insu ffi cient MaNGA coverage (IFU coverage is too small). For 2923 (51%) non-detections, we measure the median RMS flux within a 12 arcsec diameter aperture around the MaNGApositions in LoTSS images. We adopt 8 times the RMS flux density in one beam ( F RMS) as a secure flux density upper limit for each non-detection, since the catalog source completeness at this cut level reaches more than 95% (Hale et al. 2024).  \nWe calculate the rest-frame 144MHz luminosity or upper limit using the formula L 144MHz = F LoTSS × 4 π D 2 L × (1 + z ) ( -α -1) ,  \nwhere DL is the luminosity distance, z is the galaxy redshift from MaNGAobservation, and α is assumed radio power-law index (0.7, see Section 1). F LoTSS is the total flux density from LoTSSVAC for detections, or 8 × F RMS for non-detections. This restframe conversion only correct ∼ 2% of the value at MaNGA's peak redshift z ∼ 0 . 03, which is smaller than the level of most flux density errors, thus does not a ff ect our analysis and results.  \nFig. 1 shows how the radio luminosity detection threshold varies with redshift for our sample of MaNGA galaxies with LoTSS-DR2 overlap. Blue dots represent LoTSS-detected galaxies and red upper limits are non-detections. The rest-frame 144MHz luminosity varies between 10 20 -10 26 WHz -1 . LoTSS DR2 reaches 90% completeness at ∼ 0.8 mJy (Shimwell et al. 2022), resulting a limit of L 144MHz ∼ 5 × 10 22 WHz -1 at z = 0 . 15. We note that the exact limiting sensitivity also depends on the sky position, which causes the dispersion for the upper limits in Fig. 1. As a comparison, 72% and 41% of LoTSS detections will fall below the detection limits of NVSS (dashed line, Condon et al. 1998) and FIRST (dash-dotted line, Becker et al. 1995), respectively.", '3.1. The L 144MHz -SFR relation': 'As mentioned in Section 1, synchrotron continuum luminosity is tightly correlated with the star formation rate in SFGs. Using LoTSS data, the radio-SFR relation has been investigated based on di ff erent SFR tracers and over di ff erent spatial scales. For example, Gürkan et al. (2018), Smith et al. (2021), and Best et al. (2023) used SFRs from SED-fitting for SFG populations out to z ∼ 1, while Heesen et al. (2022) used SFRs converted from total infrared luminosity for resolved local group SFGs. Shenoy et al. (in prep) used both SED-fitted SFRs as well as integrated H α derived SFRs. Up to now, there has been no relation derived from IFU-based H α SFRs, despite the higher accuracy of this method. Taking advantage of the high-quality H α maps from MaNGA, we derive and examine this radio-SFR relation for our LoTSSMaNGAsample, and then use this relation to select radio-excess AGN (or RDAGN for short).  \nThe details of how we derive this relation can be found in Appendix A. In brief, we select a pure star-forming galaxy sample without AGN contamination of both the H α and radio continuum luminosities in two steps. Firstly we use the widely known emission line diagnostic diagrams (e.g., Kau ff mann et al. 2003) to select galaxies where the H α emission is dominated by H ii regions. The emission lines used in this classification are measured from the MaNGA spectra. We also perform visual classification of the LoTSS images of these star-forming galaxies and remove those with jet-like or extended radio emission that is clearly larger than the galaxy. Our L 144MHz-SFR relation is then derived by performing a linear fit to the rest-frame 144MHz luminosities and SFRs, inspired by the e ff orts in Gürkan et al. (2018). The intrinsic errors σ I of this relation are determined using the emcee (Foreman-Mackey et al. 2013) Markov chain Monte Carlo (MCMC) method.  \nOur derived radio-SFR relation can be expressed as Equation 1.  \nlog( L 144MHz WHz -1 ) = 1 . 16 × log( SFR M ⊙ yr -1 ) + 21 . 99 ± 0 . 23 (1)  \nFig. 2 shows that our results generally agree with previous low redshift relations based on di ff erent samples. For comparison, Brown et al. (2017) (blue line) used shallow TGSS sample with  \nFig. 2. The correlation between rest-frame 144MHz luminosity and SFR. Black dots with errors are the pure star-forming galaxies used for linear fitting. These SFGs are selected based on optical line diagnostic and radio image visual classification (see Appendix A for details). The SFRs are integrated from MaNGA H α maps and corrected for dust attenuation as mentioned in Section 2.1. Red solid lines are the MCMC linear fitting results. Intrinsic errors, ± 3 σ I, are shown in red dashed lines. Blue, cyan, green, and orange dashed lines are the linear fitting results in Brown et al. (2017), Smith et al. (2021), Heesen et al. (2022), and Best et al. (2023), respectively. Our result is in good consistency with most literature results.  \n<!-- image -->  \nSFRs from single fiber H α ; Smith et al. (2021) (cyan line) and Best et al. (2023) (orange line) used a sample with deep radio observations and SFRs from multi-wavelength SED fitting; and Heesen et al. (2022) (green line) used a sample of local galaxies with SFRs measured from total infrared luminosities. Our results suggest an intrinsic scatter of σ I ∼ 0 . 23 dex in this relation, consistent with other LoTSS samples (e.g., Smith et al. 2021; Cochrane et al. 2023). The slope is larger than one, which supports the prediction of calorimetry models (e.g., Chi & Wolfendale 1990). This relation was found to also depend on the stellar mass (e.g., Smith et al. 2021; Heesen et al. 2022, Shenoy et al. in prep). Since the mass dependence is weak and more significant in low-mass systems (Das et al. 2024), we do not include the mass parameter in our fitting.', '3.2. Radio-excess AGN and their jet luminosities': 'We classify a MaNGA galaxy as a radio-excess AGN host if its L 144MHz is at least 3 σ higher than the L 144MHz predicted by its SFR and Equation 1. Considering the uncertainty of these measurements, the classification can be expressed as follows: log( L 144MHz) > 1 . 16 × log(SFR) + 21 . 99 + 3 σ I. This method results in a new sample of 616 (11%) radio AGN hosts among 5578 LoTSS-MaNGA galaxies. Other detections and non-detections are considered as galaxies without secure evidence of radio excess (hereafter referred to as \'normal galaxies\' for convenience)."  \nWe also calculate the radio jet luminosity L AGN by subtracting the star formation contribution from the total radio luminosity: L AGN = L observed 144MHz -L SFR 144MHz , where L SFR 144MHz is the 144MHz lu-  \nFig. 3. Radio AGN classification for the whole LoTSS-MaNGA sample. Black solid and dashed lines are the radio-SFR relation (Equation 1) and the 3 σ I limit, respectively. Detections with observed L 144MHz larger than the limit are classified as radio-excess AGN (red stars). Other detections (blue) and non-detections (gray) are considered as radio normal galaxies with an upper limit of jet luminosity. We plot the matched radio AGN classified in Best & Heckman (2012) and Comerford et al. (2020) as a comparison (green stars). Our sample includes more low luminosity radio AGN and can distinguish some high SFR SFGs, and 77% of radio AGN in our sample are newly classified.  \n<!-- image -->  \nminosity predicted by Equation 1. The error on the L AGN, σ L AGN estimate is derived from the observed uncertainty in L observed 144MHz and the uncertainty in L SFR 144MHz , and thus includes both σ SFR and σ I. It is important to note that some star-forming galaxies (SFGs) may have negative L AGN values if they lie below the radio-SFR relation. This is not physical and to address this, we adopt 3 × σ L AGN as the upper limit of L AGN for these systems. We note that the high SFR SFGs will then have higher L AGN upper limits. For non-detections, the upper limit of L AGN is set equal to the upper limit of L 144MHz. The consequences of these selection e ff ects are discussed in Section 5.1.  \nThere are two existing MaNGA radio AGN samples in the literature (Comerford et al. 2020; Mulcahey et al. 2022). The key improvements that we have implemented in this work are, 1) classifying AGN based on the self-consistent MaNGA-derived L 144MHz-SFR relation, 2) including new measurements of L AGN as well as upper limits in the case of non-detections. Our sample is therefore better suited to select a non-radio AGN control sample with quantified L AGN (or upper limits) and is more accurate at distinguishing some high SFR, radio-luminous SFGs from RDAGN. Compared to Comerford et al. (2020), where the sample is matched to the NVSS / FIRST selected radio AGN catalog (Best & Heckman 2012), the new deep LoTSS observations that include many more star-forming galaxies allow us to use the more physical L 144MHz-SFR selection rather than the L 1 . 4GHzDn4000 classification proposed in Best et al. (2005b). In Mulcahey et al. (2022), the radio AGN sample is selected from LoTSS DR2, but the radio classification uses an empirical relation based on a non-IFU sample (Sabater et al. 2019).  \nFig. 3 illustrates our radio AGN classification for the entire LoTSS-MaNGA sample. Detections above the 3 σ I limit  \nare classified as radio-excess AGN (red), while other detections (blue) and non-detections (gray) are classified as normal galaxies with an upper limit for jet luminosity. We also show the radio AGN classified in Best & Heckman (2012) using NVSS and FIRST data, i.e., the Comerford et al. (2020) sample (green stars), demonstrating not only that our sample probes radio AGN to significantly lower luminosities, but also that some high SFR SFGs may be misclassified as AGN using their methods. 77% of radio AGN in our sample are newly classified.', '3.3. Control sample selection': 'It is well-established that galaxy age and star formation rate (SFR) are strongly correlated with stellar mass (e.g., Gallazzi et al. 2005; Guo et al. 2015). To evaluate possible di ff erent star formation histories of radio AGN host galaxies, it is essential to construct mass-controlled samples for comparison. For each radio AGN host, we create a control sample consisting of normal galaxies (no confirmed radio excess) that meet the following criteria:  \n- -Jet luminosity: upper-limit( L control AGN ) < 0 . 2 × L AGN\n- -Stellar mass: | log( M AGN ∗ / M control ∗ ) | < 0.3\n- -Physical e ff ective radius: | log( R AGN e / R control e ) | < 0.2\n- -Angular diameter distance: | log( D AGN A / D control A ) | < 0.2  \nThese criteria are set to select as many control sample as possible while considering the uncertainty level of the measurements.  \nSince radio AGN tend to be more massive than normal galaxies, there are typically more less-massive galaxies available in the control sample for a given AGN. To maintain a roughly equal median stellar mass between the AGN and control samples, for each AGN we select an equal number of more massive galaxies and less massive galaxies that meet the above criteria. Out of the 616 radio AGN, only three lack any control galaxies that meet these criteria and are discarded.  \nThe left panel of Fig. 4 illustrates the comparison of the stellar masses of each radio AGN ( M AGN ∗ ) and the mean stellar masses of their control samples ( M control ∗ ). 469 (77%) radio AGN have at least four control galaxies. Most radio AGN hosts exhibit matched stellar mass with their control samples. We also plot a similar comparison for the redshift and 90% light radius in Fig. 4, which shows that the RDAGN share consistent properties with their control sample. In the left panel of Fig. 4, the few dots with slightly larger M AGN ∗ -M control ∗ o ff sets are the radio AGN hosts with only one control galaxy. These galaxies constitute a small fraction (14%), and their o ff sets are less than 0.3 dex, thus not significantly impacting the scientific results of this study.  \nWe do not constrain the control sample to have similar SFR with the RDAGN hosts, because our focus is on the star formation history dating back to the the quenching of radio AGN host galaxies. Therefore, SFR is considered a free parameter. Nevertheless, the median di ff erence in SFR between radio AGN hosts and their control sample is only ∼ 0.23 dex, which is marginal compared to the standard deviation of the radio AGN SFRs ( ∼ 1 dex).', '4.1. Radio AGN prefer massive quiescent hosts': "Fig. 5 illustrates the global star formation rate of our RDAGN sample. The majority of RDAGN hosts (represented by red stars) are situated below the star-forming galaxy main sequence  \n(SFMS, depicted by the black solid line). Galaxies below the 3 σ SFMS lower limit of the SFMS are defined as 'quenched', as they have transitioned from the SFMS to the quiescent population. Notably, the RDAGN hosts are predominantly composed of quenched galaxies (567 of 616, 92%). Furthermore, we investigated the occurrence of RDAGN in the quenched galaxy population. As shown in the upper panel of Fig. 5, the fraction of RDAGN among all quenched galaxies, f RDAGN, exhibits an increasing trend with stellar mass, reaching at least 50% at M ∗ ∼ 10 11 . 5 M ⊙ . We note here that this fraction f RDAGN can only be considered as a lower limit at the LoTSS sensitivity, because LoTSS is still not deep enough to confirm if some weak radio excess exists in these non-detected galaxies. Deeper radio continuum surveys in the future will probe fainter radio AGN.  \nThese results are consistent with our current knowledge about RDAGN in the local universe. Previous studies have indicated a preference for RDAGN to be hosted in massive, old, and elliptical galaxies (Best et al. 2005a). Recent LOFAR data also suggest that all the M ∗ > 10 11 M ⊙ massive galaxies have a RDAGN inside (Sabater et al. 2019). The fraction observed in our sample is considerably smaller (41%), but is still reasonable considering that we use very di ff erent RDAGN classifications and the fraction definition compared to theirs. These results all suggested that the radio AGN hosts currently have old stellar populations and have a early and fast assembly history, which we will investigate in detail in Section 4.2.  \nIn Fig. 6, we explore if there is a relationship between global quenching and the power of radio jets. We quantify the degree of quenching by measuring how far galaxies lie below the SFMS: ∆ log(SFR) = log(SFRobserved) -log(SFRSFMS), i.e. smaller (more negative) ∆ log(SFR) indicates a more quenched galaxy. Galaxies below the 3 σ threshold of the SFMS (the green dashed line) are classified as quenched. The upper panel of Fig. 6 displays the fraction of quenched galaxies among all RDAGN hosts ( f quenched) across di ff erent L AGN bins. Due to the limits of L AGN measurements, our sample is complete only when the RDAGN are more luminous than ∼ 10 24 W , Hz -1 . At this jet luminosity, ∼ 95% (140 out of 147) of RDAGN host galaxies are quenched, indicating that nearly all hosts of luminous RDAGN are quenched. For less luminous RDAGN, the range of f quenched (the shadow region in the upper panel) is determined by considering two extreme assumptions. First, as the lower limit that all L AGN upper limits indicate that their hosts do not host RDAGN. Second, as the upper limit that all hosts host radio jets with L AGN below the upper limits. Even under the first assumption, the fraction remains at least ∼ 50% down to AGN luminosities of ∼ 10 23 WHz -1 . These fractions support the hypothesis that there are connections between the existence of RDAGN and the quiescence of their hosts. However, the Pearson coe ffi cient between ∆ log(SFR) and L AGN is approximately -0.1, indicating that the quenching level is irrelevant to the radio AGN power.  \nWe note that there are some galaxies with L AGN upper limits in Fig. 6 (blue arrows). This is because star formation dominates the total radio luminosity in those galaxies, making it hard to classify weak radio AGN based on radio luminosity. For these galaxies, the LoTSS sensitivity is no longer the limitation to confirm if there is radio AGN activity. Higher resolution star formation and radio continuum maps would be needed to decompose the AGN jets from star formation at sub-galactic scales.  \nIn summary, quiescent galaxies dominate the RDAGN hosts, with f quenched increasing with L AGN while ∆ log(SFR) shows no correlation with L AGN. These results suggest that radio AGN feedback is more likely to maintain galaxy quiescence rather  \n<!-- image -->  \n<!-- image -->  \nFig. 4. Left panel: The stellar mass of each radio AGN host, M AGN ∗ , compared to the mean stellar mass of its control sample, M control ∗ . The black dashed line is the 1:1 relation. M control ∗ matches with M AGN ∗ for most galaxies. A few galaxies with only one control galaxy have slightly larger o ff sets, but our scientific results are not a ff ected. The middle and right panels show similar comparisons for the redshift and 90 percent light radius. Both parameters are also well controlled.  \n<!-- image -->  \nFig. 5. The main panel is the SFR versus stellar mass diagram for the LoTSS-MaNGA sample. Background gray-scale density map shows the bimodal distribution of star formation main sequence and the quenched population. Radio AGN are plotted as red stars while galaxies without confirmed radio excess (normal galaxies) are plotted as blue dots. The black solid line is the star formation main sequence (SFMS). Galaxies below the 3 σ SFMS lower limit of SFMS (black dashed line) are considered as 'quenched'. Radio AGN host galaxies are dominated by massive and quenched populations. The upper panel shows the fraction of radio AGN in all quenched galaxies. The fraction increases with stellar mass to > 50% at high mass end (10 11 . 5 M ⊙ ).  \n<!-- image -->  \nthan drive the galaxy quenching from the SFMS, which is consistent with Mulcahey et al. (2022).  \n'Radio-mode' AGN feedback is believed to be necessary to regulate the cooling flows in dense cluster environment and help massive galaxies maintain quiescent (e.g., Fabian 2012). Radiomode AGN feedback models have been implemented in cosmological hydrodynamical simulations, where the existence of jet mode feedback is crucial for preventing galaxies from becom-  \nf  \nFig. 6. The main panel presents the quenching level ( ∆ SFR compared to the main sequence SFR at the same stellar mass) of MaNGA galaxies as a function of their radio AGN luminosities (or the upper limits). The L AGN upper limits of non-detections and are plotted as gray arrows. The upper limits of non-RDAGN detections are calculated based on the star formation contribution to the total radio luminosity and are shown in blue arrows. Below the green line (3 σ lower than the SFMS) are quenched galaxies. The lack of galaxies in the upper right panel indicates that almost all the hosts of luminous radio AGN are quenched. At L AGN > 10 23 WHz -1 , the fraction of radio AGN hosts that are quenched galaxies, f quenched, increases with L AGN from ∼ 50% to 100%, as shown in the upper panel. The uncertainty shown as the gray region is due to the L AGN limits. ∆ log(SFR) shows no correlation with L AGN (Pearson correlation coe ffi cient ρ ∼ -0 . 11).  \n<!-- image -->  \ning too massive (Torrey et al. 2014). Because the jets dump most of their energy at large distances from the galaxy and because the radio jet power varies on very short timescales compared to the cooling time of the gas in dark matter halos, the luminosity of the jet may not correlate very strongly with the star  \nFig. 7. Mass assembly across the cosmic lookback time for di ff erent regions of RDAGN hosts and their controls. Solid red lines are the median SFHs of radio AGN hosts and the blue dashed lines are for their control samples' median. We also plot the average mass assembly history of galaxies with halo masses of 10 13 M ⊙ from the Illustris simulation (Rodriguez-Gomez et al. 2016). Although the simulation relation is for the total stellar mass, it is kept fixed in all the panels for reference. Panels from left to right are the results for the regions of the whole galaxy, 0-0.5 Re , 0.5-1 Re , and 1-1.5 Re , respectively. RDAGN hosts formed faster than their controls at all radii, especially in the central region. Our spectra-fitted total mass assembly history is reasonably matched by the cosmological simulation which incorporates the radio AGN feedback model.  \n<!-- image -->  \nformation rate in the galaxy. In addition, several observational studies have found weak correlations between the radio jet luminosity and both the kinetic power of the jet and the SMBH accretion rate (e.g., Fabian 2012; Russell et al. 2013), suggesting that the energy transfer from radio jets to surrounding gas is ine ffi cient. These factors may explain why the radio luminosity of our RDAGN sample is irrelevant to the quenching level of the host galaxy.", '4.2. Radio AGN host galaxies quenched earlier': "In this subsection, we investigate the mass assembly history of the RDAGN host galaxies. It has been widely argued in simulations that negative AGN feedback e ff ects are necessary to halt the growth of massive galaxies (e.g., Kau ff mann & Haehnelt 2000; Springel et al. 2005; Schaye et al. 2015; Nelson et al. 2019). If negative feedback is universally present in real galaxies, we should observe AGN-related suppression of star formation in the star formation histories (SFHs) of galaxies.  \nAs mentioned in Section 2.1, we employ the full-spectrum fitting method to obtain radially-resolved non-parametric SFHs. In Section 4.1 we demonstrated that RDAGN hosts are mostly massive quiescent galaxies, with predominantly old stellar populations that are insensitive to recent star formation. To better illustrate the SFHs, we derive the mass accumulation history instead of the SFR history by quantifying the fraction of a galaxy's stellar mass that was formed at di ff erent lookback times. We construct the mass assembly histories for each RDAGN host and their control galaxies in three radial bins: 0-0.5 Re to represent the unresolved central regions, 0.5-1 Re for the middle regions, and 1-1.5 Re for the outskirts. The mass assembly history of individual galaxies can be somewhat uncertain, so we combine them to compare the average di ff erence between radio galaxies and the control sample. The mass assembly histories are normalized at the 'observed time' of t lookback = 0, corresponding to a median redshift of z ∼ 0 . 07 (0.9 Gyr before today). For each RDAGN host, the controlled history is the median of its control sample's  \nSFHs. Then the median of all controlled histories are considered as the final results, and uncertainties are estimated using the error of the median (standard deviation divided by the square root of the sample size).  \nFig. 7 shows the comparison of median mass assembly histories between RDAGN hosts and their controls. For both radio AGN hosts (red solid lines) and their controls (blue dashed lines), galaxies form the central region (0-0.5 Re ) earlier than the middle region (0.5-1 Re ) and outskirts (1-1.5 Re ), following an 'inside-out' formation scenario. At all radii, RDAGN built their mass faster and quenched earlier, with the early quenching more pronounced in the central region. Note that this di ff erence does not necessarily imply a direct connection between RDAGN and the evolution of their hosts, because of the very di ff erent timescales of radio jet evolution compared to the buildup of the stellar mass. It is possible that similar conditions prevail during the bulk of the stellar mass build-up of both the radio AGN host galaxies and the control sample galaxies. Faster growth could be a consequence of radio AGN being located in denser environments (e.g., Peng et al. 2010). This scenario is also favored by the more significant impact in the central region; in the standard Λ CDMcosmological paradigm where structure forms hierarchically, the formation time of the inner region of the galaxy is boosted to earlier epochs in dense environments. RDAGN activity may only be triggered after their hosts exceed a certain mass threshold and may only play an important role in maintaining the quiescence at a late stage of the host galaxies' evolution. Such a scenario is in keeping with the implementation of radio mode feedback in semi-analytical models of galaxy formation (e.g., Croton et al. 2006).  \nOur SFHs derived from stellar population synthesis fitting are consistent with some simulations including radio AGN feedback models. In Fig. 7, we plot the mass assembly history of ∼ 10 11 . 5 M ⊙ galaxies in a 10 13 M ⊙ halo from the Illustris cosmology simulation (Rodriguez-Gomez et al. 2016). This simulation includes a 'radio-mode' AGN feedback model that is found to be important in suppressing star formation in massive galaxies.  \nFig. 8. Distributions of the di ff erence between the t 90 from RDAGN and their controls. Three panels from top to bottom are the results for the inner, middle, and outer regions of galaxies. The median di ff erence and its error (standard deviation divided by the square root of the sample size) are noted in the top left of each panel. Larger t 90s indicate that RDAGN hosts globally become quenched earlier.  \n<!-- image -->  \nThese authors also found that strong and weak radio jets create similar impacts on the result (Torrey et al. 2014), which is consistent with the lack of correlation between radio luminosity and the quenching level, as discussed in Section 4.1. The mass assembly of the simulated galaxies (black line in Fig. 7) generally agrees with our observational results. The discrepancy between simulated and spectra-derived SFHs at t lookback > 10 Gyr is due to that the stellar population synthesis is not sensitive to the oldest stars, i.e. the SFH at early universe.  \nWith the mass accumulation curves, we calculate the lookback time t X when the galaxy accumulates X percent of the current mass. These lookback times are often used to quantify how quickly galaxies quench or how early galaxies become quenched (e.g., Pacifici et al. 2016). Since our sample predominantly consists of quiescent galaxies with no significant recent star formation, we consider t 90 as the lookback time when galaxies cease rapid growth. The di ff erence can be determined through the values from RDAGN hosts and their control sample's median values, as ∆ t 90 (positive means that the t 90 of RDAGN hosts is larger, i.e., these galaxies formed earlier). We calculate the ∆ t 90 for each RDAGN host compared to its controls, and plot the distributions in Fig. 8. Panels in Fig. 8 from top to bottom are the results in radial bins 0-0.5 Re , 0.5-1 Re , and 1-1.5 Re , respectively. The median values and errors on the median (the standard deviation divided by the square root of the sample size) are listed in the top left of each panel to indicate the significance of the di ff erences. In Fig. 8, the distribution of ∆ t 90 is shifted towards positive values in all three radial bins, especially in the central one, consistent with the results of mass assembly histories. This indicates that the RDAGN hosts tend to become quenched ∼ 0.40.6 Gyr earlier.  \nFig. 9. Illustration of the stacked di ff erential spectrum between all RDAGN hosts and their controls from the nuclear regions ( ∼ 2 . 5 '' diameter). The spectrum is shown over the restframe wavelength range 3700Å-8800Å. This wavelength range covers the most prominent emission and absorption lines from [O ii ] λ 3727 to Ca ii λ 8662, which are indicated by green dashed lines. The 'emission'- or 'absorption'-like features indicate that those emission lines are stronger or weaker (respectively) in RDAGN hosts than in their control galaxy stacks. The most prominent features of emission line excess are from [N ii ] λ 6550,6585 and H α . This kind of di ff erential stacked spectra are created for di ff erent regions and di ff erent RDAGN populations, and analyzed in Section 4.3.  \n<!-- image -->  \nrest", '4.3. The impact of radio AGN on ISM revealed by the spatially resolved spectra': "Previous analyses have shown relatively marginal di ff erences in star formation properties between RDAGN hosts and their controls. In this subsection, we directly compare the observed spectra of RDAGN hosts and their controls, focusing particularly on the emission lines. Radio jets have long been known to ionize the ISM and create observable emission lines (e.g., Blandford et al. 2019). High-resolution jet simulations show that the kinetic energy in radio jets can be transferred to the surrounding gas by shocks in supersonic outflows (Weinberger et al. 2017).  \nMost massive quiescent galaxies do not have strong emission line features. To enhance the signal-to-noise ratio (S / N) of the emission lines, i.e., reduce the noise, we leverage the abundant spectra from IFU observations and stack (median) them in radial bins for both RDAGN hosts and their controls. During the stacking process, all spectra are converted to the rest frame. Spectra in each radial bin of a galaxy are first stacked by observed flux, which ensures that each galaxy contributes equally to the population stack. This approach highlights di ff erences in emission and absorption lines between RDAGN hosts and controls. In the di ff erential spectra, stronger emission lines in RDAGN hosts appear as 'emission', while weaker lines appear as 'absorption', and vice versa for absorption lines.  \nAs an illustration, Fig. 9 shows the stacked di ff erential spectra from the nuclear (within a 2 . 5 '' diameter) regions of the radio AGN and their controls over the wavelength interval 3700Å8800Å. The strong optical emission and absorption lines are indicated in green lines. In general, RDAGN hosts show redder spectra and several emission line excess or deficiency features in their nuclear regions. The most prominent features are the [N ii ] λ 6550,6585 and H α emission line excess. This excess is also confirmed by other less prominent lines, such as H β and [S ii ] λ 6718,6733 doublets. For absorption lines, RDAGN hosts have clearly weaker Ca lines (CaH λ 3934, CaK λ 3968, and Ca ii λ 8498,8542,8662), appearing as emission-like features. In contrast, the Mg b and Na D indices show absorption-like features, indicating RDAGN hosts have lower Na and Mg abundance. These absorption line features are not strong enough  \nFig. 10. The stacked di ff erential spectra between RDAGN hosts and their controls and the fitting results, are shown in the [N ii ] doublets + H α (green dashed lines) wavelength range. Stacking is done in sub-samples with four L AGN bins (powerful to weak from top to bottom) and in four radial bins (center to outskirts from left to right). Red lines are the fitting results for the emission lines. During the fitting, we assume that the three emission lines have individual Gaussian profiles. The equivalent width of the H α and its signal-to-noise ratio derived from the fitting results are listed in each panel. RDAGN hosts have weak emission line excess only in their nuclear regions (the leftmost panels), while the low luminosity RDAGN hosts have clear emission line deficiency in their outskirts (lower right panels).  \n<!-- image -->  \nto accurately constrain the metallicity di ff erences, so we only model the [N ii ] and H α features in this work.  \nTo investigate which population of RDAGN are contributing to the stacked emission line excess and deficiency, we divide the RDAGN sample into di ff erent subsamples by jet luminosity, radio morphology, and stellar mass, respectively. In each category, we create 16 stacked di ff erent spectra from these four subsamples and from four radial bins (0-0.5 Re , 0.5-1 Re , 1-1.5 Re , > 1 . 5 Re ). We then focus on the wavelength region between 6380Å and 6670Å to quantify the width and strength of the H α + [N ii ] features. We subtract the continuum by fitting it polynomially and then use the single component Gaussian model to fit the equivalent width and dispersion of these three lines. Fig. 10 illustrates this approach when we stack the spectra from RDAGN with di ff erent L AGN. RDAGN are divided into four L AGN bins: < 10 22 . 2 , 10 22 . 2 -10 23 , 10 23 -10 24 , and > 10 24 WHz -1 . There are 173, 165, 130, and 144 RDAGN in these four luminosity bins, respectively. Panels from top to bottom represent sub-samples of four L AGN bins, from powerful RDAGN to weak RDAGN. Within each luminosity bin, the di ff erential spectra are plotted for four radial bins (0-0.5 Re , 0.5-1 Re , 1-1.5 Re , > 1 . 5 Re ) from left to right. We note that the outermost region, r > 1 . 5 Re , is based on incomplete samples because of the field of view limit of MaNGA IFUs. The equivalent width and the signal-to-noise ratio of H α are listed in each panel, where positive and nega-  \nvalues represent stronger or weaker H α in RDAGN hosts, respectively. It can be seen that stacking can reveal equivalent width di ff erences of less than 0.5Å.  \nWe use a similar approach for the other two categories, radio morphology and stellar mass, and summarize the equivalent width measurements in Fig 11. The three panels from top to bottom show the results when dividing the RDAGN host sample by L AGN, radio morphology, and stellar mass. The calculation of equivalent width ( ∆ W H α + [N ii ]) is based on the same method as in DAP (Belfiore et al. 2019). For radio morphology, we visually classify the RDAGN into FR I, FR II, di ff use, and unresolved morphology based on the 6 '' resolution LoTSS images. The number of RDAGN in each morphology category is 78, 93, 43, and 404, respectively. In the lowest panel, we divide the RDAGN hosts into four stellar mass bins ( < 10 10 . 9 M ⊙ , 10 10 . 9 -10 11 . 2 M ⊙ , 10 11 . 2 -10 11 . 4 M ⊙ , and > 10 11 . 4 M ⊙ ), which include 132, 145, 186, and 150 galaxies, respectively. Fig 11 shows the radial profiles of the line excess. Among di ff erent subsamples, the lower mass RDAGN (median M ∗ : 10 10 . 7 M ⊙ ) and compact radio sources ( < 6 '' ) contribute most of the H α + [N ii ] excess in the nuclear regions. This indicates that the the connection between radio AGN activities and optical emission is more common when the RDAGN hosts are less massive, and only exists in small regions in the galaxy center. In the outskirts ( R > 0 . 5 Re ), we find emission line deficiency, mainly contributed by the low-  \nFig. 11. The equivalent width radial profile of the H α + [N ii ] excess or deficiency ( ∆ W H α + [N ii ]) in di ff erent RDAGN subsamples. Panels from top to bottom show the results when dividing RDAGN by jet luminosity, radio morphology, and stellar mass, respectively. Profiles of di ff erent subsamples are shown in di ff erent colors and markers. Positive ∆ W H α + [N ii ] represents that RDAGN have stronger emission lines and vice versa. Compact RDAGN ( < 6 '' ) and lower mass RDAGN (10 10 . 0 -10 10 . 9 M ⊙ ) contribute most to the nuclear excess. Low power RDAGN hosts ( L AGN < 10 22 . 2 WHz -1 ) show clear emission line deficiency in the outskirts regions.  \n<!-- image -->  \nwhich is possibly related to di ff erent star formation conditions.  \nExcess emission lines in RDAGN hosts are only found in the innermost inner bins, which indicates that the excess is likely related to the central AGN. On the other hand, the deficiency is found in the outskirts at radii greater than a few kpcs, where the emission lines are not likely to be a ff ected by the central AGN, so this likely indicates a star formation deficiency in the RDAGNhosts. To examine this assumption, we examine the ionization condition of the ISM based on the velocity dispersion of H α ( σ H α ) and the [N ii ] / H α ratio.  \nIn Fig 12, we plot the distribution of the nuclear [N ii ] / H α versus σ H α of all MaNGA galaxies using a logarithm scale (background gray contours). Emission lines from H ii regions and AGN or shocks are marked by blue and red contours, which are used to classify galaxies according to location in the BPT diagram (e.g., Kau ff mann et al. 2003). The red arrow indicates the  \nFig. 12. Ionization condition diagnostic of the emission line excess found in the nuclear regions of RDAGN hosts (green circle) as well as the deficiency found in the outskirts (green square). The green upper limits on σ H α are due to the unknown level of line broadening after stacking the spectra. The background gray-scale map is the distribution of the [N ii ] / H α versus σ H α for the whole MaNGA sample. Starforming-like emission and AGN or shock dominated emission regions as classified in the BPT diagram are plotted as blue and red contours, respectively. The red arrow indicates the direction in which the ionization becomes harder due to the AGN or shock contribution. In RDAGN hosts, the line ratio suggests that the nuclear emission line excess is created by AGN or shocks, while weaker star formation may be the reason for the emission line deficiency in the outskirts.  \n<!-- image -->  \ndirection where AGN or shock ionization becomes more dominant. We measure the the line ratio and σ H α of the emission excess for the whole RDAGN sample in the nuclear bin and the deficiency in the outskirts, and plot them as a green circle and square respectively. We note that the σ H α measurements are shown as upper limits, because the stacking procedure will bring an unknown level of line broadening. The central line excess shows a high [N ii ] / H α ratio and is located in the region predicated by AGN or shock models (e.g., D'Agostino et al. 2019). This supports the hypothesis that the central RDAGN is heating and ionizing the nuclear gas. However, the excess is weak ( ≤ 3Å) and not correlated with jet luminosity, e.g., the most powerful RDAGN population ( L AGN > 10 24 WHz -1 ) do not show significant line excess. This suggests that the RDAGN have a weak and complex impact on the ISM properties in the central region of the galaxy. It is worth noting that the resolution of the LoTSS images and MaNGA IFUs is at the kiloparsec level, necessitating future high-resolution observations to confirm whether stronger e ff ects are seen at smaller distances from the SMBH. In addition, high-resolution images are also key to distinguishing whether the emission is from the jet-related shock or from AGN photoionization.  \nCompared to the central region, the deficiency in the outskirts is located much closer to the star-forming region. This deficiency seems to be stronger in the lower luminosity RDAGN sub-samples, so weaker star formation in the outskirts of RDAGN hosts is a likely explanation. We note that the lower luminosity RDAGN hosts are more likely to be found at lower redshifts due to the survey sensitivity, and the fact that they are  \nfound in less massive host galaxies is partially a selection effect. Nevertheless, the significant absorption-like features in the low power RDAGN host di ff erential spectra still suggest that in ∼ 10 10 . 9 M ⊙ galaxies, RDAGN hosts have weaker outer region star formation than their controls.", '5. Discussion': 'In this section, we discuss in more detail some of the main unsolved problems related to the interpretation of the results in this paper and o ff er some ideas about how these may be solved in the future.', '5.1. Selection effects': 'In studies focusing on the selection and analysis of RDAGN hosts, addressing the potential biases introduced by the nondetections is crucial. Simply defining the non-RDAGN sample based on the absence of radio detection or radio excess may lead to improper control samples. For instance, a higher redshift radio non-detected galaxy might still have higher luminosity jets compared to a lower redshift weak RDAGN. A SFG with an observed L 144MHz = 10 23 WHz -1 without significant radio excess might conceal an L AGN = 10 22 WHz -1 AGN jet drowned in the emission from HII regions. Both of these two galaxies are not appropriate to be selected as part of the control sample of L AGN = 10 22 WHz -1 RDAGN, but they have been selected to be part of the control sample in most previous studies. For the sensitivity of LoTSS, this e ff ect is only negligible at L 144MHz > 10 24 WHz -1 , as shown in Fig. 6.  \nIn this work, we avoid this bias by calculating the L AGN upper limits of all the non-detections and non-RDAGN. The upper limits can help us to select control samples that are certain to either contain no jets or, at worst, jets which are much fainter than those they are being controlled against. Nonetheless, this approach may introduce bias against galaxies with higher SFRs. For example, an L 144MHz = 10 23 WHz -1 pure SFG without any AGN activity will not be selected as the control of an L AGN = 10 23 WHz -1 RDAGN with the same stellar mass. Despite this bias against higher SFRs, our control sample still exhibits SFRs about 0.2 dex higher than the RDAGN hosts, as also demonstrated in Section 4.3. In addition, the RDAGN hosts are dominated by massive galaxies, as shown in 5, and the high SFR SFGs are rare at M ∗ > 10 11 M ⊙ . These considerations ensure that our control sample selection is appropriately tailored to mitigate selection biases and provide robust comparisons with RDAGN hosts.', '5.2. Disparity between the jet age and quenching time': "If the 'radio-mode' AGN feedback can indeed suppress star formation, we would expect to observe a correlation between the time when the jet activity and the quenching occurred. The timing of galaxies becoming quenched can be inferred from their mass assembly history. On the other hand, estimating the age of radio jets is more complex and typically involves two popular methods: spectral age and dynamical age estimation. The spectral age method relies on the shape of the synchrotron energy spectrum. The synchrotron radiation in a fixed magnetic field will have energy losses that scale as ∂ E /∂ t ∝ ν 2 . So if there is no source driving constant particle acceleration, the spectrum will become steeper because the flux density at high frequencies will decrease faster (e.g., Harwood et al. 2015). The dynamical age  \nis based on the size of a radio jet, because the jet speed can be derived from the environment density (e.g., Falle 1991), then the time scale can be calculated by the jet size and jet speed. We note that these two ages are often observed to have large disparity (e.g., Harwood et al. 2013).  \nMost of the RDAGN in this study lack su ffi cient frequency coverage and spatial information to accurately determine their spectral and dynamical jet ages. However, even for extremely old jets with well-calibrated dynamical and spectral ages, the jet ages are less than 1 Gyr (Turner et al. 2018), which is significantly shorter than the quiescent period observed in our RDAGN hosts. As depicted in Fig. 7, RDAGN hosts are observed to have become quenched approximately 3 Gyr ago. If both timescale measurements are accurate within factors of a few, our results suggest that the onset of radio jet activity likely occurred after the host galaxy became quenched, contradicting the scenario where AGN appear and then suppress star formation.  \nThis then implies that the observed RDAGN activity is not responsible for the host quenching. Several recent studies have argued that di ff erent AGN populations may represent di ff erent evolution phases of AGN, and the radio AGN represent the very late stages of a cycle of AGN activity (e.g., Klindt et al. 2019). If so, this would explain why the radio jet activities may occur later than the quenching, since the star formation suppression happened in AGN's early stages when the radiation feedback is strong. Even with the short timescale of radio jet activity, we still find high RDAGN incidence in the most massive galaxies ( > 50%, see Fig. 5), which indicates that the radio mode AGNin massive galaxies are switching on and o ff rapidly with a high duty cycle to be observed. And the current outburst is only one of the many AGN activities which can date back closer to the quenching time. The timescales of AGN evolution are still poorly constrained, however.", '5.3. The triggering of radio AGN': 'In Figure 5, we showed that the fraction of galaxies that host radio-loud AGN is a very strong function of the stellar mass of the galaxy. In this section, we attempt to pinpoint the underlying cause for why radio AGN activity is more common in massive galaxies by including additional parameters in the analysis, namely SMBH mass, the cosmic environment, and the galaxy morphology. The SMBH mass is estimated by the M BH -σ ∗ relation used in McConnell & Ma (2013). The σ ∗ is fitted from the MaNGA spectra using DAP (Westfall et al. 2019). We adopt the numbers of neighbors within the projected 200 kpc radius and line-of-sight ∆ v < 500 km s -1 as an approximation for the environmental impact, which are taken from the MaNGA-GEMA catalog 3 (Argudo-Fernádez et al. in prep). We use the Hubble type visually classified by Vázquez-Mata et al. (2022) and divided galaxies into elliptical, S0, and late-type (spiral and irregular galaxies).  \nWecalculate the incidence of RDAGN as a function of stellar mass, and plot the results for subsamples divided by the 3 additional parameters in Fig.13. In the upper panel, the RDAGN incidence is clearly higher in high σ ∗ systems at fixed stellar mass. The middle and lower panels indicate that at fixed stellar mass, RDAGN prefer denser cosmic environment and late-type galaxies, which is consistent with previous findings (e.g., Best et al. 2005a). The trends as a function of σ ∗ at fixed stellar mass are by far the strongest ones, suggesting that black hole mass is an im-  \nFig. 13. Incidence of RDAGN as a function of stellar mass, shown for di ff erent galaxy populations. From top to bottom, the galaxies are divided by stellar velocity dispersion (an indicator of the black hole mass), the number of neighbors within 200 kpc (an indicator of the cosmic environment), and Hubble type (galaxy morphology), respectively. RDAGN tend to be located in host galaxies with larger stellar velocity dispersions, denser environments, and early-type morphologies. We find that most galaxies with the largest stellar dispersion ( σ ∗ > 264 km s -1 ) host RDAGN, which suggests that the most massive SMBHs are always accreting in the radio mode.  \n<!-- image -->  \nt parameter, after stellar mass, that controls the fraction of galaxies with radio mode AGN activity. We note that at a similar Eddington ratio, the more massive black holes will have higher luminosity and thus are more likely to be detected. Sabater et al. (2019) used a larger single-fiber observed sample and showed that the RDAGN incidence dpendence on MBH is marginal. This inconsistency is partly due to that they made a radio luminosity cut on the radio AGN sample. After applying a similar cut ( L 150MHz > 10 22 . 5 WHz -1 ), our fraction values generally agree with the results in Sabater et al. (2019) ( f RDAGN ∼ 5% -10% at M ∗ ∼ 10 11 M ⊙ ).', '5.4. Implications for the AGN feedback scenario': 'Combining all the observation results found in this paper, we discuss some possible new implications for the AGN feedback scenario. We note that this discussion focuses on the moderate and faint radio AGN, where a direct connection between the ra-  \ndio AGN and the emission-line properties of the ISM is clearly seen. The more luminous radio jets may dump most of their energy at large distances from the galaxy, and the link to quenching e ff ects may not be as apparent.  \nBecause radio AGN are located in denser environments, at fixed mass, they are likely to have assembled earlier and faster. The observed higher stellar dispersion suggests that their central SMBHs are more massive, indicating possible stronger AGN activity in the past. This past AGN activity may have played an important role in quenching the host galaxies through gas heating, fast consumption of the gas, or gas outflows (e.g., Silk et al. 2024). The early-type morphology and low angular momentum (Zheng et al. 2023) indicates past galaxy-galaxy merger events, which may trigger the past AGN activity and also the fast mass growth, as well as the morphological transition from disk to spheroid (e.g. Rothberg & Joseph 2004).  \nAt a later stage, the galaxy becomes quiescent due to the lack of cold gas fueling. This also prevents the central SMBH from accreting e ffi ciently and radiatively, and the current most massive SMBHs tend to appear as radio-mode AGN. In our sample, the RDAGN hosts are dominated by quiescent galaxies and show weaker star formation activities in the outskirts, which suggests that the radio AGN may help the host galaxies to maintain quiescence. The AGN- or shock like emission excess found in the nuclear regions of RDAGN hosts indicates that radio AGN ionize and heat the surrounding gas. One remaining mystery is exactly how the weak and compact jets associated with the central excess phenomenon can maintain the quiescence of the host galaxies globally.  \nFinally, although a large-scale connection between radio AGN and the heating of surrounding gas has been observed in many central galaxies of massive clusters (e.g., Fabian 2012), we still need more observational evidence of the jet-gas connection in faint radio AGN on galaxy scales to obtain a full view of such physical processes in di ff erent galaxy environments and populations.', '5.5. Future directions': 'This work is based on the radio images and optical IFUs with spatial resolutions on the order of arcseconds. In the future, new telescopes and the update of current facilities can carry out large radio sky surveys with sub-arcsec resolution, e.g., The International LOFAR Two-metre Sky Survey 4 , the Next Generation Very Large Array (ngVLA, Di Francesco et al. 2019), the Square Kilometre Array 5 (SKA), etc.. At low redshifts, they can resolve the jet features on physical scales of a few hundred of parsecs. As discussed in Section 4.1, the higher resolution is also essential to decompose the faint radio AGN in star-forming galaxies, which can help us to understand the radio AGN luminosity function in the faint end. The wide frequency coverage of di ff erent instruments can also help us build the full synchrotron SED of radio AGN, which is essential for constraining jet ages.  \nMeanwhile, there are more and more deep and highresolution IFU samples. These improvements can reveal the detailed process about how the jets from AGN interact with ISM. High-resolution IFU is also necessary to distinguish the jetrelated emission and the AGN photoionization emission. In addition to advancements in radio and optical observations, future large-scale surveys at other wavelengths, particularly in the Xray and infrared, are expected to match the resolution and sensi-  \ntivity achieved at optical and radio bands. This multi-wavelength approach will provide comprehensive information about the different component structures of AGN, allowing for a more complete understanding of the structure and the evolution of AGN.', '6. Summary': "We build the largest optical IFU - radio continuum sample to date consisting of 5578 galaxies by matching the MaNGA survey with LoTSS-DR2 observations. We revisit the tight linear SFR - radio luminosity relation using IFU data and find an intrinsic error of ∼ 0 . 23 dex. Using this relation, we identify 616 radio AGN with excessive radio emission, and calculate their jet luminosities. We analyze their global star formation rates and their correlation with jet luminosity. We then derive the radially resolved mass assembly history by fitting the IFU spectra in radial bins and comparing the di ff erence between radio AGN hosts and their control samples We also stack the spectra in di ff erent radial bins to investigate the impact of radio AGN on the emission lines of their host galaxies. Our results can be summarized as follows:  \n- 1. The linear relation in the SFR and L 144MHz found by LoTSSMaNGA sample is tight and can be described by Equation 1: log( L 144MHz WHz -1 ) = 1 . 16 × log( SFR M ⊙ yr -1 ) + 21 . 99 , which is in very good agreement with previous results based on nonIFU samples.\n- 2. At least 41% M ∗ > 10 11 M ⊙ galaxies are found to host a radio AGN. Radio AGN host galaxies are dominated by massive quiescent galaxies, i.e., 92% lie below the -3 σ of star formation main sequence. The quenching level, ∆ SFR, is not related to the jet luminosity (Pearson correlation coe ffi cient ρ ∼ -0 . 1).\n- 3. The mass assembly history of radio AGN hosts follows an 'inside-out' scenario, similar to normal massive galaxies. Compared to a mass-matched control sample, radio AGN hosts grow faster at all radii, especially in their central regions. They grew to 90 percent of current mass at lookback times of 4-6 Gyr, and 0.4-0.6 Gyr earlier than their controls. The mass assembly history reconstructed from the optical spectra is consistent with that in simulations incorporating the radio-mode AGN feedback model.\n- 4. Stacked spectra comparisons reveal weak emission line excess exclusively in the central region of radio AGN hosts, especially in low mass RDAGN. The high ratio of the excessive [N ii ] and H α supports the scenario that the emission line excess is linked to AGN or shock ionization, but it remains to be understood why the excess is not dependent upon jet luminosity. Low luminosity radio AGN hosts show emission line deficiencies in their outskirts, likely indicating that RDAGN have weaker star formation in those regions.  \nConsidering that the timescale of jet activities is usually less than 1 Gyr, the quenching of their host galaxies that happened several Gyrs ago was likely not due to the current RDAGN. However, episodic cycles of radio AGN may play an important role in maintaining the global quiescence of the host galaxies and preventing the most massive galaxies from further growth. This conjecture is supported by the high fraction of quiescent galaxies in RDAGN hosts, as well as the high incidence of RDAGN in massive galaxies. The lack of a clear correlation between jet luminosity and feedback features suggests that energy transfer from radio jets to the ISM is an ine ffi cient and complex process. Exactly how radio jets a ff ect the star formation and interact with  \nthe gas in galaxies is yet to be fully understood. Future studies with larger samples and higher spatial resolution observations at di ff erent wavelengths are expected to shed more light on the detailed physical processes underlying 'radio-mode' AGN feedback.  \nAcknowledgements. PNB is grateful for support from the UK STFC via grants ST / V000594 / 1 and ST / Y000951 / 1. SS is grateful for support from the UK Science and Technology Facilities Council (STFC) via grant ST / X508408 / 1. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy O ffi ce of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is www.sdss4.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics | Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University. LOFAR (van Haarlem et al. 2013) is the Low Frequency Array designed and constructed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefited from the following recent major funding sources: CNRS-INSU, Observatoire de Paris and Université d'Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy. This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (einfra 180169) and the LOFAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for Computing (NIC). This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the University of Hertfordshire and supported by STFC [ST / P000096 / 1], and of the Italian LOFAR IT computing infrastructure supported and operated by INAF, and by the Physics Department of Turin university (under an agreement with Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre, Italy. Part of this work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number Ts ˜ 17 / 2-1.", 'References': "- Abdurro'uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35 Baldwin, J. A. 1997, in Astronomical Society of the Pacific Conference Series, Vol. 113, IAU Colloq. 159: Emission Lines in Active Galaxies: New Methods and Techniques, ed. B. M. Peterson, F.-Z. Cheng, & A. S. Wilson, 80 Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5 Barvainis, R. 1987, ApJ, 320, 537 Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559 Begelman, M. C., Blandford, R. D., & Rees, M. J. 1984, Reviews of Modern Physics, 56, 255 Belfiore, F., Westfall, K. B., Schaefer, A., et al. 2019, AJ, 158, 160 Best, P. N. & Heckman, T. M. 2012, MNRAS, 421, 1569 Best, P. N., Kau ff mann, G., Heckman, T. M., et al. 2005a, MNRAS, 362, 25 Best, P. N., Kau ff mann, G., Heckman, T. M., & Ivezi'c, Ž. 2005b, MNRAS, 362, 9 Best, P. N., Kondapally, R., Williams, W. L., et al. 2023, MNRAS, 523, 1729 Biermann, P. 1976, A&A, 53, 295  \nBlandford, R., Meier, D., & Readhead, A. 2019, ARA&A, 57, 467  \nBlanton, M. R., Kazin, E., Muna, D., Weaver, B. A., & Price-Whelan, A. 2011, AJ, 142, 31  \nBlanton, M. R. & Roweis, S. 2007, AJ, 133, 734 Brown, M. J. I., Moustakas, J., Kennicutt, R. C., et al. 2017, ApJ, 847, 136 Bundy, K., Bershady, M. A., Law, D. R., et al. 2015, ApJ, 798, 7 Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682 Chabrier, G. 2003, PASP, 115, 763 Chi, X. & Wolfendale, A. W. 1990, MNRAS, 245, 101  \n- Cid Fernandes, R., Stasi'nska, G., Mateus, A., & Vale Asari, N. 2011, MNRAS, 413, 1687  \nCochrane, R. K., Kondapally, R., Best, P. N., et al. 2023, MNRAS, 523, 6082 Comerford, J. M., Negus, J., Müller-Sánchez, F., et al. 2020, ApJ, 901, 159 Condon, J. J., Anderson, M. L., & Helou, G. 1991, ApJ, 376, 95 Condon, J. J., Cotton, W. D., & Broderick, J. J. 2002, AJ, 124, 675 Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693 Croston, J. H., Hardcastle, M. J., Mingo, B., et al. 2019, A&A, 622, A10 Croton, D. J., Springel, V., White, S. D. M., et al. 2006, MNRAS, 365, 11 D'Agostino, J. J., Kewley, L. J., Groves, B. A., et al. 2019, MNRAS, 487, 4153 Dai, Y. S., Wilkes, B. J., Bergeron, J., et al. 2018, MNRAS, 478, 4238 Das, S., Smith, D. J. B., Haskell, P., et al. 2024, MNRAS, 531, 977 de Jong, T., Klein, U., Wielebinski, R., & Wunderlich, E. 1985, A&A, 147, L6 Di Francesco, J., Chalmers, D., Denman, N., et al. 2019, in Canadian Long Range Plan for Astronomy and Astrophysics White Papers, Vol. 2020, 32 Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604 Dubois, Y., Devriendt, J., Slyz, A., & Teyssier, R. 2010, MNRAS, 409, 985 Fabian, A. C. 2012, ARA&A, 50, 455  \n- Falle, S. A. E. G. 1991, MNRAS, 250, 581\n- Fanaro ff , B. L. & Riley, J. M. 1974, MNRAS, 167, 31P\n- Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306\n- Gallazzi, A., Charlot, S., Brinchmann, J., White, S. D. M., & Tremonti, C. A. 2005, MNRAS, 362, 41\n- Garofalo, D. & Singh, C. B. 2019, ApJ, 871, 259  \nGoddard, D., Thomas, D., Maraston, C., et al. 2017, MNRAS, 466, 4731  \nGuo, K., Zheng, X. Z., Wang, T., & Fu, H. 2015, ApJ, 808, L49  \nGürkan, G., Hardcastle, M. J., Smith, D. J. B., et al. 2018, MNRAS, 475, 3010  \nHale, C. L., Schwarz, D. J., Best, P. N., et al. 2024, MNRAS, 527, 6540  \nHardcastle, M. J., Horton, M. A., Williams, W. L., et al. 2023, A&A, 678, A151  \nHarwood, J. J., Hardcastle, M. J., & Croston, J. H. 2015, MNRAS, 454, 3403  \nHarwood, J. J., Hardcastle, M. J., Croston, J. H., & Goodger, J. L. 2013, MN-  \nRAS, 435, 3353  \n- Heckman, T. M. & Best, P. N. 2014, ARA&A, 52, 589  \nHeckman, T. M., Kau  \nff  \nmann, G., Brinchmann, J., et al. 2004, ApJ, 613, 109  \nHeesen, V., Sta  \nff  \nehl, M., Basu, A., et al. 2022, A&A, 664, A83  \nHogg, D. W., Bovy, J., & Lang, D. 2010, arXiv e-prints, arXiv:1008.4686  \nHotan, A. W., Bunton, J. D., Chippendale, A. P., et al. 2021, PASA, 38, e009  \nJi, X. & Yan, R. 2020, MNRAS, 499, 5749  \n- Jin, G., Dai, Y. S., Pan, H.-A., et al. 2021, ApJ, 923, 6\n- Jonas, J. & MeerKAT Team. 2016, in MeerKAT Science: On the Pathway to the SKA, 1\n- Kau ff mann, G. & Haehnelt, M. 2000, MNRAS, 311, 576\n- Kau ff mann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055 Kennicutt, R. C. & Evans, N. J. 2012, ARA&A, 50, 531\n- Klindt, L., Alexander, D. M., Rosario, D. J., Lusso, E., & Fotopoulou, S. 2019, MNRAS, 488, 3109\n- Li, Z.-J., Dai, Y. S., Huang, J. S., Wuyts, S., & Cao, T.-W. 2024, ApJ, 963, 99 Madau, P. & Dickinson, M. 2014, ARA&A, 52, 415\n- Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285  \nMaraston, C., Hill, L., Thomas, D., et al. 2020, MNRAS, 496, 2962  \nMcConnell, N. J. & Ma, C.-P. 2013, ApJ, 764, 184  \nMohan, N. & Ra ff erty, D. 2015, PyBDSF: Python Blob Detection and Source Finder, Astrophysics Source Code Library, record ascl:1502.007 Mulcahey, C. R., Leslie, S. K., Jackson, T. M., et al. 2022, A&A, 665, A144 Nelson, D., Pillepich, A., Springel, V., et al. 2019, MNRAS, 490, 3234 Neumann, J., Thomas, D., Maraston, C., et al. 2022, MNRAS, 513, 5988 Osterbrock, D. E. 1989, Astrophysics of gaseous nebulae and active galactic nu-  \n- clei  \nPacifici, C., Oh, S., Oh, K., Lee, J., & Yi, S. K. 2016, ApJ, 824, 45  \nPadovani, P., Alexander, D. M., Assef, R. J., et al. 2017, A&A Rev., 25, 2  \nPeng, Y.-j., Lilly, S. J., Kovaˇc, K., et al. 2010, ApJ, 721, 193  \n- Penney, J. I., Blain, A. W., Assef, R. J., et al. 2020, MNRAS, 496, 1565  \nRodriguez-Gomez, V., Pillepich, A., Sales, L. V., et al. 2016, MNRAS, 458, 2371  \nRothberg, B. & Joseph, R. D. 2004, AJ, 128, 2098  \n- Russell, H. R., McNamara, B. R., Edge, A. C., et al. 2013, MNRAS, 432, 530\n- Sabater, J., Best, P. N., Hardcastle, M. J., et al. 2019, A&A, 622, A17\n- Salomé, Q., Salomé, P., & Combes, F. 2015, A&A, 574, A34\n- Schaye, J., Crain, R. A., Bower, R. G., et al. 2015, MNRAS, 446, 521\n- Schutte, Z. & Reines, A. E. 2022, Nature, 601, 329\n- Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2022, A&A, 659, A1\n- Shimwell, T. W., Röttgering, H. J. A., Best, P. N., et al. 2017, A&A, 598, A104\n- Silk, J., Begelman, M. C., Norman, C., Nusser, A., & Wyse, R. F. G. 2024, ApJ, 961, L39\n- Silverman, J. D., Green, P. J., Barkhouse, W. A., et al. 2008, ApJ, 679, 118 Smee, S. A., Gunn, J. E., Uomoto, A., et al. 2013, AJ, 146, 32 Smith, D. J. B., Haskell, P., Gürkan, G., et al. 2021, A&A, 648, A6 Springel, V., Di Matteo, T., & Hernquist, L. 2005, MNRAS, 361, 776 Ste ff en, J. L., Fu, H., Brownstein, J. R., et al. 2023, ApJ, 942, 107 Sun, W.-H. & Malkan, M. A. 1989, ApJ, 346, 68 Torrey, P., Vogelsberger, M., Genel, S., et al. 2014, MNRAS, 438, 1985 Turner, R. J., Shabala, S. S., & Krause, M. G. H. 2018, MNRAS, 474, 3361 van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2 Vázquez-Mata, J. A., Hernández-Toledo, H. M., Avila-Reese, V., et al. 2022, MNRAS, 512, 2222  \nWake, D. A., Bundy, K., Diamond-Stanic, A. M., et al. 2017, AJ, 154, 86 Wang, L., Norberg, P., Gunawardhana, M. L. P., et al. 2016, MNRAS, 461, 1898 Weinberger, R., Springel, V., Hernquist, L., et al. 2017, MNRAS, 465, 3291 Westfall, K. B., Cappellari, M., Bershady, M. A., et al. 2019, AJ, 158, 231 Wilkinson, D. M., Maraston, C., Goddard, D., Thomas, D., & Parikh, T. 2017, MNRAS, 472, 4297  \nWilliams, W. L., Hardcastle, M. J., Best, P. N., et al. 2019, A&A, 622, A2 Yan, R., Chen, Y., Lazarz, D., et al. 2019, ApJ, 883, 175 Yang, H. Y. K. & Reynolds, C. S. 2016, ApJ, 829, 90  \n- Zheng, X., Röttgering, H., van der Wel, A., & Cappellari, M. 2023, A&A, 673, A12", 'Appendix A: Fitting the L 144MHz -SFR relation': "To build the L 144MHz-SFR relation, the key is to select a sample of pure star-forming galaxies with reliable SFR measurement and without radio jet contribution. Using the integral field spectra from MaNGA, the SFR can be derived from the H α line, and corrected for dust attenuation on sub-galactic scales. There are galaxies in which the H α is not dominated by star formation but instead is possibly contaminated by narrow-line AGN or diffuse ionized gas. We exclude these galaxies using the widely used emission line diagnostic (BPT diagram, Baldwin et al. 1981) based on the [N ii ] λ 6585 / H α and [O iii ] λ 5008 / H β line ratios measured from the central 2.5 '' MaNGA spaxels. Specifically, our 'pure-SFG' sample only include galaxies locating in the star-forming region of the BPT diagram, using the separation diagnostic derived by (Kau ff mann et al. 2003) as well as showing nuclear H α equivalent width larger than 3Å (Cid Fernandes et al. 2011). Then we visually check the LoTSS image of these galaxies and exclude those showing jet-like features and require the signal-to-noise ratio of radio detection larger than 5. This way we get a sample of 906 secure SFGs with reliable SFR and radio luminosity measurements. Fig. A.1 shows the emission line selection of this SFG sample. ∆ BPT is the distance to the division line in the BPT diagram (Equation 1 in Kau ff mann et al. 2003), and the negative values represent that galaxies locate in the star-forming region. As a result of all the constrains, this SFG sample has a SFR limit about 0.1 M ⊙ yr -1 (see Fig. 2), thus our result about this relation may not be applicable for SFGs with SFRs lower than this value.  \nWe set three parameters in the linear fitting of the L 144MHzSFR relation. In addition to the slope and constant, we introduce a intrinsic scatter parameter, which should be the scatter level of the L 144MHz-SFR relation after excluding the e ff ect from measurement errors. Our fitting follows the method in Hogg et al. (2010). The Markov chain Monte Carlo (MCMC) sampling result is shown in Fig. A.2. The intrinsic error is found to be small, about 0.23 dex, which indicates that the radio emission is good tracer for galaxy global SFR. The relation is listed in Equation 1. At the 3 σ level, our result is consistent with previous results based on di ff erent SFR tracers and radio data from di ff erent frequencies (Wang et al. 2016; Brown et al. 2017; Gürkan et al. 2018; Smith et al. 2021; Heesen et al. 2022; Best et al. 2023).  \n<!-- image -->  \nΔ  \nFig. A.1. The 'pure SFG' sample selected by the emission line diagnostic and radio morphology. The y-axis is the equivalent width of H α in the nuclear region measured from MaNGA spectra. The x-axis is the distance to the division line in the BPT diagram (Equation 1 in Kau ff -mann et al. 2003), based on the [N ii ] λ 6585 / H α and [O iii ] λ 5008 / H β ratios. Negative and positive ∆ BPT mean that galaxies locate in the 'starforming' region and 'AGN' region in BPT diagram, respectively. This H α -∆ BPT diagram can classify the galaxies into SFG, AGN, and quiescent galaxies. Our 'pure SFG' sample are plotted as stars and colorcoded by their radio luminosities. Background gray-scale contour is the distribution of the whole MaNGA sample.Fig. A.2. The Markov chain Monte Carlo sampling of our fitting for the L 144MHz-SFR relation. Three parameters are the slope, the constant value, and the intrinsic scatter in logarithm scale, respectively.  \n<!-- image -->"}