The MAGPI Survey: Evolution of radial trends in star formation activity across cosmic time
Marcie Mun Emily Wisnioski Andrew J. Battisti J. Trevor Mendel Sara L. Ellison Edward N. Taylor Claudia D. P. Lagos Katherine E. Harborne Caroline Foster Scott M. Croom Sabine Bellstedt Stefania Barsanti Anshu Gupta Lucas M. Valenzuela Qian-Hui Chen Kathryn Grasha Tamal Mukherjee Hye-Jin Park Piyush Sharda Sarah M. Sweet Rhea-Silvia Remus Tayyaba Zafar


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This work is supported by The National Natural Science Foundation of China (No. 62172155). Corresponding authors: Yeting Guo and Fang Liu. 

    1st Changjuan Ran
School of Design 

Hunan University

Changsha, China 

s220800533@hnu.edu.cn
2nd Yeting Guo
College of Computer 

National University of Defense Technology

Changsha, China 

guoyeting13@nudt.edu.cn
3rd Fang Liu
School of Design 

Hunan University

Changsha, China 

fangl@hnu.edu.cn 

4th Shenglan Cui
School of Design 

Hunan University

Changsha, China 

cuisl@hnu.edu.cn
5th Yunfan Ye
College of Computer 

National University of Defense Technology

Changsha, China 

yunfan951202@gmail.com











    
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Using adaptive optics with the Multi-Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT), the Middle Ages Galaxy Properties with Integral Field Spectroscopy (MAGPI) survey allows us to study the spatially resolved Universe at a crucial time of ∼4 Gyr ago (z ∼ 0.3) when simulations predict the greatest diversity in evolutionary pathways for galaxies. We investigate the radial trends in the star formation (SF) activity and luminosity-weighted stellar ages as a function of offset from the star-forming main sequence (SFMS) for a total of 294 galaxies. Using both Hα emission and the 4000 Å break (i.e., D4000) as star formation rate (SFR) tracers, we find overall flat radial profiles for galaxies lying on and above the SFMS, suggestive of physical processes that enhance/regulate SF throughout the entire galaxy disc. However, for galaxies lying below the SFMS, we find positive gradients in SF suggestive of inside-out quenching. Placing our results in context with results from other redshift regimes suggests an evolution in radial trends at z ∼ 0.3 for SF galaxies above the SFMS, from uniformly enhanced SF at z∼1 and z ∼ 0.3 to centrally enhanced SF at z ∼ 0 (when averaged over a wide range of mass). We also capture higher local SFRs for galaxies below the SFMS compared to that of z ∼ 0, which can be explained by a larger population of quenched satellites in the local Universe and/or different treatments of limitations set by the D4000-sSFR relation. 







galaxies: evolution – galaxies: general – galaxies: star formation – galaxies: statistics.








§ INTRODUCTION


Galaxies are some of the most complex structures in the Universe. The formation and evolutionary pathways galaxies take throughout their lifetimes are multifold. Despite the diversity of such pathways, populations of galaxies as a whole have been observed to follow tight scaling relations across cosmic time, such as the correlation between star formation rates (SFRs) and stellar masses (M⋆), otherwise known as the star-forming main sequence (SFMS; e.g., ). The existence of such a tight relation (∼0.2 – 0.35 dex in scatter) observed up to redshifts as high as z ∼ 6 <cit.> suggests that galaxies are able to maintain their star formation in a quasi-steady manner across cosmic time <cit.>. Galaxies not on the SFMS are considered to be outliers, where galaxies above the main sequence are undergoing starbursts and galaxies below are either in the process of or have already quenched their star formation. While the SFMS has been in place across cosmic time, the normalisation of the relation has evolved together with the cosmic star formation rate density <cit.>. This suggests that there may be differences in the star-forming conditions between the early Universe and today, such that galaxies hosted much more gas-rich and star-forming discs in the past <cit.>. Scaling relations between various galaxy properties, along with multi-wavelength studies of galaxies at different redshift regimes, provide us with the big picture of galaxy evolution across cosmic time. However, in order to understand the processes governing these global relationships, we need to spatially resolve galaxies and their environments to uncover their underlying physics.

Various mechanisms are known to regulate the star formation activity of galaxies, which include those pertaining to internal structures such as bars (e.g., ), spiral arms <cit.>, and bulges (i.e., `morphological quenching'; ), active galactic nuclei (AGN; e.g., ; see  for a review), and environmental processes such as interactions with neighbouring galaxies <cit.>, some of which can lead to mergers <cit.>, gas stripping due to the surrounding medium <cit.>, and starvation/strangulation <cit.>. By nature, bars and AGN are expected to have a more noticeable impact on the galaxy centre, either potentially leading to funnelling of gas towards the centre and consequently a nuclear starburst <cit.>, or the outflow of gas followed by earlier onset of quenching <cit.>. AGN can also suppress star formation on a global scale by injecting kinetic energy into the gas distributed throughout the halo, which leads to both a decrease in cold gas inflow and increase in stability of the gas against fragmentation <cit.>. On the other hand, environmental processes add more complexities to the overall picture, where ram pressure stripping acts to preferentially strip gas from galaxy outskirts, quenching the galaxy outside-in <cit.>, whereas starvation/strangulation can quench galaxies on a global scale by cutting off cold gas accretion entirely <cit.>. As such, the distribution of the gas, stars, and metals are expected to exhibit variations from the centre towards the outskirts of galaxies <cit.>. This is further complicated by the evolution of environments and build-up of the densest environments at late times <cit.>.

Distinguishing the different physical mechanisms at play requires a wealth of observational information, among which spatially resolved photometry and/or spectroscopy covering a broad range of wavelengths prove to be crucial. Integral field spectroscopy (IFS) has been particularly useful in this sense, where large integral field unit (IFU) galaxy surveys have used spatially resolved spectroscopy to measure radial variations in galaxy properties. In particular, many studies have analysed radial trends in SFR surface density (Σ_SFR) and specific star formation rates (sSFR = SFR/M⋆) as a function of morphology, environment, stellar mass, and offset with respect to the SFMS <cit.>. Such analyses have demonstrated the power of combining global and local information, where comparing radial trends in local star formation as a function of location with respect to the global SFMS has been particularly insightful. 

Studies based on the local Universe (z ∼ 0) suggests that galaxies above and below the SFMS show enhanced and quenched star formation activity, respectively, in the galaxy centre <cit.>. Multiple scenarios have been proposed to explain this; for example, a central starburst may precede inside-out quenching in galaxies <cit.> due to processes such as galaxy mergers and AGN feedback. On the other hand, it may not necessarily be physical processes, but moreso radial variations in SF efficiencies manifesting in positive/negative gradients in SF <cit.>. Some studies have attempted to distinguish between internal and external mechanisms – <cit.> find that central and high-mass satellite galaxies quench inside-out primarily due to AGN feedback, whereas low-mass satellites quench outside-in due to environmental mechanisms such as ram pressure stripping and galaxy-galaxy interactions. Putting radial trends in SF in context with environments ranging from low-mass galaxy groups to clusters have also shown that galaxies show stronger trends of outside-in quenching with increasing environmental density <cit.>. However, features of outside-in quenching (i.e., a negative gradient in SF) can also be interpreted as central rejuvenation due to increased gas accretion rates from galaxy-galaxy interactions, such that both processes might be occurring in concert <cit.>. The combination of analysing multiple parameters, such as Σ_SFRs and sSFRs, has proved helpful towards favouring one scenario over the other <cit.>. 

At higher redshifts (z ∼ 1 - 2), high spatial resolution imaging taken with the Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) grism from the 3D-HST <cit.> survey has made similar analyses possible. Stacked images of both Hα and stellar continuum emission show that galaxies above the SFMS are enhanced everywhere throughout the disc, galaxies on the SFMS have on average flat profiles, whereas those below are quenched everywhere <cit.>. However, centrally suppressed sSFRs are observed in the centre of their most massive (10.5 < log_10(M⋆/M) < 11) galaxies, which suggests signs of inside-out quenching. Similar results are found from the SINS/zC-SINF <cit.> survey with evidence that the most massive (log_10(M⋆/M) ≳ 11) galaxies are undergoing inside-out quenching, whereas lower mass galaxies show flat sSFR profiles <cit.>. 

Together, the results at z = 0 and z = 2 suggest an evolution in radial trends over the last ∼10 Gyr for galaxies above and below the SFMS. Understanding which changes (e.g. environment, accretion rates, gas fractions, etc.) have contributed to this evolution requires investigating galaxies at the epoch where the cosmic SFRD is winding down. However, studies tracing this evolution have been limited. Observationally, they require large areas and deep high-resolution imaging or imaging spectroscopy. The Multi-Unit Spectroscopic Explorer (MUSE) instrument on the Very Large Telescope (VLT) however is opening up this space with surveys that tile over larger regions of the sky. The natural seeing MUSE-WIDE survey <cit.> has made it possible to measure the radial variations in star formation and gas-phase metallicities at 0.1 < z < 0.42, but has been limited in sample statistics <cit.>. The Middle Ages Galaxy Properties with Integral Field Spectroscopy (MAGPI[Based on observations obtained at the VLT of the European Southern Observatory (ESO), Paranal, Chile (ESO program ID 1104.B-0526)]; ) survey has been designed to resolve these issues, by achieving comparable spatial resolution to that achieved with local IFS surveys in both stars and ionised gas for ∼400 galaxies at z ∼ 0.3, with the use of adaptive optics (AO) capabilities on MUSE. 

In this paper, we study the radial trends in the star formation activity of MAGPI galaxies at z ∼ 0.3 to address two key questions: (1) Do we observe an evolution in star formation activity with redshift at z ∼ 0.3?; and (2) What regulates and/or quenches star formation at z ∼ 0.3? We use both the global and resolved SFMS (rSFMS; i.e., resolved counterpart of the global SFMS measured on kiloparsec scales, showing a tight correlation between SFR and stellar mass surface densities; e.g., ) to measure the radial variation in local SF. Specifically, we measure radial trends in ΔΣ_SFR, the logarithmic offset from the rSFMS, as a function of varying offsets from the global SFMS. We also complement our results with luminosity-weighted stellar age (AgeL) profiles. We also ensure that our sample is not biased towards star-forming galaxies with strong emission lines by using D4000 to indirectly measure SFRs for passive spaxels/galaxies. In this paper, we introduce the MAGPI survey in more depth in Section <ref>, followed by a description of our methodology behind the SFRs and stellar masses, along with global and local star formation metrics in Section <ref>. We show our resulting ΔΣ_SFR and luminosity-weighted age profiles in Section <ref>. We then discuss the potential physical mechanisms governing MAGPI galaxies, along with the implications of our results in context with similar studies at different redshift regimes in Section <ref>. Finally, we summarise our results and discuss planned future work in Section <ref>. Throughout this paper, we assume a <cit.> initial mass function (IMF) and adopt a flat ΛCDM cosmology with H_0 = 70 km s-1 Mpc-1, Ω_m = 0.3, and Ω_Λ = 0.7.  



§ THE MAGPI SURVEY


MAGPI is a VLT/MUSE Large Program (Program ID: 1104.B-0536) aimed at studying the spatially resolved spectroscopy of stars and ionized gas in galaxies at 0.25 < z < 0.35, translating to lookback times of 3 - 4 Gyrs. A main motivation of the MAGPI survey is to trace the morpho-kinematic evolution of galaxies between z∼1 and z∼2. With the aid of Ground Layer Adaptive Optics (GLAO) on MUSE, MAGPI is able to probe both stellar and gas kinematics at a comparable relative spatial resolution to those probed by IFS surveys at lower redshifts, such as MaNGA <cit.> and SAMI <cit.>. The survey targets a total of 60 primary galaxies (M⋆ > 7 × 10^10 M_) and their neighbouring galaxies (`secondary' galaxies; about ∼400) within the MUSE field-of-view (FOV) at z ∼ 0.3 (∼270 kpc) in a broad range of environments, spanning 12 ≲log (M_halo / M_) ≲ 15 <cit.>. 

56 of the 60 primary galaxies were sampled from the G12, G15, and G23 fields of the Galaxy and Mass Assembly survey (GAMA; ), with the remaining 4 from MUSE archival fields of Abell 370 (z = 0.375; Program ID: 096.A-0710, PI: Bauer) and Abell 2744 (z = 0.308; Program IDs: 095.A-0181 and 096.A-0496, PI: Richard). The sample selection based on the GAMA survey is also supported by the availability of ancillary imaging data ranging from the ultraviolet (UV) to near-infrared (NIR) from the Hyper Suprime Cam Subaru Strategic Program (HSC SSP; ), Kilo-Degree Survey (KiDS; ), and the VISTA Kilo degree Infrared Galaxy (VIKING; ). Centred on a primary target, each of the MAGPI fields covers roughly a 1 × 1 arcmin FOV with 0.2 arcsecond per pixel spatial sampling. Each field is observed in six observing blocks of 2 × 1320 s exposures, totaling to 4.4 hours in the wide-field mode (WFM) with GLAO (total of 246 hours on-source). The nominal mode is used such that wavelength coverage ranges from 4700 to 9300 Å, where spectra are sampled in 1.25 Å pixel-1. The use of GLAO results in a laser gap at 5780 - 6050 Å due to the GALACSI system sodium laser notch filter <cit.>. 

Data reduction on the MUSE data are done using pymusepipe[<https://github.com/emsellem/pymusepipe>], a Python wrapper for the MUSE reduction pipeline <cit.>. pymusepipe takes care of the major data processing which includes wavelength calibration and measurement of the instrumental line-spread function. cubefix <cit.> and the Zurich Atmosphere Purge (ZAP; ) are used for illumination correction and sky subtraction, respectively. The post-processed data cubes are then run through ProFound[<https://github.com/asgr/ProFound>] <cit.> for source detection, which additionally produces segmentation maps and measures structural parameters such as effective radii and position angles. The `dilated' segmentation maps are used to set the size of data cubes for individual galaxies (i.e., `minicubes') with mpdaf[<https://github.com/musevlt/mpdaf>], such that the data cubes fully encompass both the full light distribution from the galaxies and sufficient coverage of the background. Dilated segmentation maps are created by expanding the segmentation maps to reach a particular source magnitude limit below the estimated sky level. Further details are provided in <cit.> and Mendel et al (in prep). 

At the time of writing, observations are still ongoing and a total of 48 fields (∼86 per cent completion rate) have been observed, among which 35 of them have been fully reduced with relevant data products. The 4 archival fields of Abell 370 and Abell 2744 are not included in this analysis. While the main redshift range of interest for MAGPI is centred around z ∼ 0.3, for the purposes of sampling as many star-forming galaxies as possible, the redshift range is extended such that the galaxies selected for this study are located at 0.25 ≤ z ≤ 0.424, where the upper bound for redshift is set by the MUSE detection limit for the Hα line. 



§ METHODS





 §.§ Emission line fits



Emission lines are fit using the Galaxy IFU Spectroscopy Tool (gist; ) code, which is a Python wrapper for pPXF <cit.> and GandALF <cit.>, for which the former is specialized for stellar continuum fitting and the latter for emission line fitting. For stellar continuum measurements, we used the luminosity-weighted spectral templates from the C3K library (Charlie Conroy, private communication) that are based on the Modules for Experiments in Stellar Astrophysics (mesa) Isochrones and Stellar Tracks (mist; ). Prior to fitting, we convolve these templates to match the wavelength-dependent MUSE spectral resolution derived from sky lines (e.g., ). We have adopted a multiplicative Legendre polynomial of order 12 when fitting the stellar continuum. We adopted a S/N threshold of 10 when Voronoi binning <cit.> the stellar continuum; for galaxies with low continuum S/N, we use a single integrated bin. When choosing which spaxels to include in the continuum binning process, we take into account two criteria: 

    
  * Reside inside the dilated ProFound mask
    
  * Have integrated S/N ≥ 2 for 6050 Å < λ_obs < 7750 Å; corresponding roughly to the peak MUSE sensitivity range

For emission line fitting, we have used a customized version of pyGandALF where errors on fluxes, velocities, and widths for the emission lines are estimated based on a Monte Carlo approach. We also implemented a grid search of initial fitting parameters to improve fitting in the low S/N galaxy outskirts. Velocities of the emission lines are restricted to be within ±600 km/s relative to the stellar continuum velocity of the nearest Voronoi bin and the widths are restricted to be in the range from 1 - 300 km/s. These data products will be made publicly available in the future (Battisti et al. in prep). 



 §.§ Stellar masses


We derive resolved stellar mass maps directly from the MAGPI data itself, which provides uniform coverage across all of the target fields (i.e., GAMA G12, G15, and G23). This is done in two steps. We first derive stellar mass-to-light ratios (M/L) based on spectral energy distribution (SED) fitting to pixel-matched imaging from HSC where available[The deepest imaging available for MAGPI come from HSC (∼2.1 mag deeper than KiDS in the overlapping gri bands on average, in terms of 5σ detection limits measured in apertures of 2 arcsec diameters), however HSC imaging is not available in 12/56 of the MAGPI fields.], which provides broadband coverage over the grizy bands following the method described by <cit.> and <cit.>; and summarised briefly below. Next, we construct a relationship between g-r colour and M/L ratio in the r-band that can be applied consistently across the full dataset. 

Prior to SED fitting, we match the available imaging in both World Coordinate System (WCS) and pixel scale to the MUSE data cubes. We use the <cit.> template library to create composite stellar populations (CSPs), where we make assumptions of exponentially declining star formation histories (SFHs) and a single-screen dust attenuation law using <cit.>. A fully Bayesian approach is adopted such that probability-weighted averages are taken as the most likely values of stellar mass per pixel, in contrast to adopting the best-fit value derived via maximum likelihood (see Section 3.4 in ). We assume uniform priors on a total of 4 parameters - age, e-folding time, metallicity, and dust obscuration. 

The resulting M/L maps are then used to construct a relationship between g - r colour and M/Lr. We do this non-parametrically by taking the median M/L in bins of g - r colour 0.03 mag wide. We adopt the standard deviation of M/L within these bins as indicative of the uncertainty in mapping a single optical colour to M/L, which is of order 0.15 dex regardless of colour. We include this uncertainty in quadrature in our final mass estimates. The colour-M/L relationship derived in this way is applied to rest-frame g - r colour maps computed directly from the MAGPI data themselves using the measured redshifts, and is applied to spaxels that fall within the dilated segmentation maps produced by ProFound. Uncertainties on the MUSE-based rest-frame colours are computed using the uncertainties on the spectral data. The stellar mass maps are derived based on the colour-M/L relationship, where we also make uncertainty cuts on a pixel-by-pixel basis. To choose a reasonable cut, we reference the corresponding S/N resulting from reliable SED fitting of HSC imaging (i.e., S/N ≥ 10), which translates roughly into a maximum uncertainty of 0.5 dex. We also measure a total stellar mass by summing the stellar masses per pixel for the pixels that satisfy both the uncertainty and dilated mask cuts. We calculate stellar mass surface densities (Σ_⋆) using: 

    Σ_⋆ (M_ kpc^-2) = M_⋆ (M_)/(0.2 ×D_A)^2,

where the MUSE WFM pixel scale is 0.2 arcsec/pixel and D_A refers to the angular diameter distance in kpc/arcsec based on our spectroscopic redshifts and the adopted cosmology.



 §.§ Star formation rates

 
The main goal of this study is to understand the different physical mechanisms governing the star formation activity of galaxies in different global star-forming states. It is crucial, therefore, to have a complete sample of measured SFRs such that the sample is not biased towards star-forming galaxies. As such, we use two kinds of SFR indicators for this work - we use the Hα line for spaxels/galaxies with high S/N in their emission lines (see Section <ref>) and D4000 for all other spaxels/galaxies (see Section <ref>). Details regarding the methodology for measuring each SFR indicator are given in the following sections. 



  §.§.§ Star-forming spaxels/galaxies


For galaxies with well-detected emission lines, we use the Hα line to estimate SFRs. Hα emission traces hydrogen ionized by a variety of sources including star formation, active galactic nuclei (AGN), and shocks. Ionized hydrogen traced by stars roughly translates to star formation timescales of ∼10 Myr (e.g., ), i.e., the typical lifetimes of the young and massive O- and B-type stars. As such, Hα emission is a recent star formation tracer. In order to ensure that the Hα emission is devoid of contamination from other ionization sources (AGN in particular), we use the Baldwin, Phillips & Terlevich (BPT; ) emission line diagnostic diagram to identify purely star-forming spaxels within galaxies. For the BPT diagram, shown in Figure <ref>, we use the line ratios [OIII]λ5007/Hβ and [NII]λ6584/Hα, and require all 4 emission lines to have S/N ≥ 3 for a spaxel to be used in the analysis. However, we observe spaxels with good detection (i.e., S/N ≥ 3) in Hα but weak (i.e., S/N < 3) signal in [NII]λ6584, which suggests that we may be missing out on additional SF. To recover as many star-forming spaxels as possible, we take 3 times the error as an upper limit of the [NII]λ6584 flux <cit.> for spaxels with S/N < 3 in [NII]λ6584. We then plot the spaxels with upper limits on the BPT diagram, where we include those that fall in the SF region, whereas those that fall in the composite or AGN regions are excluded entirely from the analysis due to concerns of noise contamination (e.g., this method often results in spaxels in the outskirts being classified as AGN). This results in a total of 16,511 spaxels, where 12,882 (3,055 being upper limits) of them are classified as star-forming. We use the Hα emission line to measure SFRs for the 12,882 spaxels classified as star-forming. 



We correct Hα flux maps for dust extinction with the Balmer decrement, i.e., the Hα/Hβ flux ratio. We first correct for foreground extinction due to the Milky Way using the E(B - V) values from <cit.>. To correct for intrinsic extinction, we adopt the Galactic extinction curve from <cit.> with R_V = 3.1 and assume an intrinsic Hα/Hβ value of 2.86, which corresponds to Case B recombination under the conditions of temperature T = 104 K and electron density n_e = 102 cm-3 <cit.>. 

The dust-corrected Hα fluxes are then converted to luminosities with luminosity distances from measured spectroscopic redshifts. We use the SFR conversion recipe from <cit.>, which is given below:

    SFR_Hα (M_ yr^-1) = L_Hα/1.26 × 10^41 erg  s^-1× 1.53,

where L_Hα denotes the Hα luminosity. The factor of 1.53 (see Table 1 in ) converts the recipe from a <cit.> to a <cit.> IMF.

We measure local SFR surface densities, Σ_SFR, for each of the spaxels classified as SF with the following equation:

    Σ_SFR, Hα (M_⊙ yr^-1 kpc^-2) = SFR_Hα (M_ yr^-1)/(0.2 ×D_A)^2,

where the MUSE WFM pixel scale is 0.2 arcsec/pixel and D_A refers to the angular diameter distance in kpc/arcsec. In addition to the spaxel SFR surface densities, we also compute total SFRs for each galaxy by summing up all star-forming spaxels with measured SFRs. Uncertainties on both SFR and Σ_SFR are measured via error propagation on the measured uncertainties in Hα and Hβ fluxes.



  §.§.§ Passive spaxels/galaxies


For galaxies with either weak emission lines or lack of star formation as classified by the BPT diagram, we use D4000 to measure SFRs. Previous studies <cit.> have derived an empirical relation between D4000 and sSFR, that can be used in galaxies with regions either (1) classified as either composite or AGN by the BPT diagram, or (2) with weak S/N in their emission lines. We follow a similar methodology with the MAGPI data, where we exclude spaxels classified as AGN in the definition of the relation but use the relation to measure D4000-based SFRs for all spaxels with no Hα-based SFRs, including AGN spaxels[At low S/N, there may be some potential contamination from AGN in the stacking analysis described in this section. However, it is also possible that `retired' (i.e., no longer actively forming stars) regions are falsely classified as AGN <cit.> due to hot post-asymptotic giant branch (AGB) stars and white dwarfs.]. We measure D4000 on a spaxel-by-spaxel basis using the GIST stellar continuum fits, and adopt the broad D4000 definition provided by <cit.> for consistency with low-redshift results (e.g., ).

With the gist-derived D4000 values and the reduced spectra, we measure the resolved D4000-sSFR relation by stacking the spectra in a range of D4000 bins to improve the S/N of weak emission lines as shown in Figure <ref>. This is in contrast to previous methods which used individual spaxels for the calibration, such that with stacking we are able to calibrate the relation down to lower sSFRs/higher D4000. We use the following criteria to choose the spaxels/spectra going into the stack: 

    
  * have a measured D4000 with S/N ≥ 5,
    
  * have a measured M⋆ with uncertainties ≤ 0.5 dex,
    
  * not classified as AGN by the BPT classification scheme.


With regards to the first criterion, we have tested with different S/N cuts on D4000 up to S/N ≥ 20 to find that the resulting D4000-sSFR relation does not change significantly. Prior to stacking spectra on a spaxel-by-spaxel basis, we subtract the best-fit continuum measured with gist and de-redshift each spectrum based on their spectroscopic redshifts and velocity field maps. To ensure that all the spectra are matched to an identical range of wavelengths, the de-redshifted spectra are then interpolated (nearest neighbour) to a common grid of rest-frame wavelengths, the range of which is determined from the longest wavelength on the blue side and the shortest wavelength on the red side of all spectra. The spectra are then normalised by stellar mass, such that the unique stellar masses measured for each spaxel are carried through when calculating sSFRs directly from the stacked fluxes. Finally, the spectra are median combined in D4000 bins of fixed width δ_D4000 = 0.05, ranging in values from 0.9 to 1.45. The selected bin width results in each bin having >200 spectra with the maximum number of spectra in a bin being ≃2100. We also tested with different bin widths and did not see significant changes in the stacked D4000-sSFR relation. Beyond D4000 > 1.45, the S/N drops dramatically such that we use a wider bin width. We stack spectra for D4000 > 1.45 in 3 bins of 1.45 < D4000 < 1.5, 1.5 < D4000 ≤ 1.7, and 1.7 < D4000 ≤ 1.9. Despite using a wider bin width resulting in ≳6000 spectra per bin for the latter two bins, we are unable to obtain robust fits for Hα and Hβ except for the first bin of 1.45 < D4000 < 1.5, resulting in a D4000 limit of ≃1.475. Previous studies such as <cit.> and <cit.> have also found that robust SFR measurements for spaxels/galaxies of D4000 > 1.45 were not feasible. Both studies attribute the reason to a steep decline in sSFR at D4000 > 1.4, such that the sSFR varies by ≈1 dex over a δ_D4000 of 0.1. However, see <cit.> and <cit.> for a continuous derivation at D4000 > 1.45. 

After median stacking the spectra in bins of D4000, we fit Gaussian profiles to both the Hα and Hβ lines for each stacked spectrum using the code lmfit[<https://lmfit.github.io/lmfit-py/>] <cit.>. We fit single Gaussian profiles to 4 emission lines: Hα, [NII]λλ6549,6584, and Hβ. When fitting the emission lines, we take on the following constraints on the fitting parameters: (1) a single line width is fit to all the lines based on the brightest line (i.e., Hα for the [NII] doublet), (2) the ratio of [NII]λ6584/[NII]λ6549 is fixed to 3.071:1 <cit.>, and (3) corresponding wavelengths for the emission lines of interest are allowed to vary within ± 5 Å of the rest-frame wavelengths in vacuum. While the constraint placed on the wavelengths are not strict, the median offsets of the fits are ≃ 0.8 Å and ≃ 0.3 Å for the Hα and Hβ lines respectively, suggesting that the constraint of 5 Å is not an issue. We first fit the lines using the Levenberg-Marquardt algorithm, then use the Markov Chain Monte Carlo (MCMC) method to refine our best-fit and uncertainty estimates. The median and 1σ values of the posterior probability distributions of the fitted parameters are then used to measure integrated fluxes and their errors. The integrated Hα fluxes for each bin are then dust-corrected for both foreground and intrinsic extinction via the same method outlined in Section <ref>, using the integrated Hβ fluxes to measure the Balmer decrement. Foreground extinction is corrected for by using the median E(B - V) of the stack. We then use the median spectroscopic redshift of each bin to convert the extinction-corrected Hα fluxes to luminosities, and then to sSFRs. 



The resulting resolved D4000-sSFR relation for 0.25 ≤ z ≤ 0.424 is shown in Figure <ref>. The blue contours represent the distribution of spaxels with measurements of both Hα-derived SFRs and D4000 (7,788 spaxels), whereas the grey circles along with the black solid line indicate the stacked D4000-sSFR relation. The black line is given by a one-dimensional smoothing spline fit to the data points. To convert D4000 to SFRs, each spaxel with a measured D4000 is first matched to the closest value in D4000 on the D4000-sSFR relation. Then, a sample of possible sSFR values are generated based on the input D4000 and its error via Monte Carlo, where the median of the distribution is taken as the output sSFR. The median absolute deviation (MAD) standard deviation of the sSFR distribution and the standard deviation of the scatter in the recovery of SFRs with D4000 (see Figure <ref>) are added in quadrature to obtain uncertainties on the sSFRs. The latter uncertainty is measured from comparing Σ_SFR, D4000 and Σ_SFR, Hα for the same spaxels, where the standard deviation of Δlog(Σ_SFR) [≡ log(Σ_SFR, D4000) - log(Σ_SFR, Hα)] is added in quadrature to reflect how well Σ_SFR, Hα measurements are recovered with D4000. Additional discussion along with tests performed on the reliability of D4000 as a SFR indicator are presented in Appendix <ref>. The chosen sSFR is then converted to a Σ_SFR using the following equation: 

    Σ_SFR, D4000 (M_⊙ yr^-1 kpc^-2) = sSFR×Σ_⋆,

where the units of Σ_⋆ are in M kpc-2. SFRs are measured in the same manner, except in units of M yr-1. Total SFRs are then measured by summing up all the spaxels with measured D4000-derived SFRs that lie in the dilated masks, similarly done with the Hα SFRs. 



 §.§ Global and local star formation metrics


To compare different subsamples of galaxies in our analysis, we consider the known dependencies of SFRs on other properties (e.g., ), most notably stellar mass. Similar in definition to the commonly measured sSFR, we choose to use ΔΣ_SFR and ΔSFR parameters (e.g., ). The parameters are defined as the following:

    ΔΣ_SFR   = log_10(Σ_SFR, spax) - log_10(Σ_SFR, MS) 
    ΔSFR   = log_10(SFR_gal) - log_10(SFR_MS)

where both parameters describe the logarithmic offsets from the resolved and global SFMS, respectively. The parameters are defined such that any galaxy/spaxel above the main sequence has positive Δ-parameter indicating higher levels of star formation activity than a galaxy/spaxel on the main sequence, and vice versa. While ΔSFR measures how star-forming a galaxy is overall for its stellar mass, ΔΣ_SFR is defined in a similar way except that it measures the level of star formation activity on a local scale equivalent to that of a MUSE spaxel. 



Given the definitions of the Δ-parameters, we measure both the global and resolved star-forming main sequences. We assume that the dependence of SFR on stellar mass can be well described by a single power-law such that the SFMS is a linear relation in log-log space. We use the code ltsfit[<https://pypi.org/project/ltsfit/>] <cit.> to measure a best linear fit to the SFMS. 

To define the resolved SFMS, we only use the spaxels with Hα-based Σ_SFR (total of 12,198 spaxels) measurements to ensure that the resolved SFMS best represents a population of star-forming spaxels. We show the resulting fit along with all the spaxels with measured Σ_SFR and Σ_⋆ (including D4000-derived Σ_SFR brings the total up to 13,504 spaxels) in Figure <ref>, where each hexagonal bin is colour-coded by ΔΣ_SFR as defined by Equation <ref>. The best-fit equation is given below:

    log_10(Σ_SFR) [M_⊙ yr^-1 kpc^-2] = 0.918 ×log_10(Σ_⋆) - 9.196,

with the root-mean-square error on the fit being ∼0.338 dex, shown by the blue dashed line in Figure <ref>. The errors on the slope and intercept are 0.005 and 0.006, respectively. The global SFMS is defined similarly such that we only use galaxies with SFRHα (total of 211 galaxies) for the fit. We show the resulting global SFMS fit, along with the distribution of a total of 302 galaxies with measured SFR (including D4000-based) and M⋆ in Figure <ref>. The equation for the global SFMS is given below:

    log_10(SFR) [M_⊙ yr^-1] = 0.748 ×log_10(M_⋆) - 7.726,

with the root-mean-square error on the fit being ∼0.551 dex, and the slope and intercept errors being 0.038 and 0.055, respectively. 



We define global SF states as a function of logarithmic offset from the SFMS using the following definitions to classify galaxies in our sample:  

    
  * Above the SFMS: ΔSFR > 0.5 dex,
    
  * SFMS: -0.5 dex < ΔSFR < 0.5 dex,
    
  * Just below the SFMS: -1.1 dex < ΔSFR < -0.5 dex,
    
  * Far below the SFMS: ΔSFR < -1.1 dex.

These classifications are comparable to those used for the MANGA sample, allowing a fair comparison with results based on the local Universe <cit.>. The distribution of ΔSFR values for our sample are shown in Figure <ref>, colour-coded by the different SF states as defined above. These classifications result in a total of 301 galaxies. Finally, 8 galaxies are removed from the sample that have a global measurement of SFR and stellar mass but individually do not have spaxels that meet our S/N criteria in both the stellar mass and SFR maps simultaneously. This results in our final sample of 294, such that we have 27 galaxies in the ΔSFR > 0.5 bin, 131 galaxies in the main sequence bin, 42 galaxies in the -1.1 < ΔSFR < -0.5 bin, and 94 galaxies in the least star-forming bin.  





 §.§ Derivation of radial profiles


Following the definitions of ΔΣ_SFR and ΔSFR, we construct radial profiles of star formation activity as a function of global SF state to probe the physical mechanisms at play within MAGPI galaxies. We apply the same methodology towards measuring radial profiles in AgeL as well, where stellar ages are derived based on stellar continuum fits using the C3K spectral templates (Section <ref>). We use the structural parameters derived with ProFound, which include effective radii (i.e., R_ e), position angles, and axial ratios, to define radial bins of elliptical annuli. These parameters were measured using i-band MUSE images reconstructed with the SDSS i-band filter transmission curve. The structural parameters given by ProFound are PSF-convolved measurements, as ProFound does not take either the size or shape of the PSF into account in source detection. 

Fixing the locations of peak flux in the white light image as the galaxy centre, we calculate galactocentric distances for each spaxel in units of R_ e for each galaxy. We choose to use fixed discrete bins of width 0.5 R_ e from 0 to 3.0 R_ e to bin values of ΔΣ_SFR from all galaxies with measured ΔΣ_SFR maps. The radial extent out to which we probe is set by the number of galaxies and spaxels contributing to each radial bin, such that only bins with at least 10 galaxies (N_gal≥ 10) and 50 spaxels (N_spax≥ 50) were included. The cuts are chosen to exclude bins with low number statistics in either the number of galaxies or spaxels. Details on the total number of galaxies and spaxels contributing to each bin for both ΔΣ_SFR and AgeL profiles are given in Appendix <ref>. We confirm that our results are not significantly affected by the choice of fixed versus smoothed binning approaches or bin width, consistent with <cit.>. To measure a population-averaged radial profile, we take the median of all spaxels belonging to all galaxies within each global SF state for each radial bin. We then measure the standard error on the median ΔΣ_SFR with bootstrap. 



Due to our relatively small sample we do not apply an inclination cut. Using a larger sample, <cit.> have shown that their radial profiles are robust against restrictions to face-on galaxies or adopting Euclidean distance formula rather than elliptical aperture bins consistent with <cit.>. 





§ RESULTS


In this section, we explore radial trends in both star formation rates and stellar ages as a function of global SF state, to understand what potential processes govern our sample of MAGPI galaxies at z ∼ 0.3. We compare the radial trends in a qualitative and quantitative manner, where for the latter we measure radial slopes with Monte Carlo derived uncertainties by making linear fits to the profiles. The slopes and errors are shown in Table <ref>. We show the ΔΣ_SFR profiles in Section <ref> and put them in context with the AgeL profiles in Section <ref>. 



 §.§ deltasigmasfr profiles
 
The ΔΣ_SFR radial profiles are shown in Figure <ref>, colour-coded in the same manner as shown in Figure <ref>. For the ΔSFR > 0.5 bin (pink), galaxies exhibit enhanced star formation activity with respect to the resolved SFMS (i.e., positive ΔΣ_SFR), where the overall trend is flat (slope = -0.05 ± 0.01 dex R_ e-1) across all radial distances probed. The flatness of the profile suggests that the physical processes at play do not enhance specific regions in galaxies above the SFMS at z ∼ 0.3. For all galaxies in this bin, all spaxels have Hα-measured Σ_SFR - indicating that the star formation probed in these galaxies is recent. 

For galaxies on the main sequence (i.e., -0.5 < Δ SFR < 0.5; blue), the profile shows a slightly positive gradient with a measured slope of 0.11 ± <0.01 dex R_ e-1. We find 3 galaxies with notably high spaxel contribution fractions to be responsible for the small enhancement at the outskirts (R ≳ 2 R_ e). Two of these galaxies are among the more highly star-forming galaxies in this bin (ΔSFR ≃ 0.42 and 0.49 dex), and all 3 of them exhibit on average higher Σ_SFR with increasing galactocentric radii. While it is not trivial to interpret this as a sign of inside-out quenching and/or preferential enhancement of SF in the outskirts, we are able to confirm that the uptick in the outskirts is statistically robust. Removing these three galaxies results in a flatter profile but drops the last radial bin out to 3 R_ e below our criteria of a minimum of 10 galaxies. It is also noteworthy that this uptick has not been observed in previous studies, such as those based on the local Universe <cit.>, showcasing the strength of MAGPI in probing the far outskirts of galaxies. The inner flat (slope = 0.06 ± 0.01 dex R_ e-1 for R ≤ 1.5 R_e; refer to Table <ref>) profile suggests that if there are any competing physical mechanisms at play, they balance each other such that the level of star formation activity stays fairly uniform from the galaxy centre towards the outskirts. Despite the galaxies in this bin lying on or near the SFMS, the majority of the average radial profile overall sits below ΔΣ_SFR = 0 (grey dashed line). This suggests that what is observed in the ΔΣ_SFR does not necessarily align with what is suggested by a galaxy's ΔSFR, such that it is important to investigate galaxy-wide star formation activity on both local and global scales. Similar results have been observed with local (e.g., MaNGA; ) galaxies, in particular, satellite galaxies on the main sequence exhibit a flat ΔΣ_SFR profile at ΔΣ_SFR∼ -0.1 at all radial distances probed up to 1.5 R_ e <cit.>. 

We observe a positive (slope = 0.17 ± 0.02 dex R_ e-1) radial gradient in ΔΣ_SFR out to 2 R_ e within the -1.1 < ΔSFR < -0.5 bin (green). The entire profile is located at ΔΣ_SFR∼ -0.65, which together with the positive gradient, is suggestive of inside-out quenching. Moreover, the contribution of Hα-detected spaxels begins to decrease to ∼40 per cent for galaxies in this bin and to <10 per cent in the ΔSFR < -1.1 bin (red), further supporting the onset of quenching (Appendix <ref>). In contrast to what is measured for the ΔSFR > 0.5 (pink) and -0.5 < ΔSFR < 0.5 (blue) bins, we are only able to robustly measure the profile out to 2 R_ e. For ∼34 per cent of spaxels in this bin, we only measure an upper limit on ΔΣ_SFR because they have D4000 > 1.475. As we do not include these upper limits into consideration for the profile measurement, the profile shown in Figure <ref> is an upper limit (Appendix <ref>).

In our lowest ΔSFR bin (red), we observe an overall positive gradient with a slope of 0.11 ± 0.01 dex R_ e-1, again suggestive of inside-out quenching. These results are similar to that of the -1.1 < ΔSFR < -0.5 bin (green), with the exception that galaxies in this bin exhibit lower values of ΔΣ_SFR across all radial bins probed. Moreover, the contribution of Hα-detected spaxels is far lower in this bin, reaching an average of ∼10 per cent per radial bin. As such, galaxies in this bin are also subject to the same limitations imposed by the measured D4000-sSFR relation, where the fraction of spaxels with upper limits are high towards the galaxy centre (∼97 per cent in the 0 – 0.5 R_ e bin, compared to ∼84 percent in the 2 – 2.5 R_ e bin). This is expected given that older stellar populations (and as such larger D4000) likely reside in galaxy centres. Given that quite a few galaxies have measured D4000 values higher than that limit, we are potentially biasing our sample of `quenched' galaxies to those with some residual star formation. We explore this further in Section <ref> and Appendix <ref>. 



 §.§ Luminosity-weighted stellar ages


We show the luminosity-weighted stellar age (AgeL) profiles, following the same methodology of stellar continuum fitting with gist as described in Section <ref>, in Figure <ref>. Starting with the highest star-forming bin (i.e., ΔSFR > 0.5; pink), we observe an overall uniform distribution of stellar ages with a slope of -0.01 ± 0.01 Gyr R_ e-1. Galaxies in this bin consist of the youngest stellar ages out of all global SF states, which is in line with what we observe with the ΔΣ_SFR profile. 



On the other hand, we observe a negative gradient (slope = -0.18 ± < 0.01 Gyr R_ e-1) in the stellar ages for the main sequence (i.e., -0.5 < ΔSFR < 0.5; blue) population, consistent with inside-out growth <cit.>. This is in contrast to the slightly positive gradient we observe out to 2.5 Re in ΔΣ_SFR (slope = 0.11 ± < 0.01 dex R_ e-1), where we may be capturing lower levels of recent SF and older stellar populations in the centre. 

For the -1.1 < ΔSFR < -0.5 bin (green), we observe a flat profile with a slope of -0.04 ± 0.02 Gyr R_ e-1. This is in contrast to the positive gradient observed in ΔΣ_SFR, where the galaxy centre is less star-forming than the outskirts. Given that the ΔΣ_SFR profile arises from a combination of Hα and D4000, any residual SF probed by Hα is not being captured in the AgeL profile likely due to timescale differences (≲10 Myr for Hα vs. ≲1 Gyr for the stellar continuum). 

A flat profile is observed in the ΔSFR < -1.1 (red) bin as well (slope = -0.02 ± 0.01 Gyr R_ e-1), where the oldest ages out of all 4 global SF states are observed. We observe similar trends with the -1.1 < ΔSFR < -0.5 bin, where in addition to a flat AgeL profile, we observe a positive gradient in ΔΣ_SFR despite the significantly decreased fraction of Hα spaxels in this bin. The difference in radial trends may also stem from the use of Voronoi binning for stellar continuum fitting. As Voronoi binning is not applied to the emission line fluxes or D4000 measurements, the spatial variation we are able to probe is not as fine with the ages. Nevertheless, the overall increase in range of stellar ages with decreasing ΔSFR is in line with the expectation of galaxies hosting older stellar populations with decreased SFRs. 



§ DISCUSSION


We have investigated the ΔΣ_SFR and luminosity-weighted stellar ages of galaxies across different regions of the SFMS within the MAGPI sample. In this section, we first address the probability of a potential redshift evolution of galaxy properties among local (z ∼ 0), intermediate (z ∼ 0.3; this study), and high (z ∼ 2) redshift regimes. We then focus on understanding the potential physical mechanisms at play while also connecting our results to those of other similar IFS-based studies. We also put our results in context with what has been found with cosmological simulations. 



 §.§ Do we observe an evolution in star formation activity with redshift at sim 0.3?


Galaxy evolution studies indicate that mass-averaged galaxy populations have evolved significantly from z∼ 2 to the present day (e.g., ; and references therein). These changes are likely driven by the evolution of accretion, environment, and the build up of passive galaxies through quenching. Here we explore our ΔΣ_SFR profiles in the context of this evolution.

Starting with z ∼ 0, we overplot the radial profiles from MaNGA data (solid and dashed lines; ) on top of our results in Figure <ref> to examine any differences in ΔΣ_SFR. We measure slopes for the MaNGA and MAGPI profiles, the latter for which we re-measure the slopes only up to 1.5 R_ e for direct comparison to MaNGA. The slopes are given in Table <ref>. Given that the majority of our MAGPI sample (∼76 per cent) belong to groups identified using the algorithm introduced by <cit.>, we plot MaNGA radial profiles for satellites only for fairer comparison. Aside from the main sequence (i.e., -0.5 < ΔSFR < 0.5; blue) profile, all star-forming bins show distinctive profiles in overall shape and/or normalisation of ΔΣ_SFR values. 

Notably, the ΔSFR > 0.5 bin (pink) as measured with MaNGA shows a strong negative gradient (slope = -0.34 ± 0.02 dex R_ e-1) in star formation, whereas the profile measured with MAGPI is flat across the same radial distances probed (slope = -0.02 ± 0.02 dex R_ e-1 for R ≤ 1.5 R_ e). The negative gradient has been observed in star-forming galaxies in other MaNGA-based studies <cit.>, which seems to suggest that this is a common trend in the local Universe. In particular, <cit.> find this central enhancement to become more distinct with increasing stellar mass. A similar trend is seen with SAMI galaxies <cit.>, showing centrally concentrated SF in galaxies located >1σ above the main sequence (however, we note that this study used Σ_SFR and not sSFR, where the latter is a much more comparable parameter to ΔΣ_SFR). In contrast, <cit.> find a flattening with increasing stellar mass for the above MS profile with logM_⋆=10.5-11 galaxies being consistent with a flat profile. While we do not split our sample in stellar mass bins due to low number statistics, we note that the majority of MAGPI galaxies above the MS are in the mass ranges of logM_⋆=9-9.5 or lower (Figure <ref>), therefore implying evolution within this sample.

At z∼1, <cit.> find overall flat Hα surface brightness profiles when normalised by the SFMS, such that SF is enhanced everywhere in galaxies above the SFMS. However, they also find increasingly centrally depressed profiles in sSFR and Hα equivalent width with increasing stellar mass. For a more direct comparison, we re-measure the radial profiles in sSFR (≡Σ_SFR / Σ_⋆) in 3 different star-forming bins, across 4 bins of stellar mass, as done in <cit.>. We show the definitions of the star-forming bins below, where the upper bound on the `above the SFMS' bin and the lower bound on the `below the SFMS' bin has been modified to include the rest of the MAGPI sample.

    
  * Above the SFMS: ΔSFR > 0.4 dex,
    
  * SFMS: -0.4 dex < ΔSFR ≤ 0.4 dex,
    
  * Below the SFMS: ΔSFR ≤ -0.4 dex,

Similarly done with the ΔΣ_SFR profiles, we impose galaxy and spaxel cuts such that only radial bins with at least 5 galaxies (Ngal ≥ 5) and 25 spaxels (Nspax ≥ 25) are included. The cuts imposed are less stringent here (see Section <ref>) due to reduced sample statistics coming from binning the profiles into multiple stellar mass regimes. The profiles, along with those from <cit.> (bottom panel of Figure 14 in their study), are shown in Figure <ref>. We have normalised all profiles by the measured sSFR value of the SFMS profile at r ≈ 1 kpc, to facilitate easier comparison. Starting with galaxies in the lowest mass bin, we observe overall flat profiles for galaxies above (blue; slope = 0.03 ± <0.01 dex kpc-1) the SFMS, in line with what is observed with the 3D-HST results <cit.>. However, with increasing stellar mass, we do not observe the same trend of increasingly centrally depressed profiles; we measure similar slopes of 0.02 ± <0.01 and 0.01 ± <0.01 dex kpc-1 for the 9.5 < logM_⋆ < 10 and 10 < logM_⋆ < 10.5 bins, respectively. For the highest mass bin, we are unable to measure a statistically robust profile with the imposed galaxy and spaxel cuts. Similar trends are found for a handful of galaxies at z ∼ 2 <cit.>, where flat profiles[We note that profiles from <cit.> are also measured in terms of sSFRs, different from the offset from the rSFMS used in this work and with work from MaNGA. While we do not perform the same sSFR comparison with their sample as we've done with <cit.>, they are still comparable in that both measurements are normalised by stellar mass.] are observed on average for above MS galaxies but arising from a large variety for individual systems that appears to be mass dependent. Together, these results suggest that SF profiles of low to intermediate mass galaxies above the MS are flat out to ∼2-3R_e from cosmic noon until at least ∼4 Gyrs ago perhaps indicative of efficient gas accretion and transport throughout galaxies. While at z∼0, galaxies above the MS may more regularly have centrally enhanced SF due to central starbursts partly driven by mergers. 

On the other hand, there is a strong agreement in the range of ΔΣ_SFR values probed by the main sequence galaxies (blue) at z∼0.3 and z∼0. The two profiles are both flat within R ≤ 1.5 R_ e, where the MaNGA and MAGPI profiles measure slopes of 0.00 ± 0.01 and 0.06 ± 0.01 dex R_ e-1, respectively. While there is a statistically significant difference in the slopes based on the measured uncertainties, we note that the difference mainly stems from the profiles diverging from one another beyond R ∼ 1  R_ e. This suggests that galaxies on the SFMS across the epochs probed are regulating their SF activity in a similar manner in the inner regions of galaxies. However, the uptick observed in the outskirts of the MAGPI sample may hint at external mechanisms, highlighting the importance of mapping SF activity out to large galactocentric radii. The positive slope in the MAGPI sample at large galactic radii is driven by a small number of galaxies (Section <ref>) but is consistent with average sSFR profiles of massive galaxies at z∼1 <cit.> and individual profiles measured of massive galaxies at z∼2 <cit.> which have also been measured to ∼3 R_ e. In particular, when converted to sSFRs, the MS (black) profiles measure flat slopes across all stellar mass bins (averaging ≈0.03 ± <0.01 dex kpc-1), which is in agreement with the profiles from <cit.> (slopes averaging <0.1 dex kpc-1).





The two lowest ΔSFR bins (i.e., green and red profiles) show larger differences in ΔΣ_SFR between z = 0 and z = 0.3. In general, we observe higher levels of star formation activity in our MAGPI sample for the same ΔSFR bins.[Barring differences in the loci of the SFMS, which can rise from differences in methodology (<cit.> uses the definition from <cit.>, which does not require a pre-selection of SF galaxies as done in this study) and/or evolution of the SFMS over time, the bins are considered to be identical in ranges of ΔSFR.] The offset in ΔΣ_SFR could be due to differences in populations probed at the two epochs; recent results from the EAGLE simulation <cit.> show that galaxies with centrally concentrated SF below the SFMS are more common at z = 0 than at z ≈ 0.3. Centrally concentrated SF suggests relatively quenched outskirts of these galaxies due to environmental mechanisms, such that these findings suggest that there are more quenched satellites in the local Universe than at the MAGPI redshift regime. In terms of the measured slopes, there is good agreement between the MaNGA and MAGPI profiles within R ≤ 1.5  R_ e for the -1.1 < ΔSFR < -0.5 bin (green), with measurements of 0.12 ± 0.01 and 0.08 ± 0.03 dex R_ e-1, respectively. The MaNGA profile shows a stronger hint of inside-out quenching (i.e., steeper positive gradient), but we note that the MAGPI profile does measure a steeper gradient (slope = 0.17 ± 0.02 dex R_ e-1) out to R ∼ 2  R_ e. On the other hand, the MaNGA profile for the ΔSFR < -1.1 bin (red) is overall flat (slope = -0.02 ± <0.01 dex R_ e-1), whereas the MAGPI profile measures a slightly steeper negative gradient (slope = -0.09 ± 0.02 dex R_ e-1) for R ≤ 1.5  R_ e. Similar to the -1.1 < ΔSFR < -0.5 bin, the MAGPI profile shows a stronger hint of potential inside-out quenching with a measured slope of 0.11 ± 0.01 dex R_ e-1 when measured out to 3 R_ e.

However, the caveat here is that the flatness of the ΔSFR < -1.1 profile from MaNGA largely rises from assigning a constant value to all D4000 > 1.45 measurements. When a similar treatment is done on the -1.1 < ΔSFR < -0.5 and ΔSFR < -1.1 bins for the MAGPI sample, the profiles become much flatter and reside around ΔΣ_SFR∼ -1.5. Given the considerable fraction of upper limits that exist in both bins, in particular for the ΔSFR < -1.1 bin (see Figure <ref>), the contrast in ΔΣ_SFR between z = 0 and z = 0.3 does not necessarily indicate an evolution in SF. 

At z∼1-2, a central (within ∼1 R_e) depression is seen in sSFR profiles of galaxies below the SFMS particularly for the most massive galaxies (; see also the red dashed lines in the panels with logM_⋆>10 in Figure <ref>). We observe mixed results with the sSFR profiles for MAGPI galaxies below the MS (red), in that the profiles in the 9 < logM_⋆ < 9.5 and 10 < logM_⋆ < 10.5 bins show positive gradients (slopes of 0.10 ± 0.02 and 0.08 ± 0.01 dex kpc-1, respectively), whereas the profiles in the 9.5 < logM_⋆ < 10 and 10.5 < logM_⋆ < 11 bins show flatter profiles (slopes of -0.02 ± 0.01 and 0.01 ± <0.01 dex kpc-1). The lack of a trend with increasing stellar mass may come from a lack of robust statistics per radial bin, as apparent by the larger uncertainties and shorter radial distances probed. We also note that given the distribution of MAGPI galaxies below the SFMS in SFR-M⋆ space (see Figure <ref>), stellar mass bin widths of 0.5 dex in the range of 9 < logM_⋆ < 11 naturally limit the number of available galaxies for analysis. However, when considered over the entire stellar mass range, galaxies at z ∼ 1 do show flat MS-normalised Hα profiles, which is in line with the MAGPI and MaNGA results seen with the ΔΣ_SFR profiles.





 §.§ What regulates and/or quenches star formation at sim 0.3?



We observe enhanced star formation at all radial distances probed with respect to the resolved SFMS in the most star-forming bin (i.e., ΔSFR > 0.5). Given that all galaxies contributing to the profile have Hα-measured Σ_SFR, this suggests that MAGPI galaxies in this bin have sufficient cold gas reservoirs to fuel star formation as traced at this epoch. The overall flatness (slope = -0.05 ± 0.01 dex R_ e-1) of the profile suggests that the physical processes at play for these galaxies do not lead to a preferred radial trend in star formation enhancement. 

Previous studies () have proposed that gravitational torques can transport the newly accreted gas from these interactions towards the centre, eventually leading to a starburst. This can be caused partly by galaxy-galaxy and/or tidal interactions, triggering inflow of cold gas external to the galaxy. To test this hypothesis, we search for nearby neighbours in both redshift and on-sky separations. Following the findings of <cit.>, we first search for nearby galaxies with line-of-sight velocities of Δ v < 1000 km s-1 and projected distances of ≲150 kpc - the maximum projected separation out to which <cit.> found statistically significant SF enhancements. This simple test indicates that ∼78 per cent (21/27) of galaxies in the ΔSFR > 0.5 bin have at least one nearby neighbour, some having as many as 11 potential neighbours. We also confirm these results with a preliminary group finding analysis, where we find ∼85 per cent (23/27) of galaxies belong to groups ranging between 2 to 12 members. If galaxy-galaxy interactions are the dominant process at play, the median profile for this bin would show a negative gradient due to the central starburst. Given the flatness of the profile, this suggests that interactions with nearby neighbours cannot be the sole physical process at work for star-forming galaxies residing above the SFMS. 

In contrast, a generally negative trend in star formation activity with increasing galactocentric radii for galaxies above the SFMS has been observed in the local Universe (i.e., z ∼ 0). In particular, the central enhancement of star formation activity in MaNGA galaxies can be associated with metal-poor gas accretion <cit.>. This suggests that major and minor mergers, along with interactions with dwarf satellites, are some of the likely causes of the inflow of pristine gas towards the centre. The central enhancement is confirmed by <cit.>, where they find shorter gas depletion times centrally compared to the outskirts. Assuming a simple gas regulator model, these results suggest that spatial variation in SFRs in galaxies may simply be due to variation in SF efficiencies, such that any changes in gas accretion rates are immediately reflected upon the measured SFRs. On the other hand, <cit.> do not find evidence for strong radial trends in star formation as probed by EW(Hα) at z ∼ 1. They instead find that star formation is enhanced throughout the galaxy disc for galaxies located above the main sequence, which is suggestive of physical processes not exclusive to major mergers and galaxy interactions. We find our results to be more consistent with those of <cit.>, which suggests that radial trends already start to evolve at the MAGPI redshift regime. This could also be explained by the fact that gas accretion rates are overall higher at higher redshifts <cit.>. 

Galaxies on the main sequence (i.e., -0.5 < ΔSFR < 0.5) show a positive gradient in ΔΣ_SFR with a slope of 0.11 ± <0.01 dex R_ e-1. Generally small bootstrap uncertainties of the median profile suggest that local variation in Σ_SFR is minimal and that values are generally distributed around ΔΣ_SFR = 0. Relatively small uncertainties in the luminosity-weighted age profile also suggest that the increase in age with decreasing radius towards the centre is likely real. These results are consistent with an inside-out growth scenario, where galaxies start building up their stellar mass in the centre. 

A model based on high-redshift (z ∼ 2 - 4) simulations suggests that galaxies on the SFMS undergo multiple cycles of gas inflow and depletion in the centre, which results in oscillations about the SFMS and as such scatter about the main sequence <cit.>. It is not until galaxies reach a critical virial mass of ∼1011.5 M, where galaxies then begin a full quenching process triggered by shock heating of the halo. On the other hand, analysis based on the EAGLE simulations <cit.> at z ∼ 0.1 suggests that the scatter of the SFMS is mostly modulated by long timescale (∼10 Gyr) variations that depend on the halo's assembly history. Fluctuations due to self-regulation processes such as cooling, SF, and outflows run on shorter timescales and are only important for less massive galaxies. Both scenarios apply to our sample, in that any competing physical mechanisms at play likely cancel one another out and that any long timescale processes will not be reflected in Hα-based measurements, given that Hα traces timescales as short as ∼10 Myr. With the former, this implies a balance between gas accretion and depletion due to star formation and/or galactic winds, which is unsurprising for galaxies located on the SFMS. Furthermore, our nearby neighbour search suggests that 65 per cent (85/131) of galaxies in this ΔSFR bin have neighbours within projected separations of 150 kpc or lower, giving further support for external cold gas accretion. Results from the group finding analysis give similar numbers, where some groups consist of as many as 20 members. 

Similar conclusions were reached in another study at a similar redshift range of 0.1 < z < 0.42 with the MUSE-Wide survey, which show evidence for inside-out growth in star-forming galaxies based on observing a positive gradient in dust-corrected Hα-based sSFRs <cit.>. Furthermore, observations of extended Hα emission compared to the stellar continuum, along with increasingly centrally depressed Hα equivalent widths with stellar mass, at z ∼ 1 suggests that inside-out assembly of galaxy discs are ubiquitous across a broad range of redshifts <cit.>.

While galaxies in the higher star-forming bins show evidence of star formation fueled by consistent cold gas accretion, galaxies in the -1.1 < ΔSFR < -0.5 bin begin to show signs of quenching across all radial bins probed. The positive gradient in ΔΣ_SFR suggests inside-out quenching, with relatively higher SF measured in the outskirts. This trend suggests that it is moreso internal rather than external mechanisms dominating the SF activity in these galaxies. As mentioned previously in Section <ref>, the MAGPI sample selected for this study do not include galaxies in the most dense environments, i.e., galaxy clusters. Majority of our galaxies (∼76 per cent) belong to groups, where environmental mechanisms such as ram pressure stripping <cit.>, viscous stripping <cit.>, and starvation/strangulation <cit.>, are not expected to be as strong as they are in cluster environments. Gas stripping mechanisms in particular are expected to be more efficient in the galaxy outskirts, where the gas is less tightly confined to the galaxy's gravitational potential. The aftermath of such mechanisms would manifest itself in a negative gradient in SF, characteristic of quenching starting from outside-in. For this ΔSFR bin in particular, ∼69 per cent (29/42) of them belong to groups, some with as many as 20 members. Given that we do not observe a negative gradient, we attribute the overall low levels of SF and the positive gradient in ΔΣ_SFR, to `pre-processing' <cit.> – where galaxies are subject to interactions with other galaxies and the group potential itself, leading to SF quenching. 

Clear features of environmental mechanisms at play are observed in the local Universe. For MaNGA, notable differences in ΔΣ_SFR profiles between the centrals and satellites for green valley (i.e., galaxies in the -1.1 < ΔSFR < -0.5 bin) galaxies have been observed <cit.>. While both centrals and satellites exhibit quiescent cores, satellites do not have star-forming outskirts as centrals do. Nevertheless, satellites in the MaNGA sample do exhibit positive ΔΣ_SFR gradients (slope = 0.12 ± 0.01 dex R_ e-1; Table <ref>) overall. Evidence for outside-in quenching is only captured in low-mass (i.e., M⋆ < 1010 M) satellites for the MaNGA sample. These results imply that environmental processes play a more dominant role for low-mass satellites, which may explain for the lack of a clear outside-in quenching feature in the MAGPI sample. Due to current sample statistics in both galaxies and spaxels, we are unable to perform a similar analysis for the current MAGPI sample. 

We also mentioned previously that the entire ΔΣ_SFR profile for this bin is considered an upper limit, given the limitation of the D4000-sSFR relation. In Appendix <ref>, we show that the majority of spaxels with upper limits are distributed around ΔΣ_SFR ≃ -1.5, with the largest fraction being in the 0.5 – 1.0 R_ e bin. In terms of the ratio of detections vs. non-detections, the contribution from both are comparable such that the entire profile will likely be shifted to lower ΔΣ_SFR with proper consideration of upper limits. We do not expect to see a different trend other than the previously observed positive gradient (i.e., inside-out quenching). We also address the effects of combining Hα- and D4000-based Σ_SFR measurements on the ΔΣ_SFR profile in Appendix <ref>. Our comparison of Hα- and D4000-only profiles show that while D4000 alone does systematically underestimate the level of SF, there is in general a good agreement between the two measurements (Figures <ref> and <ref>). 

Finally, we discuss the implications of the galaxies in the least star-forming bin, i.e., ΔSFR < -1.1 (red). The measured slope of 0.11 ± 0.01 dex R_ e-1 of the ΔΣ_SFR profile suggests that the central region is relatively quenched in comparison to the outskirts. The profile suggests physical processes that are preferentially at work within the galaxy centre, which may include AGN feedback and/or expedited use of star-forming gas. While we have removed any spaxels classified as optical AGN, it is possible that we may have missed out on weaker AGN emission due to lack of sufficient S/N (i.e., S/N ≥ 3) in one or more emission lines, or AGN identifiable by multi-wavelength tracers. The lack of a current optical AGN signature also does not preclude previous activity of an AGN that is currently not active <cit.>. 

In local galaxies, ΔΣ_SFR profiles in the most and least star-forming bins mirror one another in that there is a clear central enhancement in the former and suppression in the latter <cit.>. This has been interpreted as an indication of inside-out mass growth triggered by gas inflow preferentially towards the central regions, followed by eventual quenching propagating from inside-out. A variety of scenarios could explain this phenomenon, which include gas depletion and AGN feedback. On the other hand, <cit.> associate central enhancement/suppression in galaxies above/below the SFMS with different response rates to changes in gas accretion rates from the halo; positive/negative SF gradients are thus not necessarily hinting towards different physical processes at play. However with the same parent dataset, <cit.> observe a much flatter profile for galaxies of the same bin (i.e., their ΔSFR < -1.1 bin), where the lack of a clear trend seem to come from their choice of extending the D4000-sSFR relation to higher D4000 (i.e., D4000 > 1.45) by assigning the same artificial value of sSFR = 10-12 yr-1 <cit.>. We can see this effect at work within our own sample. When we include only the spaxels with D4000 ≤ 1.475 where the relation can be defined, we see the central depression. However, when we include spaxels with a measured D4000 beyond this limit as upper limits defined by a floor in sSFR at high D4000, we obtain a flat profile consistent with <cit.>. As shown in Appendix <ref>, we observe a higher fraction of upper limits towards the galaxy centre (i.e., 0 – 1.5 R_ e). This suggests that with improved measurements on the upper limits, the ΔΣ_SFR profile is likely to show a steeper positive gradient consistent with inside-out quenching. 



§ SUMMARY


In this study, we have investigated the radial trends in ΔΣ_SFR and AgeL as a function of location with respect to the SFMS (i.e., ΔSFR) to constrain the physical processes enhancing, regulating, and quenching MAGPI galaxies. We use D4000 in addition to the Hα emission line to ensure that we capture low levels of SF, such that our sample is as complete as possible in the ranges of global SF states probed. We also place our results in context with galaxies at low- (z ∼ 0) and high-redshift (z ∼ 1 and z ∼ 2) to investigate the possibility of an evolution in radial trends in SF activity across these redshift regimes. We summarise our key results below: 

    
  * Star-forming galaxies above the SFMS (i.e., ΔSFR > 0.5) at the MAGPI redshift regime show uniformly enhanced SF throughout all radial distances probed, suggesting a mixture of physical processes (e.g., galaxy-galaxy interactions) at play along with a sufficient cold gas reservoir to fuel SF. 
    
  * Galaxies along the SFMS (i.e., -0.5 < ΔSFR < 0.5) show a slightly positive gradient in ΔΣ_SFR, where the uptick towards the outskirts is associated with a few highly star-forming galaxies. Otherwise, the inner regime of the profile is flat as expected from MS galaxies maintaining their SF via both a balance between gas accretion and depletion <cit.> and long timescale variations due to differences in halo assembly histories <cit.>. The negative gradient in luminosity-weighted stellar ages (i.e., AgeL) also suggests inside-out growth <cit.>, in agreement with other studies <cit.> as well. 
    
  * Galaxies just below the SFMS (i.e., -1.1 < ΔSFR < -0.5) show a positive gradient in SF, suggestive of inside-out quenching. Our results suggest that galaxies likely have undergone pre-processing from interactions with other galaxies and the group gravitational potential. We also compare Hα and D4000-only profiles to find that D4000-measured ΔΣ_SFR profiles are systematically lower but do not completely dominate in spaxel contribution in any specific radial bin. 
    We attribute the lack of outside-in quenching feature to the majority of our sample galaxies being in the central regions of group environments.
    
  * Quenched galaxies (i.e., ΔSFR < -1.1) in the MAGPI sample show a positive gradient in ΔΣ_SFR as well, where the central dip in SF suggests the aftermath of AGN feedback or expedited use of star-forming gas due to a nuclear starburst. We also consider the possibility of simply lower SF efficiencies leading to lower levels of SF in the centre <cit.>. Given that the majority of galaxies in this bin have ΔΣ_SFR measured from D4000, we acknowledge that we are missing a large fraction of the quenched population due to limitations in the measured D4000-sSFR relation (see Section <ref>, but also ). With proper consideration of upper limits, we expect to see stronger hints of inside-out quenching for quenched MAGPI galaxies. 
    
  * We capture a potential evolution in the radial trends in SF for star-forming galaxies from z ∼ 2 to z ∼ 0. The flat ΔΣ_SFR observed in star-forming MAGPI galaxies is in contrast to the results observed in the local Universe <cit.>, where galaxies clearly show centrally enhanced SF and thus a negative gradient in SF. Agreements with observations at z ∼ 1-2 <cit.> suggest that this may be an indicator of an evolution in the radial trends in SF over the last 4 Gyrs.
    


In future work, we plan to place constraints on the physical mechanisms governing MAGPI galaxies by exploring matched samples within a suite of cosmological simulations (Harborne et al. in prep) and to complete a more statistical environmental analysis using environmental metrics probed out to 5 Mpc (Barsanti et al. in prep). 



§ ACKNOWLEDGEMENTS

We would like to thank the anonymous referee for their helpful comments that improved the manuscript. MM thanks Mallory D. Thorp for helpful discussions on the use of D4000 as a SFR indicator. MM thanks Asa F. L. Bluck for sharing his MaNGA radial profiles as a comparison set with the MAGPI results. MM also extends thanks to Erica J. Nelson for approving the use of her 3D-HST profiles as a comparison set. We wish to thank the ESO staff, and in particular the staff at Paranal Observatory, for carrying out the MAGPI observations. MAGPI targets were selected from GAMA. GAMA is a joint European-Australasian project based around a spectroscopic campaign using the Anglo-Australian Telescope. GAMA was funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. GAMA photometry is based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 179.A-2004, ID 177.A-3016. The MAGPI team acknowledge support by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. CL, JTM and CF are the recipients of ARC Discovery Project DP210101945. CF is the recipient of an Australian Research Council Future Fellowship (project number FT210100168) funded by the Australian Government. AG would like to acknowledge support by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. LMV acknowledges support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and the Marianne-Plehn-Program of the Elite Network of Bavaria. KG is supported by the Australian Research Council through the Discovery Early Career Researcher Award (DECRA) Fellowship (project number DE220100766) funded by the Australian Government. PS is supported by the Leiden University Oort Fellowship and the International Astronomical Union TGF Fellowship. SMS acknowledges funding from the Australian Research Council (DE220100003).

This work made use of Astropy:[http://www.astropy.orghttp://www.astropy.org] a community-developed core Python package and an ecosystem of tools and resources for astronomy <cit.>. This research has made use of the NASA/IPAC Infrared Science Archive <cit.>, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. Parts of the results in this work make use of the colormaps in the CMasher <cit.> package.




§ DATA AVAILABILITY

All MUSE data present in this work are publicly available on the ESO archive. Data products such as fully reduced datacubes and emission line fits will be made available as part of a MAGPI team data release (Mendel et al. in prep; Battisti et al. in prep). 





mnras
 


















§ USING D4000 AS A SFR INDICATOR





 §.§ Reliability of D4000 derived SFRs

We investigate the reliability of D4000 as a SFR indicator to ensure that the use of D4000 is not introducing significant bias in the analysis. In Figure <ref>, we show a plot comparing the Σ_SFR, Hα and Σ_SFR, D4000 for all spaxels with reliably measured Σ_SFR, Hα in our sample. With the exception of some scatter as shown by the black hexagonal bins, the general trend is that both measurements agree well with one another with a bias of approximately -0.116 dex. We also present the scatter in standard deviation and the MAD standard deviation in the bottom panel, where both measurements are generally in good agreement as well. We use the standard deviation of the scatter to take into consideration the uncertainty rising from the recovery of Hα-based SFRs from D4000, by adding this value in quadrature when measuring errors on D4000-based SFRs, as explained in Section <ref>. 

An important caveat to the ΔΣ_SFR profile in the -1.1 < ΔSFR < -0.5 (green) bin is that we use a combination of Hα- and D4000-based measurements. While the two have been shown to be well calibrated to each other (see Figure <ref>), it is possible that combining the different indicators may affect the radial profile. In total, ∼45 per cent of spaxels from galaxies in this bin consist of Hα-measured SFRs. In contrast, the ΔSFR > 0.5 (pink) bin and the -0.5 < ΔSFR < 0.5 (blue) bin are dominated by spaxels with SFRs measured by Hα, 100 per cent and 99 per cent, respectively. While the ΔSFR < -1.1 bin (red) is dominated by spaxels with SFRs measured by D4000, ∼92 per cent. In Figure <ref>, we split the -1.1 < ΔSFR < -0.5 bin into Hα- (N = 27) and D4000-measured (N = 15) galaxies to investigate the implications of the resulting median ΔΣ_SFR profiles. The D4000-based profile is systematically lower than that of Hα, as expected. However, both profiles span the full radial range of the -1.1 < ΔSFR < -0.5 bin, suggesting that neither SFR indicator is biased towards either the centre or the outskirts. 

We re-calculate the ΔΣ_SFR median profiles for 11 galaxies with measurements in both SFR tracers, as shown in Figure <ref>. There is in general good agreement in the range of ΔΣ_SFR measured by the two tracers for the same galaxies, although Hα-based Σ_SFR measurements do indicate slightly higher SF activity. Moreover, while the D4000 profile does show a slightly decreasing trend with radial distance, the number of spaxels with measured Σ_SFR also tapers off towards the outskirts, such that the profiles do agree within the range of uncertainties. 









 §.§ Radial distribution of SFR indicators

We explore whether D4000 measurements are preferentially located in certain radial regimes of our sample galaxies for the lower star-forming bins of -1.1 < ΔSFR < -0.5 and ΔSFR < -1.1, where the contribution of D4000 measurements notably increase. We investigate the fraction of D4000-measured Σ_SFR (i.e., fD4000) as a function of galactocentric radii (R/R_ e) and show the resulting histograms in Figure <ref>, where the top panel is for the -1.1 < ΔSFR < -0.5 (green) bin and the bottom for the ΔSFR < -1.1 (red) bin. For the -1.1 < ΔSFR < -0.5 bin, we find that fD4000 is uniform across all radial bins, suggesting that D4000 measurements are not introducing any biases in the ΔΣ_SFR profile. For the ΔSFR < -1.1 bin, fD4000 is notably higher across all radial bins, with relatively higher fractions observed in the 1.5 – 2.5 R_ e regimes. However, the fractional contribution of D4000 measurements is still comparable among all radial bins, such that we reach the same conclusion that the use of D4000 as an SFR indicator is not biasing our measurements to particular spatial regimes within our galaxy sample. 





 §.§ Upper limits on D4000-based SFRs


In the main body of the paper, we do not include spaxels that have D4000 > 1.475 as the D4000-sSFR relation is not defined beyond this limit (Section <ref>). In this section, we assign upper limits to spaxels with D4000 measurements beyond the defined D4000-sSFR relation. More specifically, we assign spaxels in this regime with the sSFR value associated with the D4000 limit, which is log_10(sSFR) ≃ -11.3 yr-1. We do this for all galaxies in our sample defined in Section <ref>. We then plot the distribution of these upper limits with that of the detections (both Hα and D4000-based ΔΣ_SFR) and the median profiles for the two ΔSFR bins with significant contribution of D4000 measurements: -1.1 < ΔSFR < -0.5 (left panel of Figure <ref>) and ΔSFR < -1.1 (right panel of Figure <ref>). 



For both ΔSFR bins, it is expected that the majority of the upper limits are commonly distributed around a low ΔΣ_SFR value (∼ -1.5). In terms of distribution along the radial axes, the probabilty density distributions of detections and non-detections are strikingly similar for the -1.1 < ΔSFR < -0.5 bin (green), such that the peak of both distributions lie in the 0.5 – 1.0 R_ e bin. It seems fair to assume that with reliable measurements in place for these upper limits, the entire profile would be normalised towards lower ΔΣ_SFR. We do not expect the overall trend to change considerably. On the other hand, for the ΔSFR < -1.1 bin (red), non-detections are found to mainly occupy regimes around 0.5 – 1.5 R_ e, whereas detections are concentrated around 1 – 2.5 R_ e. This suggests that with the inclusion of upper limits, we will likely measure lower ΔΣ_SFR in the centre, leading to a stronger positive gradient. Furthermore, while the number of detections vs. non-detections are comparable for the -1.1 < ΔSFR < -0.5 bin, the number of non-detections significantly outnumber that of the detections in the 0 - 2.0 R_ e regime for the ΔSFR < -1.1, averaging around ∼2500 spaxels per bin compared to ∼150 spaxels for the detections. The overal normalisations of the profiles are thus upper-limits in the -1.1 < ΔSFR < -0.5 (green) and ΔSFR < -1.1 (red) bins.




§ BIN STATISTICS OF THE RADIAL PROFILES



This section presents information on the number of galaxies and spaxels that contribute to each radial bin for the ΔΣ_SFR and AgeL profiles shown in Section <ref>. Tables <ref> and <ref> show the statistics for the ΔΣ_SFR and AgeL profiles, respectively, where the first number of each column indicates the total number of galaxies (Ngal) contributing spaxels to that bin, and the second number the total number of spaxels (Nspax) in each bin.  







§ MAPS OF MEASURED PROPERTIES



In this section, we show the maps of measured physical properties for example galaxies belonging to each global SF state in Figure <ref>. In each row of panels, we show the maps of the collapsed MUSE spectrum (i.e., white light image), dilated mask (as derived with ProFound, see Section <ref>), the stellar mass surface density (Σ_⋆; see Section <ref>), SFR surface density (Σ_SFR; see Section <ref>), and ΔΣ_SFR (see Section <ref>).


 







