The fundamental metallicity relation (FMR) of galaxies is a 3D relationbetween the gas-phase metallicity, stellar mass and star-formation rate (SFR).It has been studied so far only for galaxies identified as star-forming (SF) onthe BPT diagrams (BPT-SF), but not for galaxies with LI(N)ER/AGN classification(BPT-non-SF), mainly due to the lack of diagnostics for estimating theirgas-phase metallicities in the latter cases. We extend the FMR to BPT-non-SFgalaxies. To this end, we exploit the recent nebular line empiricalcalibrations derived specifically for galaxies classified as non-SF in the BPTdiagrams. Moreover, we study an alternative representation of the FMR where weconsider the offsets in metallicity and SFR with respect to Main Sequence (MS)galaxies. We find that galaxies with SFR higher than the MS are more metal-poorthan their counterparts on the MS, which is interpreted in terms of gasaccretion, boosting star formation and diluting the metallicity. Low-massgalaxies below the MS (i.e. towards quiescence) have metallicities higher thantheir MS counterparts, which is interpreted in terms of starvation, (i.e.suppression of fresh gas supply) hampering star formation and reducing thedilution effect, hence resulting in a higher level of internal chemicalenrichment. Massive galaxies below the MS have gas metallicity much closer totheir MS counterparts and much lower than expected from their stellarmetallicities; this result suggests a scenario where massive nearly-quiescentgalaxies with LI(N)ER-like nebular emission have recently accreted gas from thecircum/intergalactic medium.

The gas needed to sustain star formation in galaxies is supplied by thecircumgalactic medium (CGM), which in turn is affected by accretion from largescales. In a series of two papers, we examine the interplay between a galaxy'sambient CGM and central star formation within the context of the large-scaleenvironment. We use the IllustrisTNG-100 simulation to show that the influenceexerted by the large-scale galaxy environment on the CGM gas angular momentumresults in either enhanced (Paper I) or suppressed (Paper II, this paper) starformation inside a galaxy. We find that for present-day quenched galaxies, boththe large-scale environments and the ambient CGM have always had higher angularmomenta throughout their evolutionary history since at least $z=2$, incomparison to those around present-day star-forming disk galaxies, resulting inless efficient gas inflow into the central star-forming gas reservoirs. Asufficiently high CGM angular momentum, as inherited from the larger-scaleenvironment, is thus an important factor in keeping a galaxy quenched, once itis quenched. The process above naturally renders two key observationalsignatures: (1) a coherent rotation pattern existing across multiple distancesfrom the large-scale galaxy environment, to the circumgalactic gas, to thecentral stellar disk; and (2) an anti-correlation between galaxy star-formationrates and orbital angular momenta of interacting galaxy pairs or groups.

We present the kinematics and stellar population properties of a sample of 53galaxies (50 are Early-Type galaxies, ETGs) with Counter-Rotating Disks (CRD)extracted from a sample of about 4000 galaxies of all morphological types inthe MaNGA survey (DR16). The kinematic maps were used to select galaxies basedon evidence of counter-rotation in the velocity maps or two peaks in thevelocity dispersion maps. For about 1/3 of the sample, the counter-rotatingcomponents can also be separated spectroscopically. We then produced the ageand metallicity maps, and compared the stellar population properties to thoseof the general ETGs population. We found that CRDs have similar trends in ageand metallicity, but they are generally less metallic at low masses. Themetallicity gradients are similar; instead, age gradients are typically flatterand confined within a smaller range of values. We compared the velocity fieldsof the ionized gas and the stars, and found that in 25 cases the gas corotateswith either the inner (13 cases) or the outer (12 cases) disk, and in 9 casesthe gaseous and stellar disks are misaligned. With one exception, allmisaligned cases have stellar masses less than $3 \times 10^{10}$M$_\odot$. Wealso compared stellar and gaseous disks with age maps and found that in mostcases the gas corotates with the younger disk. We looked for evidences ofmultimodality in the stellar populations, and found it in 25 galaxies, plus 11cases with evidences of ongoing star formation, and the latter are the youngestand least massive galaxies; 13 galaxies, instead, exhibit unimodality, and arethe oldest and most massive CRDs. As a general result, our work supportsdifferent formation scenarios for the kinematic class of counter-rotators.