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The Parameterised Post-Newtonian (PPN) approach is the default framework for performing precision tests of gravity in nearby astrophysical systems. In recent works we have extended this approach for cosmological applications, and in this paper we use observations of the anisotropies in the Cosmic Microwave Background to constrain the time variation of the PPN parameters $\alpha$ and $\gamma$ between last scattering and the present day. We find their time-averages over cosmological history should be within $\sim 20\%$ of their values in GR, with $\bar{\alpha}=0.89^{+0.08}_{-0.09}$ and $\bar{\gamma}=0.90^{+0.07}_{-0.08}$ at the $68\%$ confidence level. We also constrain the time derivatives of these parameters, and find that their present-day values should be within a factor of two of the best Solar System constraints. Many of these results have no counter-part from Solar System observations, and are entirely new constraints on the gravitational interaction. In all cases, we find that the data strongly prefer $\bar{\alpha}\simeq \bar{\gamma}$, meaning that observers would typically find local gravitational physics to be compatible with GR, despite considerable variation of $\alpha$ and $\gamma$ being allowed over cosmic history. This study lays the groundwork for future precision tests of gravity that combine observations made over all cosmological and astrophysical scales of length and time., Comment: Comments welcome

Carbon- and Oxygen-rich stars populating the Thermally-Pulsing Asymptotic Giant Branch (TP-AGB) phase of stellar evolution are relevant contributors to the spectra of ~1 Gyr old populations. Atmosphere models for these types are uncertain, due to complex molecules and mass-loss effects. Empirical spectra are then crucial, but samples are small due to the short (~3 Myr) TP-AGB lifetime. Here we exploit the vastness of the MaNGA Stellar library MaStar (~60,000 spectra) to identify C,O-rich type stars. We define an optical colour selection with cuts of (g-r)>2 and (g-i)<1.55(g-r)-0.07, calibrated with known C- and O- rich spectra. This identifies C-,O-rich stars along clean, separated sequences. An analogue selection is found in V,R,I bands. Our equation identifies C- and O-rich spectra with predictive performance metric F1-scores of 0.72 and 0.74 (over 1), respectively. We finally identify 41 C- and 87 O-rich type AGB stars in MaStar, 5 and 49 of which do not have a SIMBAD counterpart. We also detect a sample of non-AGB, dwarf C-stars. We further design a fitting procedure to classify the spectra into broad spectral types, by using as fitting templates empirical C and O-rich spectra. We find remarkably good fits for the majority of candidates and categorise them into C- and O-rich bins following existing classifications, which correlate to effective temperature. Our selection models can be applied to large photometric surveys (e.g. Euclid, Rubin). The classified spectra will facilitate future evolutionary population synthesis models., Comment: 16 pages, 13 figures, MNRAS in press

The iMaNGA project uses a forward-modelling approach to compare the predictions of cosmological simulations with observations from SDSS-IV/MaNGA. We investigate the dependency of age and metallicity radial gradients on galaxy morphology, stellar mass, stellar surface mass density ($\Sigma_*$), and environment. The key of our analysis is that observational biases affecting the interpretation of MaNGA data are emulated in the theoretical iMaNGA sample. The simulations reproduce the observed global stellar population scaling relations with positive correlations between galaxy mass and age/metallicity quite well and also produce younger stellar populations in late-type in agreement with observations. We do find interesting discrepancies, though, that can inform the physics and further development of the simulations. Ages of spiral galaxies and low-mass ellipticals are overestimated by about 2-4 Gyr. Radial metallicity gradients are steeper in iMaNGA than in MaNGA, a discrepancy most prominent in spiral and lenticular galaxies. Also, the observed steepening of metallicity gradients with increasing galaxy mass is not well matched by the simulations. We find that the theoretical radial profiles of surface mass density $\Sigma_*$ are steeper than in observations except for the most massive galaxies. In both MaNGA and iMaNGA [Z/H] correlates with $\Sigma_*$, however, the simulations systematically predict lower [Z/H] by almost a factor of 2 at any $\Sigma_*$. Most interestingly, for galaxies with stellar mass $\log M_*\leq 10.80 M_\odot$ the MaNGA data reveal a positive correlation between galaxy radius and [Z/H] at fixed $\Sigma_*$, which is not recovered in iMaNGA. Finally, the dependence on environmental density is negligible in both the theoretical iMaNGA and the observed MaNGA data.

Several prominent forthcoming Cosmic Microwave Background polarisation experiments will employ a Continuously Rotating Half-Wave Plate (CRHWP), the primary purpose of which is to mitigate instrumental systematic effects on relatively large angular scales, where the $B$-mode polarisation signal generated by primordial gravitational waves is expected to peak. The use of a CRHWP necessitates demodulating the time-ordered data during the early stages of data processing. The standard approach is to ``lock in'' on the polarisation signal using the known polarisation modulation frequency and then use Fourier techniques to filter out the remaining unwanted components in the data. However, an alternative less well-studied option is to incorporate the demodulation directly into the map-making step. Using simulations, we compare the performance of these two approaches to determine which is most effective for $B$-mode signal recovery. Testing the two techniques in multiple experimental scenarios, we find that the lock-in technique performs best over the full multipole range explored. However, for the recovery of the largest angular scales ($\ell < 100$) we find essentially no difference in the recovery of the signal between the lock-in and map-making approaches, suggesting that a parallel analysis based on the latter approach could represent a powerful consistency check for primordial $B$-mode experiments employing a CRHWP. We also investigate the impact of a detector-differencing step, implemented prior to demodulation, finding that in most scenarios it makes no difference whether differencing is used or not. However, analysing detectors individually allows the point at which information from multiple detectors is combined to be moved to later stages in the analysis pipeline. This presents alternative options for dealing with instrumental systematic effects that are not mitigated by the CRHWP.

Model-independent tests of gravity with cosmology are important when testing extensions to the standard cosmological model. To maximise the impact of these tests one requires predictions for the matter power spectrum on non-linear scales. In this work we validate the \texttt{ReACT} approach to the non-linear matter power spectrum against a suite of phenomenological modified gravity N-body simulations with a time-varying gravitational constant, covering a wider range of parameter space than previously examined. This vanilla application of \texttt{ReACT} has limited range and precision due to the different concentration-mass relation $c(M)$ that occurs when gravity is modified. We extend this approach with a fitting function for a modified concentration-mass relation, allowing for accurate (1$\%$) computation of the matter power spectrum up $k=2\,h\,{\rm Mpc}^{-1}$ across a substantial range of parameter space. This fitting function allows precision model-independent tests of modified gravity to be carried out using the data from upcoming large scale structure surveys., Comment: 28 pages, 13 figures Comments Welcome!

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating., Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 71

Direct numerical simulations are used to elucidate the interplay of wettability and fluid viscosities on immiscible fluid displacements in a heterogeneous porous medium.We classify the flow regimes based using qualitative and quantitative analysis into viscous fingering (low $M$), compact displacement (high $M$), and an intermediate transition regime ($M \approx 1$). We use stability analysis to obtain theoretical phase boundaries between these regimes, which agree well with our analyses. At the macroscopic (sample) scale, we find that wettability strongly controls the threshold $M$ (at which the regimes change). At the pore scale, wettability alters the dominant pore-filling mechanism. At very small $M$ (viscous fingering regime), smaller pore spaces are preferentially invaded during imbibition, with flow of films of invading fluid along the pore walls. In contrast, during drainage, bursts result in filling of pores irrespective of their size. As $M$ increases, the effect of wettability decreases as cooperative filling becomes the dominant mechanism regardless of wettability. This suggest that for imbibition at a given contact angle, decreasing $M$ is associated with change in effective wetting from neutral-wet (cooperative filling) to strong-wet (film flow).

We study the prospects for detection of continuous gravitational signals from "normal" Galactic neutron stars, i.e. non-recycled ones. We use a synthetic population generated by evolving stellar remnants in time, according to several models. We consider the most recent constraints set by all-sky searches for continuous gravitational waves and use them for our detectability criteria. We discuss detection prospects for the current and the next generation of gravitational wave detectors. We find that neutron stars whose ellipticity is solely caused by magnetic deformations cannot produce any detectable signal, not even by 3rd-generation detectors. Currently detectable sources all have $B\lesssim10^{12}$ G and deformations not solely due to the magnetic field. For these in fact we find that the larger the magnetic field is, the larger is the ellipticity required for the signal to be detectable and this ellipticity is well above the value induced by the magnetic field. Third-generation detectors as the Einstein Telescope and Cosmic Explorer will be able to detect up to $\approx 250$ more sources than current detectors. We briefly treat the case of recycled neutron stars, with a simplified model. We find that continuous gravitational waves from these objects will likely remain elusive to detection by current detectors but should be detectable with the next generation of detectors.

General relativity manifests very similar equations in different regimes, notably in large scale cosmological perturbation theory, non-linear cosmological structure formation, and in weak field galactic dynamics. The same is not necessarily true in alternative gravity theories, in particular those that possess MONDian behaviour ("relativistic extensions" of MOND). In these theories different regimes are typically studied quite separately, sometimes even with the freedom in the theories chosen differently in different regimes. If we wish to properly and fully test complete cosmologies containing MOND against the $\Lambda$CDM paradigm then we need to understand cosmological structure formation on all scales, and do so in a coherent and consistent manner. We propose a method for doing so and apply it to generalised Einstein-Aether theories as a case study. We derive the equations that govern cosmological structure formation on all scales in these theories and show that the same free function (which may contain both Newtonian and MONDian branches) appears in the cosmological background, linear perturbations, and non-linear cosmological structure formation. We show that MONDian behaviour on galactic scales does not necessarily result in MONDian behaviour on cosmological scales, and for MONDian behaviour to arise cosmologically, there will be no modification to the Friedmann equations governing the evolution of the homogeneous cosmological background. We comment on how existing N-body simulations relate to complete and consistent generalised Einstein-Aether cosmologies. The equations derived in this work allow consistent cosmological N-body simulations to be run in these theories whether or not MONDian behaviour manifests on cosmological scales., Comment: Typo corrected on page 14; submitted to JCAP

Strengthening the synergy between simulations and observations is essential to test galaxy formation and evolution theories. To achieve this goal, in the first paper of this series, we presented a method to generate mock SDSS-IV/MaNGA integral-field spectroscopic galaxy observations from cosmological simulations. In this second paper, we build the iMaNGA catalogue consisting of $\sim$1,000 unique galaxies from the TNG50 cosmological simulations, selected to mimic the SDSS-IV/MaNGA-Primary sample selection. Here we present and discuss the iMaNGA sample and its comparison to the MaNGA Primary catalogue. The iMaNGA sample well recovers the MaNGA-Primary sample in terms of stellar mass vs angular size relation and spatial resolution. The S\'ersic index vs angular size relation, instead, is not reproduced well by the simulations, mostly because of a paucity of high-mass elliptical galaxies in TNG50. We also investigate our ability to recover the galaxy kinematics and stellar population properties with full-spectral fitting. We demonstrate that 'intrinsic' and `recovered' stellar kinematics, stellar ages and metallicities are consistent, with residuals compatible with zero within 1$-{\sigma}$. Also`intrinsic' and `recovered' star formation histories display a great resemblance. We conclude that our mock generation and spectral fitting processes do not distort the `intrinsic' galaxy properties. Therefore, in the third paper of this series, we can meaningfully test the cosmological simulations, comparing the stellar population properties and kinematics of the iMaNGA mock galaxies and the MaNGA observational results., Comment: Published on MNRAS: 03 May 2023 https://doi.org/10.1093/mnras/stad1337

We present a stellar parameter catalog built to accompany the MaStar Stellar Library, which is a comprehensive collection of empirical, medium-resolution stellar spectra. We constructed this parameter catalog by using a multicomponent $\chi^{2}$ fitting approach to match MaStar spectra to models generated by interpolating the ATLAS9-based BOSZ model spectra. The total $\chi^{2}$ for a given model is defined as the sum of components constructed to characterize narrow-band features of observed spectra (e.g., absorption lines) and the broadband continuum shape separately. Extinction and systematics due to flux calibration were taken into account in the fitting. The $\chi^{2}$ distribution for a given region of model space was sampled using a Markov Chain Monte Carlo (MCMC) algorithm, the data from which were then used to extract atmospheric parameter estimates ($T_{eff}$, log g, [Fe/H], and [$\alpha$/Fe]), their corresponding uncertainties, and direct extinction measurements. Two methods were used to extract parameters and uncertainties: one that accepts the MCMC's prescribed minimum-$\chi^{2}$ result, and one that uses Bayesian inference to compute a likelihood-weighted mean from the $\chi^{2}$ distribution sampled by the MCMC. Results were evaluated for internal consistency using repeat observations where available and by comparing them with external data sets (e.g., APOGEE-2 and Gaia DR2). Our spectral-fitting exercise reveals possible deficiencies in current theoretical model spectra, illustrating the potential power of MaStar spectra for helping to improve the models. This paper represents an update to the parameters that were originally presented with SDSS-IV DR17. The MaStar parameter catalog containing our BestFit results is available on the SDSS-IV DR17 website as part of version 2 of the MaStar stellar parameter value-added catalog., Comment: 22 pages, 21 figures. A&A in press

There has been substantial commentary on the role of cyberattacks carried out by low-level cybercrime actors in the Russia-Ukraine conflict. We analyse 358k website defacement attacks, 1.7M UDP amplification DDoS attacks, 1764 posts made by 372 users on Hack Forums mentioning the two countries, and 441 Telegram announcements (with 58k replies) of a volunteer hacking group for two months before and four months after the invasion. We find the conflict briefly but notably caught the attention of low-level cybercrime actors, with significant increases in online discussion and both types of attacks targeting Russia and Ukraine. However, there was little evidence of high-profile actions; the role of these players in the ongoing hybrid warfare is minor, and they should be separated from persistent and motivated 'hacktivists' in state-sponsored operations. Their involvement in the conflict appears to have been short-lived and fleeting, with a clear loss of interest in discussing the situation and carrying out both website defacement and DDoS attacks against either Russia or Ukraine after just a few weeks.

Parameterised Post-Newtonian Cosmology (PPNC) is a theory-agnostic framework for testing gravity in cosmology, which connects gravitational physics on small and large scales in the Universe. It is a direct extension of the Parameterised Post-Newtonian (PPN) approach to testing gravity in isolated astrophysical systems, and therefore allows constraints on gravity from vastly different physical regimes to be compared and combined. We investigate the application of this framework to a class of example scalar-tensor theories of gravity in order to verify theoretical predictions, and to investigate for the first time the scale-dependence of the gravitational couplings that appear within its perturbation equations. In doing so, we evaluate the performance of some simple interpolating functions in the transition region between small and large cosmological scales, as well as the uncertainties that using such functions would introduce into the calculation of observables. We find that all theoretical predictions of the PPNC framework are verified to high accuracy in the relevant regimes, and that simple interpolating functions perform well (but not perfectly) between these regimes. This study is an important step towards being able to use the PPNC framework to analyse cosmological datasets, and to thereby test if/how the gravitational interaction has changed as the Universe has evolved., Comment: 28 pages, 16 figures

We spectroscopically detected candidate emission-lines of 8 likely, 17 probable, and 69 possible strong galaxy-galaxy gravitational lens candidates found within the spectra of ~10,000 galaxy targets contained within the completed Mapping of Nearby Galaxies at Apache Point Observatory (MaNGA) survey. This search is based upon the methodology of the Spectroscopic Identification of Lensing Objects (SILO) project, which extends the spectroscopic detection methods of the BOSS Emission-Line Lensing Survey (BELLS) and the Sloan Lens ACS Survey (SLACS). We scanned the co-added residuals that we constructed from stacks of foreground subtracted row-stacked-spectra (RSS) so a sigma-clipping method can be used to reject cosmic-rays and other forms of transients that impact only a small fraction of the combined exposures. We also constructed narrow-band images from the signal-to-noise of the co-added residuals to observe signs of lensed source images. We also use several methods to compute the probable strong lensing regime for each candidate lens to determine which candidate background galaxies may reside sufficiently near the galaxy centre for strong lensing to occur. We present the spectroscopic redshifts within a value-added catalogue (VAC) for data release 17 (DR17) of SDSS-IV. We also present the lens candidates, spectroscopic data, and narrow-band images within a VAC for DR17. High resolution follow-up imaging of these lens candidates are expected to yield a sample of confirmed grade-A lenses with sufficient angular size to probe possible discrepancies between the mass derived from a best-fitting lens model, and the dynamical mass derived from the observed stellar velocities., Comment: Accepted for publication in MNRAS, June 20, 2022. In press. 30 pages, 8 figures, 3 tables, 2 appendices with 15 tables

Galaxy formation and evolution simulations are essential tools to probe poorly known astrophysics processes, but particular care is needed to compare simulations with galaxy observations, as observed data need to be modelled as well. We present a method to generate mock galaxies from the hydro-dynamical IllustrisTNG simulations which are suited to compare with integral field spectroscopic observation of galaxies from the SDSS-IV/MaNGA survey. Firstly, we include the same instrumental effects and procedures as adopted in the acquisition and analysis of real data. Furthermore, we generate the galaxy spectra from the simulations using new stellar population models based on the MaNGA stellar library (MaStar). In this way, our mock data cubes have the same spatial sampling, cover the same wavelength range (3600-10300 \r{A}), and share the same spectral resolution ($R\approx1800$) and flux calibration of real MaNGA galaxy spectra. In this first paper, we demonstrate the method over an early-type and a late-type simulated galaxy from TNG50. We analyse the correspondent mock MaNGA-like data cubes with the same full spectral fitting code, \textsc{FIREFLY}, which was used for the observed spectra. We find that the intrinsic and recovered age and metallicity gradients are consistent within 1${\sigma}$, with residuals over all tassels consistent with $0$ at the 68$\%$ confidence level. We also perform the challenging test at comparing intrinsic and recovered star formation histories, finding a close resemblance between input and output. In follow-up papers, we will present a full simulated MaNGA-like catalogue ($\approx10,000$ galaxies) with a comprehensive comparison of TNG50 simulations to MaNGA observational results.

Stellar radial migration plays an important role in reshaping a galaxy's structure and the radial distribution of stellar population properties. In this work, we revisit reported observational evidence for radial migration and quantify its strength using the age--[Fe/H] distribution of stars across the Milky Way with APOGEE data. We find a broken age--[Fe/H] relation in the Galactic disc at $r>6$ kpc, with a more pronounced break at larger radii. To quantify the strength of radial migration, we assume stars born at each radius have a unique age and metallicity, and then decompose the metallicity distribution function (MDF) of mono-age young populations into different Gaussian components that originated from various birth radii at $r_{\rm birth}<13$ kpc. We find that, at ages of 2 and 3 Gyr, roughly half the stars were formed within 1 kpc of their present radius, and very few stars ($<5$%) were formed more than 4 kpc away from their present radius. These results suggest limited short distance radial migration and inefficient long distance migration in the Milky Way during the last 3 Gyr. In the very outer disc beyond 15~kpc, the observed age--[Fe/H] distribution is consistent with the prediction of pure radial migration from smaller radii, suggesting a migration origin of the very outer disc. We also estimate intrinsic metallicity gradients at ages of 2 and 3 Gyr of $-0.061$ dex kpc$^{-1}$ and $-0.063$ dex kpc$^{-1}$, respectively., Comment: 18 pages, 12 figures, MNRAS in press

We present the MaNGA FIREFLY Value-Added-Catalogue (VAC) - a catalogue of ~3.7 million spatially resolved stellar population properties across 10,010 nearby galaxies from the final data release of the MaNGA survey. The full spectral fitting code firefly is employed to derive parameters such as stellar ages, metallicities, stellar and remnant masses, star formation histories, star formation rates and dust attenuation. In addition to Voronoi-binned measurements, our VAC also provides global properties, such as central values and radial gradients. Two variants of the VAC are available: presenting the results from fits using the M11-MILES and the novel MaStar stellar population models. MaStar allows to constrain the fit over the whole MaNGA wavelength range, extends the age-metallicity parameter space, and uses empirical spectra from the same instrument as MaNGA. The fits employing MaStar models find on average slightly younger ages, higher mass-weighted metallicities and smaller colour excesses. These differences are reduced when matching wavelength range and converging template grids. We further report that FIREFLY stellar masses are systematically lower by ~0.3 dex than masses from the MaNGA PCA and Pipe3D VACs, but match masses from the NSA best with only ~0.1 dex difference. Finally, we show that FIREFLY stellar ages correlate with spectral index age indicators H$\delta_A$ and $D_n$(4000), though with a clear additional metallicity dependence., Comment: 20 pages, 16 figures (+appendix). Accepted for publication in MNRAS. The accepted version now also includes star formation rates and performance tests. The MaNGA FIREFLY VAC is publicly available at the SDSS webpage https://www.sdss.org/dr17/manga/manga-data/manga-firefly-value-added-catalog and at ICG Portsmouth's website http://www.icg.port.ac.uk/manga-firefly-vac

This paper documents the seventeenth data release (DR17) from the Sloan Digital Sky Surveys; the fifth and final release from the fourth phase (SDSS-IV). DR17 contains the complete release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, which reached its goal of surveying over 10,000 nearby galaxies. The complete release of the MaNGA Stellar Library (MaStar) accompanies this data, providing observations of almost 30,000 stars through the MaNGA instrument during bright time. DR17 also contains the complete release of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) survey which publicly releases infra-red spectra of over 650,000 stars. The main sample from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), as well as the sub-survey Time Domain Spectroscopic Survey (TDSS) data were fully released in DR16. New single-fiber optical spectroscopy released in DR17 is from the SPectroscipic IDentification of ERosita Survey (SPIDERS) sub-survey and the eBOSS-RM program. Along with the primary data sets, DR17 includes 25 new or updated Value Added Catalogs (VACs). This paper concludes the release of SDSS-IV survey data. SDSS continues into its fifth phase with observations already underway for the Milky Way Mapper (MWM), Local Volume Mapper (LVM) and Black Hole Mapper (BHM) surveys., Comment: 40 pages, 8 figures, 6 tables. In press at ApJSS (arxiv v2 corrects some minor typos and updates references)

The MaNGA Stellar Library (MaStar) is a large collection of high-quality empirical stellar spectra designed to cover all spectral types and ideal for use in the stellar population analysis of galaxies observed in the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. The library contains 59,266 spectra of 24,130 unique stars with spectral resolution $R\sim1800$ and covering a wavelength range of $3,622-10,354$ \r{A}. In this work, we derive five physical parameters for each spectrum in the library: effective temperature ($T_{eff}$), surface gravity ($\log g$), metalicity ($[Fe/H]$), micro-turbulent velocity ($\log(v_{micro})$), and alpha-element abundance ($[\alpha/Fe]$). These parameters are derived with a flexible data-driven algorithm that uses a neural network model. We train a neural network using the subset of 1,675 MaStar targets that have also been observed in the Apache Point Observatory Galactic Evolution Experiment (APOGEE), adopting the independently-derived APOGEE Stellar Parameter and Chemical Abundance Pipeline (ASPCAP) parameters for this reference set. For the regions of parameter space not well represented by the APOGEE training set ($7,000 \leq T \leq 30,000$ K), we supplement with theoretical model spectra. We present our derived parameters along with an analysis of the uncertainties and comparisons to other analyses from the literature., Comment: 16 figures, 3 tables, accepted to AJ

We calculate the fundamental stellar parameters effective temperature, surface gravity and iron abundance - T$_{\rm eff}$, log g, [Fe/H] - for the final release of the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar), containing 59,266 per-visit-spectra for 24,290 unique stars at intermediate resolution ($R\sim1800$) and high S/N (median = 96). We fit theoretical spectra from model atmospheres by both MARCS and BOSZ-ATLAS9 to the observed MaStar spectra, using the full spectral fitting code pPXF. We further employ a Bayesian approach, using a Markov Chain Monte Carlo (MCMC) technique to map the parameter space and obtain uncertainties. Originally in this paper, we cross match MaStar observations with Gaia photometry, which enable us to set reliable priors and identify outliers according to stellar evolution. In parallel to the parameter determination, we calculate corresponding stellar population models to test the reliability of the parameters for each stellar evolutionary phase. We further assess our procedure by determining parameters for standard stars such as the Sun and Vega and by comparing our parameters with those determined in the literature from high-resolution spectroscopy (APOGEE and SEGUE) and from lower-resolution matching template (LAMOST). The comparisons, considering the different methodologies and S/N of the literature surveys, are favourable in all cases. Our final parameter catalogue for MaStar cover the following ranges: $2592 \leq $ T$_{\rm eff} \leq 32983\;$K; $-0.7 \leq $ log g $ \leq 5.4\;$dex; $-2.9 \leq $ [Fe/H] $\leq 1.0\;$dex and will be available with the last SDSS-IV Data Release, in December 2021., Comment: 22 pages, 25 figures. MNRAS in press. Stellar parameters will be made available with the Data Release 17 of the SDSS, planned for December 2021