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Hosein Haghi

Publications and source records attributed to Hosein Haghi.

At least 19 recordsLinked to original sources

Microlensify: a Transformer Based Machine Learning Classifier for Microlensing Events Trained on TESS Light Curves

Microlensing can reveal populations of faint compact objects that are otherwise difficult to detect. Depending on their design, all-sky surveys have the potential to search for these objects across the sky. The Transiting Exoplanet Survey Satellite (TESS), primarily designed to detect transiting exoplanets, also provides near all-sky coverage with high cadence. In this work, we use TESS data to search for microlensing candidates using both traditional and machine-learning methods and to identify associated false positives in high-cadence surveys. Microlensify is a physics-informed, transformer-based variational autoencoder trained on simulated single-lens microlensing light curves and real TESS Sector 12 data. The model classifies events, reconstructs light curves, and estimates microlensing event durations. Applied to $\sim 5.6$ million TESS light curves, it identified between $0.036\%$ and $1.89\%$ as microlensing candidates across different TESS pipelines. After applying microlensing detection metrics and cross-matching with SIMBAD, we obtained a final list of candidates and identified false positives including long-period variables, Mira variables, cataclysmic variables, red giants, and transients. We also found Gaussian-like peaks caused by asteroid crossings, a potential source of false positives in high-cadence microlensing surveys. The model also predicts event duration with an accuracy of $R^2 = 0.97$. The model was further tested on published events from different ground-based microlensing surveys, confirming 92.7% as microlensing, demonstrating its applicability across surveys with different cadences.

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CatBoost versus Spectral Energy Distribution-Fitting: Estimating Galaxy Properties under Controlled Photometric Incompleteness

Estimating galaxy physical parameters from photometric data is fundamentally challenged by missing measurements that are endemic to astronomical surveys. Using a mock catalog from the Horizon-AGN hydrodynamical simulation that provides the true physical parameters, we evaluate CatBoost, a gradient-boosting algorithm that natively handles missing data, under a deliberately adversarial scenario: we train it on 12 photometric bands with increasing levels of injected missingness (10%, 20%, 30% missing per band) and compare its performance against an idealised parametric spectral energy distribution (SED)-fitting reference that uses complete 26-band photometry (no missing data, all bands available). This asymmetric design represents an upper-bound, best-case baseline for traditional methods. Despite this intentional disadvantage, CatBoost's performance degradation is limited: moving from complete data to 30% missing, mass RMSE increases from 0.08 to 0.18 dex, SFR RMSE from 0.41 to 0.53 dex, and redshift RMSE from 0.20 to 0.28, while bias remains near zero. Against the ideal SED-fitting reference, CatBoost trained on only 12 bands with 30% missing values achieves lower errors for mass (0.18 vs. 0.28 dex) and SFR (0.53 vs. 0.57 dex) and removes the systematic biases present in the SED-fitting results. For redshift, the SED-fitting reference has lower NMAD (0.030 vs. 0.093 at extreme missingness) while CatBoost maintains smaller bias. These results suggest that CatBoost's native handling of missing values can offer practical advantages for extracting galaxy properties from imperfect photometric surveys, at least under the conditions explored here.

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COSMOS2025: A Machine Learning Census of Massive Quiescent Galaxies at $2.5 < \text{z} < 5$

The existence of massive quiescent galaxies at high redshifts ($ \text{z} \gtrsim 2$) strongly constrains the rapid quenching mechanisms in galaxy evolution models. We present a machine learning framework to identify massive ($\log(\text{M}_*/\text{M}_\odot) > 9.5$) quiescent galaxies at $2.5 < \text{z} < 5$ in the COSMOS2025 catalog. We train a \texttt{CatBoostClassifier} on mock photometry from the Santa Cruz semi-analytic models (SAMs), incorporating key JWST NIRCam bands and realistic noise to transfer the SAM-derived quiescent label (based on specific star-formation rate) to the observational space. When validated against the SAM ground truth, our classifier achieves a significantly higher recall (completeness) of 78\% (compared to 53\% for spectral energy distribution (SED)-fitting), while maintaining a high purity of 82\%. Applied to the COSMOS2025 sample, and assuming the SAM definition of quiescence transfers to the real Universe, the model identifies 1111 quiescent candidates, a population 2.6 times larger than the 427 candidates identified via the catalog's simple SED-fitting configuration. Under the SAM definition of quiescence, this consistent pattern of high purity but poor completeness suggests that the SED-fitting methods, constrained by simplified parametric star-formation histories, may miss a significant fraction of the quiescent population, likely galaxies in crucial transitional evolutionary stages. The trained classifier and classified COSMOS2025 sample are publicly available.

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Baryonic mass budgets in the central regions of the Bullet Cluster and their consistency with strong lensing in MOND

Strong lensing observations of the Bullet Cluster have traditionally been regarded as strong evidence for dark matter and a major challenge to Milgromian dynamics (MOND). The offset between the lensing mass and the X-ray gas centroids implies a substantial amount of unseen mass near the brightest cluster galaxies (BCGs). However, the high metallicities observed in both the intracluster gas and the massive early-type member galaxies suggest a past stellar population dominated by massive stars, whose evolved remnants contribute additional baryonic mass. This effect is naturally incorporated in the integrated galaxy-wide initial mass function (IGIMF) theory, which predicts substantially larger baryonic masses than a canonical IMF. In this work, we re-estimate the baryonic masses of the three BCG-centred core regions of the Bullet Cluster using recent JWST photometry and compare them with MOND strong-lensing masses. We derive IGIMF masses using stellar population synthesis models with constant and (self-) enriched metallicities, representing lower and upper mass limits, respectively. We find that the MOND strong-lensing masses of all three cores lie within the range predicted by the IGIMF models. These results suggest that the baryonic mass budget is consistent with MOND requirements from strong-lensing observations in the core regions of the Bullet Cluster. However, the physical viability of this scenario also depends on the spatial distribution and dynamical behavior of the remnant population, which remain to be established. More generally, regardless of the validity of MOND, the results imply that less dark matter may be required than previously inferred.

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The fingerprint of primordial mass segregation on the tidal tails of star clusters

We investigate the effect of primordial mass segregation (PMS) in shaping the tidal tail structures of star clusters, searching for any trace of PMS on the tails at both early and late evolutionary stages. Through N-body simulations, we analyze clusters with two different degrees of PMS at various Galactocentric distances (R_G), considering two black hole retention scenarios. Our findings reveal that PMS influences early cluster expansion and the formation of tidal tails with a bottom-heavy stellar mass function, this being more pronounced at smaller R_G but diminishes over time. Primordially segregated clusters exhibit denser, unified, and longer tail structures compared to non-segregated clusters. The mean stellar mass distribution along the tails shows distinct patterns for primordially segregated and non-segregated clusters, converging at later evolutionary stages. The retention of stellar remnants has a weak impact on the mean mass distribution along the tails and on its morphology. We find that although mean mass differences persist along the tidal tails, the rate of change in primordially mass-segregated clusters eventually converges with that of non-segregated clusters, suggesting that the influence of primordial mass segregation on the tidal tails gradually diminishes over the course of cluster evolution.

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The mmax-Mecl relation in the LEGUS clusters

The relation between the maximum stellar mass in a very young cluster (mmax) and the total stellar mass of the cluster (Mecl), known as the mmax-Mecl relation, remains debated in the literature. To test the validity of this relation, we modelled young star clusters with masses between 102.5 and 105.0 M_sun and ages of 1-4 Myr using the galIMF code, in which stellar masses are optimally sampled from a varying initial stellar mass function. We compared the results with literature observations of extragalactic young star clusters. We incorporated stellar evolution via PARSEC and COLIBRI tracks and computed Halpha luminosities using the Pegase code. To account for dynamical ejections, we stochastically removed stars based on their spectral type, following previous N-body simulations. Additional sources of scatter, including uncertainties in age determination and contamination by field stars, were considered. Our results indicate that, under the assumptions explored here, optimal sampling is consistent with the extragalactic star cluster observations considered, whereas purely random sampling produces distributions that are not in agreement. These findings support a highly self-regulated interpretation of cluster formation in which stellar masses align optimally with the initial mass function rather than being drawn independently at random.

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COSMOS-Web: Estimating Physical Parameters of Galaxies Using Self-Organizing Maps

The COSMOS-Web survey, with its unparalleled combination of multiband data, notably, near-infrared imaging from JWST's NIRCam (F115W, F150W, F277W, and F444W), provides a transformative dataset down to $\sim28$ mag (F444W) for studying galaxy evolution. In this work, we employ Self-Organizing Maps (SOMs), an unsupervised machine learning method, to estimate key physical parameters of galaxies -- redshift, stellar mass, star formation rate (SFR), specific SFR (sSFR), and age -- directly from photometric data out to $z=3.5$. SOMs efficiently project high-dimensional galaxy color information onto 2D maps, showing how physical properties vary among galaxies with similar spectral energy distributions. We first validate our approach using mock galaxy catalogs from the HORIZON-AGN simulation, where the SOM accurately recovers the true parameters, demonstrating its robustness. Applying the method to COSMOS-Web observations, we find that the SOM delivers robust estimates despite the increased complexity of real galaxy populations. Performance metrics ($σ_{\mathrm{NMAD}}$ typically between $0.1$--$0.3$, and Pearson correlation between $0.7$ and $0.9$) confirm the precision of the method, with $\sim$ $70\%$ of predictions within 1$σ$ dex of reference values. Although redshift estimation in COSMOS-Web remains challenging (median $σ_{\mathrm{NMAD}} = 0.04$), the overall success of the highlights its potential as a powerful and interpretable tool for galaxy parameter estimation. A key advance of this work is the use of JWST/NIRCam photometry, particularly the F444W band, which enhances SOM training and allows more accurate estimation of stellar mass, SFR, and age compared to previous studies using IRAC/Spitzer filters.

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Machine Learning vs. Spectral Energy Distribution Fitting: A Comparative Analysis of Accuracy in Stellar Mass Estimation

Traditional spectral energy distribution (SED)-fitting methods for stellar mass estimation face persistent challenges including systematic biases and computational constraints. We present a controlled comparison of machine learning (ML) and SED-fitting methods, assessing their accuracy, robustness, and computational efficiency. Using a sample of COSMOS-like galaxies from the Horizon-AGN simulation as a benchmark with known true masses, we evaluate the Parametric t-SNE (Pt-SNE) algorithm -- trained on noise-injected BC03 models -- against the established SED-fitting code LePhare. Our results demonstrate that Pt-SNE achieves superior accuracy, with a root-mean-square error (sigma_F) of 0.169 dex compared to LePhare's 0.306 dex. Crucially, Pt-SNE exhibits significantly lower bias (0.029 dex) compared to LePhare (0.286 dex). Pt-SNE also shows greater robustness across all stellar mass ranges, particularly for low-mass galaxies (10^9 to 10^10 solar masses), where it reduces errors by 47-53 %. Even when restricted to only six optical bands, Pt-SNE outperforms LePhare using all 26 available photometric bands, underscoring its superior informational efficiency. Computationally, Pt-SNE processes large datasets approximately 3.2 x 10^3 times faster than LePhare. These findings highlight the fundamental advantages of ML methods for stellar mass estimation, demonstrating their potential to deliver more accurate, stable, and scalable measurements for large-scale galaxy surveys.

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Universal depletion of metal-poor globular clusters in inner galaxy regions: Fossil record of black hole retention

We analyzed the spatial distribution of globular cluster (GC) systems across 37 host galaxies in a two dimensional parameter space defined by projected galactocentric distance Rg and metallicity Fe/H. We identified a universal triangular depleted region characterized by a lack of metal poor GCs in the inner parts of host galaxies. The morphology of this depleted region correlates with the luminous mass of the host galaxies; more massive galaxies consistently exhibit more extended depleted regions. We attribute this phenomenon to the combined influence of large scale galactic assembly and internal GC dynamics, particularly the initial retention of black holes within GCs. Metal poor GCs contain a more massive and compact black hole subsystem, which drives more energetic few body encounters and injects greater kinetic energy into the stellar population. This extra energy, combined with strong tidal forces in central galactic regions, accelerates the dissolution of low metallicity GCs, producing the triangular depleted pattern in the Rg - Fe/H space. Stronger tidal fields in more massive galaxies confine surviving metal poor GCs to larger radii, broadening the depleted region. The morphology of this region may serve as a potential distance indicator for host galaxies. Our results also suggest that scenarios with substantial black hole natal kicks are unlikely, as too few retained black holes would erase the metallicity dependent cluster dissolution required to form the observed depletion region.

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Massive Star Formation at Supersolar Metallicities: Constraints on the Initial Mass Function

Metals enhance the cooling efficiency of molecular clouds, promoting fragmentation. Consequently, increasing the metallicity may boost the formation of low-mass stars. Within the integrated galaxy initial mass function (IGIMF) theory, this effect is empirically captured by a linear relation between the slope of the low-mass stellar IMF, $α_1$, and the metal mass fraction, $Z$. This linear $α_1$-$Z$ relation has been calibrated up to $\approx 2 \, Z_{\odot}$, though higher metallicity environments are known to exist. We show that if the linear $α_1$-$Z$ relation extends to higher metallicities ($[Z] \gtrsim 0.5$), massive star formation is suppressed entirely. Alternatively, fragmentation efficiency may saturate beyond some metallicity threshold if gravitational collapse cascades rapidly enough. To model this behavior, we propose a logistic function describing the transition from metallicity-sensitive to metallicity-insensitive fragmentation regimes. We provide a user-friendly public code, pyIGIMF, which enables the instantaneous computation of the IGIMF theory with the logistic $α_1$-$Z$ relation.

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Machine Learning Classification of COSMOS2020 Galaxies: Quiescent vs. Star-Forming

Accurately distinguishing between quiescent and star-forming galaxies is essential for understanding galaxy evolution. Traditional methods, such as spectral energy distribution (SED) fitting, can be computationally expensive and may struggle to capture complex galaxy properties. This study aims to develop a robust and efficient machine learning (ML) classification method to identify quiescent and star-forming galaxies within the Farmer COSMOS2020 catalog. We utilized JWST wide-field light cones from the Santa Cruz semi-analytical modeling framework to train a supervised ML model, the CatBoostClassifier, using 28 color features derived from 8 mutual photometric bands within the COSMOS catalog. The model was validated against a testing set and compared to the SED-fitting method in terms of precision, recall, F1-score, and execution time. Preprocessing steps included addressing missing data, injecting observational noise, and applying a magnitude cut (ch1 < 26 AB) along with a redshift range of 0.2 < z < 3.5 to align the simulated and observational datasets. The ML method achieved an F1-score of 89\% for quiescent galaxies, significantly outperforming the SED-fitting method, which achieved 54%. The ML model demonstrated superior recall (88% vs. 38%) while maintaining comparable precision. When applied to the COSMOS2020 catalog, the ML model predicted a systematically higher fraction of quiescent galaxies across all redshift bins within 0.2 < z < 3.5 compared to traditional methods like NUVrJ and SED-fitting. This study shows that ML, combined with multi-wavelength data, can effectively identify quiescent and star-forming galaxies, providing valuable insights into galaxy evolution. The trained classifier and full classification catalog are publicly available.

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Semi-supervised classification of stars, galaxies and quasars using K-means and random-forest approaches

Classifying stars, galaxies, and quasars is essential for understanding cosmic structure and evolution; however, the vast data from modern surveys make manual classification impractical, while supervised learning methods remain constrained by the scarcity of labeled spectroscopic data. We aim to develop a scalable, label-efficient method for astronomical classification by leveraging semi-supervised learning (SSL) to overcome the limitations of fully supervised approaches. We propose a novel SSL framework combining K-means clustering with random forest classification. Our method partitions unlabeled data into 50 clusters, propagates labels from spectroscopically confirmed centroids to 95% of cluster members, and trains a random forest on the expanded pseudo-labeled dataset. We applied this to the CPz catalog, containing multi-survey photometric and spectroscopic data, and compared performance with a fully supervised random forest. Our SSL approach achieves F1 scores of 98.8%, 98.9%, and 92.0% for stars, galaxies, and quasars, respectively, closely matching the supervised method with F1 scores of 99.1%, 99.1%, and 93.1%, while outperforming traditional color-cut techniques. The method demonstrates robustness in high-dimensional feature spaces and superior label efficiency compared to prior work. This work highlights SSL as a scalable solution for astronomical classification when labeled data is limited, though performance may be degraded in lower dimensional settings.

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Origin of High Dark Remnant Fractions in Milky Way Globular Clusters: The Crucial Role of Initial Black Hole Retention

Comparing the dynamical and stellar masses of Milky Way (MW) globular clusters (GCs) reveals a discrepancy exceeding a factor of two. Since this substantial invisible mass is concentrated in the cluster centre, it is attributed to stellar remnants. The majority of mass in remnants consists of white dwarfs (WDs). Allocating over half of a GC's current mass to WDs could significantly restrict the dynamical evolution scenarios governing stellar clusters. As the most massive stars in GCs, black holes (BHs) exert a substantial effect on the escape rate of lower mass stars, such as WDs. This paper aims to identify which scenarios of BH natal kicks can accurately reproduce the notable dark remnant fraction observed in MW GCs. We compare the observed remnant fraction of MW GCs with a comprehensive grid of direct \Nbody simulations while adjusting the natal kick received by BHs. Our results reveal that simulations employing low natal kicks to BHs are the only ones capable of mirroring the remnant fraction of MW GCs. According to the Spitzer instability, the presence of a BH population prompts the formation of a BH sub-system (BHSub) at the centre of a star cluster. The BHSub serves as an energetic power plant, continually releasing kinetic energy through few-body encounters between single and binary BHs, and transferring the generated energy to the entire stellar population. This energy induces a significant difference in the ejection rate of stellar remnants and luminous stars, ultimately increasing the fraction of dark remnants within the star cluster.

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Dark Star Clusters or Ultra-Faint Dwarf galaxies? Revisiting UMa3/U1

Owing to sparse spectroscopic observations, the classification of faint satellites as either dark matter-dominated dwarf galaxies or self-gravitating star clusters remains unresolved. The recently discovered Ursa Major III/UNIONS 1 (UMa3/U1) object, with its measured velocity dispersion, provides a rare observational anchor in this regime. Despite its cluster-like compactness, its inferred dynamical mass-to-light ratio (M_dyn/L) suggests a dark matter-dominated nature, prompting interpretations of UMa3/U1 as a microgalaxy, though current measurements remain inconclusive. Thousand-level M_dyn/L values are not unique to galaxies; self-gravitating dark star clusters (DSCs) can reach comparable levels via energy injection driven by a centrally segregated black hole subsystem (BHSub), which accelerates the evaporation of luminous stars and leads to a super-virial appearance with elevated velocity dispersion. To assess whether UMa3/U1 is a DSC, we conducted direct N-body simulations and identified a model that successfully reproduces both its compact structure and elevated M_dyn/L, supporting a self-gravitating cluster origin. We find the cluster entered the DSC phase around 4 Gyr ago, with its luminous stars expected to be depleted within the next 1 Gyr, followed by the gradual disruption of the central BHSub over the subsequent Gyr. We broaden our analysis by mapping DSC evolutionary tracks in the size versus total luminosity (L) and M_dyn/L-L spaces, showing that DSCs occupy a region overlapping with faint, ambiguous satellites. In the M_dyn/L-L diagram, DSCs trace a transitional channel bridging globular clusters and dwarf galaxies as they rise from M_dyn/L ~ 2 to 10^4 M_sun/L_sun.

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The effect of the environment-dependent stellar initial mass function on the baryonic Tully Fisher relation

We investigate the impact of an environment-dependent galaxy-wide stellar initial mass function (gwIMF) on the baryonic Tully-Fisher relation (BTFR). The integrated galaxy-wide IMF (IGIMF) theory, which incorporates variations in stellar populations due to star formation history (SFH) and metallicity, provides a more accurate framework for understanding systematic deviations in galaxy scaling relations than that given by an invariant gwIMF. By considering how the mass-to-light ratio of the stellar population is influenced by metallicity and SFH, we show that high-mass galaxies have their masses in stars and remnants underestimated under the assumption of a constant mass-to-light ratio. In contrast, low-mass, gas-dominated galaxies are less affected. Our results suggest that the discrepancies between the true and observed BTFR are primarily driven by the evolving nature of the stellar IMF, particularly in galaxies with slowly declining SFHs. The IGIMF theory offers a solution to the observed offsets in the BTFR, especially for high-mass galaxies, where the rotational velocities are higher than predicted by MOND. We conclude that incorporating the IGIMF provides a more accurate description of galaxy dynamics, revealing the importance of stellar population characteristics in refining our understanding of the baryonic mass-velocity relationship. This study underscores the necessity of accounting for the variation of the gwIMF when interpreting the BTFR, particularly in the context of alternative gravitational theories like MOND.

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Are the ONC, Pleiades, and Hyades snapshots of the same embedded cluster?

Using direct $N$-body simulations, we investigate the initial conditions and evolution of a star-forming region resembling the Orion Nebula Cluster (ONC) with the advanced \textsc{NBODY6} code. By varying the initial conditions, we aim to identify a model that closely aligns with observed parameters such as the half-mass radius, core radius, and total mass. Additionally, we examine the cluster's evolution over 800 Myr to determine whether it could reproduce the present-day properties of the Pleiades and Hyades along its evolutionary path. Under the influence of a Milky Way-like tidal field, the ONC experiences significant mass loss, primarily due to rapid gas expulsion, retaining approximately 47\% of its initial 4200 stars by about 100 Myr and only 9\% by about 700 Myr. These evolutionary stages closely match the properties of the Pleiades and Hyades, suggesting that an ONC-like cluster may have been their precursor. Additional models with varying degrees of primordial mass segregation indicate that the ONC likely had an initial half-mass radius of 0.2-0.3 pc, a total mass of 1200 - 2000 M$_\odot$, and a high degree of mass segregation. Models with an initial stellar count of about $N_{\text{in}} \approx 4 \times 10^3 - 5 \times 10^3$, rich in binaries and exhibiting mass segregation, show excellent agreement with observed cluster properties.

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Leveraging Machine Learning for Accurate and Fast Stellar Mass Estimation of Galaxies

Unveiling the evolutionary history of galaxies necessitates a precise understanding of their physical properties. Traditionally, astronomers achieve this through spectral energy distribution (SED) fitting. However, this approach can be computationally intensive and time-consuming, particularly for large datasets. This study investigates the viability of machine learning (ML) algorithms as an alternative to traditional SED-fitting for estimating stellar masses in galaxies. We compare a diverse range of unsupervised and supervised learning approaches including prominent algorithms such as K-means, HDBSCAN, Parametric t-Distributed Stochastic Neighbor Embedding (Pt-SNE), Principal Component Analysis (PCA), Random Forest, and Self-Organizing Maps (SOM) against the well-established LePhare code, which performs SED-fitting as a benchmark. We train various ML algorithms using simple model SEDs in photometric space, generated with the BC03 code. These trained algorithms are then employed to estimate the stellar masses of galaxies within a subset of the COSMOS survey dataset. The performance of these ML methods is subsequently evaluated and compared with the results obtained from LePhare, focusing on both accuracy and execution time. Our evaluation reveals that ML algorithms can achieve comparable accuracy to LePhare while offering significant speed advantages (1,000 to 100,000 times faster). K-means and HDBSCAN emerge as top performers among our selected ML algorithms. Supervised learning algorithms like Random Forest and manifold learning techniques such as Pt-SNE and SOM also show promising results. These findings suggest that ML algorithms hold significant promise as a viable alternative to traditional SED-fitting methods for estimating the stellar masses of galaxies.

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Stellar population synthesis models with a physically varying IMF

Interpreting galactic luminosity requires assumptions about the galaxy-wide initial mass function (gwIMF), often assumed invariant in most stellar population synthesis (SPS) models. If stars form in clusters with metallicity- and density-dependent \textit{stellar IMFs}, the integrated galaxy-wide IMF (IGIMF) can be calculated, with its shape depending on the star formation rate (SFR) and metallicity. The shape of the IGIMF thus depends on the star formation rate (SFR) and metallicity. We develop the \texttt{SPS-VarIMF} code which enables us for the first time to compute the spectra, luminosities, and remnant populations of galaxies in the context of the varying gwIMF with time, SFR, and an assumed metallicity. Using the \texttt{SPS-VarIMF} code one can calculate how the interpretation from the integrated galactic light may change if the underlying galaxy-wide IMF is assumed to be environmentally dependent instead of being invariant. In particular, we compare the time evolution of the galaxy color and the stellar mass-to-light ratio in different bands for the IGIMF and invariant canonical gwIMF assuming constant and delayed-$τ$ star formation histories. We show that the underlying gwIMF can be determined by examining the colors and luminosities of late-type galaxies in UV and optical bands. On the other hand, for early-type galaxies, it is difficult to distinguish which gwIMF is valid since adopting the different gwIMFs yields almost identical colors. However, their gwIMF-dependent $M/L$ ratios differ by up to an order of magnitude. Massive present-day elliptical galaxies would have been $10^4$ times as bright as at present when they were forming.

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