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We present the first steps toward applying causal representation learning to astronomy. Following up on previous work that introduced causal discovery to the field for the first time, here we solve a long standing conundrum by identifying the direction of the causal relation between supermassive black hole (SMBH) mass and their host galaxy properties. This leverages a score-based causal discovery approach with an exact posterior calculation. Causal relations between SMBHs and their host galaxies are further clarified by Independent Component Analysis (ICA). The astrophysical problem we focus on is one of the most important open issues in the field and one that has not seen a definitive resolution in decades. We consider the space of six physical properties of galaxies, subdivided by morphology: elliptical, lenticular, and spiral, plus SMBH mass. We calculate an exact posterior over the space of directed acyclic graphs for these variables based on a flat prior and the Bayesian Gaussian equivalent score. The nature of the causal relation between galaxy properties and SMBH mass is found to vary smoothly with morphology, with galaxy properties determining SMBH mass in ellipticals and vice versa in spirals. This settles a long-standing debate and is compatible with our theoretical understanding of galaxy evolution. ICA reveals a decreasing number of meaningful Independent Components (ICs) from ellipticals and lenticular to spiral. Moreover, we find that only one IC correlates with SMBH mass in spirals while multiple ones do in ellipticals, further confirming our finding that SMBH mass causes galaxy properties in spirals, but the reverse holds in ellipticals., Comment: Accepted by NeurIPS 2024 Causal Representation Learning Workshop. arXiv admin note: substantial text overlap with arXiv:2410.00965

Correlations between galaxies and their supermassive black holes (SMBHs) have been observed, but the causal mechanisms remained unclear. The emerging field of causal inference now enables examining these relationships using observational data. This study, using advanced causal discovery techniques and a state-of-the-art dataset, reveals a causal link between galaxy properties and SMBH masses. In elliptical galaxies, bulge properties influence SMBH growth, while in spiral galaxies, SMBHs affect host galaxy properties, potentially through feedback in gas-rich environments. For spiral galaxies, SMBHs progressively quench star formation, whereas in elliptical galaxies, quenching is complete, and the causal connection has reversed. These findings support theoretical models of active galactic nuclei feedback regulating galaxy evolution and suggest further exploration of causal links in astrophysical and cosmological scaling relations., Comment: 34 pages, 20 figures, submitted for peer-review

Context. Computational astronomy has reached the stage where running a gravitational N-body simulation of a stellar system, such as a Milky Way star cluster, is computationally feasible, but a major limiting factor that remains is the ability to set up physically realistic initial conditions. Aims. We aim to obtain realistic initial conditions for N-body simulations by taking advantage of machine learning, with emphasis on reproducing small-scale interstellar distance distributions. Methods. The computational bottleneck for obtaining such distance distributions is the hydrodynamics of star formation, which ultimately determine the features of the stars, including positions, velocities, and masses. To mitigate this issue, we introduce a new method for sampling physically realistic initial conditions from a limited set of simulations using Gaussian processes. Results. We evaluated the resulting sets of initial conditions based on whether they meet tests for physical realism. We find that direct sampling based on the learned distribution of the star features fails to reproduce binary systems. Consequently, we show that physics-informed sampling algorithms solve this issue, as they are capable of generating realisations closer to reality., Comment: Accepted to A&A (4th Sep 2024)

We present the first application of data-driven techniques for dynamical system analysis based on Koopman theory to variable stars. We focus on light curves of RRLyrae type variables, in the Galactic globular cluster $\omega$ Centauri. Light curves are thus summarized by a handful of complex eigenvalues, corresponding to oscillatory or fading dynamical modes. We find that variable stars of the RRc subclass can be summarized in terms of fewer ($\approx 8$) eigenvalues, while RRab need comparatively more ($\approx 12$). This result can be leveraged for classification and reflects the simpler structure of RRc light curves. We then consider variable stars displaying secular variations due to the Tseraskaya-Blazhko effect and find a change in relevant eigenvalues with time, with possible implications for the physical interpretation of the effect., Comment: Accepted (spotlight) at the Scaling AI for Science workshop at ICML 2024

Third-generation (3G) gravitational-wave detectors such as the Einstein Telescope (ET) will observe binary black hole (BBH) mergers at redshifts up to $z\sim 100$. However, an unequivocal determination of the origin of high-redshift sources will remain uncertain because of the low signal-to-noise ratio (S/N) and poor estimate of their luminosity distance. This study proposes a machine-learning approach to infer the origins of high-redshift BBHs. We specifically differentiate those arising from Population III (Pop. III) stars, which probably are the first progenitors of star-born BBH mergers in the Universe, and those originated from Population I-II (Pop. I-II) stars. We considered a wide range of models that encompass the current uncertainties on Pop. III BBH mergers. We then estimated the parameter errors of the detected sources with ET using the Fisher information-matrix formalism, followed by a classification using XGBoost, which is a machine-learning algorithm based on decision trees. For a set of mock observed BBHs, we provide the probability that they belong to the Pop. III class while considering the parameter errors of each source. In our fiducial model, we accurately identify $\gtrsim 10\%$ of the detected BBHs that originate from Pop. III stars with a precision $>90\%$. Our study demonstrates that machine-learning enables us to achieve some pivotal aspects of the ET science case by exploring the origin of individual high-redshift GW observations. We set the basis for further studies, which will integrate additional simulated populations and account for further uncertainties in the population modeling., Comment: Published in Astronomy & Astrophysics. 15 pages, 9 Figures and 6 tables. Comments are welcome

In astronomy, spectroscopy consists of observing an astrophysical source and extracting its spectrum of electromagnetic radiation. Once extracted, a model is fit to the spectra to measure the observables, leading to an understanding of the underlying physics of the emission mechanism. One crucial, and often overlooked, aspect of this model is the background emission, which contains foreground and background astrophysical sources, intervening atmospheric emission, and artifacts related to the instrument such as noise. This paper proposes an algorithmic approach to constructing a background model for SITELLE observations using statistical tools and supervised machine learning algorithms. We apply a segmentation algorithm implemented in photutils to divide the data cube into background and source spaxels. After applying a principal component analysis (PCA) on the background spaxels, we train an artificial neural network to interpolate from the background to the source spaxels in the PCA coefficient space, which allows us to generate a local background model over the entire data cube. We highlight the performance of this methodology by applying it to SITELLE observations obtained of a SIGNALS galaxy, \NGC4449, and the Perseus galaxy cluster of galaxies, NGC 1275. We discuss the physical interpretation of the principal components and noise reduction in the resulting PCA-based reconstructions. Additionally, we compare the fit results using our new background modeling approach to standard methods used in the literature and find that our method better captures the emission from HII regions in NGC 4449 and the faint emission regions in NGC 1275. These methods also demonstrate that the background does change as a function of the position of the datacube., Comment: Accepted to RASTI

Cosmological galaxy formation simulations are powerful tools to understand the complex processes that govern the formation and evolution of galaxies. However, evaluating the realism of these simulations remains a challenge. The two common approaches for evaluating galaxy simulations is either through scaling relations based on a few key physical galaxy properties, or through a set of pre-defined morphological parameters based on galaxy images. This paper proposes a novel image-based method for evaluating the quality of galaxy simulations using unsupervised deep learning anomaly detection techniques. By comparing full galaxy images, our approach can identify and quantify discrepancies between simulated and observed galaxies. As a demonstration, we apply this method to SDSS imaging and NIHAO simulations with different physics models, parameters, and resolution. We further compare the metric of our method to scaling relations as well as morphological parameters. We show that anomaly detection is able to capture similarities and differences between real and simulated objects that scaling relations and morphological parameters are unable to cover, thus indeed providing a new point of view to validate and calibrate cosmological simulations against observed data., Comment: 13 pages, 16 figures, published in MNRAS

Future gravitational wave observatories can probe dark matter by detecting the dephasing in the waveform of binary black hole mergers induced by dark matter overdensities. Such a detection hinges on the accurate modelling of the dynamical friction, induced by dark matter on the secondary compact object in intermediate and extreme mass ratio inspirals. In this paper, we introduce NbodyIMRI, a new publicly available code designed for simulating binary systems within cold dark matter `spikes'. Leveraging higher particle counts and finer timesteps, we validate the applicability of the standard dynamical friction formalism and provide an accurate determination of the maximum impact parameter of particles which can effectively scatter with a compact object, across various mass ratios. We also show that in addition to feedback due to dynamical friction, the dark matter also evolves through a `stirring' effect driven by the time-dependent potential of the binary. We introduce a simple semi-analytical scheme to account for this effect and demonstrate that including stirring tends to slow the rate of dark matter depletion and therefore enhances the impact of dark matter on the dynamics of the binary., Comment: 11 pages, 9 figures + appendices. Companion paper to "Sharpening the dark matter signature in gravitational waveforms I: Accretion and eccentricity evolution" (arXiv:2402.13053). NbodyIMRI code available here: https://github.com/bradkav/NbodyIMRI

Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to realistically simulate GCs, the simulation physics or initial conditions may fail to fully reflect reality. Therefore our training data may be biased, leading to a failure in generalization on observational data. Both the first issue -- explainability/interpretability -- and the second -- out of distribution generalization and fairness -- are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an XGBoost classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost and a global rule from CORELS., Comment: ApJ accepted

The upcoming facilities like the Vera C. Rubin Observatory will provide extremely deep photometry of thousands of star clusters to the edge of the Galaxy and beyond, which will require adequate tools for automatic analysis, capable of performing tasks such as the characterization of a star cluster through the analysis of color-magnitude diagrams (CMDs). The latter are essentially point clouds in N-dimensional space, with the number of dimensions corresponding to the photometric bands employed. In this context, machine learning techniques suitable for tabular data are not immediately applicable to CMDs because the number of stars included in a given CMD is variable, and equivariance for permutations is required. To address this issue without introducing ad-hoc manipulations that would require human oversight, here we present a new CMD featurization procedure that summarizes a CMD by means of a quadtree-like structure through iterative partitions of the color-magnitude plane, extracting a fixed number of meaningful features of the relevant subregion from any given CMD. The present approach is robust to photometric noise and contamination and it shows that a simple linear regression on our features predicts distance modulus (metallicity) with a scatter of 0.33 dex (0.16 dex) in cross-validation., Comment: 10 pages, 6 figures. Submitted to the International Conference on Machine Learning 2023

RR Lyrae (RRL) are old, low-mass radially pulsating variable stars in their core helium burning phase. They are popular stellar tracers and primary distance indicators, since they obey to well defined period-luminosity relations in the near-infrared regime. Their photometric identification is not trivial, indeed, RRL samples can be contaminated by eclipsing binaries, especially in large datasets produced by fully automatic pipelines. Interpretable machine-learning approaches for separating eclipsing binaries from RRL are thus needed. Ideally, they should be able to achieve high precision in identifying RRL while generalizing to new data from different instruments. In this paper, we train a simple logistic regression classifier on Catalina Sky Survey (CSS) light curves. It achieves a precision of 87% at 78% recall for the RRL class on unseen CSS light curves. It generalizes on out-of-sample data (ASAS/ASAS-SN light curves) with a precision of 85% at 96% recall. We also considered a L1-regularized version of our classifier, which reaches 90% sparsity in the light-curve features with a limited trade-off in accuracy on our CSS validation set and -- remarkably -- also on the ASAS/ASAS-SN light curve test set. Logistic regression is natively interpretable, and regularization allows us to point out the parts of the light curves that matter the most in classification. We thus achieved both good generalization and full interpretability., Comment: To appear on The Astrophysical Journal. 13 pages, 8 figures, 3 tables

We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with $N$, based on the Multi-Particle Collision (MPC) scheme, previously applied in Plasma Physics. We simulate globular clusters with a realistic number of stellar particles (at least up to several times $10^6$) on a standard workstation. We simulate clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH-average-star mass ratios, unrestricted by the computational constraints affecting direct N-body codes. We use either single mass models or models with a Salpeter mass function, with the IMBH initially sitting at the centre. The force exerted by and on the IMBH is evaluated with a direct scheme. We measure the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we study the evolution of the velocity anisotropy profiles. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function. For the models with Salpeter MF we observe that equipartition of kinetic energies is never achieved. Orbital anisotropy at large radii appears driven by energetic escapers on radial orbits. We measure the wander radius. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-center more frequently than expected, with implications on observational IMBH detection., Comment: 11 pages, 10 figures. Matching the version of the ms accepted in A&A

We use Gaia DR3 data to study the Collinder 132-Gulliver 21 region via the machine learning algorithm StarGO, and find eight subgroups of stars (ASCC 32, Collinder 132 gp 1--6, Gulliver 21) located in close proximity. Three co-moving populations were identified among these eight subgroups: (i) a coeval 25 Myr-old moving group (Collinder 132); (ii) an intermediate-age (50--100 Myr) group; and (iii) the 275 Myr-old dissolving cluster Gulliver 21. These three populations form parallel diagonal stripe-shape over-densities in the U--V distribution, which differ from open clusters and stellar groups in the solar neighborhood. We name this kinematic structure the Collinder 132-Gulliver 21 stream, as it extends over 270 pc in the 3D space. The oldest population Gulliver21 is spatially surrounded by the Collinder 132 moving group and the intermediate-age group. Stars in the Collinder 132-Gulliver 21 stream have an age difference up to 250 Myr. Metallicity information shows a variation of 0.3 dex between the youngest and oldest populations. The formation of the Collinder132-Gulliver 21 stream involves both star formation and dynamical heating. The youngest population (Collinder 132 moving group) with homogeneous metallicity is probably formed through filamentary star formation. The intermediate-age and the oldest population were then scatted by the Galactic bar or spiral structure resonance to intercept Collinder 132's orbit. Without mutual interaction between each population, the three populations are flying by each other currently and will become distinct three groups again in approximately ~50Myr., Comment: Accepted to ApJL, 15 pages, 7 figures

Although active galactic nuclei (AGN) feedback is required in simulations of galaxies to regulate star formation, further downstream effects on the dark matter distribution of the halo and stellar kinematics of the central galaxy can be expected. We combine simulations of galaxies with and without AGN physics from the Numerical Investigation of a Hundred Astrophysical Objects (NIHAO) to investigate the effect of AGN on the dark matter profile and central stellar rotation of the host galaxies. Specifically, we study how the concentration-halo mass ($c-M$) relation and the stellar spin parameter ($\lambda_R$) are affected by AGN feedback. We find that AGN physics is crucial to reduce the central density of simulated massive ($\gtrsim 10^{12}$ M$_\odot$) galaxies and bring their concentration to agreement with results from the Spitzer Photometry & Accurate Rotation Curves (SPARC) sample. Similarly, AGN feedback has a key role in reproducing the dichotomy between slow and fast rotators as observed by the ATLAS$^{3\text{D}}$ survey. Without star formation suppression due to AGN feedback, the number of fast rotators strongly exceeds the observational constraints. Our study shows that there are several collateral effects that support the importance of AGN feedback in galaxy formation, and these effects can be used to constrain its implementation in numerical simulations., Comment: Accepted for publication in MNRAS. 15 pages, 10 figures

We identify members of 65 open clusters in the solar neighborhood using the machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members of twenty clusters from previous studies (Pang et al. 2021a,b; Li et al. 2021) we obtain 85 clusters, and study their morphology and kinematics. We classify the substructures outside the tidal radius into four categories: filamentary (f1) and fractal (f2) for clusters $<100$ Myr, and halo (h) and tidal-tail (t) for clusters $>100$ Myr. The kinematical substructures of f1-type clusters are elongated; these resemble the disrupted cluster Group X. Kinematic tails are distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); ten among these are new. The hierarchical groups form filament networks. Two regions (Alessi 20, LP 2373) exhibit global "orthogonal" expansion (stellar motion perpendicular to the filament), which might cause complete dispersal. Infalling-like flows (stellar motion along the filament) are found in UBC 31 and related hierarchical groups in the IC 348 region. Stellar groups in the LP 2442 region (LP 2442 gp 1-5) are spatially well-mixed but kinematically coherent. A merging process might be ongoing in the LP 2442 subgroups. For younger systems ($\lesssim30$ Myr), the mean axis ratio, cluster mass and half-mass radius tend to increase with age values. These correlations between structural parameters may imply two dynamical processes occurring in the hierarchical formation scenario in young stellar groups: (1) filament dissolution and (2) sub-group mergers., Comment: Accepted to ApJ, 33 pages, 14 figures. OC 3D interactive visualization included on http://3doc-morphology.lowell.edu

Dynamical interactions in dense star clusters are considered one of the most effective formation channels of binary black holes (BBHs). Here, we present direct $N-$body simulations of two different star cluster families: low-mass ($\sim{500-800}$ M$_\odot$) and relatively high-mass star clusters ($\ge{5000}$ M$_\odot$). We show that the formation channels of BBHs in low- and high-mass star clusters are extremely different and lead to two completely distinct populations of BBH mergers. Low-mass clusters host mainly low-mass BBHs born from binary evolution, while BBHs in high-mass clusters are relatively massive (chirp mass up to $\sim{100}$ M$_\odot$) and driven by dynamical exchanges. Tidal disruption dramatically quenches the formation and dynamical evolution of BBHs in low-mass clusters on a very short timescale ($\lesssim{100}$ Myr), while BBHs in high-mass clusters undergo effective dynamical hardening until the end of our simulations (1.5 Gyr). In high-mass clusters we find that 8\% of BBHs have primary mass in the pair-instability mass gap, all of them born via stellar collisions, while only one BBH with primary mass in the mass gap forms in low-mass clusters. These differences are crucial for the interpretation of the formation channels of gravitational-wave sources., Comment: 14 pages, 9 figures, 2 tables. Revised version submitted after fixing typos. Comments welcome

XMM-Newton provides unprecedented insight into the X-ray Universe, recording variability information for hundreds of thousands of sources. Manually searching for interesting patterns in light curves is impractical, requiring an automated data-mining approach for the characterization of sources. Straightforward fitting of temporal models to light curves is not a sure way to identify them, especially with noisy data. We used unsupervised machine learning to distill a large data set of light-curve parameters, revealing its clustering structure in preparation for anomaly detection and subsequent searches for specific source behaviors (e.g., flares, eclipses). Self-organizing maps (SOMs) achieve dimensionality reduction and clustering within a single framework. They are a type of artificial neural network trained to approximate the data with a two-dimensional grid of discrete interconnected units, which can later be visualized on the plane. We trained our SOM on temporal-only parameters computed from more than 100,000 detections from the EXTraS catalog. The resulting map reveals that about 2500 most variable sources are clustered based on temporal characteristics. We find distinctive regions of the SOM map associated with flares, eclipses, dips, linear light curves, and others. Each group contains sources that appear similar by eye. We single out a handful of interesting sources for further study. The condensed view of our dataset provided by SOMs allowed us to identify groups of similar sources, speeding up manual characterization by orders of magnitude. Our method also highlights problems with fitting simple temporal models to light curves and can be used to mitigate them to an extent. This will be crucial for fully exploiting the high data volume expected from upcoming X-ray surveys, and may also help with interpreting supervised classification models., Comment: Accepted in Astronomy & Astrophysics (A&A). Main part: 12 pages, 12 figures, 1 video (appendix: 5 pages and 4 figures)