A Deep Learning Approach for Characterizing Major Galaxy Mergers
Skanda Koppula, Victor Bapst, Marc Huertas-Company, Sam Blackwell, Agnieszka Grabska-Barwinska, Sander Dieleman, Andrea Huber, Natasha Antropova, Mikolaj Binkowski, Hannah Openshaw, Adria Recasens, Fernando Caro, Avishai Deke, Yohan Dubois, Jesus Vega Ferrero, David C. Koo, Joel R. Primack, Trevor Back
AA Deep Learning Approach for CharacterizingMajor Galaxy Mergers
Skanda Koppula , Victor Bapst , Marc Huertas-Company , , , Sam Blackwell , Agnieszka Grabska-Barwinska , Sander Dieleman Andrea Huber , Natasha Antropova , Mikolaj Binkowski , Hannah Openshaw Adria Recasens , Fernando Caro , Avishai Dekel , Yohan Dubois Jesus Vega Ferrero , , David C. Koo , Joel R. Primack , Trevor Back DeepMind, London, UK N1C 4AG LERMA, Observatoire de Paris, PSL Research University, CNRS,Sorbonne Universités, UPMC Univ. Paris 06,F-75014 Paris, France Univeristé de Paris, 5 Rue Thomas Mann - 75013, Paris, France Departamento de Astrofísica, Universidad de La Laguna,E-38206 La Laguna, Tenerife, Spain Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain Racah Institute of Physics, The Hebrew University, Jerusalem 91904 Israel Institut d’Astrophysique de Paris, Sorbonne UniversitéCNRS, UMR 7095, 98 bis bd Arago, 75014 Paris, France IFCA, Instituto de Fiésica de Cantabria (UC-CSIC), Av. de Los Castros s/n 39005 Santander, Spain, Artificial Intelligence Research Institute (IIIA-CSIC), Campus UAB, Bellaterra, Spain UCO/Lick Observatory, Department of Astronomy and Astrophysics,University of California, Santa Cruz, CA 95064, USA Physics Department, University of California, Santa Cruz, CA 95064, USA
Abstract
Fine-grained estimation of galaxy merger stages from observations is a key problemuseful for validation of our current theoretical understanding of galaxy formation.To this end, we demonstrate a CNN-based regression model that is able to predict,for the first time, using a single image, the merger stage relative to the first perigeepassage with a median error of 38.3 million years (Myrs) over a period of 400Myrs. This model uses no specific dynamical modeling and learns only fromsimulated merger events. We show that our model provides reasonable estimateson real observations, approximately matching prior estimates provided by detaileddynamical modeling. We provide a preliminary interpretability analysis of ourmodels, and demonstrate first steps toward calibrated uncertainty estimation.
Galaxy merging plays a fundamental role in our current theoretical understanding of galaxy formation.Mergers significantly affect galaxy morphology, converting rotationally-supported disk galaxies intovelocity-dispersion-supported elliptical galaxies [Toomre, 1964]. Gas-rich mergers at high redshifthave also been shown to trigger central gas inflow, starburst, and galactic bulge formation [Zolotovet al., 2015], and gas-poor mergers enlarge the radii of elliptical galaxies [Oser et al., 2012].Although mergers are present in all theoretical models, observational evidence of their potential effectson galaxies remains elusive. A key challenge in correlating observations with galaxy transformationsis calibrating the merger stage: galaxy merging is by definition a dynamical process that takes severalmillion years, and observations that we can record in our lifetime provide only a single time-slicesnapshot of such a process. The two approaches used to identify mergers in the sky — counting pairsof galaxies through deep spectroscopy [Duncan et al., 2019] and identifying indicative morphological
Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada. a r X i v : . [ a s t r o - ph . GA ] F e b erturbations [Bluck et al., 2012] — both present biases based on the assumed observability ofmerger stages. Accurate merger stage estimation is also useful for measuring a global merger rate :the number of mergers per unit time and volume in the universe. Determining the observabilitytime scale is crucial to measuring these merger rates. This rate is useful for validating cosmologicalmodels [Lotz et al., 2011].In recent years, there have been several attempts to calibrate galaxy merger detection using state-of-the art simulations that provide dynamical information which is lacking in observations [Lotz et al.,2008, Snyder et al., 2019]. Machine learning has emerged as a strong tool to learn merger propertiesin simulations [Pearson et al., 2019, Snyder, 2019, Ferreira et al., 2020]. These preliminary workshave shown that deep learning can successfully classify galaxies into interacting and non-interactingsystems using simulation-provided labels. The domain shift to observations still remains a challengethough, as by definition, there is no available ground truth in the observations. Indirect sanity checkssuch as visual example inspection or comparing with standard morphologies can be undertaken, butit is still difficult to control for all possible systematics [Ferreira et al., 2020, Pearson et al., 2019].In this work, we go several steps further into the characterization of galaxy mergers using deeplearning. First, we move from a classification to a regression problem to predict the exact time ofa given image of a merger within a merger process. We show that merger stage prediction with amedian absolute error of 38.3 million years (Myrs) over a window of 400 Myrs is possible based on asingle image and without using any dynamical modeling. Second, we test our model on a well-knownsystem, the Antennae galaxies. Our models trained on simulation snapshots successfully predict themerger stage to the the correct order of magnitude on real observations, matching estimates producedby detailed dynamical modeling. We also explore first steps to measure model uncertainty, anduncover visual indicators on which the model relies. We use the cosmological hydrodynamical simulation Horizon-AGN[Dubois et al., 2014]. The simulation employs an adaptive mesh refinement Eulerian hydrodynamicsprocedure using RAMSES [Teyssier, 2002]. Galaxies are then identified using the AdaptaHOPstructure finder [Aubert et al., 2004] over the stellar distribution, using a minimum stellar mass of solar masses. The merger trees for the identified galaxies are then built using the procedureoutlined in Tweed et al. [2009]. More details on the Horizon-AGN simulation and structure findingare provided in the Appendix. We consider only galaxies more massive than solar massesin the redshift range z = [0 . , . This is intended to match current deep Hubble Space Telescopeobservations such as the CANDELS survey [Grogin et al., 2011]. We then use the galaxy merger treesfrom the simulation to select major galaxy mergers following a standard approach of thresholdingthe stellar mass ratio between the secondary and main progenitor galaxies such that M /M < [Rodriguez-Gomez et al., 2015].After this initial selection, we build merger sequences which are a complete tracking of the mergerprocess with a time resolution of ∼ Myrs. To do so, we first follow each progenitor backward intime, until the progenitors reach a calibrated distance from each other prior to merging (Appendix5.2). We call t s the time between the sequence’s beginning and the first encounter between galaxies( t first pass ). We follow the sequence forward in time by the same amount, so that the duration ofthe entire merger sequence is ∆ T = 2 × t s . The i th snapshot in the sequence occurs at a time t i .Snapshots with time − t s < t i < are considered to be pre-merger, and snapshots with a time < t i < + t s are considered to be post-merger. Since the absolute duration of a merger depends atfirst order on the dynamical time, we normalize all values by the cosmological dynamical time whichwe estimate to be t dyn ∼ . t H . Here, t H is the Hubble time /H ( z ) at the observation’s redshift. We generate observed images of all the snapshots of the selected mergersequences. Images are produced to replicate properties of Hubble Space Telescope imaging of theCANDELS survey in seven different filters going from the near UV to the near IR (F435W-F160W).We use SUNSET for image generation [Kaviraj et al., 2017, Laigle et al., 2019], which models theemission of all galaxy photons to produce an image in the observed-frame. We generate three differentprojections along the main axes of the simulations ( X, Y, Z ) . For this work, dust effects in the imagegeneration are not included for computational reasons. We use noiseless images since we want to test2hether deep networks can generalize well enough to learn the properties of galaxy mergers basedonly on examples. We therefore want to maximize the amount of signal in this proof-of-concept work.An example of a merger sequence is shown in Figure 1. Figure 1: 17 samples from a galaxy merge sequence with 34 observations, with an average redshift of 2.146. Weshow two channels of seven. The first observation ( t − ) corresponds to a normalized time of -0.24, and the last t +17 corresponds to . . The observation at time t first pass is indicated by t = 0 . In addition to simulation data, we use archival Hubble Space Telescope observations of the Antennaegalaxies (NGC 4038/NGC 4039) to test our model . This well-known system is an archetypal majormerger at redshift z = 0 . which has been extensively modeled [Karl et al., 2008, Lahén et al.,2018]. Observations have two channels: F160W and F850LP. In order to better match the propertiesof the higher redshift training set, we modify the Antennae system observations as if it was observedat high redshift. Given that we are not interested in the absolute flux, we simply apply a spatialscaling to match the angular scale at z = 1 . . We do not apply dimming to match the high SNR inthe training set. Images produced by the Horizon-AGN simulation go through a multi-step pre-processing pipeline.Views from each filter (F160W-F435W) are stacked in the channel dimension of each image. Imagesare then cropped to a × window centered around the point with maximum total intensity.We take this approach to avoid regression target leakage; a simple rescaling would yield an imagewith apparent galaxy size that correlates with merge state. This resolution-label correlation is notpresent in real galaxy views, so we take care to avoid label leakage and model degeneracy. Imagesare augmented before being fed as model input: randomly flipped, rotated in increments of °,jittered, and rescaled. Regression labels are produced through the normalization procedure describedin Section 2.1.Our Horizon-AGN simulation dataset consists of 6337 galaxy merge sequences, with an averagesequence length of 32 time-steps symmetrically straddling t . Across all sequences, there are 203667individual observations, with three views per observation. We divide our simulation images into train,validation, and test datasets with a 80%-10%-10% split. Projections from the same merger neveroccur in more than one split. We use a convolutional neural network to regress merger time. In particular, we employ a standardResNet-50 architecture [He et al., 2016] to process each input image and produce two regressionoutputs: the merge time estimate t and an uncertainty score σ . For models with mass and redshift,we add in a fully-connected layer to embed the mass and redshift features before adding this to eachResNet-block output. We also train models specifically to evaluate Antennae observations, only usingthe F160W and F850LP channels in our training dataset to match the Antennae samples.To simultaneously learn uncertainty ( σ ) and merger time ( t ), we minimize the sum of a scaled MSEand σ estimate, as in Lakshminarayanan et al. [2017]: log σ + ( t − ˆ t ) σ . This is effectively minimizingthe log-likelihood criterion for a normal mean/variance estimate. We also add in an 0.0001-weightedL2 regularization term on the trainable weights, yielding our final loss criterion.We use a standard Momentum SGD optimizer with global norm-based gradient clipping set to 5.0[Sutskever et al., 2013]. We set an initial learning rate of 0.025 and use a stepwise-decay schedule,reducing by a factor of 0.1 after 50K and 100K steps. Each model completes training after 150Ksteps, roughly 7 hours using 2 V100 GPUs. igure 2: Alignment of ground truth and predictions for ± Myrs (left) and ± Myrs (right). Red dashedline: perfect alignment. Black dotted line: the median prediction. Black dashed lines: the prediction variance.
For our Antennae evaluation, we employ the test-time augmentation methodology proposed in Sunet al. [2020] to better address the simulated-to-real domain gap. We use their self-consistency lossacross augmented image views to fine-tune the model for an additional twenty steps.
We first evaluate trained models on our test split of simulation images. On the full range of mergersequence snapshot times ( ± Myrs), our regression models obtain an root mean square error of144.1 Myrs. We find that our model’s largest errors skew toward the edges of the time interval; thelargest errors are early pre-mergers, and the median absolute error is 69.35 Myrs. Interestingly, we findthat we obtain slightly better estimation accuracy using a model trained on samples ± Myrs rangearound the merge. On this time window, the model obtains an RMSE of 68.153 Myrs and medianabsolute error of 38.391 Myrs. When classifying mergers as either pre- and post-merger (thresholdingthe predictions and ground truth by t > or t ≤ ), our model obtains 86% classification accuracyon our full range of merger sequences, comparable to prior work [Ferreira et al., 2020].Figure 2 shows alignment between ground truth and predictions for both these models, along witheach model’s scaled uncertainty estimate. As previously observed on the full range, our model’smedian prediction diverges from targets for early pre-mergers. Otherwise, we find reasonable groundtruth/prediction alignment, especially for our half-range models. Our uncertainty estimate seems tovisually indicate examples outside the scatter (dark brown in the full-range interval, light blue in thehalf-range interval), and grows more uncertain toward the weakest parts of the alignment. We tested our two-filter, simulation-trained model on four redshift variants of the Hubble spaceTelescope observations of the Antennae galaxy ( z = 0 . , . , . and . ). Our model re-gressed normalized time estimates of µ = { . , . , . , . } with a model estimated σ = { . , . , . , . } , respectively. Similar regression estimates suggest stability of themodel across redshifts. Existing dynamical models of the system [Karl et al., 2008, Lahén et al., 2018]estimate that the time of observation is between 500-600 Myrs after first passage. This corresponds tonormalized times of . − . at z = 0 . (Figure 3). Our predictions are therefore in agreementwithin 1 σ despite resulting from crude approximations in simulation (lacking dust, noise, etc.). Thisis extremely encouraging, as this is the first time a model trained on cosmological simulation hasbeen applied to an observed merger snapshot that has independent measurements. Figure 3: Normalized time predictions for the four redshift variants of the Antennae observation, with priorestimates highlighted in red (left) and the two-filter Antennae observations for z = 0 . , . , and . (right). We examined regions of input used by the model to produce its predictions. In Figure 4, we visualiseinput gradients, which reflect the sensitivity of the network prediction to small changes in the input.4e show five channels of three snapshots within a merge sequence (pre-, middle-, and post- from topto bottom) with redshifts of 0.98, 0.84, and 0.70, respectively.We observe that the patterns of attention depend on wavelength and on the merger stage as expected.Infrared filters (optical rest-frame) tend to focus on the central parts of the galaxies where most ofthe stellar light comes from. In the pre-merger phase, we clearly see the cores of the two galaxieshighlighted. UV rest-frame bands focus more of their attention in the outskirts of the system. This isparticularly visible in the post-merger phase. It is likely capturing young stars being formed in theouter regions as a consequence of the interaction. - F160W F125W F105W F606W F435W ± ± ± Figure 4: Example of input gradients within amerge sequence. Rows show different timesin the sequence (image+activation). Columnsindicate different filters from near -infrared(F160W) to near-UV (F435W).
Our work shows that temporal constraints on astrophysi-cal observations can be established. We provide evidencethat such approaches can be effectively applied to realworld observations, while providing some measure of in-terpretability. We encourage study of the effects of merg-ers on galaxy evolution from a computational perspective.
Horizon-AGN was run with a co-moving box size of Lbox= h − Mpc, that contains DM particles, andthat was run considering initial conditions drawn fromthe WMAP-7 cosmology. The simulation employs theadaptive mesh refinement Eulerian hydrodymamics code,RAMSES [Teyssier, 2002], and the initially coarse 10243grid is adaptively refined, in a quasi-Lagrangian manner,down to a spatial resolution of 1 proper kpc. The Adap-taHOP structure finder [Aubert et al., 2004] was used toidentify galaxies, using a minimum threshold of 50 stellarparticles (corresponding to a minimum stellar mass of solar masses). The merger trees were builtconsidering 758 time steps that cover a redshift range spanning from z = 7 to z = 0 and with a timedifference of ∼ Myrs on average between two successive time steps.
We look for an increase in the mass of a galaxy due to the contribution ofmore than one progenitor from the previous time step. If a galaxy has more than one progenitor andthe ratio between the stellar mass provided by the secondary and the main progenitor is equal orlarger than 1:4, the galaxy is considered as a major merger, and therefore enters our selection. Toconstruct the entire merger sequence from t first pass , we fellow the progenitors until the secondaryprogenitor is separated from the main progenitor by a distance larger than four times its effectiveradius. This is an arbitrary selection that defines the beginning of our merger sequence. It has beencalibrated empirically to properly bracket all the different phases of a merger For each identified galaxy in the simulation, we define a cubic volumecentered around the galaxy with an edge length of eight times the radius of the galaxy (in this case,defined as the average between the three semi-axes obtained when fitting an ellipsoid to the stellarmass distribution of the galaxy). This volume should contain the stellar particles from the maingalaxy as well as those from any close companion, in order to capture both galaxies involved in themerger. The stellar particles contained within the volume are used as an input to SUNSET, alongwith the spectral response of the different filters. SUNSET computes the fluxes corresponding to theinputs using the stellar models of Bruzual and Charlot [2003] and a Chabrier [2003] IMF. Finally, theintegration of the SED in each pixel and the redshift of the galaxy are used to generate an image inthe observed frame.
This work proposes an approach for fine-grained estimation of galaxy mergerstage using astrophysical simulations. We believe that this work will allow astronomers to improveunderstanding of galaxy formation by tracking down with unprecedented accuracy the impact ofmergers on galaxy transformations over cosmic time. More broadly, this work may be of interest toresearchers in computational astronomy and applied machine learning. We believe there is little scopeto misuse the artifacts of this work, which uses computational methods to analyze astrophysical data.5 eferences
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