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Giulia Despali

Publications and source records attributed to Giulia Despali.

At least 19 recordsLinked to original sources

Resolving the Assembly of Disk Galaxies from the Epoch of Reionisation to Cosmic Noon

Most of the mass and angular momentum of today's disk galaxies assembled at $z>1$. Yet, it remains unclear how these galaxies acquired their gas, how their baryons and dark matter coevolved, and how feedback and radial gas transport shaped their disks. Addressing these gaps requires resolved observations of cold gas, which carries most of the mass and angular momentum involved in galaxy assembly. By resolving CO and [C II] at kpc scales, ALMA revealed a surprising population of rotation-dominated disks, even at $z>2$, exhibiting kinematic signatures consistent with spiral arms, bars, and tidal tails. Yet, these studies are limited to massive ($M_\star>10^{10.5}$ M$_\odot$) and highly star-forming (SFRs$\gtrsim 100$ M$_\odot$yr$^{-1}$) galaxies, the progenitors of today's most massive elliptical and disk galaxies. To understand how most present-day spirals (like the Milky Way) assembled, it is crucial to resolve their low-mass progenitors, which dominate the star-forming galaxy population by number at $z>1$. Achieving this goal demands a tenfold increase in line sensitivity and hence a next-generation sub-/millimetre facility: ALMA2040. This leap in sensitivity will enable routine resolved studies of hundreds of $M_\star>10^9$ M$_\odot$ galaxies, including those on and below the main sequence of star-forming galaxies, providing representative, statistical galaxy samples with sub-kpc constraints on the cold gas kinematics and morphology. By uniquely providing resolved CO, [C I], and [C II] observations across $z=1-6$, ALMA2040 will trace a much larger fraction of the cold-gas reservoir than is accessible today, extending resolved studies from rare massive and/or lensed systems to representative galaxy populations. In this way, ALMA2040 will transform our understanding of how galaxy disks formed and evolved.

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Tracing small-scale structure formation through cosmic time with strong gravitational lensing: A case for a next-generation sub-millimetre/millimetre interferometer

The nature of dark matter and the growth of supermassive black holes (SMBHs) remain major open questions in modern astrophysics. Both leave a key signature in an overlapping, largely unexplored mass range: $<10^7$ M$_{\odot}$ dark haloes and wandering black holes. These may be undetectable directly, but detectable through gravitational perturbation of strongly lensed images, and partly or entirely distinguishable from one another through lensing data alone. We demonstrate through realistic simulations that a 255-element sub-mm/mm interferometer could probe this critical mass regime, detecting gravitational perturbations in strongly lensed dusty star-forming galaxies (DSFGs) from objects down to at least $10^5$ M$_{\odot}$. Combined with lens-galaxy characterisation from the European Extremely Large Telescope (ELT), which strengthens the physical interpretation of detected perturbers, and the unprecedented lens samples expected from Euclid and the Square Kilometre Array (SKA), this facility could deliver a census of low-mass dark matter haloes and wandering massive black holes across cosmic time.

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TNGC-SIDM I: Evolution of massive cluster mergers under the self-interacting dark matter paradigm

Merging galaxy clusters provide an ideal laboratory for testing the self-interacting nature of dark matter. In this paper, we present a pilot study of magnetohydrodynamical cosmological zoom-in simulations of two cluster mergers selected from TNG-Cluster, with $M_{\rm 200c} \sim 9\times10^{14}~M_\odot$ and $M_{\rm 200c}\sim 2\times10^{14}~M_\odot$. The simulations are performed with both standard collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM), assuming an isotropic, velocity-independent cross-section of $σ_{\rm T}/m_χ= 1~\rm cm^2~g^{-1}$, with an additional $0.5~\rm cm^2~g^{-1}$ run for the low-mass system, and the mass resolution and galaxy formation model are unchanged from TNG-Cluster. We show how dark matter self-interactions produce an isothermal core in the dark matter halo, generate unique substructures in the intracluster light, and introduce variation in the multi-wavelength observables of the intracluster plasma. Using these simulations, we test the validity of observational probes for dark matter self-interactions in cluster mergers. We find that the shock-to-shock separation shows similar evolution in the self-interaction models tested here, providing a reference for distinguishing the $\sim100-200~\rm kpc$-scale difference in halo separation induced by self-interactions. Moreover, the dark matter halo centroid of the main cluster in the massive cluster merger is offset from the brightest cluster galaxy by as much as $\sim20~\rm kpc$, larger than the offset in the sub-cluster. This offset persists beyond 4 Gyr after the first pericenter passage. Our results indicate that sample selection plays a key role in testing the possible self-interacting nature of dark matter using cluster mergers, and that double radio relic cluster mergers and massive clusters with evidence of an ancient major merger offer a promising testbed for this purpose.

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Can third- and fourth-order multipoles plus radial variation of iso-density ellipses explain the observed flux ratios in B1422$+$231? YES, and a lesson learned from a TNG100 lensing galaxy sample

Flux ratio anomalies in multiply-imaged quasar lenses are a long-standing issue. Using a classical system B1422+231 as a case study, we investigate how typical non-clumpy perturbations beyond elliptical shapes -- multipoles $m_3, m_4$ and radial variations in $q, ϕ_q$ -- can account for the observed image positions and flux ratios under different observational precisions. We extract these perturbations from a pre-selected strong-lensing galaxy sample from the TNG100 simulation. Smooth macroscopic models (SIE+$γ$, EPL+$γ$) are then fitted to the observed image positions alone and to both positions and flux ratios, with and without including the extracted perturbations. With astrometric uncertainty of $σ_{p}=10$ mas, both macro-models alone can already successfully fit image positions within $3σ_{p}$. At $σ_{p}=2$ mas, however, 'astrometric anomalies' appear if smooth macro-models alone are adopted. In this case, adding the extracted perturbations can explain the anomalous image positions. When both positions and flux ratios are adopted, the SIE+$γ$ model family already shows 'flux ratio anomalies' at photometric uncertainty $σ_{f} \le 10\%$ (keeping $σ_{p}=10$ mas). When EPL+$γ$ is used, the smooth model alone can simultaneously fit both positions and flux ratios with $σ_{f}=10\%, 5\%$, but not with $σ_{f}=2\%$, where 'flux ratio anomalies' appear. Adding all four types of extracted perturbations can rescue the macro-models and explain the observed anomalous flux ratios. We present important lessons learned regarding model flexibility and degeneracy.

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Galaxy and Halo Assembly Bias in Alternative Dark Matter Models

The clustering of dark matter halos depends not only on halo mass but also on secondary halo properties, a phenomenon known as halo assembly bias. Coupled with variations in halo occupation, this dependence impacts galaxy clustering, an effect termed galaxy assembly bias. While previous studies have found only weak cosmological dependence of assembly bias within the $Λ$CDM framework, its sensitivity to the underlying dark matter physics remains largely unexplored. We use the matched dark-matter-only and hydrodynamical simulations from the AIDA-TNG suite to measure assembly bias across four dark matter models: cold dark matter, warm dark matter, and self-interacting dark matter with constant cross-sections and velocity-dependent cross-sections. We find that at z = 0, halo assembly bias is nearly identical across the four models for concentration-selected halos, as is the concentration dependence of the halo occupation distribution. The resulting galaxy assembly bias signals likewise show only weak model dependence. For stellar-mass-selected galaxy samples with $n = 0.0586 h^{3} Mpc^{-3}$ at z = 0, the velocity-dependent self-interacting dark matter scenario exhibits the largest deviation from the fiducial cold dark matter model: its assembly bias contribution to galaxy clustering is enhanced by up to $\sim 6\%$, corresponding to a $\sim 3\%$ difference in the assembly bias amplitude. Although statistically distinguishable, this difference is small and unlikely to be detected in current analyses. The weak model dependence persists across different galaxy number densities and redshifts. Overall, within the TNG galaxy-formation framework, these results indicate that assembly bias is largely insensitive to the dark matter models explored here, providing a robust baseline for future studies of the galaxy-halo connection in alternative dark matter scenarios.

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Lower central dark matter densities in nearby galaxies than predicted by simulations

Baryonic feedback in hydrodynamical simulations is typically invoked to alleviate the core--cusp problem in dwarf galaxies. Yet baryonic processes also induce adiabatic contraction of dark matter, producing overly steep density profiles and excessively high dark matter fractions in the inner regions of massive galaxies. The dark matter distribution of galaxies across a wide stellar-mass range is therefore a critical test for such simulations, but a comprehensive benchmark has remained absent. Here, we consistently measure the dark matter distribution from galaxy centres out to radii of 20--50 kpc for 136 nearby galaxies that together span the local mass--size relation over the stellar mass interval $10^9$--$10^{11.5}\,M_{\odot}$. We identify central regions with lower dark matter densities relative to $Λ$CDM simulation expectations---whose extent grows from about 10 kpc to $>50$ kpc as stellar mass increases from $10^{10} M_{\odot}$ to $10^{11.5} M_{\odot}$. Although their physical origin remains unclear, these low--dark matter regions are clearly indicated by the data. Our results provide an important observational benchmark for future hydrodynamical simulations that explore alternative dark matter models and feedback processes.

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Gas distributions inside and around haloes in the alternative dark matter simulations AIDA-TNG

The nature of Dark Matter (DM) is one of the greatest mysteries of modern astrophysics. While the standard Cold DM (CDM) model successfully explains observations on most astrophysical scales, DM particles have not yet been detected, leaving room for a plethora of different models. In order to identify their observable signatures, we use the AIDA-TNG cosmological simulation suite to predict the distributions of gas and neutral hydrogen (HI) in the CDM, Self-Interacting DM (SIDM), velocity-dependent SIDM (vSIDM), and Warm DM (WDM) models. We find that the DM models investigated have very limited impact on the median gas and HI profiles of haloes. Nevertheless, for the most massive haloes ($M_{\rm vir}\sim10^{14}\,\mathrm{M}_\odot$), we find that DM self-interactions can reduce the central potential, thereby lowering gravitational heating and the central gas temperature. We find that, in all models, the halo-to-halo variation in the HI profiles is explained by AGN feedback, and that the specific characteristics of the DM model are largely subdominant. Nevertheless, we detect some systematic difference in the case of SIDM, with more HI surviving close to the centre with respect to other models. We provide fitting functions for the gas and HI profiles. We investigate the galaxy-Ly$α$ cross-correlation function (\galacc) for different halo masses, redshifts and observational strategies. We find that at $z=0$ vSIDM can be distinguished from CDM in haloes with $10^{12}\lesssim M_{\rm vir}\lesssim10^{13}\,{\rm M}_\odot$, while SIDM1 can be distinguished from CDM in haloes with $M_{\rm vir}\gtrsim10^{13}\,{\rm M}_\odot$. We estimate that statistically-robust detection requires sampling $\sim160$ haloes with $\sim20$ sightlines each, a task that can be achieved with current and future facilities like WEAVE, 4MOST, PFS, ELT and WST.

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The assembly and fate of a giant disc galaxy in a protocluster at $z = 3$

Recent JWST observations revealed two massive ($M_{\star} \gtrsim 10^{11}\,M_{\odot}$), unexpectedly large spiral galaxies at $z \sim 3$, both in overdense environments. We focus on one of these, ADF22.1 at $z = 3.09$, which hosts an active galactic nucleus (AGN), exploiting its extended [CII] emission ($\sim$30 kpc in diameter) with high-resolution observations from the Atacama Large Millimetre Array and JWST. We find a flat outer rotation curve reaching $\sim$530 km s$^{-1}$, and perform, for the first time for a system of this type, a rotation-curve decomposition. We infer a dark-matter halo mass of $\log(M_{200}/M_{\odot})=12.9^{+0.4}_{-0.3}$, a baryon-to-halo mass ratio of $0.4^{+0.6}_{-0.3}$ in units of the cosmological baryon fraction, and a ratio between the baryonic and dark-matter halo specific angular momentum of $1.0^{+0.7}_{-0.5}$. Comparing these quantities with those of local galaxies, we find that ADF22.1 is indistinguishable from $z=0$ giant discs, pointing to the inefficiency of AGN feedback in halting disc growth. Using the Mapping Nearby Galaxies at Apache Point Observatory survey, we identify potential $z=0$ descendants of ADF22.1, suggesting it will evolve into an extreme (in either mass or angular momentum) early-type galaxy. Finally, we argue that cold-stream accretion, invoked to explain disc formation at $z > 1$, cannot simultaneously account for its size, dynamical properties, high specific angular momentum, and baryon-to-halo mass ratio. Instead, sustained accretion from the hot circumgalactic medium, either via spontaneous or fountain-driven condensation, offers a more physically plausible formation pathway.

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The AIDA-TNG project. Abundance, radial distribution, and clustering properties of halos in alternative dark matter models

Warm and self-interactive dark matter cosmologies have been proposed as nonbaryonic solutions to the tensions between the $Λ$ cold dark matter model and observations at the kiloparsec scale. In this paper, we used the dark matter-only runs of the \textsc{aida-tng} project, a set of cosmological simulations of different sizes and resolutions, to analyze the macroscopic impact of alternative dark matter models on the abundance, radial distribution, and clustering properties of halos. We adopted the halo occupation distribution formalism to characterize the evolution of its parameters $M_1$ and $α$ with the mass and redshift selection of our sample. By dividing the halo population into centrals and satellites, we were able to study their spatial density profile. We found that a Navarro-Frenk-White model is not accurate enough to describe the radial distribution of subhalos and that a generalized Navarro-Frenk-White model is required instead. Warm dark matter models, in particular, present a cuspier distribution of satellites, whereas self-interacting dark matter exhibits a shallower density profile. Moreover, we found that the small-scale clustering of dark matter halos provides a powerful tool for distinguishing among alternative dark matter scenarios, in preparation for a more detailed study that fully incorporates baryonic effects and for a comparison with observational data from galaxy clustering.

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The AIDA-TNG project: dark matter profiles and concentrations in alternative dark matter models

In the standard Cold Dark Matter (CDM) scenario, the density profiles of dark matter haloes are well described by analytical models linking their concentration to halo mass. Alternative scenarios, such as warm dark matter (WDM) and self-interacting dark matter (SIDM), modify the inner structure of haloes and predict different profile shapes and central slopes. We employ the AIDA-TNG simulations to investigate how alternative dark matter physics and baryonic processes jointly shape the internal structure of haloes. Using dark-matter-only and full-physics runs, we measure the dark matter density profiles of haloes spanning six orders of magnitude in mass, from 10^9.5 Msun to 10^14.5 Msub, and characterise them with multiple analytical models. We provide the distribution of the best-fitting parameters, as well as the concentration-mass relation in WDM and SIDM. The Einasto profile well reproduces the inner flattening produced in WDM models, both in the collisionless and in the full-physics runs. In SIDM dark-matter-only runs, haloes are better described by explicitly cored profiles, with core sizes that depend on mass and on the self-interaction model. When baryons are included, the differences between CDM and SIDM decrease, and such large dark-matter cores no longer form because adiabatic contraction in the baryon-dominated region counteracts self-interactions. Nevertheless, the coupling between baryons and self-interactions induces a broader range of inner slopes, including cases that are steeper than CDM at Milky Way masses. Alternative dark matter physics thus leaves clear signatures in the inner halo structure, even if baryons significantly reshape these differences. Our results are useful for future studies that need to predict the properties of haloes in multiple dark matter models.

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Self-interacting dark matter in the center of a Local Group dwarf galaxy and its satellites

We present a detailed comparison of a Local Group dwarf galaxy analogue evolved in two cosmological models: the standard $Λ$CDM and a self-interacting dark matter (SIDM) model with a velocity-dependent cross-section. Both simulations are run with the high-resolution, hydrodynamical LYRA galaxy formation model, allowing us to explore the global and substructure properties of the dwarf in a consistent context. While the overall halo growth, final mass, and subhalo mass functions remain largely unchanged across models, SIDM produces a central dark matter core extending to $\sim$1 kpc, which does not significantly vary with the inclusion of baryons. Baryonic properties, however, differ notably. The SIDM model leads to a 25% reduction in stellar mass and retains more gas within the stellar half-mass radius due to a prolonged quiescent phase in star formation. The stellar distribution is less centrally concentrated, and a population of in-situ star clusters form at late times. Substructure analysis reveals fewer luminous satellites and more stellar-only systems in SIDM, driven in part by tidal stripping that affects the dark matter more than the stars. A subset of satellites undergoes tidal-triggered core collapse after infall, enhancing the diversity of SIDM satellite rotation curves. These differences offer potential observational signatures of SIDM in low-mass galaxies.

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SHARP -- IX. The dense, low-mass perturbers in B1938+666 and J0946+1006: implications for cold and self-interacting dark matter

We present an extended analysis of the gravitational lens systems SDSS J0946+1006 and JVAS B1938+666. We focus on the properties of two low-mass dark matter haloes previously detected in these systems and compare them with predictions from different dark matter models. In agreement with previous studies, we find that the object H detected in J0946+1006 is a dark-matter-dominated subhalo. Object A, in B1938+666, is a foreground halo at $z = 0.13\pm0.07$, contradicting previous analyses which suggested this object to be located either within or at higher redshift than the lens. Given the new redshift for this object, we update the 3$σ$ upper limit on its luminosity to $L_V < 6.3 \times 10^5 {(z/0.13)}^2 L_{V,\odot}$. By selecting central galaxies from the TNG50 hydrodynamical simulation, we find that analogues with projected mass density profiles around the robust radius of $\sim$ 91 pc and luminosities consistent with detection A can be found, although they lie near the edge of the halo distribution in the relevant mass and redshift ranges. We conclude, therefore, that this object is an atypical but possible event in $Λ$CDM. The projected mass density profile of both detections over the well-constrained range of radii may be consistent with expectations from SIDM gravothermal fluid model if the effective self-interaction cross-section $σ_{c,0}/m_{\rm{dm}}$ is of order $300 \ \rm{cm}^2 g^{-1}$ or larger.

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Introducing the AIDA-TNG project: galaxy formation in alternative dark matter models

We introduce the AIDA-TNG project, a suite of cosmological magnetohydrodynamic simulations that simultaneously model galaxy formation and different variations of the underlying dark matter model. We consider the standard cold dark matter model and five variations, including three warm dark matter scenarios and two self-interacting models with constant or velocity-dependent cross-section. In each model, we simulate two cosmological boxes of 51.7 and 110.7 Mpc on a side, with the same initial conditions as TNG50 and TNG100, and combine the variations in the physics of dark matter with the fiducial IllustrisTNG galaxy formation model. The AIDA-TNG runs are thus ideal for studying the simultaneous effect of baryons and alternative dark matter models on observable properties of galaxies and large-scale structures. We resolve haloes in the range between $10^{8}$ and $4\times10^{14}\,$M$_{\odot}$ and scales down to the nominal resolution of 570 pc in the highest resolution runs. This work presents the first results on statistical quantities such as the halo mass function and the matter power spectrum; we quantify the modification in the number of haloes and the power on scales smaller than 1 Mpc, due to the combination of baryonic and dark matter physics. Despite being calibrated on cold dark matter, we find that the TNG galaxy formation model can produce a realistic galaxy population in all scenarios. The stellar and gas mass fraction, stellar mass function, black hole mass as a function of stellar mass and star formation rate density are very similar in all dark matter models, with some deviations only in the most extreme warm dark matter model. Finally, we also quantify changes in halo structure due to warm and self-interacting dark matter, which appear in the density profiles, concentration-mass relation and galaxy sizes.

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Non-halo structures and their effects on gravitationally lensed galaxies

While the $Λ$CDM model succeeds on large scales, its validity on smaller scales remains uncertain. Recent works suggest that non-halo dark matter structures, such as filaments and walls, could significantly influence gravitational lensing and that the importance of these effects depends on the dark matter model: in warm dark matter scenarios, fewer low-mass objects form and thus their mass is redistributed into the cosmic-web. We investigate these effects on galaxy-galaxy lensing using fragmentation-free Warm Dark Matter (WDM) simulations with particle masses of m$_χ$ = 1 keV and m$_χ$ = 3 keV. Although these cosmological scenarios are already observationally excluded, the fraction of mass falling outside of haloes grows with the thermal velocity of the dark matter particles, which allows for the search for first-order effects. We create mock datasets, based on gravitationally-lensed systems from the BELLS-Gallery, incorporating non-halo contributions from these simulations to study their impact in comparison to mocks where the lens has a smooth mass distribution. Using Bayesian modelling, we find that perturbations from WDM non-halo structures produce an effect on the inferred parameters of the main lens and shift the reconstructed source position. However, these variations are subtle and are effectively absorbed by standard elliptical power-law lens models, making them challenging to distinguish from intrinsic lensing features. Most importantly, non-halo perturbation does not appear as a strong external shear term, which is commonly used in gravitational lensing analyses to represent large-scale perturbations. Our results demonstrate that while non-halo structures can affect the lensing analysis, the overall impact remains indistinguishable from variations of the main lens in colder WDM and CDM scenarios, where non-halo contributions are smaller.

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The Three Hundred Project hydrodynamical simulations: Hydrodynamical weak-lensing cluster mass biases and richnesses using different hydro models

The mass of galaxy clusters estimated from weak-lensing observations is affected by projection effects, leading to a systematic underestimation compared to the true cluster mass, varying with both mass and redshift. The magnitude depends on the criteria used to select clusters and the spatial scale over which their mass is measured. We leverage hydrodynamical simulations of galaxy clusters carried out with GadgetX and GIZMO-SIMBA as part of the Three Hundred project. We used them to quantify weak-lensing mass biases with respect also to the results from dark matter-only simulations. We also investigate how the biases propagate into the richness-mass relation. We aim to shed light on the effect of the presence of baryons on the weak-lensing mass bias and also whether this bias depends on the galaxy formation recipe; we seek to model the richness-mass relation that can be used as guidelines for observational experiments for cluster cosmology. We produced weak-lensing simulations of random projections to model the expected excess surface mass density profile of clusters up to redshift $z=1$. We then estimated the observed richness by counting the number of galaxies in a cylinder and correcting by projected contaminants. We derived the weak-lensing mass-richness relation and found consistency across hydrodynamical simulations. The intercept parameter of the relation is independent of redshift but varies with the minimum of the stellar mass to define the richness. At the same time, the slope is relatively constant up to $z=0.55$. The scatter in observed richness at a fixed weak-lensing mass increases linearly with redshift at a fixed stellar mass cut. As expected, we observed that the scatter in richness at a given true mass is smaller than at a given weak-lensing mass. Our results for the weak-lensing mass-richness relation align well with SDSS redMaPPer cluster analyses. [Abridged]

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Detecting low-mass haloes with strong gravitational lensing II: constraints on the density profiles of two detected subhaloes

Strong gravitational lensing can detect the presence of low-mass haloes and subhaloes through their effect on the surface brightness of lensed arcs. We carry out an extended analysis of the density profiles and mass distributions of two detected subhaloes, intending to determine if their properties are consistent with the predictions of the cold dark matter (CDM) model. We analyse two gravitational lensing systems in which the presence of two low-mass subhaloes has been previously reported: SDSSJ0946+1006 and JVASB1938+66. We model these detections assuming four different models for their density profiles and compare our results with predictions from the IllustrisTNG50-1 simulation. We find that the detected subhaloes are well-modelled by steep inner density slopes, close to or steeper than isothermal. The NFW profile thus needs extremely high concentrations to reproduce the observed properties, which are outliers of the CDM predictions. We also find a characteristic radius within which the best-fitting density profiles predict the same enclosed mass. We conclude that the lens modelling can constrain this quantity more robustly than the inner slope. We find that the diversity of subhalo profiles in TNG50, consistent with tidally stripping and baryonic effects, is able to match the observed steep inner slopes, somewhat alleviating the tension reported by previous works even if the detections are not well fit by the typical subhalo. However, while we find simulated analogues of the detection in B1938+666, the stellar content required by simulations to explain the central density of the detection in J0946+1006 is in tension with the upper limit in luminosity estimated from the observations. New detections will increase our statistical sample and help us reveal more about the density profiles of these objects and the dark matter content of the Universe.

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A deep learning model for the density profiles of subhaloes in IllustrisTNG

We present a machine-learning-based model for the total density profiles of subhaloes with masses $M \gtrsim 7\times 10^8\,h^{-1}{\rm M}_\odot$ in the IllustrisTNG100 simulation. The model is based on an interpretable variational encoder (IVE) which returns the independent factors of variation in the density profiles within a low-dimensional representation, as well as the predictions for the density profiles themselves. The IVE returns accurate and unbiased predictions on all radial ranges, including the outer region profile where the subhaloes experience tidal stripping; here its fit accuracy exceeds that of the commonly used Einasto profile. The IVE discovers three independent degrees of freedom in the profiles, which can be interpreted in terms of the formation history of the subhaloes. In addition to the two parameters controlling the normalization and inner shape of the profile, the IVE discovers a third parameter that accounts for the impact of tidal stripping onto the subhalo outer profile; this parameter is sensitive to the mass loss experienced by the subhalo after its infall onto its parent halo. Baryonic physics in the IllustrisTNG galaxy formation model does not impact the number of degrees of freedom identified in the profile compared to the pure dark matter expectations, nor their physical interpretation. Our newly proposed profile fit can be used in strong lensing analyses or other observational studies which aim to constrain cosmology from small-scale structures.

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The energy shear of protohaloes

As it collapses to form a halo, the shape of a protohalo patch is deformed by the initial shear field. This deformation is often modeled using the "deformation" tensor, constructed from second derivatives of the gravitational potential, whose trace gives the initial overdensity. However, especially for lower mass protohalos, this matrix is not always positive definite: one of its eigenvalues has a different sign from the others. We show that the evolution of a patch is better described by the "energy shear" tensor, which is positive definite and plays a direct role in the evolution. This positive-definiteness simplifies models of halo abundances, assembly and of the cosmic web.

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