arXiv subjects

Sébastien Peirani

Publications and source records attributed to Sébastien Peirani.

At least 19 recordsLinked to original sources

arXiv2026

Starbursts hiding in the main sequence: a pathway toward quenching?

Star-forming galaxies spend most of their lifetimes on the star-forming main sequence, which establishes a tight empirical and statistical relation between stellar mass and star-formation rate. Occasional episodes of rapid star formation can push them temporarily above this sequence, turning them into starbursts. Yet some galaxies display starburst-like traits -- rapid, dense, and compact star formation -- while still remaining within the scatter of the main sequence. These "starbursts in the main sequence" (SBMSs) reveal the complexity and diversity of star formation modes, making them crucial for understanding how galaxies evolve and transition between different regimes. In this paper, we identify SBMSs in the cosmological simulation NewHorizon and follow their evolution across time to uncover their physical origins and the role of this special regime in shaping galaxy evolution. We explain the existence of SBMSs by a comparatively earlier assembly of their stellar mass, driven in particular by more frequent and repeated mergers as the other galaxies, as well as exceptionally productive starburst events triggered by these interactions. As a result, this regime appears preferentially -- though not exclusively -- in the most massive galaxies. The SBMS behavior is not continuous within individual galaxies but instead arises intermittently as a short-lived (~ 30 Myr) evolutionary mode. Nevertheless, such SBMS episodes exist throughout cosmic time across the galaxy population... [abridged]

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arXiv2026

Kinematic scaling of thin and thick discs from SAMI to NewHorizon

We revisit the relation between disc stellar mass and disc velocity dispersion (M_*-σ_e) and extend it to thin and thick subcomponents using orbit-based dynamical models of 161 SAMI galaxies and counterpart measurements for 31 disc galaxies in the NewHorizon simulation. On the observational side, we apply Schwarzschild orbit superposition to recover orbital circularity distributions and component kinematics. On the simulation side, we sample thin and thick discs by circularity and, separately, by stellar age to test classification dependence. Our analysis reveals three main results. (1) Discs follow a tight M_*-σ_e relation, nearly parallel to the bulge relation. (2) For both circularity- and age-based definitions, the thick-disc component is systematically hotter than the thin-disc component, and the thin-thick dispersion ratio varies only weakly with mass. However, age cuts yield a smaller kinematic contrast, indicating that stellar age and orbital circularity do not map one-to-one and that no single global age threshold reproduces the circularity-based split. (3) Method and data systematics are present, with Schwarzschild modelling returning slightly higher disc σ_e than spectroscopic bulge-disc decompositions, and simulated discs showing lower σ_e at fixed mass than observed. All these results are consistent with a baseline set by vertical-equilibrium scalings, with secular heating accumulating over time and modulating the dispersion at fixed mass. Occasional minor interactions may add localised heating but do not appear to be essential for explaining the qualitative, global trends reported here. Future tests with chemo-dynamical modelling and higher-resolution, chemistry-tracking simulations will provide stronger constraints on disc substructures in external galaxies.

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arXiv2025

On the Origin of Gas-stripping of Galaxies in Group Environments

We investigate how low-mass group environments ($M_{\rm vir} \sim 10^{12-13}\,M_{\odot}$) influence the gas content of their satellite galaxies with $M_* > 10^{7}\,M_{\odot}$ using the \NHtwo\ simulation. Many satellite galaxies preserve substantial gas reservoirs, yet show signs of outer gas stripping, reminiscent of jellyfish galaxies in clusters. In contrast, low-mass satellites ($<10^8 \, M_{\odot}$) are largely gas-deficient, and some of them undergo gas removal within their host group by external pressure triggered by either galaxy interactions or ram pressure exerted by the hot intragroup medium. Complete gas removal in these satellite galaxies occurs when the external hydrodynamic pressure exceeds the gravitational restoring force, typically due to stochastic events such as galaxy-galaxy interaction or nearby galactic outflows. The emergence of a characteristic stellar mass of $10^8 \, M_{\odot}$ which determines the efficiency of gas removal in groups, likely reflects the differing scaling relations of external pressure with halo mass and gravitational restoring force with stellar mass. While tidal interactions can be a significant cause of gas loss in satellite galaxies, those severe enough to affect the gas content in the central regions typically lead to the complete disruption of the galaxy. Consequently, gas loss driven by tidal interactions may be underestimated in the studies focusing solely on surviving galaxies. Group environments, where environmental effects are weaker and satellite galaxies tend to have lower restoring forces due to their low masses, exhibit complex manifestations of gas loss that are not seen in more massive environments such as clusters.

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arXiv2024

On the Origin of Star Formation Quenching of Galaxies in Group Environments using the NewHorizon simulation

We study star formation (SF) quenching of satellite galaxies with $M_{*} > 10^7\,M_{\odot}$ within two low-mass groups ($M_{\rm vir}=10^{12.9}$ and $10^{12.7} \,M_{\odot}$) using the NewHorizon simulation. We confirm that satellite galaxies ($M_{*}\lesssim10^{10}\,M_{\odot}$) are more prone to quenching than their field counterparts. This quenched fraction decreases with increasing stellar mass, consistent with recent studies. Similar to the findings in cluster environments, we note a correlation between the orbital motions of galaxies within these groups and the phenomenon of SF quenching. Specifically, SF is suppressed at the group center, and for galaxies with $M_{*} > 10^{9.1}\,M_{\odot}$, there is often a notable rejuvenation phase following a temporary quenching period. The SF quenching at the group center is primarily driven by changes in star formation efficiency and the amount of gas available, both of which are influenced by hydrodynamic interactions between the interstellar medium and surrounding hot gas within the group. Conversely, satellite galaxies with $M_{*} < 10^{8.2}\,M_{\odot}$ experience significant gas removal within the group, leading to SF quenching. Our analysis highlights the complexity of SF quenching in satellite galaxies in group environments, which involves an intricate competition between the efficiency of star formation (which depends on the dynamical state of the gas) on the one hand, and the availability of cold dense gas on the other hand. This challenges the typical understanding of environmental effects based on gas stripping through ram pressure, suggesting a need for a new description of galaxy evolution under mild environmental effects.

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arXiv2023

Emergence and cosmic evolution of the Kennicutt-Schmidt relation driven by interstellar turbulence

The scaling relations between the gas content and star formation rate of galaxies provide useful insights into processes governing their formation and evolution. We investigate the emergence and the physical drivers of the global Kennicutt-Schmidt (KS) relation at $0.25 \leq z \leq 4$ in the cosmological hydrodynamic simulation NewHorizon capturing the evolution of a few hundred galaxies with a resolution of $\sim$ 40 pc. The details of this relation vary strongly with the stellar mass of galaxies and the redshift. A power-law relation $Σ_{\rm SFR} \propto Σ_{\rm gas}^{a}$ with $a \approx 1.4$, like that found empirically, emerges at $z \approx 2 - 3$ for the most massive half of the galaxy population. However, no such convergence is found in the lower-mass galaxies, for which the relation gets shallower with decreasing redshift. At the galactic scale, the star formation activity correlates with the level of turbulence of the interstellar medium, quantified by the Mach number, rather than with the gas fraction (neutral or molecular), confirming previous works. With decreasing redshift, the number of outliers with short depletion times diminishes, reducing the scatter of the KS relation, while the overall population of galaxies shifts toward low densities. Using pc-scale star formation models calibrated with local Universe physics, our results demonstrate that the cosmological evolution of the environmental and intrinsic conditions conspire to converge towards a significant and detectable imprint in galactic-scale observables, in their scaling relations, and in their reduced scatter.

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arXiv2021

Supermassive black holes in cosmological simulations II: the AGN population and predictions for upcoming X-ray missions

In large-scale hydrodynamical cosmological simulations, the fate of massive galaxies is mainly dictated by the modeling of feedback from active galactic nuclei (AGN). The amount of energy released by AGN feedback is proportional to the mass that has been accreted onto the BHs, but the exact sub-grid modeling of AGN feedback differs in all simulations. Whilst modern simulations reliably produce populations of quiescent massive galaxies at z<2, it is also crucial to assess the similarities and differences of the responsible AGN populations. Here, we compare the AGN population of the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA simulations. The AGN luminosity function (LF) varies significantly between simulations. Although in agreement with current observational constraints at z=0, at higher redshift the agreement of the LFs deteriorates with most simulations producing too many AGN of L_{x, 2-10 keV}~10^43-10^44 erg/s. AGN feedback in some simulations prevents the existence of any bright AGN with L_{x, 2-10 keV}>=10^45 erg/s (although this is sensitive to AGN variability), and leads to smaller fractions of AGN in massive galaxies than in the observations at z<=2. We find that all the simulations fail at producing a number density of AGN in good agreement with observational constraints for both luminous (L_{x, 2-10 keV}~10^43-10^45 erg/s) and fainter (L_{x, 2-10 keV}~10^42-10^43 erg/s) AGN, and at both low and high redshift. These differences can aid us in improving future BH and galaxy subgrid modeling in simulations. Upcoming X-ray missions (e.g., Athena, AXIS, and LynX) will bring faint AGN to light and new powerful constraints. After accounting for AGN obscuration, we find that the predicted number density of detectable AGN in future surveys spans at least one order of magnitude across the simulations, at any redshift.

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arXiv2021

Supermassive black holes in cosmological simulations I: M_BH-M_star relation and black hole mass function

The past decade has seen significant progress in understanding galaxy formation and evolution using large-scale cosmological simulations. While these simulations produce galaxies in overall good agreement with observations, they employ different sub-grid models for galaxies and supermassive black holes (BHs). We investigate the impact of the sub-grid models on the BH mass properties of the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA simulations, focusing on the M_BH-M_star relation and the BH mass function. All simulations predict tight M_BH-M_star relations, and struggle to produce the lowest (M_BH< 10^7.5 Msun) in galaxies of M_star~10^10.5-10^11.5 Msun. While the time evolution of the mean M_BH-M_star relation is mild (<1 dex in BH mass for 0 10^9 Msun in most of the simulations. The BH mass function is dominated by efficiently accreting BHs (log10 f_Edd >-2$) at high redshifts, and transitions progressively from the high-mass to the low-mass end to be governed by inactive BHs. The transition time and the contribution of active BHs are different among the simulations, and can be used to evaluate models against observations.

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arXiv2021

Introducing the NewHorizon simulation: Galaxy properties with resolved internal dynamics across cosmic time

Hydrodynamical cosmological simulations are increasing their level of realism by considering more physical processes and having greater resolution or larger statistics. However, usually either the statistical power of such simulations or the resolution reached within galaxies are sacrificed. Here, we introduce the NewHorizon project in which we simulate at high resolution a zoom-in region of $\sim(16\,\rm Mpc)^3$ that is larger than a standard zoom-in region around a single halo and is embedded in a larger box. A resolution of up to 34 pc is reached within galaxies; this allows the simulation to capture the multi-phase nature of the interstellar medium and the clumpy nature of the star formation process in galaxies. In this introductory paper, we present several key fundamental properties of galaxies and their black holes, including the galaxy mass function, cosmic star formation rate, galactic metallicities, the Kennicutt-Schmidt relation, the stellar-to-halo mass relation, galaxy sizes, stellar kinematics and morphology, gas content within galaxies and its kinematics, and the black hole mass and spin properties over time. The various scaling relations are broadly reproduced by NewHorizon with some differences with the standard observables. Owing to its exquisite spatial resolution, NewHorizon captures the inefficient process of star formation in galaxies, which evolve over time from being more turbulent, gas rich, and star bursting at high redshift. These high-redshift galaxies are also more compact, and they are more elliptical and clumpier until the level of internal gas turbulence decays enough to allow for the formation of discs. The NewHorizon simulation gives access to a broad range of galaxy formation and evolution physics at low-to-intermediate stellar masses, which is a regime that will become accessible in the near future through surveys such as the LSST.

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arXiv2020

Stellar and Weak Lensing Profiles of Massive Galaxies in the Hyper-Suprime Cam Survey and in Hydrodynamic Simulations

We perform a consistent comparison of the mass and mass profiles of massive ($M_\star > 10^{11.4}M_{\odot}$) central galaxies at z~0.4 from deep Hyper Suprime-Cam (HSC) observations and from the Illustris, TNG100, and Ponos simulations. Weak lensing measurements from HSC enable measurements at fixed halo mass and provide constraints on the strength and impact of feedback at different halo mass scales. We compare the stellar mass function (SMF) and the Stellar-to-Halo Mass Relation (SHMR) at various radii and show that the radius at which the comparison is performed is important. In general, Illustris and TNG100 display steeper values of $α$ where $M_{\star}\propto M_{\rm vir}^α$. These differences are more pronounced for Illustris than for TNG100 and in the inner rather than outer regions of galaxies. Differences in the inner regions may suggest that TNG100 is too efficient at quenching in-situ star formation at $M_{\rm vir}\simeq10^{13} M_{\odot}$ but not efficient enough at $M_{\rm vir}\simeq10^{14} M_{\odot}$. The outer stellar masses are in excellent agreement with our observations at $M_{\rm vir}\simeq10^{13} M_{\odot}$, but both Illustris and TNG100 display excess outer mass as $M_{\rm vir}\simeq10^{14} M_{\odot}$ (by ~0.25 and ~0.12 dex, respectively). We argue that reducing stellar growth at early times in $M_\star \sim 10^{9-10} M_{\odot}$ galaxies would help to prevent excess ex-situ growth at this mass scale. The Ponos simulations do not implement AGN feedback and display an excess mass of ~0.5 dex at $r<30$ kpc compared to HSC which is indicative of over-cooling and excess star formation in the central regions. Joint comparisons between weak lensing and galaxy stellar profiles are a direct test of whether simulations build and deposit galaxy mass in the correct dark matter halos and thereby provide powerful constraints on the physics of feedback and galaxy growth.

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arXiv2020

Formation of compact galaxies in the Extreme-Horizon simulation

We present the Extreme-Horizon (EH) cosmological simulation: EH models galaxy formation with stellar and AGN feedback and uses a very high resolution in the intergalactic and circumgalactic medium. The high resolution in low-density regions results in smaller-size massive galaxies at redshift $z=2$, in better agreement with observations compared to other simulations. This results from the improved modeling of cold gas flows accreting onto galaxies. Besides, the EH simulation forms a population of particularly compact galaxies with stellar masses of $10^{10-11}$\,M$_\sun$ that are reminiscent of observed ultracompact galaxies at $z\simeq2$. These objects form mainly through repeated major mergers of low-mass progenitors, independently of baryonic feedback mechanisms. This formation process can be missed in simulations using a too low resolution in low-density intergalactic regions.

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arXiv2020

Shapes and alignments of dark matter haloes and their brightest cluster galaxies in 39 strong lensing clusters

We study shapes and alignments of 45 dark matter (DM) haloes and their brightest cluster galaxies (BCGs) using a sample of 39 massive clusters from Hubble Frontier Field (HFF), Cluster Lensing And Supernova survey with Hubble (CLASH), and Reionization Lensing Cluster Survey (RELICS). We measure shapes of the DM haloes by strong gravitational lensing, whereas BCG shapes are derived from their light profiles in Hubble Space Telescope images. Our measurements from a large sample of massive clusters presented here provide new constraints on dark matter and cluster astrophysics. We find that DM haloes are on average highly elongated with the mean ellipticity of $0.482\pm 0.028$, and position angles of major axes of DM haloes and their BCGs tend to be aligned well with the mean value of alignment angles of $22.2\pm 3.9$ deg. We find that DM haloes in our sample are on average more elongated than their BCGs with the mean difference of their ellipticities of $0.11\pm 0.03$. In contrast, the Horizon-AGN cosmological hydrodynamical simulation predicts on average similar ellipticities between DM haloes and their central galaxies. While such a difference between the observations and the simulation may well be explained by the difference of their halo mass scales, other possibilities include the bias inherent to strong lensing measurements, limited knowledge of baryon physics, or a limitation of cold dark matter.

astro-ph.CO↗

arXiv2020

The impact of AGN feedback on the 1D power spectra from the Ly$α$ forest using the Horizon-AGN suite of simulations

The Lyman-$α$ forest is a powerful probe for cosmology, but it is also strongly impacted by galaxy evolution and baryonic processes such as Active Galactic Nuclei (AGN) feedback, which can redistribute mass and energy on large scales. We constrain the signatures of AGN feedback on the 1D power spectrum of the Lyman-$α$ forest using a series of eight hydro-cosmological simulations performed with the Adaptative Mesh Refinement code RAMSES. This series starts from the Horizon-AGN simulation and varies the sub-grid parameters for AGN feeding, feedback and stochasticity. These simulations cover the whole plausible range of feedback and feeding parameters according to the resulting galaxy properties. AGNs globally suppress the Lyman-$α$ power at all scales. On large scales, the energy injection and ionization dominate over the supply of gas mass from AGN-driven galactic winds, thus suppressing power. On small scales, faster cooling of denser gas mitigates the suppression. This effect increases with decreasing redshift. We provide lower and upper limits of this signature at nine redshifts between $z=4.25$ and $z=2.0$, making it possible to account for it at post-processing stage in future work given that running simulations without AGN feedback can save considerable amounts of computing resources. Ignoring AGN feedback in cosmological inference analyses leads to strong biases with 2\% shift on $σ_8$ and 1\% shift on $n_s$, which represents twice the standards deviation of the current constraints on $n_s$.

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arXiv2019

The diverse galaxy counts in the environment of high-redshift massive black holes in Horizon-AGN

High-redshift quasars are believed to reside in highly biased regions of the Universe, where black hole (BH) growth is sustained by an enhanced number of mergers and by being at the intersection of filaments bringing fresh gas. This assumption should be supported by an enhancement of the number counts of galaxies in the field of view of quasars. While the current observations of quasar environments do not lead to a consensus on a possible excess of galaxies, the future missions JWST, WFIRST, and Euclid will provide new insights on quasar environments, and will substantially increase the number of study-cases. We are in a crucial period, where we need to both understand the current observations and predict how upcoming missions will improve our understanding of BH environments. Using the large-scale simulation Horizon-AGN, we find that statistically the most massive BHs reside in environments with the largest number counts of galaxies. However, we find a large variance in galaxy number counts, and some massive BHs do not show enhanced counts in their neighborhood. Interestingly, some massive BHs have a very close galaxy companion but no further enhancement of the galaxy number counts at larger scales, in agreement with recent observations. We find that AGN feedback in the surrounding galaxies is able to decrease their luminosity and stellar mass, and therefore to make them un-observable when using restrictive galaxy selection criteria. Radiation from the quasars can spread over large distances, which could affect the formation history of surrounding galaxies, but a careful analysis of these processes requires radiative transfer simulations.

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arXiv2019

Cosmological evolution of orientations of cluster-sized dark matter haloes and their central galaxies in the Horizon-AGN simulation

It is known observationally that the major axes of galaxy clusters and their brightest cluster galaxies are roughly aligned with each other. To understand the origin of the alignment, we identify 40 cluster-sized dark matter (DM) haloes with masses higher than $5\times10^{13}~M_{\odot}$ and their central galaxies (CGs) at $z\approx 0$ in the Horizon-AGN cosmological hydrodynamical simulation. We trace the progenitors at 50 different epochs between $0 1$. The alignment becomes tighter with cosmic time; the major axes of the CGs and their host DM haloes at present are aligned on average within $\sim 30^{\circ}$ in the three dimensional space and $\sim 20^{\circ}$ in the projected plane. The orientations of the major axes of DM haloes on average follow one of the eigen-vectors of the surrounding tidal field that corresponds to the {\it slowest collapsing} (or even stretching) mode, and the alignment with the tidal field also becomes tighter. This implies that the orientations of CGs and DM haloes at the present epoch are largely imprinted in the primordial density field of the Universe, whereas strong dynamical interactions such as mergers are important to explain their mutual alignment at each epoch.

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arXiv2019

The impact of the connectivity of the cosmic web on the physical properties of galaxies at its nodes

We investigate the impact of the number of filaments connected to the nodes of the cosmic web on the physical properties of their galaxies using the Sloan Digital Sky Survey. We compare these measurements to the cosmological hydrodynamical simulations Horizon-(no)AGN and Simba. We find that more massive galaxies are more connected, in qualitative agreement with theoretical predictions and measurements in dark matter only simulation. The star formation activity and morphology of observed galaxies both display some dependence on the connectivity of the cosmic web at fixed stellar mass: less star forming and less rotation supported galaxies also tend to have higher connectivity. These results qualitatively hold both for observed and virtual galaxies, and can be understood given that the cosmic web is the main source of fuel for galaxy growth. The simulations show the same trends at fixed halo mass, suggesting that the geometry of filamentary infall impacts galaxy properties beyond the depth of the local potential well. Based on simulations, it is also found that AGN feedback is key in reversing the relationship between stellar mass and connectivity at fixed halo mass. Technically, connectivity is a practical observational proxy for past and present accretion (minor mergers or diffuse infall).

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arXiv2018

Projected alignment of non-sphericities of stellar, gas, and dark matter distributions in galaxy clusters: analysis of the Horizon-AGN simulation

While various observations measured ellipticities of galaxy clusters and alignments between orientations of the brightest cluster galaxies and their host clusters, there are only a handful of numerical simulations that implement realistic baryon physics to allow direct comparisons with those observations. Here we investigate ellipticities of galaxy clusters and alignments between various components of them and the central galaxies in the state-of-the-art cosmological hydrodynamical simulation Horizon-AGN, which contains dark matter, stellar, and gas components in a large simulation box of $(100 h^{-1}$ Mpc$)^3$ with high spatial resolution ($\sim1$ kpc). We estimate ellipticities of total matter, dark matter, stellar, gas surface mass density distributions, X-ray surface brightness, and the Compton $y$-parameter of the Sunyaev-Zel'dovich effect, as well as alignments between these components and the central galaxies for 120 projected images of galaxy clusters with masses $M_{200}>5\times10^{13}M_{\odot}$. Our results indicate that the distributions of these components are well aligned with the major-axes of the central galaxies, with the root mean square value of differences of their position angles of $\sim 20^\circ$, which vary little from inner to the outer regions. We also estimate alignments of these various components with total matter distributions, and find tighter alignments than those for central galaxies with the root mean square value of $\sim 15^\circ$. We compare our results with previous observations of ellipticities and position angle alignments and find reasonable agreements. The comprehensive analysis presented in this paper provides useful prior information for analyzing stacked lensing signals as well as designing future observations to study ellipticities and alignments of galaxy clusters.

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arXiv2017

SDSS IV MaNGA: Discovery of an $H_α$ blob associated with a dry galaxy pair -- ejected gas or a `dark' galaxy candidate?

We report the discovery of a mysterious giant $H_α$ blob that is $\sim 8$ kpc away from the main MaNGA target 1-24145, one component of a dry galaxy merger, identified in the first-year SDSS-IV MaNGA data. The size of the $H_α$ blob is $\sim$ 3-4 kpc in radius, and the $H_α$ distribution is centrally concentrated. However, there is no optical continuum counterpart in deep broadband images reaching $\sim$26.9 mag arcsec$^{-2}$ in surface brightness. We estimate that the masses of ionized and cold gases are $3.3 \times 10^{5}$ $\rm M_{\odot}$ and $< 1.3 \times 10^{9}$ $\rm M_{\odot}$, respectively. The emission-line ratios indicate that the $H_α$ blob is photoionized by a combination of massive young stars and AGN. Furthermore, the ionization line ratio decreases from MaNGA 1-24145 to the $H_α$ blob, suggesting that the primary ionizing source may come from MaNGA 1-24145, likely a low-activity AGN. Possible explanations of this $H_α$ blob include AGN outflow, the gas remnant being tidally or ram-pressure stripped from MaNGA 1-24145, or an extremely low surface brightness (LSB) galaxy. However, the stripping scenario is less favoured according to galaxy merger simulations and the morphology of the $H_α$ blob. With the current data, we can not distinguish whether this $H_α$ blob is ejected gas due to a past AGN outburst, or a special category of `ultra-diffuse galaxy' (UDG) interacting with MaNGA 1-24145 that further induces the gas inflow to fuel the AGN in MaNGA 1-24145.

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arXiv2016

Anisotropic q-Gaussian velocity distributions in LambdaCDM halos

The velocity distribution function (VDF) of dark matter (DM) halos in $Λ$CDM dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in $Λ$CDM halos, built from an isotropic $q$-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass halos of a dissipationless cosmological simulation. Beyond the virial radius, $r_{\rm vir}$, our model VDF adequately reproduces that measured in the simulated halos, but no $q$-Gaussian model can adequately represent the VDF within $r_{\rm vir}$, as the speed distribution function is then flatter-topped than any $q$-Gaussian can allow. Nevertheless, our VDF fits significantly better the simulations than the commonly used Maxwellian (Gaussian) distribution, at virtually all radii within $5\,r_{\rm vir}$. Within 0.4 (1) $r_{\rm vir}$, the non-Gaussianity index $q$ is (roughly) linearly related to the slope of the density profile and also to the velocity anisotropy profile. We provide a parametrization of the modulation of $q$ with radius for both the median fits and the fit of the stacked halo. At radii of a few percent of $r_{\rm vir}$, corresponding to the Solar position in the Milky Way, our best-fit VDF, although fitting better the simulations than the Gaussian one, overproduces significantly the fraction of high velocity objects, indicating that one should not blindly use these $q$-Gaussian fits to make predictions on the direct detection rate of DM particles.

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