arXiv subjects

Nelson D. Padilla

Publications and source records attributed to Nelson D. Padilla.

At least 37 records · Page 2Linked to original sources

arXiv2021

Press-Schechter primordial black hole mass functions and their observational constraints

We present a modification of the Press-Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated to the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of super-massive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well established monochromatic constraints there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ~10^2 M_Sun, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO which are difficult to explain by stellar collapse.

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arXiv2021

Halo Merger Tree Comparison: Impact on Galaxy Formation Models

We examine the effect of using different halo finders and merger tree building algorithms on galaxy properties predicted using the GALFORM semi-analytical model run on a high resolution, large volume dark matter simulation. The halo finders/tree builders HBT, ROCKSTAR, SUBFIND and VELOCIRAPTOR differ in their definitions of halo mass, on whether only spatial or phase-space information is used, and in how they distinguish satellite and main haloes; all of these features have some impact on the model galaxies, even after the trees are post-processed and homogenised by GALFORM. The stellar mass function is insensitive to the halo and merger tree finder adopted. However, we find that the number of central and satellite galaxies in GALFORM does depend slightly on the halo finder/tree builder. The number of galaxies without resolved subhaloes depends strongly on the tree builder, with VELOCIRAPTOR, a phase-space finder, showing the largest population of such galaxies. The distributions of stellar masses, cold and hot gas masses, and star formation rates agree well between different halo finders/tree builders. However, because VELOCIRAPTOR has more early progenitor haloes, with these trees GALFORM produces slightly higher star formation rate densities at high redshift, smaller galaxy sizes, and larger stellar masses for the spheroid component. Since in all cases these differences are small we conclude that, when all of the trees are processed so that the main progenitor mass increases monotonically, the predicted GALFORM galaxy populations are stable and consistent for these four halo finders/tree builders.

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arXiv2021

Simultaneous Estimation of Large-Scale Structure and Milky Way Dust Extinction from Galaxy Surveys

The high cosmological precision offered by the next generation of galaxy surveys hinges on improved corrections for Galactic dust extinction. We explore the possibility of estimating both the dust extinction and large-scale structure from a single photometric galaxy survey, making use of the predictable manner in which Milky Way dust affects the measured brightness and colors of galaxies in a given sky location in several redshift bins. To test our method, we use a synthetic catalog from a cosmological simulation designed to model the Vera C. Rubin Observatory Legacy Survey of Space and Time. At high Galactic latitude ($|b|\gtrsim20^\circ$) and a resolution of $1^\circ$ ($7'$), we predict the uncertainty in the measurement of dust extinction, $E(B-V)$, to be $0.005\ \mathrm{mag}$ ($0.015\ \mathrm{mag}$). This is similar to the uncertainty of existing dust maps, illustrating the feasibility of our method. Simultaneous estimation of large-scale structure is predicted to recover the galaxy overdensity $δ$ with a precision of $\sim0.01$ ($\sim0.05$) at $1^\circ$ ($7'$) resolution. We also introduce a Bayesian formalism that combines prior information from existing dust maps with the likelihood of Galactic dust extinction determined from the excursion of observed galaxy properties.

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arXiv2021

Magnetic field generation from primordial black hole distributions

We introduce a statistical method for estimating magnetic field fluctuations generated from primordial black hole (PBH) populations. To that end, we consider monochromatic and extended Press-Schechter PBH mass functions, such that each constituent is capable of producing its own magnetic field due to some given physical mechanism. Assuming linear correlation between magnetic field fluctuations and matter over-densities, our estimates depend on the mass function, the physical field generation mechanism by each PBH constituent, and the characteristic PBH separation. After computing the power spectrum of magnetic field fluctuations, we apply our formalism to study the plausibility that two particular field generation mechanisms could have given rise to the expected seed fields according to current observational constraints. The first mechanism is the Biermann battery and the second one is due to the accretion of magnetic monopoles at PBH formation, constituting magnetic PBHs. Our results show that, for monochromatic distributions, it does not seem to be possible to generate sufficiently intense seed fields in any of the two field generation mechanisms. For extended distributions, it is also not possible to generate the required seed field by only assuming a Biermann battery mechanism. In fact, we report an average seed field by this mechanism of about 10^{-47} G, at z = 20. For the case of magnetic monopoles we instead assume that the seed values from the literature are achieved and calculate the necessary number density of monopoles. In this case we obtain values that are below the upper limits from current constraints.

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arXiv2020

Redshift-space effects in voids and their impact on cosmological tests. Part I: the void size function

Voids are promising cosmological probes. Nevertheless, every cosmological test based on voids must necessarily employ methods to identify them in redshift space. Therefore, redshift-space distortions (RSD) and the Alcock-Paczynski effect (AP) have an impact on the void identification process itself generating distortion patterns in observations. Using a spherical void finder, we developed a statistical and theoretical framework to describe physically the connection between the identification in real and redshift space. We found that redshift-space voids above the shot noise level have a unique real-space counterpart spanning the same region of space, they are systematically bigger and their centres are preferentially shifted along the line of sight. The expansion effect is a by-product of RSD induced by tracer dynamics at scales around the void radius, whereas the off-centring effect constitutes a different class of RSD induced at larger scales by the global dynamics of the whole region containing the void. The volume of voids is also altered by the fiducial cosmology assumed to measure distances, this is the AP change of volume. These three systematics have an impact on cosmological statistics. In this work, we focus on the void size function. We developed a theoretical framework to model these effects and tested it with a numerical simulation, recovering the statistical properties of the abundance of voids in real space. This description depends strongly on cosmology. Hence, we lay the foundations for improvements in current models of the abundance of voids in order to obtain unbiased cosmological constraints from redshift surveys.

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arXiv2020

Massive Low Surface Brightness Galaxies in the EAGLE Simulation

We investigate the formation and properties of low surface brightness galaxies (LSBGs) with $M_{*} > 10^{9.5} \mathrm{M_{\odot}}$ in the EAGLE hydrodynamical cosmological simulation. Galaxy surface brightness depends on a combination of stellar mass surface density and mass-to-light ratio ($M/L$), such that low surface brightness is strongly correlated with both galaxy angular momentum (low surface density) and low specific star formation rate (high $M/L$). This drives most of the other observed correlations between surface brightness and galaxy properties, such as the fact that most LSBGs have low metallicity. We find that LSBGs are more isolated than high surface brightness galaxies (HSBGs), in agreement with observations, but that this trend is driven entirely by the fact that LSBGs are unlikely to be close-in satellites. The majority of LSBGs are consistent with a formation scenario in which the galaxies with the highest angular momentum are those that formed most of their stars recently from a gas reservoir co-rotating with a high-spin dark matter halo. However, the most extended LSBG disks in EAGLE, which are comparable in size to observed giant LSBGs, are built up via mergers. These galaxies are found to inhabit dark matter halos with a higher spin in their inner regions ($<0.1r_{200c}$), even when excluding the effects of baryonic physics by considering matching halos from a dark matter only simulation with identical initial conditions.

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arXiv2019

A Halo Merger Tree Generation and Evaluation Framework

Semi-analytic models are best suited to compare galaxy formation and evolution theories with observations. These models rely heavily on halo merger trees, and their realistic features (i.e., no drastic changes on halo mass or jumps on physical locations). Our aim is to provide a new framework for halo merger tree generation that takes advantage of the results of large volume simulations, with a modest computational cost. We treat halo merger tree construction as a matrix generation problem, and propose a Generative Adversarial Network that learns to generate realistic halo merger trees. We evaluate our proposal on merger trees from the EAGLE simulation suite, and show the quality of the generated trees.

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arXiv2019

Tracing the Quenching History in Galaxy Clusters in the EAGLE Simulation

We use the EAGLE hydrodynamical simulation to trace the quenching history of galaxies in its 10 most massive clusters. We use two criteria to identify moments when galaxies suffer significant changes in their star formation activity: {\it i)} the instantaneous star formation rate (SFR) strongest drop, $Γ_{\rm SFR}^{\rm SD}$, and {\it ii)} a "quenching" criterion based on a minimum threshold for the specific SFR of $\lesssim$ 10$^{-11}\rm yr^{-1}$. We find that a large fraction of galaxies ($\gtrsim 60\%$) suffer their $Γ_{\rm SFR}^{\rm SD}$ outside the cluster's R$_{200}$. This ``pre-processed" population is dominated by galaxies that are either low mass and centrals or inhabit low mass hosts ($10^{10.5}$M$_{\odot} \lesssim$ M$_{\rm host} \lesssim 10^{11.0}$M$_{\odot}$). The host mass distribution is bimodal, and galaxies that suffered their $Γ_{\rm SFR}^{\rm SD}$ in massive hosts ($10^{13.5}\rm M_{\odot} \lesssim M_{host} \lesssim 10^{14.0}M_{\odot}$) are mainly processed within the clusters. Pre-processing mainly limits the total stellar mass with which galaxies arrive in the clusters. Regarding quenching, galaxies preferentially reach this state in high-mass halos ($10^{13.5}\rm M_{\odot} \lesssim M_{host} \lesssim 10^{14.5}M_{\odot}$). The small fraction of galaxies that reach the cluster already quenched has also been pre-processed, linking both criteria as different stages in the quenching process of those galaxies. For the $z=0$ satellite populations, we find a sharp rise in the fraction of quenched satellites at the time of first infall, highlighting the role played by the dense cluster environment. Interestingly, the fraction of pre-quenched galaxies rises with final cluster mass. This is a direct consequence of the hierarchical cosmological model used in these simulations.

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arXiv2018

Non-fiducial cosmological test from geometrical and dynamical distortions around voids

We present a new cosmological test using the distribution of galaxies around cosmic voids without assuming a fiducial cosmology. The test is based on a physical model for the void-galaxy cross-correlation function projected along and perpendicular to the line of sight. We treat correlations in terms of void-centric angular distances and redshift differences between void-galaxy pairs, hence it is not necessary to assume a fiducial cosmology. This model reproduces the coupled dynamical (Kaiser effect, RSD) and geometrical (Alcock-Paczynski effect, GD) distortions that affect the correlation measurements. It also takes into account the scale mixing due to the projection ranges in both directions. The model is general, so it can be applied to an arbitrary cylindrical binning scheme, not only in the case of the projected correlations. It primarily depends on two cosmological parameters: $Ω_m$, the matter fraction of the Universe today (sensitive to GD), and $β$, the ratio between the growth rate factor of density perturbations and the tracer bias (sensitive to RSD). In the context of the new generation of galaxy spectroscopic surveys, we calibrated the test using the Millennium XXL simulation for different redshifts. The method successfully recovers the cosmological parameters. We studied the effect of measuring with different projection ranges, finding robust results up to wide ranges. The resulting data covariance matrices are relatively small, which reduces the noise in the Gaussian likelihood analysis and will allow the usage of a smaller number of mock catalogues. The performance evaluated in this work indicates that the developed method is a promising test to be applied on real data.

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arXiv2018

Semi-Analytic Galaxies - I. Synthesis of environmental and star-forming regulation mechanisms

We present results from the semi-analytic model of galaxy formation SAG applied on the MultiDark simulation MDPL2. SAG features an updated supernova (SN) feedback scheme and a robust modelling of the environmental effects on satellite galaxies. This incorporates a gradual starvation of the hot gas halo driven by the action of ram pressure stripping (RPS), that can affect the cold gas disc, and tidal stripping (TS), which can act on all baryonic components. Galaxy orbits of orphan satellites are integrated providing adequate positions and velocities for the estimation of RPS and TS. The star formation history and stellar mass assembly of galaxies are sensitive to the redshift dependence implemented in the SN feedback model. We discuss a variant of our model that allows to reconcile the predicted star formation rate density at $z \gtrsim 3$ with the observed one, at the expense of an excess in the faint end of the stellar mass function at $z=2$. The fractions of passive galaxies as a function of stellar mass, halo mass and the halo-centric distances are consistent with observational measurements. The model also reproduces the evolution of the main sequence of star forming central and satellite galaxies. The similarity between them is a result of the gradual starvation of the hot gas halo suffered by satellites, in which RPS plays a dominant role. RPS of the cold gas does not affect the fraction of quenched satellites but it contributes to reach the right atomic hydrogen gas content for more massive satellites ($M_{\star}\gtrsim 10^{10}\,{\rm M}_{\odot}$).

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arXiv2018

Cosmic CARNage II: the evolution of the galaxy stellar mass function in observations and galaxy formation models

We present a comparison of the observed evolving galaxy stellar mass functions with the predictions of eight semi-analytic models and one halo occupation distribution model. While most models are able to fit the data at low redshift, some of them struggle to simultaneously fit observations at high redshift. We separate the galaxies into 'passive' and 'star-forming' classes and find that several of the models produce too many low-mass star-forming galaxies at high redshift compared to observations, in some cases by nearly a factor of 10 in the redshift range $2.5 < z < 3.0$. We also find important differences in the implied mass of the dark matter haloes the galaxies inhabit, by comparing with halo masses inferred from observations. Galaxies at high redshift in the models are in lower mass haloes than suggested by observations, and the star formation efficiency in low-mass haloes is higher than observed. We conclude that many of the models require a physical prescription that acts to dissociate the growth of low-mass galaxies from the growth of their dark matter haloes at high redshift.

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arXiv2017

Cosmic CARNage I: on the calibration of galaxy formation models

We present a comparison of nine galaxy formation models, eight semi-analytical and one halo occupation distribution model, run on the same underlying cold dark matter simulation (cosmological box of co-moving width 125$h^{-1}$ Mpc, with a dark-matter particle mass of $1.24\times 10^9 h^{-1}$ Msun) and the same merger trees. While their free parameters have been calibrated to the same observational data sets using two approaches, they nevertheless retain some 'memory' of any previous calibration that served as the starting point (especially for the manually-tuned models). For the first calibration, models reproduce the observed z = 0 galaxy stellar mass function (SMF) within 3-σ. The second calibration extended the observational data to include the z = 2 SMF alongside the z~0 star formation rate function, cold gas mass and the black hole-bulge mass relation. Encapsulating the observed evolution of the SMF from z = 2 to z = 0 is found to be very hard within the context of the physics currently included in the models. We finally use our calibrated models to study the evolution of the stellar-to-halo mass (SHM) ratio. For all models we find that the peak value of the SHM relation decreases with redshift. However, the trends seen for the evolution of the peak position as well as the mean scatter in the SHM relation are rather weak and strongly model dependent. Both the calibration data sets and model results are publicly available.

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arXiv2017

MultiDark-Galaxies: data release and first results

We present the public release of the MultiDark-Galaxies: three distinct galaxy catalogues derived from one of the Planck cosmology MultiDark simulations (i.e. MDPL2, with a volume of (1 Gpc/$h$)$^{3}$ and mass resolution of $1.5 \times 10^{9} M_{\odot}/h$) by applying the semi-analytic models GALACTICUS, SAG, and SAGE to it. We compare the three models and their conformity with observational data for a selection of fundamental properties of galaxies like stellar mass function, star formation rate, cold gas fractions, and metallicities - noting that they sometimes perform differently reflecting model designs and calibrations. We have further selected galaxy subsamples of the catalogues by number densities in stellar mass, cold gas mass, and star formation rate in order to study the clustering statistics of galaxies. We show that despite different treatment of orphan galaxies, i.e. galaxies that lost their dark-matter host halo due to the finite mass resolution of the N-body simulation or tidal stripping, the clustering signal is comparable, and reproduces the observations in all three models - in particular when selecting samples based upon stellar mass. Our catalogues provide a powerful tool to study galaxy formation within a volume comparable to those probed by on-going and future photometric and redshift surveys. All model data consisting of a range of galaxy properties - including broad-band SDSS magnitudes - are publicly available.

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arXiv2017

Quantifying the impact of mergers on the angular momentum of simulated galaxies

We use EAGLE to quantify the effect galaxy mergers have on the stellar specific angular momentum of galaxies, $j_{\rm stars}$. We split mergers into: dry (gas-poor)/wet (gas-rich), major/minor, and different spin alignments and orbital parameters. Wet (dry) mergers have an average neutral gas-to-stellar mass ratio of $1.1$ ($0.02$), while major (minor) mergers are those with stellar mass ratios $\ge 0.3$ ($0.1-0.3$). We correlate the positions of galaxies in the $j_{\rm stars}$-stellar mass plane at $z=0$ with their merger history, and find that galaxies of low spins suffered dry mergers, while galaxies of normal/high spins suffered predominantly wet mergers, if any. The radial $j_{\rm stars}$ profiles of galaxies that went through dry mergers are deficient by $\approx 0.3$~dex at $r\lesssim 10\,r_{50}$ (with $r_{50}$ being the half-stellar mass radius), compared to galaxies that went through wet mergers. Studying the merger remnants reveals that dry mergers reduce $j_{\rm stars}$ by $\approx 30$\%, while wet mergers increase it by $\approx 10$\%, on average. The latter is connected to the build-up of the bulge by newly formed stars of high rotational speed. Moving from minor to major mergers accentuates these effects. When the spin vectors of the galaxies prior to the dry merger are misaligned, $j_{\rm stars}$ decreases to a greater magnitude, while in wet mergers co-rotation and high orbital angular momentum efficiently spun-up galaxies. We predict what would be the observational signatures in the $j_{\rm stars}$ profiles driven by dry mergers: (i) shallow radial profiles and (ii) profiles that rise beyond $\approx 10\,r_{50}$, both of which are significantly different from spiral galaxies.

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arXiv2017

An ALMA survey of submillimetre galaxies in the COSMOS field: Physical properties derived from energy balance spectral energy distribution modelling

We determine the physical properties of a sample of SMGs in the COSMOS field that were pre-selected at the observed wavelength of $λ_{\rm obs}=1.1$ mm, and followed up at $λ_{\rm obs}=1.3$ mm with ALMA. We used MAGPHYS to fit the panchromatic (ultraviolet to radio) SEDs of 124 of the target SMGs, 19.4% of which are spectroscopically confirmed. The SED analysis was complemented by estimating the gas masses of the SMGs by using the $λ_{\rm obs}=1.3$ mm emission as a tracer of the molecular gas. The sample median and 16th-84th percentile ranges of the stellar masses, SFRs, dust temperatures, and dust and gas masses were derived to be $\log(M_{\star}/{\rm M}_{\odot})=11.09^{+0.41}_{-0.53}$, ${\rm SFR}=402^{+661}_{-233}$ ${\rm M}_{\odot}~{\rm yr}^{-1}$, $T_{\rm dust}=39.7^{+9.7}_{-7.4}$ K, $\log(M_{\rm dust}/{\rm M}_{\odot})=9.01^{+0.20}_{-0.31}$, and $\log(M_{\rm gas}/{\rm M}_{\odot})=11.34^{+0.20}_{-0.23}$, respectively. The median gas-to-dust ratio and gas fraction were found to be $120^{+73}_{-30}$ and $0.62^{+0.27}_{-0.23}$, respectively. We found that 57.3% of our SMGs populate the main sequence (MS) of star-forming galaxies, while 41.9% of the sources lie above the MS by a factor of >3 (one source lies below the MS). The largest 3 GHz radio sizes are found among the MS sources. Those SMGs that appear irregular in the rest-frame UV are predominantly starbursts, while the MS SMGs are mostly disk-like. The larger radio-emitting sizes of the MS SMGs compared to starbursts is a likely indication of their more widespread, less intense star formation. The irregular UV morphologies of the starburst SMGs are likely to echo their merger nature. Our results suggest that the transition from high-$z$ SMGs to local ellipticals via compact, quiescent galaxies (cQGs) at $z \sim 2$ might not be universal, and the latter population might also descend from the so-called blue nuggets.

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arXiv2017

nIFTy Cosmology: the clustering consistency of galaxy formation models

We present a clustering comparison of 12 galaxy formation models (including Semi-Analytic Models (SAMs) and Halo Occupation Distribution (HOD) models) all run on halo catalogues and merger trees extracted from a single ΛCDM N-body simulation. We compare the results of the measurements of the mean halo occupation numbers, the radial distribution of galaxies in haloes and the 2-Point Correlation Functions (2PCF). We also study the implications of the different treatments of orphan (galaxies not assigned to any dark matter subhalo) and non-orphan galaxies in these measurements. Our main result is that the galaxy formation models generally agree in their clustering predictions but they disagree significantly between HOD and SAMs for the orphan satellites. Although there is a very good agreement between the models on the 2PCF of central galaxies, the scatter between the models when orphan satellites are included can be larger than a factor of 2 for scales smaller than 1 Mpc/h. We also show that galaxy formation models that do not include orphan satellite galaxies have a significantly lower 2PCF on small scales, consistent with previous studies. Finally, we show that the 2PCF of orphan satellites is remarkably different between SAMs and HOD models. Orphan satellites in SAMs present a higher clustering than in HOD models because they tend to occupy more massive haloes. We conclude that orphan satellites have an important role on galaxy clustering and they are the main cause of the differences in the clustering between HOD models and SAMs.

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arXiv2017

An ALMA survey of submillimetre galaxies in the COSMOS field: The extent of the radio-emitting region revealed by 3 GHz imaging with the Very Large Array

We determine the radio size distribution of a large sample of 152 SMGs in COSMOS that were detected with ALMA at 1.3 mm. For this purpose, we used the observations taken by the VLA-COSMOS 3 GHz Large Project. One hundred and fifteen of the 152 target SMGs were found to have a 3 GHz counterpart. The median value of the major axis FWHM at 3 GHz is derived to be $4.6\pm0.4$ kpc. The radio sizes show no evolutionary trend with redshift, or difference between different galaxy morphologies. We also derived the spectral indices between 1.4 and 3 GHz, and 3 GHz brightness temperatures for the sources, and the median values were found to be $α=-0.67$ and $T_{\rm B}=12.6\pm2$ K. Three of the target SMGs, which are also detected with the VLBA, show clearly higher brightness temperatures than the typical values. Although the observed radio emission appears to be predominantly powered by star formation and supernova activity, our results provide a strong indication of the presence of an AGN in the VLBA and X-ray-detected SMG AzTEC/C61. The median radio-emitting size we have derived is 1.5-3 times larger than the typical FIR dust-emitting sizes of SMGs, but similar to that of the SMGs' molecular gas component traced through mid-$J$ line emission of CO. The physical conditions of SMGs probably render the diffusion of cosmic-ray electrons inefficient, and hence an unlikely process to lead to the observed extended radio sizes. Instead, our results point towards a scenario where SMGs are driven by galaxy interactions and mergers. Besides triggering vigorous starbursts, galaxy collisions can also pull out the magnetised fluids from the interacting disks, and give rise to a taffy-like synchrotron-emitting bridge. This provides an explanation for the spatially extended radio emission of SMGs, and can also cause a deviation from the well-known IR-radio correlation.

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arXiv2017

How to get cool in the heat: comparing analytic models of hot, cold, and cooling gas in haloes and galaxies with EAGLE

We use the hydrodynamic, cosmological EAGLE simulations to investigate how hot gas in haloes condenses to form and grow galaxies. We select haloes from the simulations that are actively cooling and study the temperature, distribution, and metallicity of their hot, cold, and transitioning `cooling' gas, placing these in context of semi-analytic models. Our selection criteria lead us to focus on Milky Way-like haloes. We find the hot-gas density profiles of the haloes form a progressively stronger core over time, the nature of which can be captured by a beta profile that has a simple dependence on redshift. In contrast, the hot gas that will cool over a time-step is broadly consistent with a singular isothermal sphere. We find that cooling gas carries a few times the specific angular momentum of the halo and is offset in spin direction from the rest of the hot gas. The gas loses ~60% of its specific angular momentum during the cooling process, generally remaining greater than that of the halo, and it precesses to become aligned with the cold gas already in the disc. We find tentative evidence that angular-momentum losses are slightly larger when gas cools onto dispersion-supported galaxies. We show that an exponential surface density profile for gas arriving on a disc remains a reasonable approximation, but a cusp containing ~20% of the mass is always present, and disc scale radii are larger than predicted by a vanilla Fall & Efstathiou model. These scale radii are still closely correlated with the halo spin parameter, for which we suggest an updated prescription for galaxy formation models.

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