K. Dolag

Ludwig-Maximilians-University of Munich, München, Bavaria, Germany

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Publications (325)1035.64 Total impact

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    ABSTRACT: Recent models for the large-scale Galactic magnetic fields in the literature were largely constrained by synchrotron emission and Faraday rotation measures. We select three different but representative models and compare their predicted polarized synchrotron and dust emission with that measured by the Planck satellite. We first update these models to match the Planck synchrotron products using a common model for the cosmic-ray leptons. We discuss the impact on this analysis of the ongoing problems of component separation in the Planck microwave bands and of the uncertain cosmic-ray spectrum. In particular, the inferred degree of ordering in the magnetic fields is sensitive to these systematic uncertainties. We then compare the resulting simulated emission to the observed dust emission and find that the dust predictions do not match the morphology in the Planck data, particularly the vertical profile in latitude. We show how the dust data can then be used to further improve these magnetic field models, particularly in the thin disc of the Galaxy where the dust is concentrated. We demonstrate this for one of the models and present it as a proof of concept for how we will advance these studies in future using complementary information from ongoing and planned observational projects.
    Full-text · Article · Jan 2016
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    Alexander M. Beck · Klaus Dolag
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    ABSTRACT: We present a model for the seeding and evolution of magnetic fields in galaxies by supernovae (SN). SN explosions during galaxy assembly provide seed fields, which are subsequently amplified by compression, shear flows and random motions. Our model explains the origin of microG magnetic fields within galactic structures. We implement our model in the MHD version of the cosmological simulation code Gadget-3 and couple it with a multi-phase description of the interstellar medium. We perform simulations of Milky Way-like galactic halo formation and analyze the distribution and strength of the magnetic field. We investigate the intrinsic rotation measure (RM) evolution and find RM values exceeding 1000 rad/m*m at high redshifts and RM values around 10 rad/m*m at present-day. We compare our simulations to a limited set of observational data points and find encouraging similarities. In our model, galactic magnetic fields are a natural consequence of the very basic processes of star formation and galaxy assembly.
    Preview · Article · Nov 2015
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    ABSTRACT: We present an on-the-fly geometrical approach for shock detection and Mach number calculation in simulations employing smoothed particle hydrodynamics (SPH). We utilize pressure gradients to select shock candidates and define up- and downstream positions. We obtain hydrodynamical states in the up- and downstream regimes with a series of normal and inverted kernel weightings parallel and perpendicular to the shock normals. Our on-the-fly geometrical Mach detector incorporates well within the SPH formalism and has low computational cost. We implement our Mach detector into the simulation code GADGET and alongside many SPH improvements. We test our shock finder in a sequence of shock-tube tests with successively increasing Mach numbers exceeding by far the typical values inside galaxy clusters. For the all shocks, we resolve the shocks well and the correct Mach numbers are assigned. An application to a strong magnetized shock-tube gives stable results in full magnetohydrodynamic set-ups. We simulate a merger of two idealized galaxy clusters and study the shock front. The cluster shock is well-captured by our algorithm and assigned correct Mach numbers.
    No preview · Article · Nov 2015
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    ABSTRACT: The Virgo cluster is the largest Sunyaev-Zeldovich (SZ) source in the sky, both in terms of angular size and total integrated flux. Planck's wide angular scale and frequency coverage, together with its high sensitivity, allow a detailed study of this large object through the SZ effect. Virgo is well resolved by Planck, showing an elongated structure, which correlates well with the morphology observed from X-rays, but extends beyond the observed X-ray signal. We find a good agreement between the SZ signal (or Compton paranmeter, y_c) observed by Planck and the expected signal inferred from X-ray observations and simple analytical models. Due to its proximity to us, the gas beyond the virial radius can be studied with unprecedented sensitivity by integrating the SZ signal over tens of square degrees. We study the signal in the outskirts of Virgo and compare it with analytical models and a constrained simulation of the environment of Virgo. Planck data suggest that significant amounts of low-density plasma surround Virgo out to twice the virial radius. We find the SZ signal in the outskirts of Virgo to be consistent with a simple model that extrapolates the inferred pressure at lower radii while assuming that the temperature stays in the keV range beyond the virial radius. The observed signal is also consistent with simulations and points to a shallow pressure profile in the outskirts of the cluster. This reservoir of gas at large radii can be linked with the hottest phase of the elusive warm/hot intergalactic medium. Taking the lack of symmetry of Virgo into account, we find that a prolate model is favoured by the combination of SZ and X-ray data, in agreement with predictions.
    Full-text · Article · Nov 2015
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    ABSTRACT: In the last few years, it became possible to observationally resolve galaxies with two distinct nuclei in their centre. For separations smaller than 10kpc, dual and offset active galactic nuclei (AGN) are distinguished: in dual AGN, both nuclei are active, whereas in offset AGN only one nucleus is active. To theoretically study the origin of such AGN pairs, we employ a cosmological, hydrodynamic simulation with a large volume of (182 Mpc)^3 from the set of Magneticum Pathfinder Simulations. The simulation self-consistently produces 35 resolved black hole (BH) pairs at redshift z=2, with a comoving distance smaller than 10kpc. 14 of them are offset AGN and nine are dual AGN, resulting in a fraction of (1.2 \pm 0.3)% AGN pairs with respect to the total number of AGN. In this paper, we discuss fundamental differences between the BH and galaxy properties of dual AGN, offset AGN and inactive BH pairs and investigate their different triggering mechanisms. We find that in dual AGN, the corresponding BH from the less massive progenitor galaxy always accretes with a higher Eddington ratio and that dual AGN have similar BH masses. In contrast, in offset AGN, the active BH is typically more massive than its non-active counterpart. Furthermore, dual AGN in general accrete more gas from the intergalactic medium than offset AGN and non-active BH pairs. This highlights that merger events, particularly minor mergers, do not necessarily lead to strong gas inflows and thus, do not always drive strong nuclear activity.
    No preview · Article · Oct 2015
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    ABSTRACT: By means of zoom-in hydrodynamic simulations, we quantify the amount of neutral hydrogen (H i) hosted by groups and clusters of galaxies. Our simulations, which are based on an improved formulation of smoothed particle hydrodynamics, include radiative cooling, star formation, metal enrichment and supernova feedback, and can be split into two different groups, depending on whether feedback from active galactic nuclei (AGN) is turned on or off. Simulations are analysed to account for H i self-shielding and the presence of molecular hydrogen. We find that the mass in neutral hydrogen of dark matter haloes monotonically increases with the halo mass and can be well described by a power law of the form $M_{\rm H\,\small {I}}(M,z)\propto M^{3/4}$. Our results point out that AGN feedback reduces both the total halo mass and its H i mass, although it is more efficient in removing H i. We conclude that AGN feedback reduces the neutral hydrogen mass of a given halo by ∼50 per cent, with a weak dependence on halo mass and redshift. The spatial distribution of neutral hydrogen within haloes is also affected by AGN feedback, whose effect is to decrease the fraction of H i that resides in the halo inner regions. By extrapolating our results to haloes not resolved in our simulations, we derive astrophysical implications from the measurements of $\Omega _{\rm H\,\small {I}}(z)$: haloes with circular velocities larger than ∼25 km s−1 are needed to host H i in order to reproduce observations. We find that only the model with AGN feedback is capable of reproducing the value of $\Omega _{\rm H\,\small {I}}b_{\rm H\,\small {I}}$ derived from available 21 cm intensity mapping observations.
    Preview · Article · Oct 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: We present the 8th Full Focal Plane simulation set (FFP8), deployed in support of the Planck 2015 results. FFP8 consists of 10 fiducial mission realizations reduced to 18144 maps, together with the most massive suite of Monte Carlo realizations of instrument noise and CMB ever generated, comprising $10^4$ mission realizations reduced to about $10^6$ maps. The resulting maps incorporate the dominant instrumental, scanning, and data analysis effects; remaining subdominant effects will be included in future updates. Generated at a cost of some 25 million CPU-hours spread across multiple high-performance-computing (HPC) platforms, FFP8 is used for the validation and verification of analysis algorithms, as well as their implementations, and for removing biases from and quantifying uncertainties in the results of analyses of the real data.
    Full-text · Article · Sep 2015
  • Klaus Dolag · Eiichiro Komatsu · Rashid Sunyaev
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    ABSTRACT: We calculate the one-point probability density distribution functions (PDF) and the power spectra of the thermal and kinetic Sunyaev-Zeldovich (tSZ and kSZ) effects and the mean Compton Y parameter using the Magneticum Pathfinder simulations, state-of-the-art cosmological hydrodynamical simulations of a large cosmological volume of (896 Mpc/h)^3. These simulations follow in detail the thermal and chemical evolution of the intracluster medium as well as the evolution of super-massive black holes and their associated feedback processes. We construct full-sky maps of tSZ and kSZ from the light-cones out to z=0.17, and one realization of 8.8x8.8 degree wide, deep light-cone out to z=5.2. The local universe at z<0.027 is simulated by a constrained realisation. The tail of the one-point PDF of tSZ from the deep light-cone follows a power-law shape with an index of -3.2. Once convolved with the effective beam of Planck, it agrees with the PDF measured by Planck. The predicted tSZ power spectrum agrees with that of the Planck data at all multipoles up to l~1000, once the calculations are scaled to the Planck 2015 cosmological parameters with \Omega_m=0.308 and \sigma_8=0.8149. Consistent with the results in the literature, however, we continue to find the tSZ power spectrum at l=3000 that is significantly larger than that estimated from the high-resolution ground-based data. The simulation predicts the mean fluctuating Compton Y value of =1.18x10^{-6} for \Omega_m=0.272 and \sigma_8=0.809. Nearly half (~ 5x10^{-7}) of the signal comes from halos below a virial mass of 10^{13}M_\odot/h. Scaling this to the Planck 2015 parameters, we find =1.57x10^{-6}. The PDF and the power spectrum of kSZ from our simulation agree broadly with the previous work.
    No preview · Article · Sep 2015
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    ABSTRACT: We present results obtained from a set of cosmological hydrodynamic simulations of galaxy clusters, aimed at comparing predictions with observational data on the diversity between cool-core and non-cool-core clusters. Our simulations include the effects of stellar and AGN feedback and are based on an improved version of the Smoothed-Particle-Hydrodynamics code GADGET-3, which ameliorates gas mixing and better captures gas-dynamical instabilities by including a suitable artificial thermal diffusion. In this Letter, we focus our analysis on the entropy profiles, our primary diagnostic to classify the degree of cool-coreness of clusters, and on the iron profiles. In keeping with observations, our simulated clusters display a variety of behaviors in entropy profiles: they range from steadily decreasing profiles at small radii, characteristic of cool-core systems, to nearly flat core isentropic profiles, characteristic of non cool-core systems. Using observational criteria to distinguish between the two classes of objects, we find them to occur in similar proportions in simulations and in observations. Furthermore, we also find that simulated cool-core clusters have profiles of iron abundance that are steeper than those of non-cool-core clusters, also in agreement with observational results. We show that the capability of our simulations to generate a realistic cool-core structure in the cluster population is due to AGN feedback and artificial thermal diffusion: their combined action allows to naturally distribute the energy extracted from super-massive black holes and to compensate the radiative losses of low-entropy gas with short cooling time residing in the cluster core.
    Preview · Article · Sep 2015
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    Full-text · Conference Paper · Sep 2015
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    ABSTRACT: We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the Sunyaev-Zeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planck-discovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through follow-up observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (similar to 80.6%) are spectroscopic, and associated mass estimates derived from the Y-z mass proxy. We also provide a new SZ quality flag for the remaining 280 candidates. This flag was derived from a novel artificial neural-network classification of the SZ signal. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections.
    Full-text · Article · Sep 2015
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    ABSTRACT: Comparisons between observed and predicted strong lensing properties of galaxy clusters have been used to claim either tension or consistency with ΛCDM cosmology. However, standard approaches to such tests are unable to quantify the preference for one cosmology over another. We advocate a Bayesian approach whereby the parameters defining the scaling relation between Einstein radii and cluster mass are treated as the observables. We demonstrate a method of estimating the likelihood for observing these parameters under the ΛCDM framework, using the X-ray selected z > 0.5 MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We account for cluster lens triaxiality within the modelling of the likelihood function. Cluster selection criteria is found to play as important a role as the uncertainty related to the description of star formation and feedback.
    Full-text · Article · Jul 2015 · Proceedings of the International Astronomical Union
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    ABSTRACT: This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlation functions of CMB temperature and polarization. They use the hybrid approach employed previously: pixel-based at low multipoles, $\ell$, and a Gaussian approximation to the distribution of cross-power spectra at higher $\ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models. More than doubling the data allows further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction, contributing to enhanced precision. Improvements in processing and instrumental models further reduce uncertainties. Extensive tests establish robustness and accuracy, from temperature, from polarization, and from their combination, and show that the {\Lambda}CDM model continues to offer a very good fit. We further validate the likelihood against specific extensions to this baseline, such as the effective number of neutrino species. For this first detailed analysis of Planck polarization, we concentrate at high $\ell$ on E modes. At low $\ell$ we use temperature at all Planck frequencies along with a subset of polarization. These data take advantage of Planck's wide frequency range to improve the separation of CMB and foregrounds. Within the baseline cosmology this requires a reionization optical depth $\tau=0.078\pm0.019$, significantly lower than without high-frequency data for explicit dust monitoring. At high $\ell$ we detect residual errors in E, typically at the {\mu}K$^2$ level; we thus recommend temperature alone as the high-$\ell$ baseline. Nevertheless, Planck high-$\ell$ polarization spectra are already good enough to allow a separate high-accuracy determination of the {\Lambda}CDM parameters, consistent with those established from temperature alone.
    Full-text · Article · Jul 2015
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    ABSTRACT: In the context of the formation of spiral galaxies the evolution and distribution of the angular momentum of dark matter halos have been discussed for more than 20 years, especially the idea that the specific angular momentum of the halo can be estimated from the specific angular momentum of its disk (e.g. Fall & Efstathiou (1980), Fall (1983) and Mo et al. (1998)). We use a new set of hydrodynamic cosmological simulations called Magneticum Pathfinder which allow us to split the galaxies into spheroidal and disk galaxies via the circularity parameter ϵ, as commonly used (e.g. Scannapieco et al. (2008)). Here, we focus on the dimensionless spin parameter λ = J |E|1/2 / (G M5/2) (Peebles 1969, 1971), which is a measure of the rotation of the total halo and can be fitted by a lognormal distribution, e.g. Mo et al. (1998). The spin parameter allows one to compare the relative angular momentum of halos across different masses and different times. Fig. 1 reveals a dichotomy in the distribution of λ at all redshifts when the galaxies are split into spheroids (dashed) and disk galaxies (dash-dotted). The disk galaxies preferentially live in halos with slightly larger spin parameter compared to spheroidal galaxies. Thus, we see that the λ of the whole halo reflects the morphology of its central galaxy. For more details and a larger study of the angular momentum properties of disk and spheroidal galaxies, see Teklu et al. (in prep.).
    No preview · Article · Jul 2015 · Proceedings of the International Astronomical Union
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    ABSTRACT: We present Magneticum Pathfinder, a new set of hydrodynamical cosmological simulations covering a large range of cosmological scales. Among the important physical processes included in the simulations are the chemical and thermodynamical evolution of the diffuse gas as well as the evolution of stars and black holes and the corresponding feedback channels. In the high resolution boxes aimed at studies of galaxy formation and evolution, populations of both disk and spheroidal galaxies are self-consistently reproduced. These galaxy populations match the observed stellar mass function and show the same trends for disks and spheroids in the mass–size relation as observations from the SDSS. Additionally, we demonstrate that the simulated galaxies successfully reproduce the observed specific angular-momentum–mass relations for the two different morphological types of galaxies. In summary, the Magneticum Pathfinder simulations are a valuable tool for studying the assembly of cosmic and galactic structures in the universe.
    No preview · Article · Jul 2015 · Proceedings of the International Astronomical Union
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    ABSTRACT: The total density profiles of elliptical galaxies can be fit by a single power law, i.e., ρ tot ∝ r γ with γ ≈ −2. While strong lensing observations show a tendency for the slopes to become flatter with increasing redshift, simulations indicate an opposite trend. To understand this discrepancy, we study a set of simulated spheroids formed within the cosmological framework. From our simulations we find that the steepness of the total density slope correlates with the compactness of the stellar component within the half-mass radius, and that spheroidal galaxies tend to be more compact at high redshifts than their present-day counterparts. While both these results are in agreement with observations, the observed trend of the total density slope with redshift remains in contradiction to the results from simulations.
    No preview · Article · Jul 2015 · Proceedings of the International Astronomical Union
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    ABSTRACT: (abridged) We analyse the clustering features of Large Scale Structures (LSS) in the presence of massive neutrinos, employing a set of large-volume, high-resolution cosmological N-body simulations, where neutrinos are treated as a separate collisionless fluid. The volume of 8$\cGpc$, combined with a resolution of about $8\times 10^{10}\Ms$ for the cold dark matter (CDM) component, represents a significant improvement over previous N-body simulations in massive neutrino cosmologies. We show that most of the nonlinear evolution is generated exclusively by the CDM component. We find that accounting only for the nonlinear evolution of the CDM power spectrum allows to recover the total matter power spectrum with the same accuracy as the massless case. Indeed, we show that, the most recent version of the \halofit\ formula calibrated on $\Lambda$CDM simulations can be applied directly to the linear CDM power spectrum without requiring additional fitting parameters in the massive case. As a second step, we study the abundance and clustering properties of CDM halos, confirming that, in massive neutrino cosmologies, the proper definition of the halo bias should be made with respect to the {\em cold} rather than the {\em total} matter distribution, as recently shown in the literature. Here we extend these results to the redshift space, finding that, when accounting for massive neutrinos, an improper definition of the linear bias can lead to a systematic error of about 1-$2 \%$ in the determination of the linear growth rate from anisotropic clustering. This result is quite important if we consider that future spectroscopic galaxy surveys, as \eg\ Euclid, are expected to measure the linear growth-rate with statistical errors less than about $3 \%$ at $z\lesssim1$.
    Full-text · Article · May 2015 · Journal of Cosmology and Astroparticle Physics
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    ABSTRACT: Redshift-space clustering anisotropies caused by cosmic peculiar velocities provide a powerful probe to test the gravity theory on large scales. However, to extract unbiased physical constraints, the clustering pattern has to be modelled accurately, taking into account the effects of non-linear dynamics at small scales, and properly describing the link between the selected cosmic tracers and the underlying dark matter field. We use a large hydrodynamic simulation to investigate how the systematic error on the linear growth rate, $f$, caused by model uncertainties, depends on sample selections and comoving scales. Specifically, we measure the redshift-space two-point correlation function of mock samples of galaxies, galaxy clusters and Active Galactic Nuclei, extracted from the Magneticum simulation, in the redshift range 0.2 < z < 2, and adopting different sample selections. We estimate $f\sigma_8$ by modelling both the monopole and the full two-dimensional anisotropic clustering, using the dispersion model. We find that the systematic error on $f\sigma_8$ depends significantly on the range of scales considered for the fit. If the latter is kept fixed, the error depends on both redshift and sample selection, due to the scale-dependent impact of non-linearities, if not properly modelled. On the other hand, we show that it is possible to get unbiased constraints on $f\sigma_8$ provided that the analysis is restricted to a proper range of scales, that depends non trivially on the properties of the sample. This can have a strong impact on multiple tracers analyses, and when combining catalogues selected at different redshifts.
    Preview · Article · May 2015
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    ABSTRACT: By looking at the kinetic Sunyaev-Zeldovich effect (kSZ) in Planck nominal mission data, we present a significant detection of baryons participating in large-scale bulk flows around central galaxies (CGs) at redshift $z\approx 0.1$. We estimate the pairwise momentum of the kSZ temperature fluctuations at the positions of the CGC (Central Galaxy Catalogue) samples extracted from Sloan Digital Sky Survey (DR7) data. For the foreground-cleaned maps, we find $1.8$-$2.5\sigma$ detections of the kSZ signal, which are consistent with the kSZ evidence found in individual Planck raw frequency maps, although lower than found in the WMAP-9yr W band ($3.3\sigma$). We further reconstruct the peculiar velocity field from the CG density field, and compute for the first time the cross-correlation function between kSZ temperature fluctuations and estimates of CG radial peculiar velocities. This correlation function yields a $3.0$-$3.7$$\sigma$ detection of the peculiar motion of extended gas on Mpc scales, in flows correlated up to distances of 80-100 $h^{-1}$ Mpc. Both the pairwise momentum estimates and kSZ temperature-velocity field correlation find evidence for kSZ signatures out to apertures of 8 arcmin and beyond, corresponding to a physical radius of $> 1$ Mpc, more than twice the mean virial radius of halos. This is consistent with the predictions from hydro simulations that most of the baryons are outside the virialized halos. We fit a simple model, in which the temperature-velocity cross-correlation is proportional to the signal seen in a semi-analytic model built upon N-body simulations, and interpret the proportionality constant as an "effective" optical depth to Thomson scattering. We find $\tau_T=(1.4\pm0.5)\times 10^{-4}$; the simplest interpretation of this measurement is that much of the gas is in a diffuse phase, which contributes little signal to X-ray or thermal SZ observations.
    Full-text · Article · Apr 2015
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    ABSTRACT: The evolution and distribution of the angular momentum of dark matter halos have been discussed in several studies over the last decades. In particular, the idea arose that angular momentum conservation should allow to infer the total angular momentum of the entire dark matter halo from measuring the angular momentum of the baryonic component, which is populating the center of the halo, especially for disk galaxies. To test this idea and to understand the connection between the angular momentum of the dark matter halo and its galaxy, we use the Magneticum Simulations. We successfully produce populations of spheroidal and disk galaxies self-consistently. Thus, we are able to study the dependance of galactic properties on their morphology. We find that: (I) The specific angular momentum of stars in disk and spheroidal galaxies as function of their stellar mass compares well with observational results; (II) The specific angular momentum of the stars in disk galaxies is slightly smaller compared to the specific angular momentum of the cold gas, in good agreement with observations; (III) Simulations including the baryonic component show a dichotomy in the specific stellar angular momentum distribution when splitting the galaxies according to their morphological type. This dichotomy can also be seen in the spin parameter, where disk galaxies populate halos with slightly larger spin compared to spheroidal galaxies; (IV) Disk galaxies preferentially populate halos in which the angular momentum vector of the dark matter component in the central part shows a better alignment to the angular momentum vector of the entire halo; (V) The specific angular momentum of the cold gas in disk galaxies is approximately 40 percent smaller than the specific angular momentum of the total dark matter halo and shows a significant scatter.
    Full-text · Article · Mar 2015 · The Astrophysical Journal

Publication Stats

10k Citations
1,035.64 Total Impact Points

Institutions

  • 2012-2015
    • Ludwig-Maximilians-University of Munich
      • Department of Physics
      München, Bavaria, Germany
  • 2001-2015
    • Max Planck Institute for Astrophysics
      Arching, Bavaria, Germany
  • 2012-2014
    • Technische Universität München
      München, Bavaria, Germany
  • 2007-2014
    • The Astronomical Observatory of Brera
      Merate, Lombardy, Italy
  • 2013
    • Max Planck Institute for Extraterrestrial Physics
      Arching, Bavaria, Germany
  • 2010
    • Catalan Institution for Research and Advanced Studies
      Barcino, Catalonia, Spain
  • 2009
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2003-2008
    • University of Padova
      • Department of Physics and Astronomy "Galileo Galilei"
      Padua, Veneto, Italy
  • 2004
    • Lawrence Berkeley National Laboratory
      Berkeley, California, United States
    • National Institute of Astrophysics
      • Institute of Space Astrophysics and Cosmic Physics IASF - Rome
      Roma, Latium, Italy
  • 2002
    • University of Pennsylvania
      • Department of Physics and Astronomy
      Philadelphia, Pennsylvania, United States