Probing a regular orbit with spectral dynamics

We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis code of Carpintero & Aguilar to determine the nature of an orbit (irregular, regular, resonant, periodic) from a short-time numerical integration. If the orbit is regular, we approximate it by a truncated Fourier time series of a few tens of terms per coordinate. Switching to a description in action-angle variables, this corresponds to a reconstruction of the underlying invariant torus. We then relate the uniform distribution of a regular orbit on its torus to the non-uniform distribution in the space of observables by a simple Jacobian transformation between the two sets of coordinates. This allows us to compute, in a cell-independent way, all the physical quantities needed in the study of the orbit, including the density and in the line-of-sight velocity distribution, with much increased accuracy. The resulting flexibility in the determination of the orbital properties, and the drastic reduction of storage space for the orbit library, provide a significant improvement in the practical application of Schwarzschild's orbit superposition method for constructing galaxy models. We test and apply our method to two-dimensional orbits in elongated discs, and to the meridional motion in axisymmetric potentials, and show that for a given accuracy, the spectral dynamics formalism requires an order of magnitude fewer computations than the more traditional approaches.Comment: 13 pages, 18 eps figures, submitted to MNRA

Axisymmetric Three-Integral Models for Galaxies

We describe an improved, practical method for constructing galaxy models that match an arbitrary set of observational constraints, without prior assumptions about the phase-space distribution function (DF). Our method is an extension of Schwarzschild's orbit superposition technique. As in Schwarzschild's original implementation, we compute a representative library of orbits in a given potential. We then project each orbit onto the space of observables, consisting of position on the sky and line-of-sight velocity, while properly taking into account seeing convolution and pixel binning. We find the combination of orbits that produces a dynamical model that best fits the observed photometry and kinematics of the galaxy. A key new element of this work is the ability to predict and match to the data the full line-of-sight velocity profile shapes. A dark component (such as a black hole and/or a dark halo) can easily be included in the models. We have tested our method, by using it to reconstruct the properties of a two-integral model built with independent software. The test model is reproduced satisfactorily, either with the regular orbits, or with the two-integral components. This paper mainly deals with the technical aspects of the method, while applications to the galaxies M32 and NGC 4342 are described elsewhere (van der Marel et al., Cretton & van den Bosch). (abridged)Comment: minor changes, accepted for publication in the Astrophysical Journal Supplement

The non-evolving internal structure of early-type galaxies: the case study SDSS J0728+3835 at z = 0.206

We study the internal dynamical structure of the early-type lens galaxy SDSS J0728+3835 at z = 0.206. The analysis is based on two-dimensional kinematic maps extending out to 1.7 effective radii obtained from Keck spectroscopy, on lensing geometry and on stellar mass estimates obtained from multiband Hubble Space Telescope imaging. The data are modelled under the assumptions of axial symmetry supported by a two-integral distribution function (DF), by applying the combined gravitational lensing and stellar dynamics code CAULDRON, and yielding high-quality constraints for an early-type galaxy at cosmological redshifts. Modelling the total density profile as a power-law of the form rho_tot ~ 1/r^{gamma}, we find that it is nearly isothermal (logarithmic slope gamma = 2.08^{+0.04}_{-0.02}), and quite flattened (axial ratio q = 0.60^{+0.08}_{-0.03}). The galaxy is mildly anisotropic (delta = 0.08 +/- 0.02) and shows a fair amount of rotational support, in particular towards the outer regions. We determine a dark matter fraction lower limit of 28 per cent within the effective radius. The stellar contribution to the total mass distribution is close to maximal for a Chabrier initial mass function (IMF), whereas for a Salpeter IMF the stellar mass exceeds the total mass within the galaxy inner regions. We find that the combination of a NFW dark matter halo with the maximally rescaled luminous profile provides a remarkably good fit to the total mass distribution over a broad radial range. Our results confirm and expand the findings of the SLACS survey for early-type galaxies of comparable velocity dispersion (sigma_SDSS = 214 +/- 11 km/s). The internal structure of J0728 is consistent with that of local early-type galaxies of comparable velocity dispersion as measured by the SAURON project, suggesting lack of evolution in the past two billion years.Comment: 13 pages, 10 figures. MNRAS in press. Revised to match accepted versio

On the offset of barred galaxies from the black Hole MBH-σ relationship

We use collisionless N-body simulations to determine how the growth of a supermassive black hole (SMBH) influences the nuclear kinematics in both barred and unbarred galaxies. In the presence of a bar, the increase in the velocity dispersion σ (within the effective radius) due to the growth of an SMBH is on average �10%, whereas the increase is only �4% in an unbarred galaxy. In a barred galaxy, the increase results from a combination of three separate factors: (1) orientation and inclination effects; (2) angular momentum transport by the bar that results in an increase in the central mass density; and (3) an increase in the vertical and radial velocity anisotropy of stars in the vicinity of the SMBH. In contrast, the growth of the SMBH in an unbarred galaxy causes the velocity distribution in the inner part of the nucleus to become less radially anisotropic. The increase in σ following the growth of the SMBH is insensitive to a variation of a factor of 10 in the final mass of the SMBH, showing that it is the growth process rather than the actual SMBH mass that alters bar evolution in a way that increases σ.We argue that using an axisymmetric stellar dynamical modeling code to measure SMBH masses in barred galaxies could result in a slight overestimate of the derived MBH, especially if a constant M/L ratio is assumed. We conclude that the growth of a black hole in the presence of a bar could result in an increase in σ that is roughly 4%–8% larger than the increase that occurs in an axisymmetric system. While the increase in σ due to SMBH growth in a barred galaxy might partially account for the claimed offset of barred galaxies and pseudo bulges from the MBH–σ relation obtained for elliptical galaxies and classical bulges in unbarred galaxies, it is inadequate to account for all of the offset

Dark matter in early-type galaxies: dynamical modelling of IC1459, IC3370, NGC3379 and NGC4105

We analyse long-slit spectra of four early-type galaxies which extend from ~1 to ~3 effective radii: IC1459, IC3370, NGC3379 and NGC4105. We have extracted the full line-of-sight velocity distribution (in the case of NGC3379 we also used data from the literature) which we model using the two-integral approach. Using two-integral modelling we find no strong evidence for dark haloes, but the fits suggest that three-integral modelling is necessary. We also find that the inferred constant mass-to-light ratio in all four cases is typical for early-type galaxies. Finally, we also discuss the constraints on the mass-to-light ratio which can be obtained using X-ray haloes in the case of IC1459, NGC3379 and NGC4105 and compare the estimated values with the predictions from the dynamical modelling.Comment: 42 pages, 18 figures, accepted for publication in MNRA

Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research

This review discusses the current status of supermassive black hole research, as seen from a purely observational standpoint. Since the early '90s, rapid technological advances, most notably the launch of the Hubble Space Telescope, the commissioning of the VLBA and improvements in near-infrared speckle imaging techniques, have not only given us incontrovertible proof of the existence of supermassive black holes, but have unveiled fundamental connections between the mass of the central singularity and the global properties of the host galaxy. It is thanks to these observations that we are now, for the first time, in a position to understand the origin, evolution and cosmic relevance of these fascinating objects.Comment: Invited Review, 114 pages. Because of space requirements, this version contains low resolution figures. The full resolution version can be downloaded from http://www.physics.rutgers.edu/~lff/publications.htm

Two-dimensional kinematics of SLACS lenses: III. Mass structure and dynamics of early-type lens galaxies beyond z ~ 0.1

We combine in a self-consistent way the constraints from both gravitational lensing and stellar kinematics to perform a detailed investigation of the internal mass distribution, amount of dark matter, and dynamical structure of the 16 early-type lens galaxies from the SLACS Survey, at z = 0.08 - 0.33, for which both HST/ACS and NICMOS high-resolution imaging and VLT VIMOS IFU spectroscopy are available. Based on this data set, we analyze the inner regions of the galaxies, i.e. typically within one (3D) effective radius r_e, under the assumption of axial symmetry and by constructing dynamical models supported by two-integral stellar DFs. For all systems, the total mass density distribution is found to be well approximated by a simple power-law: this profile is on average slightly super-isothermal, with a logarithmic slope = 2.074^{+0.043}_{-0.041} (68% CL) and an intrinsic scatter 0.144^{+0.055}_{-0.014}, and is fairly round, with an average axial ratio = 0.77+/-0.04. The lower limit for the dark matter fraction (fDM) inside r_e ranges, in individual systems, from nearly zero to almost a half, with a median value of 12%. By including stellar masses derived from SPS models with a Salpeter IMF, we obtain an average fDM = 31%. The fDM rises to 61% if, instead, a Chabrier IMF is assumed. For both IMFs, the dark matter fraction increases with the total mass of the galaxy (3-sigma correlation). Based on the intrinsic angular momentum parameter calculated from our models, we find that the galaxies can be divided into two dynamically distinct groups, which are shown to correspond to the usual classes of the slow and fast rotators. Overall, the SLACS systems are structurally and dynamically very similar to their nearby counterparts, indicating that the inner regions of early-type galaxies have undergone little, if any, evolution since redshift z ~ 0.35. (Abridged)Comment: 27 pages, 34 figures. MNRAS, in pres

MEMO: mass spectrometry-based sample vectorization to explore chemodiverse datasets

In natural products research, chemodiverse extracts coming from multiple organisms are explored for novel bioactive molecules, sometimes over extended periods. Samples are usually analyzed by liquid chromatography coupled with fragmentation mass spectrometry to acquire informative mass spectral ensembles. Such data is then exploited to establish relationships among analytes or samples (e.g., via molecular networking) and annotate metabolites. However, the comparison of samples profiled in different batches is challenging with current metabolomics methods since the experimental variation-changes in chromatographical or mass spectrometric conditions - hinders the direct comparison of the profiled samples. Here we introduce MEMO-MS2 BasEd SaMple VectOrization-a method allowing to cluster large amounts of chemodiverse samples based on their LC-MS/MS profiles in a retention time agnostic manner. This method is particularly suited for heterogeneous and chemodiverse sample sets. MEMO demonstrated similar clustering performance as state-of-the-art metrics considering fragmentation spectra. More importantly, such performance was achieved without the requirement of a prior feature alignment step and in a significantly shorter computational time. MEMO thus allows the comparison of vast ensembles of samples, even when analyzed over long periods of time, and on different chromatographic or mass spectrometry platforms. This new addition to the computational metabolomics toolbox should drastically expand the scope of large-scale comparative analysis

Antiprotozoal activity of natural products from Nigerien plants used in folk medicine

In the course of the screening of plants from Niger for antiprotozoal activity, the methanol extract of Cassia sieberiana, and the dichloromethane extracts of Ziziphus mauritiana and Sesamun alatum were found to be active against protozoan parasites, namely Trypanosoma brucei rhodesiense, Trypanosoma cruzi, Leishmania donovani and/or Plasmodium falciparum. Myricitrin (1), quercitrin (2) and 1-palmitoyl-lysolecithin (3) were isolated from C. sieberiana. From Z. mauritiana, the three triterpene derivatives 13, 15, and 16 are described here for the first time. Their chemical structures were determined by 1D and 2D NMR experiments, UV, IR and HRESIMS data. The absolute configurations were assigned via comparison of the experimental and calculated ECD spectra. In addition, eight known cyclopeptide alkaloids (4, 5, 7-12), and five known triterpenoids (6, 14, 17-19) were isolated. The antiprotozoal activity of the isolated compounds, as well as of eleven quinone derivatives (20-30) previously isolated from S. alatum was determined in vitro. The cytotoxicity in L6 rat myoblast cells was also evaluated. Compound 18 showed the highest antiplasmodial activity (IC(50) = 0.2 microm) and compound 24 inhibited T. b. rhodesiense with an IC(50) value of 0.007 microM. However, it also displayed significant cytotoxicity in L6 cells (IC(50) = 0.4 microm)

Isolation and structural elucidation of compounds from Pleiocarpa bicarpellata and their in vitro antiprotozoal activity

Species of the genus Pleiocarpa are used in traditional medicine against fever and malaria. The present study focuses on the isolation and identification of bioactive compounds from P. bicarpellata extracts, and the evaluation of their antiprotozoal activity. Fractionation and isolation combined to LC-HRMS/MS-based dereplication provided 16 compounds: seven indole alkaloids, four indoline alkaloids, two secoiridoid glycosides, two iridoid glycosides, and one phenolic glucoside. One of the quaternary indole alkaloids (7) and one indoline alkaloid (15) have never been reported before. Their structures were elucidated by analysis of spectroscopic data, including 1D and 2D NMR experiments, UV, IR, and HRESIMS data. The absolute configurations were determined by comparison of the experimental and calculated ECD data. The extracts and isolated compounds were evaluated for their antiprotozoal activity towards Trypanosoma brucei rhodesiense, Trypanosoma cruzi, Leishmania donovani, and Plasmodium falciparum, as well as for their cytotoxicity against rat skeletal myoblast L6 cells. The dichloromethane/methanol (1:1) root extract showed strong activity against P. falciparum (IC50 value of 3.5 microg/mL). Among the compounds isolated, tubotaiwine (13) displayed the most significant antiplasmodial activity with an IC50 value of 8.5 microM and a selectivity index of 23.4. Therefore, P. bicarpallata extract can be considered as a source of indole alkaloids with antiplasmodial activity