Photometric and fundamental plane studies of galaxies

Determining the morphological parameters that describe galaxies has always been a challenging task. The studies on the correlations between different photometric as well as spectroscopic parameters of the galaxies help in understanding their structure, properties of the stars and gas which constitute the galaxy, the various physical and chemical processes which determine the properties, and galaxy formation and evolution. In the last few decades, the advent of Charge Coupled Devices (CCDs) and near infrared arrays ha\·e provided quick and reliable digitized data acquisition, in the optical and near infrared bands. This has provided an avalanche of data, which can be processed using sophisticated image analysis techniques to obtain information about the morphology of galaxies. The photometric analysis performed in this thesis involve the extraction of structural parameters of early type gala.xies imaged in the near infrared K (2.2ttm) band, obtaining correlations between these, parameters and using them to constrain the large scale properties of galaxi,~s.

GHASP: an H alpha kinematic survey of spiral and irregular galaxies - IX. The near-infrared, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near-infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from a homogeneous Fabry-Perot sample of galaxies [the Gassendi HAlpha survey of SPirals (GHASP) survey]. The main advantage of GHASP over other samples is that the maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colours, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48 +/- 0.38 and 3.64 +/- 0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratio recipes were used. We also point out, for the first time, that the rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than the flat ones or the symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K) similar to -20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well-defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.

Can retired galaxies mimic active galaxies? Clues from the Sloan Digital Sky Survey

The classification of galaxies as star forming or active is generally done in the ([O III]/H beta, [N II]/H alpha) plane. The Sloan Digital Sky Survey (SDSS) has revealed that, in this plane, the distribution of galaxies looks like the two wings of a seagull. Galaxies in the right wing are referred to as Seyfert/LINERs, leading to the idea that non-stellar activity in galaxies is a very common phenomenon. Here, we argue that a large fraction of the systems in the right wing could actually be galaxies which stopped forming stars. The ionization in these `retired` galaxies would be produced by hot post-asymptotic giant branch stars and white dwarfs. Our argumentation is based on a stellar population analysis of the galaxies via our STARLIGHT code and on photoionization models using the Lyman continuum radiation predicted for this population. The proportion of LINER galaxies that can be explained in such a way is, however, uncertain. We further show how observational selection effects account for the shape of the right wing. Our study suggests that nuclear activity may not be as common as thought. If retired galaxies do explain a large part of the seagull`s right wing, some of the work concerning nuclear activity in galaxies, as inferred from SDSS data, will have to be revised.

Morphological properties of superclusters of galaxies

We studied superclusters of galaxies in a volume-limited sample extracted from the Sloan Digital Sky Survey Data Release 7 and from mock catalogues based on a semi-analytical model of galaxy evolution in the Millennium Simulation. A density field method was applied to a sample of galaxies brighter than M(r) = -21+5 log h(100) to identify superclusters, taking into account selection and boundary effects. In order to evaluate the influence of the threshold density, we have chosen two thresholds: the first maximizes the number of objects (D1) and the second constrains the maximum supercluster size to similar to 120 h(-1) Mpc (D2). We have performed a morphological analysis, using Minkowski Functionals, based on a parameter, which increases monotonically from filaments to pancakes. An anticorrelation was found between supercluster richness (and total luminosity or size) and the morphological parameter, indicating that filamentary structures tend to be richer, larger and more luminous than pancakes in both observed and mock catalogues. We have also used the mock samples to compare supercluster morphologies identified in position and velocity spaces, concluding that our morphological classification is not biased by the peculiar velocities. Monte Carlo simulations designed to investigate the reliability of our results with respect to random fluctuations show that these results are robust. Our analysis indicates that filaments and pancakes present different luminosity and size distributions.

Global properties of `ordinary` early-type galaxies: photometry and spectroscopy of stars and globular clusters in NGC 4494

We present a comprehensive analysis of the spatial, kinematic and chemical properties of stars and globular clusters (GCs) in the `ordinary` elliptical galaxy NGC 4494 using data from the Keck and Subaru telescopes. We derive galaxy surface brightness and colour profiles out to large galactocentric radii. We compare the latter to metallicities derived using the near-infrared Calcium Triplet. We obtain stellar kinematics out to similar to 3.5 effective radii. The latter appear flattened or elongated beyond similar to 1.8 effective radii in contrast to the relatively round photometric isophotes. In fact, NGC 4494 may be a flattened galaxy, possibly even an S0, seen at an inclination of similar to 45 degrees. We publish a catalogue of 431 GC candidates brighter than i(0) = 24 based on the photometry, of which 109 are confirmed spectroscopically and 54 have measured spectroscopic metallicities. We also report the discovery of three spectroscopically confirmed ultra-compact dwarfs around NGC 4494 with measured metallicities of -0.4 less than or similar to [Fe/H] less than or similar to -0.3. Based on their properties, we conclude that they are simply bright GCs. The metal-poor GCs are found to be rotating with similar amplitude as the galaxy stars, while the metal-rich GCs show marginal rotation. We supplement our analysis with available literature data and results. Using model predictions of galaxy formation, and a suite of merger simulations, we find that many of the observational properties of NGC 4494 may be explained by formation in a relatively recent gas-rich major merger. Complete studies of individual galaxies incorporating a range of observational avenues and methods such as the one presented here will be an invaluable tool for constraining the fine details of galaxy formation models, especially at large galactocentric radii.

A NEW METHOD TO QUANTIFY X-RAY SUBSTRUCTURES IN CLUSTERS OF GALAXIES

We present a new method to quantify substructures in clusters of galaxies, based on the analysis of the intensity of structures. This analysis is done in a residual image that is the result of the subtraction of a surface brightness model, obtained by fitting a two-dimensional analytical model (beta-model or Sersic profile) with elliptical symmetry, from the X-ray image. Our method is applied to 34 clusters observed by the Chandra Space Telescope that are in the redshift range z is an element of [0.02, 0.2] and have a signal-to-noise ratio (S/N) greater than 100. We present the calibration of the method and the relations between the substructure level with physical quantities, such as the mass, X-ray luminosity, temperature, and cluster redshift. We use our method to separate the clusters in two sub-samples of high-and low-substructure levels. We conclude, using Monte Carlo simulations, that the method recuperates very well the true amount of substructure for small angular core radii clusters (with respect to the whole image size) and good S/N observations. We find no evidence of correlation between the substructure level and physical properties of the clusters such as gas temperature, X-ray luminosity, and redshift; however, analysis suggest a trend between the substructure level and cluster mass. The scaling relations for the two sub-samples (high-and low-substructure level clusters) are different (they present an offset, i. e., given a fixed mass or temperature, low-substructure clusters tend to be more X-ray luminous), which is an important result for cosmological tests using the mass-luminosity relation to obtain the cluster mass function, since they rely on the assumption that clusters do not present different scaling relations according to their dynamical state.

Newtonian acceleration scales in spiral galaxies

We revisit the issue of the constancy of the dark matter (DM) and baryonic Newtonian acceleration scales within the DM scale radius by considering a large sample of late-type galaxies. We rely on a Markov Chain Monte Carlo method to estimate the parameters of the halo model and the stellar mass-to-light ratio and then propagate the uncertainties from the rotation curve data to the estimate of the acceleration scales. This procedure allows us to compile a catalogue of 58 objects with estimated values of the B-band absolute magnitude M-B, the virial mass M-vir, and the DM and baryonic Newtonian accelerations (denoted as g(DM)(r(0)) and g(bar)(r(0)), respectively) within the scale radius r(0) which we use to investigate whether it is possible to define a universal acceleration scale. We find a weak but statistically meaningful correlation with M-vir thus making us argue against the universality of the acceleration scales. However, the results somewhat depend on the sample adopted so that a careful analysis of selection effects should be carried out before any definitive conclusion can be drawn.

Modeling the cosmological co-evolution of supermassive black holes and galaxies

In this Thesis, we investigate the cosmological co-evolution of supermassive black holes (BHs), Active Galactic Nuclei (AGN) and their hosting dark matter (DM) halos and galaxies, within the standard CDM scenario. We analyze both analytic, semi-analytic and hybrid techniques and use the most recent observational data available to constrain the assumptions underlying our models. First, we focus on very simple analytic models where the assembly of BHs is directly related to the merger history of DM haloes. For this purpose, we implement the two original analytic models of Wyithe & Loeb 2002 and Wyithe & Loeb 2003, compare their predictions to the AGN luminosity function and clustering data, and discuss possible modifications to the models that improve the match to the observation. Then we study more sophisticated semi-analytic models in which however the baryonic physics is neglected as well. Finally we improve the hybrid simulation of De Lucia & Blaizot 2007, adding new semi-analytical prescriptions to describe the BH mass accretion rate during each merger event and its conversion into radiation, and compare the derived BH scaling relations, fundamental plane and mass function, and the AGN luminosity function with observations. All our results support the following scenario: • The cosmological co-evolution of BHs, AGN and galaxies can be well described within the CDM model. • At redshifts z & 1, the evolution history of DM halo fully determines the overall properties of the BH and AGN populations. The AGN emission is triggered mainly by DM halo major mergers and, on average, AGN shine at their Eddington luminosity. • At redshifts z . 1, BH growth decouples from halo growth. Galaxy major mergers cannot constitute the only trigger to accretion episodes in this phase. • When a static hot halo has formed around a galaxy, a fraction of the hot gas continuously accretes onto the central BH, causing a low-energy “radio” activity at the galactic centre, which prevents significant gas cooling and thus limiting the mass of the central galaxies and quenching the star formation at late time. • The cold gas fraction accreted by BHs at high redshifts seems to be larger than at low redshifts.

X-Ray studies of the physics of matter around super-massive black-holes in nearby Seyfert galaxies

Seyfert galaxies are the closest active galactic nuclei. As such, we can use them to test the physical properties of the entire class of objects. To investigate their general properties, I took advantage of different methods of data analysis. In particular I used three different samples of objects, that, despite frequent overlaps, have been chosen to best tackle different topics: the heterogeneous BeppoS AX sample was thought to be optimized to test the average hard X-ray (E above 10 keV) properties of nearby Seyfert galaxies; the X-CfA was thought the be optimized to compare the properties of low-luminosity sources to the ones of higher luminosity and, thus, it was also used to test the emission mechanism models; finally, the XMM–Newton sample was extracted from the X-CfA sample so as to ensure a truly unbiased and well defined sample of objects to define the average properties of Seyfert galaxies. Taking advantage of the broad-band coverage of the BeppoS AX MECS and PDS instruments (between ~2-100 keV), I infer the average X-ray spectral propertiesof nearby Seyfert galaxies and in particular the photon index (~1.8), the high-energy cut-off (~290 keV), and the relative amount of cold reflection (~1.0). Moreover the unified scheme for active galactic nuclei was positively tested. The distribution of isotropic indicators used here (photon index, relative amount of reflection, high-energy cut-off and narrow FeK energy centroid) are similar in type I and type II objects while the absorbing column and the iron line equivalent width significantly differ between the two classes of sources with type II objects displaying larger absorbing columns. Taking advantage of the XMM–Newton and X–CfA samples I also deduced from measurements that 30 to 50% of type II Seyfert galaxies are Compton thick. Confirming previous results, the narrow FeK line is consistent, in Seyfert 2 galaxies, with being produced in the same matter responsible for the observed obscuration. These results support the basic picture of the unified model. Moreover, the presence of a X-ray Baldwin effect in type I sources has been measured using for the first time the 20-100 keV luminosity (EW proportional to L(20-100)^(−0.22±0.05)). This finding suggests that the torus covering factor may be a function of source luminosity, thereby suggesting a refinement of the baseline version of the unifed model itself. Using the BeppoSAX sample, it has been also recorded a possible correlation between the photon index and the amount of cold reflection in both type I and II sources. At a first glance this confirms the thermal Comptonization as the most likely origin of the high energy emission for the active galactic nuclei. This relation, in fact, naturally emerges supposing that the accretion disk penetrates, depending to the accretion rate, the central corona at different depths (Merloni et al. 2006): the higher accreting systems hosting disks down to the last stable orbit while the lower accreting systems hosting truncated disks. On the contrary, the study of the well defined X–C f A sample of Seyfert galaxies has proved that the intrinsic X-ray luminosity of nearby Seyfert galaxies can span values between 10^(38−43) erg s^−1, i.e. covering a huge range of accretion rates. The less efficient systems have been supposed to host ADAF systems without accretion disk. However, the study of the X–CfA sample has also proved the existence of correlations between optical emission lines and X-ray luminosity in the entire range of L_(X) covered by the sample. These relations are similar to the ones obtained if high-L objects are considered. Thus the emission mechanism must be similar in luminous and weak systems. A possible scenario to reconcile these somehow opposite indications is assuming that the ADAF and the two phase mechanism co-exist with different relative importance moving from low-to-high accretion systems (as suggested by the Gamma vs. R relation). The present data require that no abrupt transition between the two regimes is present. As mentioned above, the possible presence of an accretion disk has been tested using samples of nearby Seyfert galaxies. Here, to deeply investigate the flow patterns close to super-massive black-holes, three case study objects for which enough counts statistics is available have been analysed using deep X-ray observations taken with XMM–Newton. The obtained results have shown that the accretion flow can significantly differ between the objects when it is analyzed with the appropriate detail. For instance the accretion disk is well established down to the last stable orbit in a Kerr system for IRAS 13197-1627 where strong light bending effect have been measured. The accretion disk seems to be formed spiraling in the inner ~10-30 gravitational radii in NGC 3783 where time dependent and recursive modulation have been measured both in the continuum emission and in the broad emission line component. Finally, the accretion disk seems to be only weakly detectable in rk 509, with its weak broad emission line component. Finally, blueshifted resonant absorption lines have been detected in all three objects. This seems to demonstrate that, around super-massive black-holes, there is matter which is not confined in the accretion disk and moves along the line of sight with velocities as large as v~0.01-0.4c (whre c is the speed of light). Wether this matter forms winds or blobs is still matter of debate together with the assessment of the real statistical significance of the measured absorption lines. Nonetheless, if confirmed, these phenomena are of outstanding interest because they offer new potential probes for the dynamics of the innermost regions of accretion flows, to tackle the formation of ejecta/jets and to place constraints on the rate of kinetic energy injected by AGNs into the ISM and IGM. Future high energy missions (such as the planned Simbol-X and IXO) will likely allow an exciting step forward in our understanding of the flow dynamics around black holes and the formation of the highest velocity outflows.

Early-type galaxies as probes of galaxy formation and cosmology

The goal of this thesis is to analyze the possibility of using early-type galaxies to place evolutionary and cosmological constraints, by both disentangling what is the main driver of ETGs evolution between mass and environment, and developing a technique to constrain H(z) and the cosmological parameters studying the ETGs age-redshift relation. The (U-V) rest-frame color distribution is studied as a function of mass and environment for two sample of ETGs up to z=1, extracted from the zCOSMOS survey with a new selection criterion. The color distributions and the slopes of the color-mass and color-environment relations are studied, finding a strong dependence on mass and a minor dependence on environment. The spectral analysis performed on the D4000 and Hδ features gives results validating the previous analysis. The main driver of galaxy evolution is found to be the galaxy mass, the environment playing a subdominant but non negligible role. The age distribution of ETGs is also analyzed as a function of mass, providing strong evidences supporting a downsizing scenario. The possibility of setting cosmological constraints studying the age-redshift relation is studied, discussing the relative degeneracies and model dependencies. A new approach is developed, aiming to minimize the impact of systematics on the “cosmic chronometer” method. Analyzing theoretical models, it is demonstrated that the D4000 is a feature correlated almost linearly with age at fixed metallicity, depending only minorly on the models assumed or on the SFH chosen. The analysis of a SDSS sample of ETGs shows that it is possible to use the differential D4000 evolution of the galaxies to set constraints to cosmological parameters in an almost model-independent way. Values of the Hubble constant and of the dark energy EoS parameter are found, which are not only fully compatible, but also with a comparable error budget with the latest results.

The gaseous environment of radio galaxies: a new perspective from high-resolution x-ray spectroscopy

It is known that massive black holes have a profound effect on the evolution of galaxies, and possibly on their formation by regulating the amount of gas available for the star formation. However, how black hole and galaxies communicate is still an open problem, depending on how much of the energy released interacts with the circumnuclear matter. In the last years, most studies of feedback have primarily focused on AGN jet/cavity systems in the most massive galaxy clusters. This thesis intends to investigate the feedback phenomena in radio--loud AGNs from a different perspective studying isolated radio galaxies, through high-resolution spectroscopy. In particular one NLRG and three BLRG are studied, searching for warm gas, both in emission and absorption, in the soft X-ray band. I show that the soft spectrum of 3C33 originates from gas photoionized by the central engine. I found for the first time WA in 3C382 and 3C390.3. I show that the observed warm emitter/absorbers is not uniform and probably located in the NLR. The detected WA is slow implying a mass outflow rate and kinetic luminosity always well below 1% the L(acc) as well as the P(jet). Finally the radio--loud properties are compared with those of type 1 RQ AGNs. A positive correlation is found between the mass outflow rate/kinetic luminosity, and the radio loudness. This seems to suggest that the presence of a radio source (the jet?) affects the distribution of the absorbing gas. Alternatively, if the gas distribution is similar in Seyferts and radio galaxies, the M(out) vs rl relation could simply indicate a major ejection of matter in the form of wind in powerful radio AGNs.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.

Kinematics of local and high-z galaxies through 3D modeling of emission-line datacubes

The kinematics is a fundamental tool to infer the dynamical structure of galaxies and to understand their formation and evolution. Spectroscopic observations of gas emission lines are often used to derive rotation curves and velocity dispersions. It is however difficult to disentangle these two quantities in low spatial-resolution data because of beam smearing. In this thesis, we present 3D-Barolo, a new software to derive the gas kinematics of disk galaxies from emission-line data-cubes. The code builds tilted-ring models in the 3D observational space and compares them with the actual data-cubes. 3D-Barolo works with data at a wide range of spatial resolutions without being affected by instrumental biases. We use 3D-Barolo to derive rotation curves and velocity dispersions of several galaxies in both the local and the high-redshift Universe. We run our code on HI observations of nearby galaxies and we compare our results with 2D traditional approaches. We show that a 3D approach to the derivation of the gas kinematics has to be preferred to a 2D approach whenever a galaxy is resolved with less than about 20 elements across the disk. We moreover analyze a sample of galaxies at z~1, observed in the H-alpha line with the KMOS/VLT spectrograph. Our 3D modeling reveals that the kinematics of these high-z systems is comparable to that of local disk galaxies, with steeply-rising rotation curves followed by a flat part and H-alpha velocity dispersions of 15-40 km/s over the whole disks. This evidence suggests that disk galaxies were already fully settled about 7-8 billion years ago. In summary, 3D-Barolo is a powerful and robust tool to separate physical and instrumental effects and to derive a reliable kinematics. The analysis of large samples of galaxies at different redshifts with 3D-Barolo will provide new insights on how galaxies assemble and evolve throughout cosmic time.

Accretion of Mass and Angular Momentum onto The Discs of Spiral Galaxies

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.