Serbian Astronomical Journal (Dec 2009)
Elliptical Galaxies: Rotationally Distorted, After All
Abstract
On the basis of earlier investigations onhomeoidally striated Mac Laurin spheroids and Jacobi ellipsoids (Caimmi and Marmo2005, Caimmi 2006a, 2007), different sequences of configurations are defined and represented in the ellipticity-rotation plane, $({sf O}hat{e}chi_v^2)$. The rotation parameter, $chi_v^2$, is defined as the ratio, $E_mathrm{rot}/E_mathrm{res}$, of kinetic energy related to the mean tangential equatorial velocity component, $M(overline{v_phi})^2/2$, to kineticenergy related to tangential equatorial component velocity dispersion, $Msigma_{phiphi}^2/2$, andresidual motions, $M(sigma_{ww}^2+sigma_{33}^2)/2$.Without loss of generality (above a thresholdin ellipticity values), the analysis is restricted to systems with isotropic stress tensor, whichmay be considered as adjoint configurationsto any assigned homeoidally striated density profile with anisotropic stress tensor, different angular momentum, and equal remaining parameters.The description of configurations in the$({sf O}hat{e}chi_v^2)$ plane is extendedin two respects, namely (a) from equilibriumto nonequilibrium figures, where the virialequations hold with additional kinetic energy,and (b) from real to imaginary rotation, wherethe effect is elongating instead of flattening,with respect to the rotation axis.An application is made toa subsample $(N=16)$ of elliptical galaxies extracted from richer samples $(N=25,~N=48)$of early type galaxies investigated within theSAURON project (Cappellari et al. 2006, 2007).Sample objects are idealized as homeoidallystriated MacLaurinspheroids and Jacobi ellipsoids, and theirposition in the $({sf O}hat{e}chi_v^2)$plane is inferred from observations followinga procedure outlined in an earlier paper(Caimmi 2009b). The position of related adjoint configurations with isotropic stresstensor is also determined. With a singleexception (NGC 3379), slow rotators arecharacterized by low ellipticities $(0lehat{e}<0.2)$, low anisotropy parameters$(0ledelta<0.15)$, and low rotationparameters $(0lechi_v^2<0.15)$, while fastrotators show large ellipticities $(0.2lehat{e}<0.65)$, large anisotropy parameters$(0.15ledelta<0.35)$, and large rotationparameters $(0.15lechi_v^2<0.5)$. Analternative kinematic classification withrespect to earlier attempts (Emsellem etal. 2007) requires larger samples for providingadditional support to the above mentionedresults. A possible interpretation of slowrotators as nonrotating at all and elongated due to negative anisotropy parameters,instead of flattened due to positiveanisotropy parameters, is exploited.Finally, the elliptical side of the Hubblemorphological sequence is interpreted as asequence of equilibrium (adjoint) configurations where the ellipticity is an increasing functionof the rotation parameter, slow rotators correspond to early classes (E0-E2 in the oblate limit and E2-E0 in the prolate limit)and fast rotators to late classes (E3-E6).In this view, boundaries are rotationally distorted regardless of angular momentumand stress tensor, where rotation has tobe intended as due to additional kinetic energy of tangential equatorial velocity components,with respect to spherical configurations with isotropic stress tensor.
