1,238 research outputs found
The Stellar Mass Fundamental Plane: The virial relation and a very thin plane for slow-rotators
Early-type galaxies -- slow and fast rotating ellipticals (E-SRs and E-FRs)
and S0s/lenticulars -- define a Fundamental Plane (FP) in the space of
half-light radius , enclosed surface brightness and velocity
dispersion . Since and are distance-independent
measurements, the thickness of the FP is often expressed in terms of the
accuracy with which and can be used to estimate sizes .
We show that: 1) The thickness of the FP depends strongly on morphology. If the
sample only includes E-SRs, then the observed scatter in is ,
of which only is intrinsic. Removing galaxies with
further reduces the observed scatter to ( intrinsic). The observed scatter increases to the usually
quoted in the literature if E-FRs and S0s are added. If the FP is defined using
the eigenvectors of the covariance matrix of the observables, then the E-SRs
again define an exceptionally thin FP, with intrinsic scatter of only
orthogonal to the plane. 2) The structure within the FP is most easily
understood as arising from the fact that and are nearly
independent, whereas the and correlations are nearly
equal and opposite. 3) If the coefficients of the FP differ from those
associated with the virial theorem the plane is said to be `tilted'. If we
multiply by the global stellar mass-to-light ratio and we account
for non-homology across the population by using S\'ersic photometry, then the
resulting stellar mass FP is less tilted. Accounting self-consistently for
gradients will change the tilt. The tilt we currently see suggests that
the efficiency of turning baryons into stars increases and/or the dark matter
fraction decreases as stellar surface brightness increases.Comment: 13 pages, 9 figures, 3 tables, accepted for publication in MNRA
Contractions of low-dimensional nilpotent Jordan algebras
In this paper we classify the laws of three-dimensional and four-dimensional
nilpotent Jordan algebras over the field of complex numbers. We describe the
irreducible components of their algebraic varieties and extend contractions and
deformations among them. In particular, we prove that J2 and J3 are irreducible
and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure
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