ABSTRACT
We examine the effectiveness of identifying distinct evolutionary histories in IllustrisTNG-100 galaxies using unsupervised machine learning with Gaussian mixture models. We focus on how ...clustering compressed metallicity histories and star formation histories produces sub-population of galaxies with distinct evolutionary properties (for both halo mass assembly and merger histories). By contrast, clustering with photometric colours fails to resolve such histories. We identify several populations of interest that reflect a variety of evolutionary scenarios supported by the literature. Notably, we identify a population of galaxies inhabiting the upper red sequence, M* > 1010 M⊙, that has a significantly higher ex-situ merger mass fraction present at fixed masses and a star formation history that has yet to fully quench, in contrast to an overlapping, satellite-dominated population along the red sequence, which is distinctly quiescent. Extending the clustering to study four clusters instead of three further divides quiescent galaxies, whereas star-forming ones are mostly contained in a single cluster, demonstrating a variety of supported pathways to quenching. In addition to these populations, we identify a handful of populations from our other clusters that are readily applicable to observational surveys, including a population related to post-starburst galaxies, allowing for possible extensions of this work in an observational context, and to corroborate results within the IllustrisTNG ecosystem.
We introduce versatile spectral analysis (VESPA): a new method which aims to recover robust star formation and metallicity histories from galactic spectra. VESPA uses the full spectral range to ...construct a galaxy history from synthetic models. We investigate the use of an adaptative parametrization grid to recover reliable star formation histories on a galaxy‐by‐galaxy basis. Our goal is robustness as opposed to high‐resolution histories, and the method is designed to return high time resolution only where the data demand it. In this paper we detail the method and we present our findings when we apply VESPA to synthetic and real Sloan Digital Sky Survey (SDSS) spectroscopic data. We show that the number of parameters that can be recovered from a spectrum depends strongly on the signal‐to‐noise ratio, wavelength coverage and presence or absence of a young population. For a typical SDSS sample of galaxies, we can normally recover between two and five stellar populations. We find very good agreement between VESPA and our previous analysis of the SDSS sample with MOPED.
We present the first quantitative detection of large-scale filamentary structure at z NOT approximately equal to 0.7 in the large cosmological volume probed by the VIMOS Public Extragalactic ...Redshift Survey (VIPERS). We use simulations to show the capability of VIPERS to recover robust topological features in the galaxy distribution, in particular the filamentary network. We then investigate how galaxies with different stellar masses and stellar activities are distributed around the filaments, and find a significant segregation, with the most massive or quiescent galaxies being closer to the filament axis than less massive or active galaxies. The signal persists even after downweighting the contribution of peak regions. Our results suggest that massive and quiescent galaxies assemble their stellar mass through successive mergers during their migration along filaments towards the nodes of the cosmic web. On the other hand, low-mass star-forming galaxies prefer the outer edge of filaments, a vorticity-rich region dominated by smooth accretion, as predicted by the recent spin alignment theory. This emphasizes the role of large-scale cosmic flows in shaping galaxy properties.
The classical Bonnet problem is to classify all immersions
f
:
M
2
→
R
3
into Euclidean three-space that are not determined, up to a rigid motion, by their induced metric and mean curvature function. ...The natural extension of Bonnet problem for Euclidean hypersurfaces of dimension
n
≥
3
was studied by Kokubu (Tôhoku Math J 44:433–442, 1992). In this article, we investigate an infinitesimal version of Bonnet problem for hypersurfaces with dimension
n
≥
3
of any space form, namely, we classify the hypersurfaces
f
:
M
n
→
Q
c
n
+
1
,
n
≥
3
, of any space form
Q
c
n
+
1
of constant curvature
c
, for which there exists a (non-trivial) one-parameter family of immersions
f
t
:
M
n
→
Q
c
n
+
1
, with
f
0
=
f
, whose induced metrics
g
t
and mean curvature functions
H
t
coincide “up to the first order," that is,
∂
/
∂
t
|
t
=
0
g
t
=
0
=
∂
/
∂
t
|
t
=
0
H
t
.
We address the problem of determining the hypersurfaces
f
:
M
n
→
Q
s
n
+
1
(
c
)
with dimension
n
≥
3
of a pseudo-Riemannian space form of dimension
n
+
1
, constant curvature
c
and index
s
∈
{
0
,
...1
}
for which there exists another isometric immersion
f
~
:
M
n
→
Q
s
~
n
+
1
(
c
~
)
with
c
~
≠
c
. For
n
≥
4
, we provide a complete solution by extending results for
s
=
0
=
s
~
by do Carmo and Dajczer (Proc Am Math Soc 86:115–119,
1982
) and by Dajczer and Tojeiro (J Differ Geom 36:1–18,
1992
). Our main results are for the most interesting case
n
=
3
, and these are new even in the Riemannian case
s
=
0
=
s
~
. In particular, we characterize the solutions that have dimension
n
=
3
and three distinct principal curvatures. We show that these are closely related to conformally flat hypersurfaces of
Q
s
4
(
c
)
with three distinct principal curvatures, and we obtain a similar characterization of the latter that improves a theorem by Hertrich-Jeromin (Beitr Algebra Geom 35:315–331,
1994
).
Abstract
We obtain constraints on cosmological parameters from the spherically averaged redshift-space correlation function of the CMASS Data Release 9 (DR9) sample of the Baryonic Oscillation ...Spectroscopic Survey (BOSS). We combine this information with additional data from recent cosmic microwave background (CMB), supernova and baryon acoustic oscillation measurements. Our results show no significant evidence of deviations from the standard flat Λ cold dark matter model, whose basic parameters can be specified by Ωm = 0.285 ± 0.009, 100 Ωb = 4.59 ± 0.09, n
s = 0.961 ± 0.009, H
0 = 69.4 ± 0.8 km s−1 Mpc−1 and σ8 = 0.80 ± 0.02. The CMB+CMASS combination sets tight constraints on the curvature of the Universe, with Ω
k
= −0.0043 ± 0.0049, and the tensor-to-scalar amplitude ratio, for which we find r < 0.16 at the 95 per cent confidence level (CL). These data show a clear signature of a deviation from scale invariance also in the presence of tensor modes, with n
s < 1 at the 99.7 per cent CL. We derive constraints on the fraction of massive neutrinos of f
ν < 0.049 (95 per cent CL), implying a limit of ∑m
ν < 0.51 eV. We find no signature of a deviation from a cosmological constant from the combination of all data sets, with a constraint of w
DE = −1.033 ± 0.073 when this parameter is assumed time-independent, and no evidence of a departure from this value when it is allowed to evolve as w
DE(a) = w
0 + w
a
(1 − a). The achieved accuracy on our cosmological constraints is a clear demonstration of the constraining power of current cosmological observations.
We develop a Ribaucour transformation for the class of conformally flat hypersurfaces
f
:
M
3
→
Q
s
4
(
c
)
with three distinct principal curvatures of a pseudo-Riemannian space form of dimension 4, ...constant curvature
c
and index
s
∈
{
0
,
1
}
, as well as for the class of hypersurfaces
f
:
M
3
→
Q
s
4
(
c
)
with three distinct principal curvatures for which there exists another isometric immersion
f
~
:
M
3
→
Q
s
~
4
(
c
~
)
with
c
~
≠
c
. It gives a process to produce a family of new elements of those classes starting from a given one and a solution of a linear system of PDE’s. This enables us to construct explicit new examples of hypersurfaces in both classes.
We obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the
L
-transformation. It allows ...to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear partial differential equations. We prove a decomposition theorem for the
L
-transformation, which is a far-reaching generalization of the classical permutability formula for the Ribaucour transformation of surfaces of constant curvature in Euclidean three space. As a consequence, we derive a Bianchi-cube theorem, which allows to produce, from
k
initial scalar
L
-transforms of a given submanifold of constant curvature, a whole
k
-dimensional cube all of whose remaining
2
k
-
(
k
+
1
)
vertices are submanifolds with the same constant sectional curvature given by explicit algebraic formulae. We also obtain further reductions, as well as corresponding decomposition and Bianchi-cube theorems, for the classes of
n
-dimensional flat Lagrangian submanifolds of
C
n
and
n
-dimensional Lagrangian submanifolds with constant curvature
c
of the complex projective space
C
P
n
(
4
c
)
or the complex hyperbolic space
C
H
n
(
4
c
)
of complex dimension
n
and constant holomorphic curvature 4c.
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