12,189 research outputs found
Separation probabilities for products of permutations
We study the mixing properties of permutations obtained as a product of two
uniformly random permutations of fixed cycle types. For instance, we give an
exact formula for the probability that elements are in distinct
cycles of the random permutation of obtained as product of two
uniformly random -cycles
Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays
Supermassive black hole -- host galaxy relations are key to the computation
of the expected gravitational wave background (GWB) in the pulsar timing array
(PTA) frequency band. It has been recently pointed out that standard relations
adopted in GWB computations are in fact biased-high. We show that when this
selection bias is taken into account, the expected GWB in the PTA band is a
factor of about three smaller than previously estimated. Compared to other
scaling relations recently published in the literature, the median amplitude of
the signal at yr drops from to
. Although this solves any potential tension between
theoretical predictions and recent PTA limits without invoking other dynamical
effects (such as stalling, eccentricity or strong coupling with the galactic
environment), it also makes the GWB detection more challenging.Comment: 6 pages 4 figures, submitted to MNRAS letter
The synchrotron foreground and CMB temperature-polarization cross correlation power spectrum from the first year WMAP data
We analyse the temperature-polarization cross-correlation in the Galactic
synchrotron template that we have recently developed, and between the template
and CMB temperature maps derived from WMAP data. Since the polarized
synchrotron template itself uses WMAP data, we can estimate residual
synchrotron contamination in the CMB angular spectrum. While
appears to be contamined by synchrotron, no evidence for
contamination is found in the multipole range which is most relevant for the
fit of the cosmological optical depth.Comment: Accepted for pubblication on MNRAS Lette
A Search for the Most Massive Galaxies. II. Structure, Environment and Formation
We study a sample of 43 early-type galaxies, selected from the SDSS because
they appeared to have velocity dispersion > 350 km/s. High-resolution
photometry in the SDSS i passband using HRC-ACS on board the HST shows that
just less than half of the sample is made up of superpositions of two or three
galaxies, so the reported velocity dispersion is incorrect. The other half of
the sample is made up of single objects with genuinely large velocity
dispersions. None of these objects has sigma larger than 426 +- 30 km/s. These
objects define rather different relations than the bulk of the early-type
galaxy population: for their luminosities, they are the smallest, most massive
and densest galaxies in the Universe. Although the slopes of the scaling
relations they define are rather different from those of the bulk of the
population, they lie approximately parallel to those of the bulk "at fixed
sigma". These objects appear to be of two distinct types: the less luminous
(M_r>-23) objects are rather flattened and extremely dense for their
luminosities -- their properties suggest some amount of rotational support and
merger histories with abnormally large amounts of gaseous dissipation. The more
luminous objects (M_r<-23) tend to be round and to lie in or at the centers of
clusters. Their properties are consistent with the hypothesis that they are
BCGs. Models in which BCGs form from predominantly radial mergers having little
angular momentum predict that they should be prolate. If viewed along the major
axis, such objects would appear to have abnormally large sigma for their sizes,
and to be abnormally round for their luminosities. This is true of the objects
in our sample once we account for the fact that the most luminous galaxies
(M_r<-23.5), and BCGs, become slightly less round with increasing luminosity.Comment: 21 pages, 19 figures, accepted for publication in MNRA
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
Allocation of risk capital in a cost cooperative game induced by a modified expected shortfall
The standard theory of coherent risk measures fails to consider individual institutions as part of a system which might itself experience instability and spread new sources of risk to the market participants. This paper fills this gap and proposes a cooperative market game where agents and institutions play the same role. We take into account a multiple institutions framework where some institutions jointly experience distress, and evaluate their individual and collective impact on the remaining institutions in the market. To carry out the analysis, we define a new risk measure (SCoES) which is a generalization of the Expected Shortfall of and we characterize the riskiness profile as the outcome of a cost cooperative game played by institutions in distress. Each institution’s marginal contribution to the spread of riskiness towards the safe institutions in then evaluated by calculating suitable solution concepts of the game such as the Banzhaf–Coleman and the Shapley–Shubik values.
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 16/12/2019, available online: http://www.tandfonline.com/10.1080/01605682.2019.168695
The ages, metallicities and star formation histories of early-type galaxies in SDSS
We use the spectra of ~ 22,000 early-type galaxies, selected from the Sloan
Digital Sky Survey, to infer the ages, metallicities and star formation
histories of these galaxies. We find clear evidence of "downsizing", i.e.
galaxies with larger velocity dispersion have older stellar populations. In
particular, most early-type galaxies with velocity dispersion exceeding 200 km
s-1 formed more than 90% of their current stellar mass at redshift z > 2.5.
Therefore, star formation was suppressed around this redshift. We also show
that chemical enrichment was rapid, lasting 1-2 Gyr and find evidence that
[Fe/H] is sub-solar. We study the robustness of these results by comparing
three different approaches: using (i) Lick absorption line indices; (ii)
fitting a single-burst stellar population model to the whole spectrum
(lines+continuum); and (iii) reconstructing the star formation and metallicity
histories in multiple age-bins, providing a method to measure mass-weighted
ages and metallicities. We find good agreement between the luminosity-weighted
ages and metallicities computed with these three methods.Comment: Submitted to Ap
PC1643+4631A,B: The Lyman-Alpha Forest at the Edge of Coherence
This is the first measurement and detection of coherence in the intergalactic
medium (IGM) at substantially high redshift (z~3.8) and on large physical
scales (~2.5 h^-1 Mpc). We perform the measurement by presenting new
observations from Keck LRIS of the high redshift quasar pair PC 1643+4631A, B
and their Ly-alpha absorber coincidences. This experiment extends multiple
sightline quasar absorber studies to higher redshift, higher opacity, larger
transverse separation, and into a regime where coherence across the IGM becomes
weak and difficult to detect. We fit 222 discrete Ly-alpha absorbers to
sightline A and 211 to sightline B. Relative to a Monte Carlo pairing test
(using symmetric, nearest neighbor matching) the data exhibit a 4sigma excess
of pairs at low velocity splitting (<150 km/s), thus detecting coherence on
transverse scales of ~2.5 h^-1 Mpc. We use spectra extracted from an SPH
simulation to analyze symmetric pair matching, transmission distributions as a
function of redshift and compute zero-lag cross-correlations to compare with
the quasar pair data. The simulations agree with the data with the same
strength (~4sigma) at similarly low velocity splitting above random chance
pairings. In cross-correlation tests, the simulations agree when the mean flux
(as a function of redshift) is assumed to follow the prescription given by
Kirkman et al. (2005). While the detection of flux correlation (measured
through coincident absorbers and cross-correlation amplitude) is only
marginally significant, the agreement between data and simulations is
encouraging for future work in which even better quality data will provide the
best insight into the overarching structure of the IGM and its understanding as
shown by SPH simulations.Comment: 15 pages, 11 figures; accepted for publication in Astronomical
Journa
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