Concepts of Optimality and Their Uses

Lecture to the memory of Alfred Nobel, December 11, 1975allocation of resources;

Gravitational Lens Time Delays in CDM

In standard CDM halo models, the time delay of a gravitational lens is determined by the cold baryon mass fraction, f, of the visible galaxy relative to the overall halo. The observed time delays in PG1115+080, SBS1520+530, B1600+434 and HE2149-2745 give Hubble constants consistent with the HST Key Project value of H0=72+/-8 km/s Mpc only if f>0.2 (1-sided 68% confidence), which is larger than the upper bound of fmax=Omega_b/Omega_0=0.15+/-0.05 estimated from the CMB. If all available baryons cool and f=fmax then the time delays imply H0=65+/-6 km/s Mpc (95% confidence). If local inventories of cold baryons, f=0.013/h70, are correct, then H0=52+/-6 km/s Mpc and the halo parameters closely match isothermal mass models. Isothermal models are also consistent with strong and weak lens studies, stellar dynamics and X-ray observations on these scales, while significantly more centrally concentrated models are not. There is a a conflict between gravitational lens time delays, the local distance scale and standard CDM halo models.Comment: Submitted to ApJ. 22 pages, 7 figure

The non-universality of the low-mass end of the IMF is robust against the choice of SSP model

We perform a direct comparison of two state-of-the art single stellar population (SSP) models that have been used to demonstrate the non-universality of the low-mass end of the Initial Mass Function (IMF) slope. The two public versions of the SSP models are restricted to either solar abundance patterns or solar metallicity, too restrictive if one aims to disentangle elemental enhancements, metallicity changes and IMF variations in massive early-type galaxies (ETGs) with star formation histories different from the solar neighborhood. We define response functions (to metallicity and \alpha-abundance) to extend the parameter space of each set of models. We compare these extended models with a sample of Sloan Digital Sky Survey (SDSS) ETGs spectra with varying velocity dispersions. We measure equivalent widths of optical IMF-sensitive stellar features to examine the effect of the underlying model assumptions and ingredients, such as stellar libraries or isochrones, on the inference of the IMF slope down to ~0.1 solar masses. We demonstrate that the steepening of the low-mass end of the Initial Mass Function (IMF) based on a non-degenerate set of spectroscopic optical indicators is robust against the choice of the stellar population model. Although the models agree in a relative sense (i.e. both imply more bottom-heavy IMFs for more massive systems), we find non-negligible differences on the absolute values of the IMF slope inferred at each velocity dispersion by using the two different models. In particular, we find large inconsistency in the quantitative predictions of IMF slope variations and abundance patterns when sodium lines are used. We investigate the possible reasons for these inconsistencies.Comment: 16 pages, 9 figures, 2 tables, accepted for publication on Ap