Four stellar populations and extreme helium variation in the massive outer-halo globular cluster NGC 2419

Recent work revealed that both the helium variation within globular clusters (GCs) and the relative numbers of first and second-generation stars (1G, 2G) depend on the mass of the host cluster. Precise determination of the internal helium variations and of the fraction of 1G stars are crucial constraints to the formation scenarios of multiple populations (MPs). We exploit multi-band Hubble Space Telescope photometry to investigate MPs in NGC 2419, which is one of the most-massive and distant GCs of the Galaxy, almost isolated from its tidal influence. We find that the 1G hosts the ~37% of the analyzed stars, and identified three populations of 2G stars, namely 2GA, 2GB, and 2GC, which comprise the ~20%, ~31% and ~12% of stars, respectively. We compare the observed colors of these four populations with the colors derived from appropriate synthetic spectra to infer the relative helium abundances. We find that 2GA, 2GB, and 2GC stars are enhanced in helium mass fraction by deltaY ~0.01, 0.06, and 0.19 with respectto 1G stars that have primordial helium (Y=0.246). The high He enrichment of 2GC stars is hardly reconcilable with most of the current scenarios for MPs. Furthermore, the relatively larger fraction of 1G stars (~37%) compared to other massive GCs is noticeable. By exploiting literature results, we find that the fractions of 1G stars of GCs with large perigalactic distance are typically higher than in the other GCs with similar masses. This suggests that NGC 2419, similarly to other distant GCs, lost a lower fraction of 1G stars.Comment: 10 pages, 8 figures, submitted to MNRAS January 22n

Statistics of biased tracers in variance-suppressed simulations

Cosmological simulations play an increasingly important role in analysing the observed large-scale structure of the Universe. Recently, they have been particularly important in building hybrid models that combine a perturbative bias expansion with displacement fields extracted from N-body simulations to describe the clustering of biased tracers. Here, we show that simulations that employ a technique referred to as "Fixing-and-pairing" (F&P) can dramatically improve the statistical precision of such hybrid models. Specifically, by numerical and analytic means, we show that F&P simulations provide unbiased estimates for all statistics employed by hybrid models while reducing, by up to two orders of magnitude, their uncertainty on large scales. This roughly implies that an EUCLID-like survey could be analysed using simulations of 2Gpc a side -- a 10% of the survey volume. Our work establishes the robustness of F&P for current hybrid theoretical models for galaxy clustering, an important step towards achieving an optimal exploitation of large-scale structure measurements.Comment: 23 pages, 8 figure

Non-universality of the mass function: dependence on the growth rate and power spectrum shape

The abundance of dark matter haloes is one of the key probes of the growth of structure and expansion history of the Universe. Theoretical predictions for this quantity usually assume that, when expressed in a certain form, it depends only on the mass variance of the linear density field. However, cosmological simulations have revealed that this assumption breaks, leading to 10-20% systematic effects. In this paper we employ a specially-designed suite of simulations to further investigate this problem. Specifically, we carry out cosmological N-body simulations where we systematically vary growth history at a fixed linear density field, or vary the power spectrum shape at a fixed growth history. We show that the halo mass function generically depends on these quantities, thus showing a clear signal of non-universality. Most of this effect can be traced back to the way in which the same linear fluctuation grows differently into the nonlinear regime depending on details of its assembly history. With these results, we propose a parameterization with explicit dependence on the linear growth rate and power spectrum shape. Using an independent suite of simulations, we show that this fitting function accurately captures the mass function of haloes over cosmologies spanning a vast parameter space, including massive neutrinos and dynamical dark energy. Finally, we employ this tool to improve the accuracy of so-called cosmology-rescaling methods and show they can deliver 2% accurate predictions for the halo mass function over the whole range of currently viable cosmologies