The first two papers appear to be a rigorous look at the relation between the mass of a cluster and the most massive star formed. The second paper highlights how to go about properly constraining the properties of a cluster within this new framework.

A CR paper examines the distribution of cosmic rays with Fermi. They find variations of CRs from cloud to cloud at the low energies responsible for CR heating. The final attacks the degeneracy between star formation history, abundance and dust properties to derive the mass of stars, gas, dust and stellar age self consistently at moderate red shift.

**Crucial aspects of the initial mass function (I): The statistical correlation between the total mass of an ensemble of stars and its most massive star** Miguel Cervino (1 and 2), Carlos Romann-Zuniga (3), Valentina Luridiana (2 and 4), Amelia Bayo (5 and 6), Nestor Sanchez (7), Enrique Perez (1) ((1) IAA-CSIC, (2) IAC, (3) IA-Ensenada UNAM, (4) Univ. La Laguna, (5) ESO, (6) MPA Heifelberg, (7) Facl. Matematicas-UCM) (Submitted on 28 Mar 2013)

Our understanding of stellar systems depends on the adopted interpretation of the IMF, phi(m). Unfortunately, there is not a common interpretation of the IMF, which leads to different methodologies and diverging analysis of observational data.We study the correlation between the most massive star that a cluster would host, mmax, and its total mass into stars, M, as an example where different views of the IMF lead to different results. We assume that the IMF is a probability distribution function and analyze the mmax-M correlation within this context. We also examine the meaning of the equation used to derive a theoretical M-char_mmax relationship, N x int[Char_mmax-mup] phi(m) dm = 1 with N the total number of stars in the system, according to different interpretations of the IMF. We find that only a probabilistic interpretation of the IMF, where stellar masses are identically independent distributed random variables, provides a self-consistent result. Neither M nor N, can be used as IMF scaling factors. In addition, Char_mmax is a characteristic maximum stellar mass in the cluster, but not the actual maximum stellar mass. A <M>-Char_mmax correlation is a natural result of a probabilistic interpretation of the IMF; however, the distribution of observational data in the N (or M)-cmmax plane includes a dependence on the distribution of the total number of stars, N (and M), in the system, Phi(N), which is not usually taken into consideration. We conclude that a random sampling IMF is not in contradiction to a possible mmax-M physical law. However, such a law cannot be obtained from IMF algebraic manipulation or included analytically in the IMF functional form. The possible physical information that would be obtained from the N (or M)-mmax correlation is closely linked with the Phi(M) and Phi(N) distributions; hence it depends on the star formation process and the assumed.

Comments: | Accepted by A&A; 16 pages, 10 figures |

Subjects: | Cosmology and Extragalactic Astrophysics (astro-ph.CO); Galaxy Astrophysics (astro-ph.GA) |

Cite as: | arXiv:1303.7237 [astro-ph.CO] |

(or arXiv:1303.7237v1 [astro-ph.CO] for this version) |

**Crucial aspects of the initial mass function (II): The inference of total quantities from partial information on a cluster** Miguel Cervino (1 and 2), Carlos Romann-Zuniga (3), Amelia Bayo (4 and 5), Valentina Luridiana (2 and 6), Nestor Sanchez (7), Enrique Perez (1) ((1) IAA-CSIC, (2) IAC, (3) IA-Ensenada UNAM, (4) ESO, (5) MPA Heifelberg, (6) Univ. La Laguna, (7) Facl. Matematicas-UCM) (Submitted on 28 Mar 2013)

In a probabilistic framework of the interpretation of the initial mass function (IMF), the IMF cannot be arbitrarily normalized to the total mass, M, or number of stars, N, of the system. Hence, the inference of M and N when partial information about the studied system is available must be revised. (i.e., the contribution to the total quantity cannot be obtained by simple algebraic manipulations of the IMF). We study how to include constraints in the IMF to make inferences about different quantities characterizing stellar systems. It is expected that including any particular piece of information about a system would constrain the range of possible solutions. However, different pieces of information might be irrelevant depending on the quantity to be inferred. In this work we want to characterize the relevance of the priors in the possible inferences. Assuming that the IMF is a probability distribution function, we derive the sampling distributions of M and N of the system constrained to different types of information available. We show that the value of M that would be inferred must be described as a probability distribution Phi[M; m_a, N_a, Phi(N)] that depends on the completeness limit of the data, m_a, the number of stars observed down to this limit, N_a, and the prior hypothesis made on the distribution of the total number of stars in clusters, Phi(N).

Comments: | Accepted by A&A; 9 pages |

Subjects: | Cosmology and Extragalactic Astrophysics (astro-ph.CO); Galaxy Astrophysics (astro-ph.GA) |

Cite as: | arXiv:1303.7238 [astro-ph.CO] |

(or arXiv:1303.7238v1 [astro-ph.CO] for this version) |

**Probing Cosmic Rays in Nearby Giant Molecular Clouds with the Fermi Large Area Telescope** Rui-zhi Yang, Emma de Oña Wilhelmi, Felix Aharonian (Submitted on 29 Mar 2013)

We report the results of our study on the energy spectra and absolute fluxes of cosmic rays (CRs) in the Local Galaxy based on three-year gamma-ray observations of ten nearby giant molecular clouds (GMCs) belongs to the Gould Belt, with the Fermi Large Area Telescope (LAT). The gamma-ray signals obtained with high statistical significance allow the determination of gamma-ray spectra above 300 MeV with adequate precision for extraction of the energy distributions of CRs in these clouds. Remarkably, both the derived spectral indices and the absolute fluxes of CR protons in the energy interval 10 – 100 GeV are in good agreement with the recent direct measurements of local CRs by the PAMELA experiment. This is a strong evidence for a quite homogeneous distribution of CRs, at least within several hundred parsecs of the Local Galaxy. Combined with the well established energy-dependent time of escape of CRs from the Galaxy, \tau(E) ~ E^{-\delta} with \delta ~ 0.5-0.6, the measured spectrum implies a CRs spectral index of the (acceleration) source of ~ E^{-2.3}. At low energies, the spectra of gamma-rays appear to vary from one cloud to another. This implies spatial variations of the energy spectra of CR below 10 GeV which at such low energies could be naturally explained by the impact of the propagation effects as well as by the contribution of CR locally accelerated inside the clouds.

Comments: | Submitted to A&A |

Subjects: | High Energy Astrophysical Phenomena (astro-ph.HE) |

Cite as: | arXiv:1303.7323 [astro-ph.HE] |

(or arXiv:1303.7323v1 [astro-ph.HE] for this version) |

**The dust properties of z ~ 3 MIPS-LBGs from photo-chemical models** X.L. Fan, A. Pipino, F. Matteucci (Submitted on 29 Mar 2013)

The stacked spectral energy distribution (SED) of Multiband Imaging Photometer for Spitzer (MIPS) 24$\mu m$ detected Lyman break galaxies (MIPS-LBGs) is fitted by means of spectro-photometric model GRASIL with an "educated" fitting approach which benefits from results of chemical evolution models. The star formation rate(SFR)-age-metallicity degeneracies of SED modelling are broken by using SFH and chemical enrichment history suggested by chemical models, which also provide dust mass, dust abundance and chemical elements locked in dust component. We derive the total mass $M_{tot}$, stellar mass $M_{\ast}$, gas mass $M_{g}$, dust mass $M_{d}$, age and SFR of the stacked MIPS-LBG in a self-consistent way. Our estimate of $M_{\ast}= 8\times 10^{10}$ agrees with other works based on UV-optical SED fitting. We suggest that MIPS-LBGs at $z\sim3$ are young (0.3-0.6 Gyr), massive ($M_{tot} \sim 10^{11} M_{\odot}$), dusty ($M_{d} \sim 10^{8} M_{\odot}$), metal rich ($Z \sim Z_{\odot} $) progenitors of elliptical galaxies suffering a strong burst of star formation (SFR $\sim 200 M_{\odot}/yr$). Our estimate of $M_{d}=7 \times 10^{7} M_{\odot}$ of the stacked MIPS-LBG is about a factor of eight lower than the estimated value based on single temperature grey-body fitting, suggesting that self-consistent SED models are needed to estimate dust mass. By comparing with the Milky Way molecular cloud and dust properties, we suggest that denser and dustier environments and flatter dust size distribution are likely in high redshift massive star forming galaxies. These dust properties, as well as the different types of SFHs, can cause different SED shapes between high redshift star-forming ellipticals and local star-burst templates. This discrepancy of SED shapes could in turn explain the non detection at submillimeter wavelengths, of IR luminous ($L_{IR} \succeq 10^{12} L_{\odot} $) MIPS-LBGs.

Comments: | 31pages,9 figures, accepted for publication in ApJ |

Subjects: | Cosmology and Extragalactic Astrophysics (astro-ph.CO) |

Cite as: | arXiv:1303.7399 [astro-ph.CO] |

(or arXiv:1303.7399v1 [astro-ph.CO] for this version) |