---
abstract: 'The young $\sigma$ Orionis cluster in the Orion Belt is an incomparable site for studying the formation and evolution of high-mass, solar-like, and low-mass stars, brown dwarfs, and substellar objects below the deuterium burning mass limit. The first version of the Mayrit catalogue was a thorough data compilation of cluster members and candidates, which is regularly used by many authors of different disciplines. I show two new applications of the catalogue and advance preliminar results on very wide binarity and the initial mass function from 18 to 0.035$M_\odot$ in $\sigma$ Orionis. The making-up of a new version of the Mayrit catalogue with additional useful data is in progress.'
author:
- 'José A. Caballero'
title: 'Stars and brown dwarfs, spatial distribution, multiplicity, X-rays, discs, and the complete mass function of the $\sigma$ Orionis cluster'
---

[address=[Departamento de Astrofísica y Ciencias de la Atmósfera, Facultad de Física, Universidad Complutense de Madrid, E-28040 Madrid, Spain]{},email=[caballero@astrax.fis.ucm.es]{}]{}

The [*Mayrit*]{} catalogue
==========================

The constellation of Orion has pulled in the attention of astronomers and sky-watchers since the ancient times: it was mentioned in the Bible, Homer’s Odyssey and Virgil’s Aeneid, has been widely used in celestial navigation, and represented important characters, deities, or tools in mythologies all over the world (it was the Babylonian Shepherd of Anu, the Finnish Väinämöinen, and the Julpan, a canoe of the Australian aborigines). Within the constellation, the prominent Orion Belt, formed by [Alnitak]{} ($\zeta$ Ori), [Alnilam]{} ($\epsilon$ Ori), and [Mintaka]{} ($\delta$ Ori), is perhaps the most famous asterism in the sky. Thought to be mapped in the Giza pyramid complex by the ancient Egyptians, the Orion Belt has also been of great significance in other cultures: it was the Scandinavian Freyja’s distaff, the Iberian Tres Marías, the Northern-European Three Kings, and the Chinese lunar mansion Shen (literally “three” in Chinese). The fourth brightest star in the Orion Belt, about 2mag fainter than the three main stars, is [$\sigma$ Ori]{}. The star, which is actually the hierarchical multiple Trapezium-like stellar system that illuminates the famous [Horsehead Nebula]{}, has taken a great importance in the last decade. Its significance lies in the very early spectral type of the hottest component ($\sigma$ Ori A, O9.5V) and in the homonymous star cluster that surrounds the system (Garrison 1967). The $\sigma$ Orionis star cluster, re-discovered due to its large number of X-ray emitters (Wolk 1996), contains one of the best known brown dwarf and planetary-mass object populations (Béjar et al. 1999; Zapatero Osorio et al. 2000; Caballero et al. 2007), and is an excellent laboratory to study the evolution of discs and angular momenta (Reipurth et al. 1998; Caballero et al. 2004; Scholz & Eislöffel 2004; Oliveira et al. 2006; Hernández et al. 2007). Approximate canonical ages, heliocentric distances and visual extinctions are $\tau \sim$ 3Ma, $d \sim$ 385pc and $A_V \sim$ 0.3mag.

The knowledge of the whole stellar and substellar populations in a cluster in general, and in $\sigma$ Orionis in particular, has serious implications on the accuracy of the determination of some important parameters, such asthe slope of the initial mass function, frequency of discs, and degree of radial concentration. These observational parameters are, in their turn, fundamental for the theoretical scenarios that predict the formation of stars, brown dwarfs, and planets. The Mayrit catalogue of stars and brown dwarfs in the $\sigma$ Orionis cluster, built by Caballero (2008b), was an effort to compile key data on confirmed and candidate cluster members. The basis of that work was an optical-near infrared correlation between the 2MASS and DENIS catalogues in a circular area of radius 30arcmin contred on the $\sigma$ Ori stellar system. The analysis was supported by an exhaustive bibliographic search of confirmed cluster members with signposts of youth and by additional X-ray, mid-infrared, and astrometric data.

*Mayrit reloaded*
=================

![[*Left:*]{} separation to the nearest Mayrit neighbour as a function of the angular separation to the $\sigma$ Orionis centre. The segmented curves denote probabilities of alignment by chance of 5 (top) and 1% (bottom). [*Right:*]{} mass function in the $\sigma$ Orionis cluster from 18 to 0.035$M_\odot$ using the Mayrit catalogue. [*Top window:*]{} cumulative number of stars and brown dwarfs per mass interval. The vertical dashed line line denotes the stellar/substellar boundary. [*Bottom window:*]{} mass spectrum. The diagonal dash-dotted lines indicate the slopes corresponding to $\alpha$ = +2.35 (at high masses) and $\alpha$ = +0.3 (at low masses). []{data-label="thefigure"}](caballero_f1a.eps "fig:"){width="55.00000%"} ![[*Left:*]{} separation to the nearest Mayrit neighbour as a function of the angular separation to the $\sigma$ Orionis centre. The segmented curves denote probabilities of alignment by chance of 5 (top) and 1% (bottom). [*Right:*]{} mass function in the $\sigma$ Orionis cluster from 18 to 0.035$M_\odot$ using the Mayrit catalogue. [*Top window:*]{} cumulative number of stars and brown dwarfs per mass interval. The vertical dashed line line denotes the stellar/substellar boundary. [*Bottom window:*]{} mass spectrum. The diagonal dash-dotted lines indicate the slopes corresponding to $\alpha$ = +2.35 (at high masses) and $\alpha$ = +0.3 (at low masses). []{data-label="thefigure"}](caballero_f1b.eps "fig:"){width="55.00000%"}

The Mayrit catalogue has turned out to be a very useful tool for studying the spatial and radial velocity distributions (Caballero 2008a, 2008c; Bouy et al. 2008), disc frequency as a function of stellar mass (Luhman et al. 2008), and X-ray emission in the $\sigma$ Orionis cluster (López-Santiago & Caballero 2008; E. Franciosoni et al., in prep.). In this proceeding, I advance some preliminar results on two new specific topics: very wide binarity and initial mass function.

#### Very wide binaries

I have searched for very wide ($\Delta >$ 1000AU) systems among the Mayrit cluster members and candidates following a simple statistical approach. The method is based on the study of the variation of the separation to the nearest neighbour, $\rho_{\rm min}$, with the separation to the cluster centre, $r$ (left window of Fig. \[thefigure\]). The shorter the $\rho_{\rm min}$ between two objects is, the larger the probability to be bound is. However, a pair of cluster members can be separated by a short angular separation but be located at different heliocentric distances due to a projection effect. I have estimated the values of $\rho_{\rm min}$ that correspond to probabilities of random alignments of 5 and 1% for a configuration with the same (symmetrical) radial profile as $\sigma$ Orionis. For that, I have used 1000 Monte Carlo simulated distributions following the power-law radial distribution quantified in Caballero (2008a), that corresponds to a volume density proportional to $r^{-2}$. Three $\sigma$ Orionis pairs of objects, listed in Table \[thetable\], have probabilities of random alignment of $\sim$1%. Interestingly, two of the “pairs” are actually hierarchical triple system candidates. Projected physical separations, of $\Delta \approx$ 2700–5100AU, are not rare in the solar neighbourhood. Compare these values with $\Delta = 1700 \pm 300$AU, which is the separation between the $\sigma$ Orionis X-ray brown dwarf [\[SE2004\] 70]{} and the L5$\pm$2-type, planetary-mass, object candidate [SOri 68]{} (Caballero et al. 2006).

  --- ------------ --------- ---------------- --------------- ------ ------- ------
  1      528005 AB    530005    7.63$\pm$0.10   287.1$\pm$0.8   2700   1.6+?   0.61
  2     1415279 AB   1416280   12.18$\pm$0.10     4.4$\pm$0.5   4400   1.3+?   0.24
  3         397060    410059   14.12$\pm$0.10    40.4$\pm$0.5   5100     1.1   0.19
  --- ------------ --------- ---------------- --------------- ------ ------- ------

  : Visual systems in $\sigma$ Orionis with probability of alignment by chance of $\sim$1%[]{data-label="thetable"}

#### Initial mass function

Béjar et al. (2001), Tej et al. (2002), González-García et al. (2006), Caballero (2007), and Caballero et al. (2007) have determined the slope of the mass spectrum ($\Delta N / \Delta M \approx a M^{-\alpha}$) at different mass intervals in $\sigma$ Orionis. In right window of Fig. \[thefigure\], I display the cluster (initial) mass function in the interval 18–0.035$M_\odot$. Individual masses were derived from the $J$-band magnitudes tabulated in the Mayrit catalogue and using the 3Ma-old theoretical isochrones of Schaller et al. (1992), Baraffe et al. (1998), and Chabrier et al. (2000) depending on the corresponding effective temperature. The majority of the investigated stars have masses between 0.12 and 1.9$M_\odot$. While the slope $\alpha$ of the mass spectrum in the range 18–0.7$M_\odot$ follows the Salpeter value ($\alpha \approx$ +2.35), it smoothly decreases down to $\alpha \approx$ +0.3 in the mass range 0.3–0.035$M_\odot$. The transition between both slope domains is not abrupt at all, and occurs at $M \sim$ 0.4–0.6$M_\odot$. A careful derivation of the $\sigma$ Orionis initial mass function in the interval $18 \le M/M_{\odot} \le 0.025$, acounting for a precise heliocentric distance, incompleteness of the Mayrit catalogue, and decontamination by late-type field dwarfs, neighbouring young stellar populations, and red quasars, is ongoing.

*Mayrit revolutions*
====================

I have used the first version of the Mayrit catalogue in Caballero (2008b) as a basis to create an updated version, Mayrit 2.0, which will be published in a forthcoming paper. I have incorporated the latest spectroscopic results from Gatti et al. (2008), Sacco et al. (2008), Maxted et al. (2008), González-Hernández et al. (2008), and Caballero et al. (2008). The new catalogue contains UKIDSS $YZJHK$ magnitudes, radial velocities, and lithium equivalent widths for about 350 $\sigma$ Orionis members and candidates.

Partial financial support was provided by the Spanish Ministerio Educación y Ciencia, the Comunidad Autónoma de Madrid, the Universidad Complutense de Madrid, the Spanish Virtual Observatory, and the European Social Fund. JAC is an [*Investigador Juan de la Cierva*]{} at the UCM.

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