Modelo para determinar la existencia de economías de escala en el proceso de beneficio de café Sistema 3

systems

Shortly after the first numerical relativity (NR) simulations of a complete BBH orbit presented in Brügmann, Tichy, and Jansen [2004], the first successful multiple orbit NR simulations of the actual merger of a BBH system were achieved in Pretorius [2005a], Campanelli et al. [2006], and Baker et al. [2006]. Since then, ever-growing computational resources and advances in the numerical methods used to simulate these systems have made the exploration of the vast initial parameter space possible (see e.g. Hinder [2010] and references therein for a recent overview of the status of BBH simulations). The initial parameters of BBH simulations are the BH mass ratio and the six components of their initial spin vectors. The investigation of these initial parameters has led to significant discoveries, as the occurrence of the orbital hang-up [Campanelli, Lousto, and Zlochower 2006] and the presence of the so-called super-kicks, where the final BH is displaced from the orbital plane after its formation with a higher speed than predicted by Post-Newtonian estimates. This happens for initial configurations with anti-aligned BH spins that lie in the orbital plane (see Brügmann et al. [2008] and references therein).

Stellar mass BH–torus systems are believed to be the end states of BNS or BHNS mergers, as well as of the rotational gravitational collapse of massive stars1_{. BNS mergers can also form an intermediate, transient structure known}

1_{We note that there are more types of mergers that might lead to the formation of post-}

merger accretion tori, such as BH–white dwarf, NS–white dwarf, and binary white dwarf mergers (see, for instance Fryer et al. [1999], Paschalidis et al. [2011], and Raskin et al. [2012]).

as a hypermassive NS after the merger, whose large differential rotation leads to a delayed collapse to a BH (see, e.g. Shibata et al. [2006]), or to a magnetar (a NS with a extremely strong magnetic field) surrounded by an accretion disc (see, e.g. Giacomazzo and Perna [2013]. Our theoretical understanding of the formation of BH–torus systems and their evolution relies strongly on numerical work. The first BNS mergers in full GR (albeit for simplified matter models) were performed by Shibata and Ury¯u [2000], and following the BBH breakthrough in 2005, Shibata and Ury¯u [2006] performed the first NR BHNS mergers. If the NS does not plunge into the BH during the final merger phase of a BHNS binary, but is rather tidally disrupted by the BH, a thick accretion torus can form around the remnant Kerr BH (see Shibata and Taniguchi [2011] and references therein). Thick accretion tori also form in unequal mass BNS mergers (see Faber and Rasio [2012] and references therein). The formation of a thick, massive accretion torus in these systems is of particular interest as the remnant BH–torus system is believed to be a possible gamma-ray burst (GRB) engine [Woosley 1993, Janka et al. 1999, Aloy, Janka, and Müller 2005]. In particular, the BH–torus systems resulting from BNS and BHNS mergers are believed to be the birthplaces of short GRBs (SGRB), as the expected lifetime of the accretion torus is of the order of the duration of SGRBs, while long GRBs are more likely to be produced by “failed” Type Ib supernovae [Woosley 1993]. BH–torus systems emit GWs, which may eventually provide the direct means to study their actual formation and evolution. Observing these GWs will help to prove whether the hypothesis that these systems form the central engine of GRBs is correct, as due to their intrinsic high density and temperature electromagnetic observations are out of reach. Furthermore, once observed, the detected gravitational waveforms of the actual inspiral and coalescence in BNS and BHNS mergers will enhance our understanding of the actual equation of state (EOS) of NS [Read et al. 2009], thus providing valuable insights about the behaviour of matter at nuclear densities. For an overview of the event rate estimates of BNS and BHNS mergers that are observable with initial and advanced LIGO see e.g. Abadie et al. [2010], Dominik et al. [2013], and Dominik et al. [2015].

In recent years a significant number of NR simulations have shown the feasi- bility of the formation of such systems from generic initial data (see e.g. Rezzolla et al. [2010], Kyutoku et al. [2011], Hotokezaka et al. [2013b], Hotokezaka et al. [2013a], and Kastaun and Galeazzi [2015] for recent progress). In particular, the 3D simulations of Rezzolla et al. [2010] (see also references therein) have shown that unequal-mass BNS mergers lead to the self-consistent formation of

necessary requirements of the GRB’s central engine hypothesis. However, if the energy released in a SGRB comes from the accretion torus, the BH–torus system has to survive for up to a few seconds [Rees and Meszaros 1994]. Any instability which might disrupt the system on shorter timescales, such as the runaway instability [Abramowicz, Calvani, and Nobili 1983] or the Papaloizou- Pringle instability (PPI) [Papaloizou and Pringle 1984], could pose a severe problem for the prevailing GRB models. Additionally, post-merger discs should be highly magnetised, due to efficient magnetic field amplification mechanisms active in BNS mergers [Kiuchi et al. 2015a]. Large accretion rates facilitated by the magneto-rotational instability (MRI), which might be active in accre- tion discs [Balbus and Hawley 1991], could further shorten the lifetime of the accretion torus.

The majority of compact merger simulations to date have led to the produc- tion of BH–torus systems in which the central BH spin and the torus angular momentum vector are aligned. This is the expected outcome for BNS mergers, where the direction of the remnant BH spin is perpendicular to the original orbital plane of the binary. For BHNS mergers, an aligned BH–torus system is produced if the BH has zero spin initially or if the BH spin is initially aligned with the orbital plane of the binary system. However, if the BH spin is initially

misalignedwith the orbital plane of the binary, tilted BH–torus systems have

been shown to form self-consistently in full NR simulations [Foucart et al. 2011, Foucart et al. 2013, Kawaguchi et al. 2015]. Another possible scenario for the formation of tilted BH–torus systems is by means of asymmetric supernova explosions in binary systems [Fragos et al. 2010]. In fact, it is believed that most BH–torus systems should be tilted (see Fragile, Mathews, and Wilson [2001], Maccarone [2002], and Fragile et al. [2007] for arguments).

As shown in Foucart [2012], the disc mass in BHNS mergers increases with a larger initial BH spin and decreases with a larger initial BH mass. This is due to the size of the innermost circular stable orbit (ISCO) of the BH in the merger. The ISCO grows with BH mass and decreases with the spin magnitude of the BH. If the ISCO is large enough, the NS will be “swallowed” entirely by the BH before being tidally disrupted, leaving no accretion torus behind. Another factor in determining the tidal disruption of the NS is its compactness (the ratio of the NS mass and its radius). As seen in Foucart [2012], the larger the NS, the more favoured are massive post-merger discs. In order to estimate disc masses resulting from BHNS mergers, one needs thus an estimate for the initial BH masses in these system. One such method, via population synthesis considerations, favour larger BH masses [Belczynski et al. 2008, Belczynski et al.

2010, Fryer et al. 2012], with a peak around 8 M⊙ and a mass gap between

the lightest expected BHs and NS masses. This means that these massive BHs would need very large initial spins in order to be able to form massive remnant discs after the BHNS merger. However, the prediction of accurate remnant BH masses via population synthesis is difficult, as the BH mass crucially depends on the detailed supernova explosion mechanism [Kreidberg et al. 2012] which in turn is very model dependent on the actual presupernova evolution of rotating massive stars [Heger, Langer, and Woosley 2000].