On the Fueling of Massive Black Holes and the Properties of their Host Spheroids

We study the relation between nuclear massive black holes and their host spheroid gravitational potential. Using simple models, we analyze how gas is expected to be transported in the nuclear regions of galaxies. When we couple it with the expected gas lifetime given by the Kennicutt-Schmidt Law, this naturally leads to the `M_BH - M_virial' and `M_BH - sigma' relations. We also numerically test, using AMR simulations, our simple models for the mass transport with satisfactory results.Comment: Reduced version that fit the 4-page limit. In press ApJ Letter

The Principle of Similitude in Biology: From Allometry to the Formulation of Dimensionally Homogenous `Laws'

Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the $\rm \Pi$ theorem (Vaschy 1892; Buckingham 1914). However, most relations in allometry do not satisfy this basic requirement, including the `3/4 Law' (Kleiber 1932) that relates the basal metabolic rate and body mass, which it is sometimes claimed to be the most fundamental biological rate (Brown et al. 2004) and the closest to a law in life sciences (West \& Brown 2004). Using the $\rm \Pi$ theorem, here we show that it is possible to construct a unique homogeneous equation for the metabolic rates, in agreement with data in the literature. We find that the variations in the dependence of the metabolic rates on body mass are secondary, coming from variations in the allometric dependence of the heart frequencies. This includes not only different classes of animals (mammals, birds, invertebrates) but also different exercise conditions (basal and maximal). Our results demonstrate that most of the differences found in the allometric exponents (White et al. 2007) are due to compare incommensurable quantities and that our dimensionally homogenous formula, unify these differences into a single formulation. We discuss the ecological implications of this new formulation in the context of the Malthusian's, Fenchel's and the total energy consumed in a lifespan relations.Comment: A accepted for publication in Theoretical Ecology. Comments are welcome ([email protected]

Multiscale mass transport in z~6 galactic discs: fueling black holes

By using AMR cosmological hydrodynamic N-body zoom-in simulations, with the RAMSES code, we studied the mass transport processes onto galactic nuclei from high redshift up to $z\sim6$. Due to the large dynamical range of the simulations we were able to study the mass accretion process on scales from $\sim50[kpc]$ to $\sim$ few $1[pc]$. We studied the BH growth on to the galactic center in relation with the mass transport processes associated to both the Reynolds stress and the gravitational stress on the disc. Such methodology allowed us to identify the main mass transport process as a function of the scales of the problem. We found that in simulations that include radiative cooling and SNe feedback, the SMBH grows at the Eddington limit for some periods of time presenting $\langle f_{EDD}\rangle\approx 0.5$ throughout its evolution. The $\alpha$ parameter is dominated by the Reynolds term, $\alpha_R$, with $\alpha_R\gg 1$. The gravitational part of the $\alpha$ parameter, $\alpha_G$, has an increasing trend toward the galactic center at higher redshifts, with values $\alpha_G\sim 1$ at radii <$\sim$ few $10^1[pc]$ contributing to the BH fueling. In terms of torques, we also found that gravity has an increasing contribution toward the galactic center at earlier epochs with a mixed contribution above $\sim 100 [pc]$. This complementary work between pressure gradients and gravitational potential gradients allows an efficient mass transport on the disc with average mass accretion rates of the order $\sim$ few $1 [M_{\odot}/yr]$. These level of SMBH accretion rates found in our cosmological simulations are needed in all models of SMBH growth that attempt to explain the formation of redshift $6-7$ quasars

A CASE STUDY OF LUNTIAN MULTI-PURPOSE COOPERATIVE IN BARANGAY LALAIG, TIAONG, QUEZON, PHILIPPINES: A VERTICAL INTEGRATION APPROACH

The Luntian Multi-Purpose Cooperative located in Tiaong, Quezon, Philippines. The Luntian Multi-Purpose cooperative focuses more on feed production as well as hog fattening. The LMC applied the vertical integration to develop the cooperative. They have their members as their primary costumers of their feeds. The cooperative’s business activity includes also meat shop, granting of production loan, micro-finance, mobilization of saving deposits, aside from feed milling and hog fattening. Different agencies, industry organizations and private institutions provide trainings, seminars, assistance, as well as credit for the cooperative.The aims of the study was to determine the present and discuss a noteworthy business issue (s) of Luntian Multipurpose Cooperative, evaluate the business environment prevailing at a particular time of this case , assess the cooperative’s performance in terms of the four business functions , define the problem relevant to the business issue(s) being studied. The study used primary and secondary data. Primary data were gathered through interviews with the key personnel, managers, and other informants of the Luntian Multipurpose Cooperative in order to obtain responses regarding the overall status of the cooperative including its problem and plans. Secondary data were taken from files and documents, especially the history, background information and financial statements. Other data were taken through research materials such as book, unpublished special problems and from some government institutions. The recommendation of this research showed that Luntian MPC should engage in establishing a communal farm as to become the primary source of hybrid piglets that their members would raised. The alternatives solution was establishing a breeding farm that would ask for initial investment. Keywords: cooperative, vertical integration, case study, por

Prototip de veles solars impulsades per làser per al viatge interestel·lar

[CATALÀ] El principal objectiu d’aquest treball és fer el disseny d’una sonda espacial que pugui ser capaç de realitzar un viatge interestel·lar. El treball té dues parts, una que consisteix en un estudi del estat del art, un plantejament determinant a on estem i quins son les principals etapes a superar per a el viatge interestel·lar, i una segona part que consisteix en tenir en compte tots els aspectes plantejats anteriorment i desenvolupar el disseny d’una vela solar no tripulada capaç de suportar un viatge interestel·lar. En el treball s’avaluen varis mètodes de propulsió i es decideix que la utilització de veles solars és el més adient per a realitzar el viatge tenint en compte la característica més important (la velocitat de desplaçament que pot assolir el mètode) ja que la velocitat determina la duració del viatge, un aspecte molt important a tenir en compte en aquest tipus de missió. Previ a la realització del disseny de la sonda s’estudien altres missions realitzades amb veles solars per a poder tenir-les en compte. Després d’estudiar les propietats de varis materials, es determina que el material òptim per a la construcció dels reflectors és un material compost pel polímer Kapton i per una prima capa reflectora d’alumini. En el treball també es determina un destí interesant a enviar-hi la sonda, el planeta potencialment habitable Pròxima b, ja que després d’un breu estudi també realitzat en el treball. Aquest exoplaneta no només presenta unes característiques idònies per a la vida, també orbita al voltant de l’estrella fora del sistema solar més propera, i enviar-hi una sonda, seria el viatge interestel·lar relativament més senzill possible de realitzar. La conclusió més destacable després de la realització del disseny de la vela solar amb 1.800 m2 de superfície i només 99,27 Kg, és que la sonda tarda més de 4.000 anys en realitzar el viatge fins a Pròxima b i aquest temps fa totalment inviable la seva utilització en el viatge interestel·lar. Per altra bada, la sonda aconsegueix assolir una velocitat de 300.000 m/s, superior a mecanismes de propulsió actuals i aquesta velocitat obre un ample ventall de noves propostes de missions amb la utilització del disseny de vela realitzat en aquest projecte.[ANGLÈS] The principal objective of this work is designing an spacecraft able to perform an interstellar travel. This work consists in two stages, one consists in a study about state of the art, an approach that determinates where we are and which ones are the principal stages for overcome an interstellar travel. The second stage consists in the development of the design of an unmanned solar sail considering all aspects studied in the first stage with the objective to apply it in the realized design to overcome an interstellar travel. Some space propulsion methods are studied in this work and solar sail propulsion is chosed for this type of travel considering the most important characteristic (màximum speed that each method can reach), speed is important because it is what can determinate the duration of the travel, an important aspect to consider in this kind of mission. Before the realization of the solar sail design, some realized missions that already used solar sails as a propulsion method are studied, this is important to consider them in the own realization of the solar sail. After studing some materials propieteies, one composed material is chosen for the construction of the solar sail reflectors, this material is composed by a thin polymide Kapton layer and another thin aluminium reflector layer. This work also determinates an interesting destiny for the solar sail, the potencially habitable planet Proxima b, this planet is chosen after a brief study also inroduced in this work. This planet not only have ideal characteristics for life, this planet also orbits around the nearest star outside solar system, and sending a solar sail there can be the most relatively simple of all possible interstellar travels. The most important conclusion after completing the design of the solar sail with 1,800 m2 of surface and only 99.27 Kg, is that the sail takes more than 4,000 years to make the trip to Proxima b, this time makes totally unviable the utilization of this sail for interstellar travel. On the other hand, the design is able to reach a speed of 300,000 m / s, higher than current propulsion mechanisms and this speed opens up a wide range of new missions proposals with the use of the design done in this project

Unveiling the role of galactic rotation on star formation

We study the star formation process at galactic scales and the role of rotation through numerical simulations of spiral and starburst galaxies using the adaptive mesh refinement code Enzo. We focus on the study of three integrated star formation laws found in the literature: the Kennicutt-Schmidt (KS) and Silk-Elmegreen (SE) laws, and the dimensionally homogeneous equation proposed by Escala (2015) $\Sigma_{\rm SFR} \propto \sqrt{G/L}\Sigma_{\rm gas}^{1.5}$. We show that using the last we take into account the effects of the integration along the line of sight and find a unique regime of star formation for both types of galaxies, suppressing the observed bi-modality of the KS law. We find that the efficiencies displayed by our simulations are anti-correlated with the angular velocity of the disk $\Omega$ for the three laws studied in this work. Finally, we show that the dimensionless efficiency of star formation is well represented by an exponentially decreasing function of $-1.9\Omega t_{\rm ff}^{\rm ini}$, where $t_{\rm ff}^{\rm ini}$ is the initial free-fall time. This leads to a unique galactic star formation relation which reduces the scatter of the bi-modal KS, SE, and Escala (2015) relations by 43%, 43%, and 35% respectively.Comment: Accepted in ApJ, 22 pages, 14 figure