Tesis postgrado Astrofísica

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    Identifying and characterising post-encounter disintegrating system
    (Universidad de Valparaíso, 2023-07) Ka Po Yip, Alexandra; Kurtev, Radostin
    Disintegrating multiple systems are thought to be very common based on numerical simulations, which predict that 50% to 95% of non-hierarchical triple systems and 10% of hierarchical triple systems undergo an ejection at some point in their evolution. However, very few of these systems have so far been observed. Kinematic studies of the Hipparcos catalogue have revealed only 10 disintegrating triple candidates. They are presumably the result of dynamical encounters taking place in the Galactic disk between single/multiple systems. In this thesis, I expanded the search for such systems to study their properties, as well as to characterize possible low-mass ejecta (i.e. brown dwarfs and planets). I have assembled a list of 20 candidate systems using astrometry from the Tycho-Gaia astrometric solution (later upgraded with Gaia DR3), and here I present the follow-up of 9 of them. I have obtained medium-resolution spectra for 4 of them and used the spectra to determine their radial velocity and metallicity. These measurements allowed me to conclude that two of the systems observed with ISIS are likely genuine disintegrating systems, for which I have reconstructed the most probable interaction scenario. I have obtained DECam imaging for 5 systems and by combining near-infrared photometry and proper motion, I searched for ultra- cool ejected components. I found that the system consisting of TYC 7731-1951-1, TYC 7731-2128-1 AB, and TYC 7731-1995-1ABC?, contains one very promising ultra-cool dwarf candidate. Using additional data from the literature, I have found that 3 out of the 5 disintegrating system candidates observed with DECam are likely to be true dis- integrating systems. Overall, this thesis demonstrates the feasibility of searching for disintegrating multiple systems with the method described, as well as the feasibility of identifying additional low-mass ejected components. Future Gaia data releases and upcoming large area near-infrared surveys and new space telescopes (e.g. LSST, EU- CLID, SPHEREX, NEOSurveyor) will enable me to search for even larger samples of disintegrating systems and more low-mass ejecta. This population will be fundamental to observationally constrain the rate at which this type of systems interact in the Galactic disk. The fundamental importance of searching for possible disintegrating multiple systems is its contribution in providing further constraints to the formation models of binaries and multiple systems and their evolution.
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    The mass range for hot subdwarf B stars from MESA simulations : dependence on metallicity and overshooting
    (Universidad de Valparaíso, 2023-04) Arancibia Rojas, Eduardo; Zorotovic, Mónica (Supervisor)
    Hot subdwarf B (sdB) stars are helium core burning stars that have lost almost their entire hydrogen envelope due to binary interaction. Their assumed canonical mass of MsdB ∼ 0.47 M⊙ has recently been debated given a broad range found both from observations as well as from the simulations. The mass range for sdBs as a function of initial mass was derived two decades ago by Han et al. (2002), using the Eggleton code, for two different metallicities (Z =0.02 and Z = 0.004). Here, I revised and refined these calculations, using the stellar evolution code MESA. An excellent agreement was obtained for low-mass progenitors, up to ∼ 2.0 M⊙. For more massive progenitors, a direct comparison was not possible due to the different prescription for overshooting these authors used, which is not available in MESA. However, I found that in general the MESA models result in a wider mass range compared to the simulations performed by Han et al. (2002) with the Eggleton code, for more massive stars. The effects of metallicity and the inclusion of core overshooting during the main sequence were also analysed. I found that the lower metallicity models predict, on average, slightly more massive sdBs (0.01 − 0.02 M⊙ larger). The inclusion of core overshooting during the main sequence mostly affected progenitors more massive than ∼ 1.5 M⊙, as expected, decreasing the maximum initial mass for which the core becomes degenerate during the red giant branch phase, and increasing the sdB mass for progenitors that ignite helium under non-degenerate conditions. The duration of the sdB phase was also calculated, finding a strong anti-correlation with the sdB mass. Finally, I discussed several factors that might affect the sdB mass distribution and should be considered in binary population synthesis models that aim to compare with observational samples.
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    The effect of non-gaussian primordial perturbations on large-scale structure
    (Universidad de Valparaíso, 2021-12) Peña Pinto, Greco; Candlish, Graeme
    The late-time effect of primordial non-Gaussianity offers a window into the physics of inflation and the very early Universe. In this thesis we study the conse- quences of a particular class of primordial non-Gaussianity that is fully characterized by initial density fluctuations drawn from a non-Gaussian probability density func- tion, rather than by construction of a particular form for the primordial bispectrum. We numerically generate multiple realisations of cosmological structure and use the late-time matter power spectrum, bispectrum and trispectrum to determine the ef- fect of these modified initial conditions. We show that the initial non-Gaussianity has only a small imprint on the first three polyspectra, when compared to a stan- dard Gaussian cosmology. Furthermore, some of our models present an interesting scale-dependent deviation from the Gaussian case in the bispectrum and trispectrum, although the signal is at most at the percent level. The majority of our models are consistent with CMB constraints, while the others are only marginally excluded. Finally, we discuss further possible extensions of our study.
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    A momentum coupling between dark matter and dark energy : consequences at small scales
    (Universidad de Valparaíso, 2021-05) Palma Palma, Daniela; Candlish, Graeme
    Dark energy is frequently modelled as an additional dynamical scalar field component in the Universe, referred to as “quintessence,” which drives the late-time acceleration. Furthermore, the quintessence field may be coupled to dark matter and/or baryons, leading to a fifth force. In this thesis we explore the consequences for non-linear cosmological structure formation arising from a momentum coupling between the quintessence field and dark matter. The coupling leads to a modified Euler equation, which we implement in an N-body cosmological simulation. We then analyse the non- linear power spectrum, comparing with the standard ΛCDM cosmology, as well as the halo mass function, and various other dark matter halo properties. We find that, for certain quintessence potentials, a positive coupling leads to a large enhancement of structure formation at small scales.
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    Understanding AGN physics through variability
    (Universidad de Valparaíso, 2023-05) López Navas, Elena; Arévalo Noordam, Patricia (Superviser)
    In recent years, the discovery of the so-called changing-look (CL) active galactic nu- clei (AGNs) has evidenced that several scenarios can lead to variations in the broad emission lines (BELs, with widths >1,000 km s−1) and so to the AGN optical classifications, which has challenged the classical view of AGNs defined by the simplest unified models (UM). This PhD thesis presents a comprehensive study of optical variability in AGNs with the aim of shedding light on the Type 1/Type 2 dichotomy and improving the search for the intriguing and rare CL AGNs. Our approach is based on the exploration of optical fluctuations of spectrally-classified Type 2 sources, that is, AGNs whose ac- cretion disc and broad line region (BLR) should be obscured, and so their BELs and optical continuum variability. For that purpose, we make use of the Zwicky Tran- sient Facility (ZTF), a state-of-the-art optical time-domain survey, and the Automatic Learning for the Rapid Classification of Events (ALeRCE), a Chilean-led broker using machine learning models, in preparation for the big data era with the arrival of the Legacy Survey of Space and Time (LSST). By analysing systematically the ZTF light curves of a large (>15,000) Type 2 sam- ple, we find that ∼ 11 per cent of sources show evidence for optical variations, which leads to the discovery of misclassified Type 1s with weak BELs and CL candidates. We then apply the same strategy (i.e., searching for optical variations in Type 2 sources) using the current light curve classifications given by ALeRCE, and find ∼ 60 new CL candidates. We took second epoch spectra of 36 candidates and confirmed 50 per cent of sources as turning-on CLs, resulting in one of the selection techniques with the highest success rate of CL confirmations up to date. Overall, this thesis strengthens the importance of variability studies in under- standing the physics of AGNs, and contributes to the use of machine learning algo- rithms together with all-sky variability surveys to search for intrinsically rare objects. The findings of this research will ultimately contribute to our understanding of the fundamental processes that drive the evolution of AGNs.
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    Particle and light propagation around stellar black holes in alternative theories of gravity and implications to general relativistic tests
    (Universidad de Valparaíso, 2023-01) Fathi, Mohsen; Villanueva Lobos, José (Superviser)
    The equations of motion for particles travelling in the gravitational fields of massive objects, as formulated by the general theory of relativity, have been receiving rigor- ous attention ever since the advent of the theory. In fact, the approximate solutions to these equations, at the time, could pave the way in figuring out the trajectories of planets and light in the solar system and finally, led to some observational evidences which confirmed general relativity’s predictions (as asserted by Eddington in his fa- mous book (Eddington, 1920)). However, the more delicate the experimental tests became, the more they raised the interest in obtaining exact solutions to the equations of motion. This necessitated employing advanced mathematical methods, mainly, because of the resultant differential equations appearing in the equations of motion, which tend to calculate the arc-lengths associated with the particle trajectories. Since the early attempts by Hagihara (Hagihara, 1930) and Darwin (Darwin, 1959, 1961) in obtaining and categorizing the particle orbits in the Schwarzschild spacetime, re- searchers have been employing different approaches to the computation of the arc- lengths swept by particle trajectories in gravitating systems. These approaches are, in general, based on manipulating elliptic integrals and the resultant elliptic func- tions, covering the Jacobi and the Weierstraß elliptic functions, as the two most com- mon forms. Ever since, the elliptic and hyper-elliptic functions have received a great deal of interest in analyzing the geodesic structure of massive and mass-less particles in black hole spacetimes (Rauch & Blandford, 1994; Kraniotis & Whitehouse, 2003; Kraniotis, 2004; Beckwith & Done, 2005; Cruz et al., 2005; Kraniotis, 2005; Hackmann & La¨ mmerzahl, 2008a,b; Bisnovatyi-Kogan & Tsupko, 2008; Kagramanova et al., 2010; Hackmann et al., 2010a,b; Kraniotis, 2011; Enolski et al., 2011; Gibbons & Vyska, 2012; Mun˜ oz, 2014a; Kraniotis, 2014; Mun˜ oz, 2014b; De Falco et al., 2016; Barlow et al., 2017; Vankov, 2017; Chatterjee et al., 2019; Uniyal et al., 2018; Jusufi et al., 2018; Ghaffarne- jad et al., 2018; Villanueva et al., 2018; Hsiao et al., 2020; Gralla & Lupsasca, 2020; Kraniotis, 2021). In this thesis, we investigate the time-like and null geodesics that propagate in the exterior geometry of static and rotating black holes. The first problems that are dealt with, is the derivation of the analytical solutions to the equations of motion, for both the radial and angular types of orbits. To achieve this purpose, we use the standard Lagrangian dynamics and identify the orbits in the context of the corresponding effec- tive potentials. The second objective is to apply the classical general relativistic tests (in particular in the solar system), to examine the relevant mathematical formulations for these tests that are given for each of the black holes spacetimes. The organization of this thesis is as follows: In chapter 1, we discuss, in detail, the elliptic integrals and their solutions in terms of the Jacobian and Weierstraßian elliptic functions in all of their forms. We also bring several examples to demonstrate their ap- plicability for the relevant problems in classical physics. In chapter 2, we explore the geometrical aspects of the Lagrangian and Hamiltonian on the base manifold. This is followed by the derivation of the geodesic equation from Euler-Lagrange equations. Furthermore, to exemplify this in black hole spacetimes, we calculate the exact so- lutions to the radial and angular geodesics for the mass-less and massive particles that travel in the exterior geometry of a Schwarzschild black hole, which necessitates the exploitation of the formerly discussed elliptic functions. These trajectories are also plotted for each of the types of orbits. Moreover, we review the derivation of a modified version of the Newman-Janis algorithm to generate the stationary coun- terparts of static spacetimes. In chapter 3, we begin our studies by investigating the geodesics in a particular spacetime, derived from the fourth order Weyl conformal gravity, under certain circumstances. This static black hole spacetime, is studied in the context of the propagation of mass-less, neutral, and charged massive particles. We also apply several general relativistic tests on this black hole, by means of the de- rived analytical expressions. Finally, by employing the aforementioned algorithm, a stationary counterpart of this black hole is generated. This black hole is investigated in terms of its ergoregion, photon spheres and shadow. In chapter 4, the propaga- tion of mass-less particles in the exterior geometry of a scale-dependent BTZ black hole is discussed, together with the simulation of the possible orbits. Chapter 5 is devoted to a more complicated case, namely to a Kerr black hole immersed in a non- magnetized plasma, which produces a dielectric medium residing in a curved mani- fold. We apply an elaboration to all the previously discussed methods, and then, we employ them to the investigation of the light ray trajectories in this medium. The orbits are discussed in both planar and three-dimensional context, by solving, in- dividually, the temporal evolution of the coordinates. In chapter 6, we consider a Schwarzschild black hole associated with quintessence and cloud of strings, which is firstly calibrated in the context of standard general relativistic tests for its parame- ters. We then continue with the derivation of exact analytical solutions for null and time-like geodesics in this spacetime. We finally switch our study, in chapter 7, to the application of Carathe´ odory’s geometrothermodynamics to a static (Hayward) and a stationary (rotating scale-dependent BTZ) black hole. This discussion, although being different from those done in the previous chapters, is of great interest since it provides a new vision to the black hole thermodynamics and helps for the creation of a boost in the development of this field of study. We construct the perspective of our future studies in chapter 8. Throughout this thesis, unless in the particular places that is adopted otherwise, we use the geometric units, in which G = c = h¯ = 1. Furthermore, in appropriate places where needed, we use the Einstein convention on summing over dummy indices, and the four-dimensional system of coordinates is adopted as xµ = (x0, x1, x2, x3 ), in which, the zero component corresponds to the time coordinate, i.e. x0 = t. All the diagrams and simulations have been generated by the software Mathematica® 12.0.
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    Constraining the duration of ram pressure stripping from the direction of optical jellyfish galaxy tails
    (Universidad de Valparaíso, 2023-04) Salinas Froemel, Vicente; Jaffé, Yara (Superviser)
    Within the field of galaxy evolution, we know the life of a galaxy can be driven by a combination of internal and external mechanisms. Amongst the latter, perhaps the most efficient mechanism affecting the gas content and star formation histories of galaxies in dense environments is ram pressure stripping, produced when a galaxy moves through the intergalactic medium within groups and clusters of galaxies. Ex- treme examples of on-going ram pressure stripping are known as jellyfish galaxies, a type of galaxy characterized by a tail of stripped material that can be directly ob- served in multiple wavelengths. Using the largest broad-band optical jellyfish can- didate sample in local clusters known to date, we measure the angle between the direction of the tails visible in the galaxies, and the direction towards the host cluster center. We find that 32.7% of the galaxy tails point away from the cluster center, 18.5% point toward the cluster center, and 48.8% point elsewhere. Moreover, we find strong signatures of ram pressure stripping happening on galaxies pointing away and to- wards the cluster center, and larger velocity dispersion profiles for galaxies with tails pointing away. These results are consistent with a scenario where ram pressure strip- ping has a stronger effect for galaxies following radial orbits on first infall. The results also suggest that in many cases, radially infalling galaxies are able to retain their tails after pericenter and continue to experience significant on-going ram pressure strip- ping. With the observational measures obtained in this work, we then constrain the lifetime of the optical tails from the moment they first appear to the moment they dis- appear, by comparing them with N-body simulations in combination with an MCMC model. We obtain that galaxy tails appear for the first time at ∼ 1.16 R200 and disap- pear ∼ 650 Myr after pericenter. Finally, this work constitutes an important base for future studies with increasingly larger samples of ram pressure stripped galaxies.
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    Formation of close binaries by triple dynamics in the context of supernovae la progenitors
    (Universidad de Valparaíso, 2018-07) Lagos Vilches, Felipe; Schreiber, Matthias (Advisor)
    The unique capabilities of Type Ia Supernovae (SN Ia), with emission bright and uniform enough to serve as yardsticks on cosmological distance scales, has resulted in them becoming some of the most important objects in the universe, and have led to the discovery of its accelerating expansion and eventually to the award of the 2011 Nobel Prize in Physics. Although it is well established that SN Ia are related to the thermonuclear ignition of a white dwarf (WD) that surpassed the Chandrasekhar mass limit, there is not yet a general consensus on the pathways leading to the explosion. While it is clear that the progenitors of SN Ia are close binaries which contain at least one WD, how these close binaries form and the detailed nature of the second stellar component remain one of the largest unsolved problems in astronomy. The two main progenitor channels that have been proposed are the single degenerate channel in which the WD accretes from a non-degenerate companion, and the double degenerate channel, which explains SN Ia explosions as the merger of two WDs. However, whether nature has a strong preference for one of these channels, or whether a combination of several evolutionary channels contributes to the observed SN Ia rate, remains an open question. The fact that we haven’t solved yet this important issue has two main reasons. First, the evolution of initial main sequence binary stars into close WD binary stars is a very complicated process and current theories are unable to simulate it in detail. Binary population models therefore rely on rather simple empirical relations with often completely unconstrained parameters, which makes it virtually impossible to make reliable predictions on SN Ia rates produced by any of the proposed channels. On top of that, it might even be that triple star dynamics produce significant numbers of close WD binaries, which is usually entirely ignored. Second, despite some significant recent progress, we still haven’t been able to provide decisive observational constraints on WD binary pathways towards SN Ia. This is largely because the direct progenitors of SN Ia explosions are either short-lived and potentially highly obscured super soft X-ray sources and/or faint and hard to detect close double WD binaries. The difficulty of providing clear constraints from surveys of the direct progenitors of SN Ia motivated us to go one step back in the evolution of the proposed progenitor systems. Before a double WD system is formed and before a WD accretes from a non-degenerate companion, these systems must have been detached binary stars consisting of a WD and an intermediate mass star (typically FGK spectral types) companion, formed in most cases after a common envelope (CE) phase. Characterizing a large sample of such detached WD plus main-sequence FGK star systems, that both classic SN Ia progenitors originally descended from, can provide crucial constraints on close WD binary evolution in general and the SN Ia progenitor problem in particular. The compact binary star group at the University of Valparaiso runs a large scale observational project aiming at identifying a large number of detached WD+FGK binary stars. Several close binaries have already been identified and some early results have been published. Interestingly, about 33 ± 12% of the identified close binaries are in eccentric orbits, which can not be explained by the main formation channel of close WD+FGK systems, the CE phase. Based on previous studies that involve hierarchical triple systems and the effect of a distant extra component perturbing the binary, we propose that those observed eccentric binaries are in fact triples systems, where the third star alters the orbital properties like the eccentricity in the so called Kozai-lidov Mechanisms (KLMs), and together with tidal forces can produce close binaries with eccentric orbits. As most of the observed systems only have spectroscopic measurements of the main sequence star component of the close binary, we have two possible configurations that locate the WD either orbiting this sun-like star or being a distant companion to an inner binary consisting of the sun-like star and an unseen low-mass main sequence star. In this thesis we estimate the amount of close WD+FGK binaries that evolved through KLMs (i.e., the binary as part of the triple systems) instead of via the CE phase, and the fraction of triple systems where the WD is either part of the binary or is the distant companion itself. To do this, we use the statistical research of hierarchical multiple stars of Tokovinin [2014b] to generate the initial conditions of a population of binary and triple systems that will be evolved using the Binary Star Evolution code (BSE). As the BSE algorithm only includes the evolution of single and binary stars, we evolve the distant companion as an isolated stars. Four simulations (assuming different eccentricity distribution) show that on average 23% of binaries of the observed sample could be potential hierarchical triple systems that evolved via KLMs, where about 79% correspond to systems where the WD is the distant companion, in agreement with the observations. Finally, we observationally study one of the binaries with eccentric orbit, and find the third component to be the white dwarf. We estimate that most likely the KLMs were active before the WD formed.
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    Multiperiodicidad de superciclos en novas enanas del tipo SU UMa
    (Universidad de Valparaíso, 2019-03) Contreras Quijada, Alexander
    Los sistemas estelares binarios compuestos por una componente primaria (enana blanca) y otra secundaria (estrella de secuencia principal) que presentan transferencia de masa son las llamadas variables cataclísmicas (CV, por sus siglas en inglés). El material que proviene desde la componente secundaria, luego de llenar su lóbulo de Roche, forma un disco de acreción alrededor de la enana blanca. Dentro de las CVs se encuentran las novas enanas que presentan erupciones de duración y frecuencia variables en sus curvas de luz, donde se distinguen 3 clases: las tipo U Gem o SS Cyg, Z Cam y las SU UMa. Éstas últimas poseen períodos orbitales menores a 3 horas y presentan erupciones normales que duran pocos días y erupciones más largas (alrededor de 2 semanas) y más brillantes llamadas supererupciones. El período de tiempo entre cada supererupción se denomina superciclo (entre 120 y 600 días) y cambia de forma cuasi-periódica. Así también, se distinguen las ER UMa que poseen superciclos más cortos cada 20 a 40 días. El presente trabajo presenta un estudio en detalle de superciclos para 23 novas enanas del tipo SU UMa y 3 del tipo ER UMa. Mediante datos observacionales, principalmente desde la base de datos de la American Association of Variable Star Observers (AAVSO) y supererupciones reportadas en la literatura, se pudieron obtener hasta 88 años de observaciones para cada estrella. En consecuencia, se contabilizaron la mayoría de las superupciones para asignarles números de ciclos E y con ello poder determinar los valores de superciclos típicos. De esta forma, mediante ajustes de mínimos cuadrados lineales de los números de ciclos E versus día juliano se obtuvieron superciclos generales promedio (PSC) de entre 42 días hasta aproximadamente 1.5 años. Sin embargo, se encuentra que los superciclos presentan 3 tipos de variaciones en distintas escalas de tiempo que van desde pocos meses hasta algunas décadas. En primer lugar, los residuos O-C muestran rangos de superciclo aproximadamente constante después de 5 o más supererupciones y que representan variaciones a corto plazo en intervalos de tiempo de 1 a 33 años aproximadamente. De esta forma, estos superciclos C (130 casos) muestran valores que van desde los 34 días hasta alrededor de 1.7 años, encontrándose además entre 2 a 11 superciclos C por objeto. En segundo lugar, mediante ajustes de mínimos cuadrados parabólicos a los residuos O-C lineales se encuentra que 17 casos presentan cambios seculares signicativos de superciclos, aumentando su valor en 11 o disminuyéndolo en 6 casos, lo que constituye variaciones a largo plazo. En tercer lugar, se encontraron variaciones a mediano plazo en todos los casos, donde a partir de ajustes de mínimos cuadrados sinusoidales a los residuos O-C parabólicos se determinaron superciclos (PSCsin) que van desde 5.4 a aproximadamente 48.4 años. Adicionalmente, se realizaron nuevos ajustes de mínimos cuadrados sinusoidales a los residuos O-C lineales, con ello se encontraron superciclos (PSCsin2) entre los 5.5 a los 58.6 años. Por otra parte, para los PSC se pudieron distinguir dos grupos bien definidos, separados por el C = 250 días. Por lo cual, se encuentra una fuerte correlación entre este parámetro versus tiempo de observación y PSCsin, para PSC menores a los 250 días. Sin embargo, para PSC > 250[d] no se encuentra ninguna correlación significativa con los parámetros ya mencionados. Así mismo, se encuentra que alrededor de un 64% de los superciclos C están bajo los 250[d]. Los valores de PSC son comparados con otros resultados reportados en la literatura. A pesar de que se encuentran similitudes también existen diferencias substanciales principalmente referentes a las variaciones seculares de los superciclos. Finalmente, se investiga una posible relación de los superciclos sinusoidales (PSCsin y PSCsin2) con ciclos de tipo solar ('22 años), debido a variaciones en la componente secundaria de la binaria producto de fuertes campos magnéticos que se producen en las zonas convectivas en su interior. Tales variaciones se manifiestan en cambios a largo plazo de la magnitud promedio, variaciones pequeñas del período orbital (Porb) y, en el caso de novas enanas, variaciones del valor promedio de los intervalos entre erupciones consecutivas. De esta forma, en este estudio se comparan 54 variables cataclísmicas (CVs) y un total de 103 períodos cíclicos (Pcic) donde el valor medio para CVs con Porb>3h es de 13.1 _ 2.6 años. Por el contrario, para Porb<3h el valor medio aumenta de forma signicativa hasta 23.6 _ 1.7 años. En consecuencia, las SU UMa podrían presentar ciclos de tipo solar con períodos mucho más largos que los de otros tipos de novas enanas.
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    Estimación del efecto microlente cromático en los sistemas QSO2237+0305 y SDSS1226-0006
    (Universidad de Valparaíso, 2022-04) Jerez Nicurcar, Ramsés; Motta, Verónica
    El efecto lente gravitacional es una poderosa herramienta que permite estudiar la estructura interna de los núcleos activos de galaxias. Este proceso es posible de realizar debido a que estas fuentes lejanas son magnificadas, accediendo a una resolución angular que de otra manera no sería posible. En esta tesis de magíster, se estudiaron los siguientes objetos lentes gravitacionales: el sistema cuádruple QSO2237+0305 (cruz de Einstein) y el sistema doble SDSS1226-0006. El primero concita gran interés debido a que la galaxia lente se encuentra a un corrimiento al rojo muy cercano. En el segundo sistema se han realizado escasos estudios, los cuales están relacionado con la distribución de materia de la galaxia lente, no habiéndose hecho estimaciones de los parámetros del disco de acreción con anterioridad. Mediante el estudio del espectro de cada imagen lentificada, se han analizado las líneas de emisión y continuo bajo éstas, así como también, se ha cuestionado la existencia de extinción en las líneas de emisión del sistema QSO2237+0305 obtenida en la literatura. Junto a este análisis, se ha encontrado efecto microlente en la región de las líneas anchas. Se ha confirmado la existencia de efecto microlente cromático entre las imágenes de los sistemas, permitiendo modelar el disco de acreción con un perfil de temperatura ( p). Dado a que existe una dependencia en la longitud de onda, es posible parametrizarla, de modo que el tamaño del disco de acreción se puede escribir siguiendo una ley de potencia, mediante la relación rs ∝ λp, donde p corresponde al perfil de temperatura. Se han encontrado los tamaños de los discos medidos a λ = 1026 Å y los perfiles de temperatura.
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    The origin of brown dwarfs
    (Universidad de Valparaíso, 2019-09) Santamaría Miranda, Alejandro; Schreiber, Matthias
    In the present thesis we study the problem of the formation of brown dwarfs, objects whose masses are in the range between planets and stars. There are four main for- mation theories for these substellar objects: turbulent fragmentation, disk fragmen- tation, ejection from filaments and photoevaporation. All these formation channels can form brown dwarfs but it remains an open question which is the one preferred by nature. Revealing this dominant formation mechanism was the main motivation of this thesis. In particular, we investigated if mass loss or accretion processes are a scaled-down versions of the same phenomena in the stellar regime. We used several astronomical techniques such as interferometry and spectroscopy at different wavelengths to study the formation of brown dwarfs. For our observational surveys of forming brown dwarfs the star forming region of Lupus and ρ Ophiuchus were chosen as their close distance and their youth enhance the possibilities of de- tecting and analysing faint objects. For objects in the earliest stages of their evolution we used ALMA for studying the cold dust envelopes which emit the released energy in the (sub)mm regime. ALMA was also used for the somewhat more evolved Class 0 and I sources, complemented with optical and infrared archival data. In one Class I/II source (Par-Lup3-4) we have used the emission of several molecular transitions to study the mass loss of a molecular outflow. We combined the ALMA emission line and continuum data with optical/infrared archival data. The further evolved Class II sources were studied using spectroscopic observations ranging from near ultraviolet to near infrared wavelengths as well as continuum emission in the (sub)mm and optical/infrared photometry. The most notable observational result is the discovery of eleven pre-substellar core can- didates that are in gravitational contraction. We found an interesting Class 0/I can- didate and resolved its structure. We measured the disk mass of the Class II sources and their properties are consistent with being scaled down versions of forming low mass stars. We detected for the first time the base of a bipolar molecular outflow in a very low mass star whose properties are a scaled-down version of the outflow properties ob- served in the stellar regime. We measured the accretion rate of the substellar companion to the stellar binary (SR 12) using several accretion indicators commonly used in the stellar regime. The companion’s radial velocity and its separation within the binary system point out that it is not very probable that this source was formed by disk fragmentation, while the accretion rate is in agreement with an extension of the relation obtained for more massive objects. Based on the mentioned scientific evidences (accretion rate, mass loss, the presence of isolated pre-substellar cores in gravitational contraction, and the relation between disk mass and central object) we conclude that it is highly probable that the main for- mation mechism of brown dwarfs is turbulent fragmentation (also known as scaled- down version of star formation).
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    Searching for gas in debris disks
    (Universidad de Valparaíso, 2020-04) Iglesias Vallejo, Daniela; Bayo, Amelia (Supervisora); Olofsson, Johan (Supervisor); Wahhaj, Zahed (Supervisor)
    A debris disk is commonly described as a second generation circumstellar disk com- posed of dust grains, planetesimals and possibly already formed giant planets. It was long thought that debris disks were systems fully depleted of gas, but in the last few years the presence of gas has been detected in a increasing number of them. The na- ture of this gas is still under debate; it may be residual gas (leftover from earlier stages of the disk) or second generation gas (generated by the sublimation of exocomets or collisions of icy bodies), however, both possibilities would have great implications in the process of planet formation and evolution. An efficient way to search for this gas in debris disks is monitoring gas tracers using multi-epoch high-resolution UV-optical spectroscopy. A detection of gas in the line of sight of the star shows up as a very narrow absorption feature superposed to the photospheric absorption of lines such as Ca ii or Na i, which are very sensitive gas tracers. This Thesis is devoted to the search for gas via high-resolution spectroscopy in a sample of 301 debris disks with the pur- pose of estimating the frequency of gas in debris disks. We collected high-resolution UV-optical spectroscopic data from our own observations and the ESO archive for 273 objects, completing 91% of our sample. We analysed the multi-epoch spectra of each object searching for variable and stable non-photospheric absorption features of circumstellar origin. Firstly, we performed a detailed analysis of a sub-sample of 27 objects having multiple stable absorption features with the aim of determining whether their features were of circumstellar or interstellar origin. In this group we found two objects; c Aql and HR 4796, with variable absorption features attributable to the presence of star-grazing exocomets, and one object; HD 110058 with a stable circumstellar gas absorption. We concluded from these preliminary results that the presence of gas in debris disks might be a common phenomenon. Secondly, we studied the presence of unusually large non-photospheric absorption features found in several ionized lines of the object HD 37306, that lasted for several days. After analysing different possibilities we concluded that the most likely explanation might be an ex- ocometary break-up releasing a stream of gas that remained in orbit for at least a week around the star. Then, we analyzed the variability found in the Ca ii K lines of 97 objects with the purpose of distinguishing variable absorption features most likely produced by exocometary activity from variability of a different nature, like stellar pulsations, spots or radial velocity shifts, for instance. We found five candidates with variability consistent with exocometary activity: c Aql, 49 Cet, gam Tri, HR 4796 and HD 37306, two of them with no previous reports of exocomets besides this work. Finally, we studied a sub-sample of 107 objects presenting stable non-photospheric features in their Ca ii K lines within our updated database of observations in addi- tion to those in our first sub-sample of analysis. Similarly, the absorption features observed in these objects were analysed in order to determine whether they were of circumstellar or interstellar origin. We confirmed an interstellar origin for the features in 104 of these objects, one of them, 49 Cet having a blended feature of combined circumstellar and interstellar origin. In addition, we found three candidates with features of yet inconclusive origin that might be circumstellar but need further study to confirm it. Putting together our results, we found six debris disks with presence of circumstellar gas, five of them presenting variable absorption features attributable to exocometary activity and one of them with a stable circumstellar gas component. Considering that our sample is unbiased with respect to inclination, that the gas is more likely to be detected when the disk is observed close to edge-on, more easily detected in the spectra of early-type stars, the many detection challenges related to the sporadical nature of exocometary transits, and the interlopers of gas detection, then the evidence of circumstellar gas is significant. Taking into account the currently increasing number of detections, this imply the possibility that most debris disks may harbor some gas, challenging the current paradigm of debris disks.
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    Understanding the life of evolved stars using modern astronomical tools and techniques : case study of pulsating GW Vir, hot subdwarf B stars and their progenitors
    (Universidad de Valparaíso, 2022-08) Uzundag, Murat; Vuckovic, Maja (Supervisora)
    With the advance of high precision and high duty cycle photometric monitoring from the Transiting Exoplanet Survey Satellite (TESS) mission, unprecedented asteroseismic measurements and tools have become available for pulsating hot subdwarf B (sdB), white dwarf (WD) and pre-white dwarf stars. In this thesis, we present a detailed asteroseismic and spectroscopic analysis of long-period pulsating sdB and GW Vir WD stars observed with TESS in order to compare the observations with model predictions based on stellar evolution computations coupled with adiabatic pulsation computations. A small percentage of the sdB population (about 10%) was discovered to be pulsating, allowing us to provide observational constraints for stellar models. Pulsating long-period sdB stars constitute a well-established class of variable stars that exhibit brightness variations with periods of up to a few hours and have amplitudes smaller than 0.1 percent of their mean brightness. The oscillation frequencies are associated with low degree (l < 3) medium to high-order (10 < n < 60) gravity(g)- modes, allowing us to investigate the deep interior of these stars. SdB asteroseismology has undergone substantial progress, thanks to the availability of space missions such as Kepler/K2 and TESS. We applied standard seismic tools for mode identification, including asymptotic period spacings and rotational frequency multiplets. For the dipole (l = 1) and quadrupole (l = 2) modes, we looked for a constant period spacing based on the results of the Kolmogorov-Smirnov and Inverse Variance tests. We computed stellar evolution models using the LPCODE stellar evolution code and computed dipole g-mode frequencies with the adiabatic nonradial pulsation code LP- PUL. Derived observational mean period spacings were then compared to the mean period spacings from detailed stellar evolution computations coupled with the adiabatic pulsation computations of g-modes. We find that the mean period spacings obtained for models with small convective cores, as predicted by a pure Schwarzschild criterion, are incompatible with the observations. The models with a standard, mod- est convective boundary mixing at the boundary of the convective core are in better agreement with the observed mean period spacings and are therefore more realistic. In the second and third part of the thesis, we aimed at searching for the hydrogen(H)-deficient pulsating pre-white dwarf stars called GW Vir stars that exhibit atmospheres rich in carbon, oxygen and helium. We processed and analyzed the high-precision TESS photometric light curves of the four target stars, and derived their oscillation frequencies. For each of these TESS targets, we obtained low- resolution spectra and fitted model atmospheres in order to derive their fundamental atmospheric parameters. We performed an asteroseismological analysis of these stars on the basis of GW Vir white dwarf evolutionary models that take into account the complete evolution of the progenitor stars. We searched for patterns of uniform period spacings in order to constrain the stellar mass of the stars, and employed a detailed model by best-matching all the observed frequencies with those computed from models. Using the high-quality data collected by the TESS space mission and follow-up spectroscopy, we discovered and characterized four new GW Vir stars. In the final part, we focused on the volume limited sample of low mass red giant stars, the progenitor systems of wide orbit hot sdB + main sequence (MS) binaries that are the product of a stable roche-lobe-overflow mechanism. With a homogeneously created list from Gaia, we aim at performing a spectroscopic survey to find binary systems that include low-mass red giants near the tip of the Red Giant Branch, which are predicted to be the direct progenitors of hot subdwarf B stars. We obtained high- resolution spectra for 88 stars out of which 38 stars were observed in two epochs in order to determine the binary fraction. Combining these measurements with DR2 ra- dial velocity and astrometric excess noise from early Data Release 3 (eDR3), we found 41 binary candidates. We presented 33 low-mass red giant stars that are in binary systems with orbital period between 100 and 900 days from both the ground base surveys and Gaia Data Release 3 (DR3). Using high-quality astrometric measurements provided by the Gaia mission coupled with high-resolution spectroscopy from the ground, we provided a powerful method to search for low-mass red giant stars in binary systems.
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    Strong gravitational lensing as a probe of structure from small to large scale
    (Universidad de Valparaíso, 2018-07) Rojas Olate, Karina; Motta, Verónica
    The gravitational lens effect occurs when the light is deflected by a gravitational field, generating multiple images or arcs. This powerful technique allows us to study structures at different scales in the universe that are usually related to different astrophysical problems. For instance, the characterization of dark objects in our galaxy (structure and mass distribution), the compact objects in the galaxy halos, the inner structure of quasars. Furthermore, it can be used to probe the cosmological model, for example through estimations of the Hubble constant (H0) and the mass distribution profile in galaxies, groups and cluster of galaxies. In this work I studied different structures that are affected or produced by grav- itational effect. In our galaxy at interstellar scale, I searched for microlensing effects in a region of the VISTA Variable in the V´ıa L´actea Survey (VVV). At galaxy-size scale, I studied the microlensing effect in lensed quasars to estimate the size (rs) and temperature profile (p) of their accretion disks and the effect of microlensing on time delay (∆t) measurements (related to H0). At cosmological scales, I performed a dynamical analysis for groups and clusters of galaxies to finally study the mass distribution profile in their halos. To reach these objectives I used visual and infrared images, spectroscopic data, models and simulations. The results presented in this thesis have been published in Rojas et al. (2014); Minniti et al. (2015); Verdugo et al. (2016); Motta et al. (2017); Courbin et al. (2018); Bonvin et al. (2018) among others, and part of the work is in preparation to be publish in Rojas et al. in prep(a,b), among others.
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    Dynamical stellar masses via high angular resolution techniques
    (Universidad de Valparaíso, 2021) Zúñiga Fernández, Sebastián; Oloffson, Johan
    Multiple stellar systems are abundant in our galaxy. Almost half of solar-like field stars have at least one companion. Multiple systems are the perfect playground to de- termine the stellar mass, which the one of the most fundamental parameter in stellar astrophysics, without having to rely heavily on models. In this thesis we present the results of detection and orbital characterisation of multiple systems in Young (∼ 5 − 100 Myr) associations. The aim is to identify binary and multiple systems in our sample and determine their dynamical masses. Ultimately, the results of this work should provide valuable information to calibrate evolutionary models of low- mass (< 0.5 M8) pre-main sequence stars. The SACY sample (Search for Association Containing Young stars) is a collection of nearby (< 200 pc) young (∼ 5 − 100 Myr) stars, mostly with estimated masses ∼ 0.1 − 1.2 M8. The sample is structured in groups consistent of separated populations known as moving group or associations, such as the β−Pic moving group and the AB Doradus association. In Chapter 2, we identify 68 spectroscopic binaries (SBs) among our sample of 410 objects and update the SB fraction of each young association. Our results hint at the possibility that the youngest associations have a higher SB fraction (∼ 30%) in com- parison with the five oldest (∼ 10%). This difference suggests could hint towards a non-universal primordial multiplicity in the youngest associations. One of the well known SB in our sample is the quadruple system HD 98800. The system is composed of two SBs orbiting each other (AaAb and BaBb), with a gas-rich disc in polar configu- ration around BaBb. We obtain new astrometric measurements using long-baseline in- frared interferometric observations with the VLTI/PIONIER instrument. Combining our new astrometry with archival observations and radial velocity measurements, we determine the orbital parameters of both subsystems. We refine the orbital solution of BaBb and derive, for the first time, the orbital solution of AaAb. In addition, we con- firm the polar configuration of the disc around BaBb. Furthermore, we present some preliminary results on astrometric measurements for seven interesting binary systems that we are monitoring with AO-imaging observations. Additionally, we also report new estimates on the astrometry of seven binaries using VLTI PIONIER observations. These astrometric measurements will be used to prepare the future work towards full orbital characterisation and dynamical masses determination in those multiple sys- tems. Finally, in Chapter 5 we describe our contribution to the commissioning of the New Adaptive Optics Module for Interferometry (NAOMI).
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    The growth of supremassive black holes in galaxies: co-evolution and rgulation of the star formation activity
    (Universidad de Valparaíso, 2021) Carraro Apablaza, Rosamaría; Arévalo, Patricia
    In this Thesis we study how the accretion of the central supermassive black hole evolves in galaxies in all their star formation life phases and through a wide range of cosmic epochs. We take two complementary approaches. First, we perform a statistical study on a large sample of galaxies from the COSMOS field where we take advantage of X- ray Chandra data to estimate black hole accretions, via a combination of stacked data and individual detections, and compare them with their star formation properties, estimated from far-infrared emission combined with ultra-violet emission. Then, we use semi-empirical models to create galaxy mock catalogs onto which we perform an analogous analysis in order to pin down which parameters control the black holes’ X-ray emission and its evolution. We find a picture in which the bulk of the black hole and stellar masses are accreted in the star forming phase through secular processes, where the average black hole ac- cretion follows a relation with stellar mass similar to the “main sequence”, i.e. the relation between the star formation rate and the stellar mass followed by star forming galaxies, having a similar evolution in time but with a more efficient accretion at high stellar masses. The starburst phase appears to have a significant enhancement of the SFR but a lesser impact on the black hole accretion, which has a samller enhancement especially at high redshift. Quiescent galaxies, on the other hand, undergo a signifi- cant decline in their star formation, while the black hole accretion is still noticeable. This observed evolution of the X-ray luminosity with time and galaxy phase is com- patible with a change in the average Eddington ratio but is mostly independent on the duty cycle. We find a super-linear relation between black hole and stellar mass which, in order to reproduce the observations, should be combined with an average Eddington ratio that depends on stellar mass. Our results point in the direction of galaxy downsizing, i.e. a fast accretion of the black hole and stellar mass at very high redshift for the most massive galaxies, followed by a steep decrease in accretion, while low-mass galaxies accrete their mass more slowly, with an accretion rate that decreases more slowly with time. On a separate note, we study the gas distribution in a sample of local active galax- ies, by analyzing their continuum and reflected X-ray light curves and reproducing the observed damping of the variations of the reflected component through Monte Carlo simulations.
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    Probing the source structure in lensed AGNs
    (Universidad de Valparaíso, 2022-04) Melo Melo, Alejandra; Motta Cifuentes, Verónica (Supervisora)
    Accurate determination of supermassive black hole masses are crucial to correctly understand the connection between supermassive black holes and their host galaxies, specially with the correlation that exists between the supermassive black hole mass and some physical parameters of the host galaxy. This connection is relatively well determined in the local universe over 4 orders of magnitude. However, at high redshifts (z > 1), due to flux limitation it is challenging to determine the physical parameters of the faintest systems. Fortunately, gravitational lensed quasars are highly magnified, and thus offers the opportunity to study a fainter population that otherwise is not accessible. In this work, I study the inner region of the lensed quasars. The mass of the black hole is determined using the single-epoch method for 15 lens systems using the Balmer lines (Hα and Hβ). In addition, I present supermassive black hole mass for MgII and CIV, and compare them with the previous masses and also with the literature. For the first time the black hole mass was obtained for WGD2038-4008 (Melo et al. 2021) and QJ0158-4325 (Melo et al. in prep I). The luminosity range obtained for all the sample was 44.1 ≤ log10(Lbol /Lsun) ≤ 47.6, which is in agreement with the correlation of Lbol vs MBH of lensed and non-lensed AGNs. In addition, chromatic microlensing was detected in three systems, which offered an alterna- tive technique to measure the accretion disk size. Our estimations does not agree with the one obtained using the single epoch method. Finally, I conclude that the new black hole masses reach a fainter and low-luminosity region in the black hole mass - luminosity plane.
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    The properties of post-novae
    (Universidad de Valparaíso, 2022-03) Fuentes Morales, Irma; Tappert, Claus
    The impact of nova eruptions on the long-term evolution of Cataclysmic Variables (CVs) is one of the least understood and intensively discussed topics in the field. A decisive ingredient to improve this would be to establish a large sample of post-novae with known properties. Novae are objects that are well studied in the maximum stage, but after the eruption a significant amount of time on large telescopes is needed to study them, due to them mostly turning into very faint objects. In order to obtain a significant sample of post-novae, Tappert et al. started a project to enlarge the sample since 2009, called “Life after eruption”. This thesis is the direct continuation of their project, which is based on observations both photometric and spectroscopically using a variety of telescopes located in Chile. The steps to recover post-novae consist of (i) identifying post-nova candidates in the field through color-color diagrams (ii) confirming them through their spectral characteristics and (iii) if possible, obtaining the orbital period through time-series data either photometrically or spectroscopically, with the ultimate goal to obtain a significant and reliable sample in order to update some general aspects of the post-nova population, such as the orbital period distribution and their spectral characteristics. In this work, we present the spectroscopic confirmation for eleven post-novae. Collecting spec- troscopic parameters from the literature including these new data, we present an updated spectral study of the post-novae. With all data from the “Life after eruption” project the observational lack of objects that erupted more than 60 years ago is significant filled. The main result points to there being no correlation between the mass transfer rate and the time since eruption, in good agree- ment with previous studies. The interpretation that strong equivalent widths would be indicators of low-mass transfer rate is not entirely correct (e.g. Patterson 1984), because they appear to be indicators of inclination rather than of the mass transfer rate. A more conclusive result for the behavior of the mass transfer can only be obtained with a larger sample of novae erupted especially more than 100 years ago. We also present an updated orbital period distribution of novae using the new orbital periods found here, identifying the false-claims ones in the literature and stated reasons why they are not reliable. We compare the observational data with a theoretical period distribution calculated using both an empirical and the classical recipe for angular momentum loss. We find that neither model reproduces the observed peak in the 3 – 4 h range, suggesting that the prescription for magnetic braking usually used in CV evolution above the period gap is not totally understood.
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    Demystifying the powering mechanism of low-luminosity active galactic nuclei
    (Universidad de Valparaíso, 2022-08) Díaz Ramírez, Yaherlyn; Arévalo, Patricia; Hernández-García, Lorena
    Despite the long history of studies of active galactic nuclei (AGN), details on the structure of the accretion mechanism are far from clear. The work presented in this thesis is directed at unveiling properties of the structures in AGN through broad- band X-ray spectroscopy, with particular emphasis on broad X-ray band using XMM- Newton+NuSTAR+Swift (0.5–110.0 keV) data. With its unprecedented spectral sensi- tivity in this energy band, the combination of these telescopes provides the key obser- vational diagnostics of the properties of the AGN X-ray source, the corona, and the surrounding gas in the accretion disk and the torus. In this thesis we focused on the study of of Low-luminosity AGN (LLAGN), aiming at disentangle their inner structure, with emphasis on the reflection and the accretion mechanism. The first part of the document is centered on the develop- ment of the methodology and its application to one particular LLAGN, NGC 3718 (L/LEdd ∼ 10−5). Developing a methodology to study properties of potential reflec- tors and explore the improvement in the spectral index estimation considering high energy data and torus or disk like reflection models. We found that the inclusion of these models and high energy data allows to place strong constraints on the geometry and physical features of the surroundings as well to obtain more restricted values of a torus and a disk reflector. Then we applied this methodology to a sample of 17 LLAGN from BASS/DR2 combining observations from XMM-Newton, NuSTAR and Swift and applying the same methodology that was previously developed in the first work in NGC 3718. From the analysis of the X-ray data of the AGN sample, we found a relation which is indicative of a change in the column density of the torus like reflector at lower ac- cretion rates. Also, we confirm an anti-correlation between Γ-Eddington ratio with smaller scatter than previously reported, thanks to the inclusion of high energy data and the reflection models. The change in the correlation Γ-λEdd at ∼10−3 that we found is in agreement with a different accretion mechanism compared with higher accretion AGN as was previously reported in the literature.
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    Non-isotropic distributions of stellar rotational velocities
    (Universidad de Valparaíso, 2021-03) Solar Yáñez, Martín; Curé, Michel (Supervisor)
    Stellar rotation is defined from the angular motion of a star about its own rotational axis and study this phenomenon is useful to constrain models of stellar formation and evolution. The equatorial velocity v is defined as the surface angular speed at latitude 0o , however, the projected rotational velocity v sin i value is one of the most straightforward and cheapest (from an observational point of view) ways to obtain the rotational velocity of a star, where i is the inclination angle between the axis of rotation with respect to the observer. This research is separated in two parts; obtain this v sin i value via Fourier Transform in an automated procedure and apply a non- isotropic distribution model for the axes on the unit sphere of observation: 1)Obtaining v sin i: There are several methods to infer v sin i data, in the case of Fourier Transform, this method consists in obtain the first zero of the Fourier Trans- form domain from a rotational kernel for the observed absorption line profile. First, an automated procedure to obtain v sin i via Fourier Transform is constructed, for multi- ple absorption lines at different epochs. The method consists in fit a Gaussian profile to the respective line and select the signal from the curve. Monte Carlo simulations are performed where theoretical lines are constructed for specific rotational velocities. Then, the noise is added and multiple repetitions are computed to analyze the consis- tence of the method. Later, our automatized Fourier Transform method is used in the BeSOS database to obtain their v sin i values. Results are in global agreement with the literature. 2) How is distributed v sin i: An integral equation that governs the two distribu- tions v and v sin i (true and apparent rotational speed distributions respectively) is given by a Fredholm integral in which an α parameter is added into the kernel of the equation to model a non-isotropic distribution, where α < 0 yields inclination angles close to the polar axis, α > 0 a non-isotropic near to the equator and α = 0 is the typical isotropic axes distribution. The true distribution is calculated via Tikhonov regularization method from the observed distribution which is estimated by a kernel density estimator. As α parameter is unknown, we made a grid of α to compute the Fredholm integral. To obtain the best α value, we minimized the mean square error of the projected kernel density estimator distribution with respect to the new grid of solutions for the Fredholm integral equation. The Monte Carlo random sampling repetitions ensures that the method, in general terms, is reliable until α ∼ 1. Theprocedure is applied to several open stellar clusters and field stars to see the behav- ior of the non-isotropy finding effectively that the different databases of stars are not isotropic rotating with respect to Earth. In summary, we have developed two novel methods; measures the v sin i values from any stellar spectrum for multiple absorption lines at different epochs where the line is broadening mainly by rotation (high rotators); the second, obtains the non-isotropy from a sample of v sin i data without any convergence criteria. As fu- ture works we want to implement this last method to binary systems (star-star or exoplanet-star) discovered by transit and also an extra parameter β can be introduced into the Fredholm integral to compute more complex distribution of axes.