Radial velocity measurements are critical in finding and confirming exoplanets. To confine the parameters of the planet we naturally want to minimise the errors on the measurement. However the observed measurement error is now on the same order as the precision of the instrument. This so called jitter is related to the stellar activity (Wright 2005), i.e. the magnetic field of the star. In this paper we investigate if we can discover any correlation between the radial velocity variation and the magnetic activity of the star using HARPSpol spectra for the two stars Epsilon Eridani and GJ674.

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean and an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell's equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere's equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles "collect" at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.

This thesis is an account of various phenomena caused by the interaction of the motion of electrically conducting fluids with magnetic fields. Such phenomena, the study of which is usually known as Magnetohydrodynamics (MHD), occur on a galactic, planetary or laboratory length scale; however in this thesis we concentrate on those phenomena which can be reproduced in the laboratory. In chapter 2 we study the laminar flow of uniformly conducting, incompressible fluids in rectangular ducts under the action of transverse magnetic fields. We begin by proving that when the duct has a constant cross-section the solution is unique and then analyse theoretically some of the curious effects on the flow of the duct's walls being electrically conducting. We find close agreement between the results of these theories and the experiments of Alty (1966) and Baylis (1966). We then analyse the flow in ducts with varying cross-sections. In chapter 3 we analyse some of the curious flows and current streamline patterns produced by placing electrodes on the non-conducting walls of a container, filled with a conducting fluid, and passing electric currents between the electrodes in the presence of a strong magnetic field. In chapter 4 we analyse some of the theoretical limitations on the use of Pitot tubes and electric potential (e.p.) probes in MHD flows, and provide some estimates of the errors to be expected. In chapter 5 we analyse the stability of parallel flows in parallel magnetic fields and also some aspects of the stability of the flows analysed in chapters 2 and 3. In chapters 6, 7 and 8 we describe our experimental apparatus, the experiments to investigate directly some of the flows analysed theoretically in chapters 2 and 3 by means of Pitot and e.p. probes, and experiments to measure the MHD errors inherent in the use of these probes. We concluded that the curious phenomena predicted actually exist. We also learnt much about the use of Pitot and e.p. probes, especially as some of the experimental results were as predicted in chapter 4.

Permanent magnets are essential components for many devices such as motors, which currently account for 45 % of global electricity consumption, generators and also superconducting magnetic bearings used for applications such as flywheel energy storage. But even the most powerful rare-earth magnets are limited to a remanent field of 1.4 T, whereas superconducting materials such as YBCO in their bulk form have the extraordinary ability to trap magnetic fields an order of magnitude higher, whilst being very compact. This gives them the potential to increase efficiency and allow significant volume and weight reductions for rotating machines despite the need for cooling. A new design of superconducting magnetic bearing has been developed which uses magnetized bulks as the field source, eliminating permanent magnets. Finite element modelling shows that the bulk – bulk design can achieve much higher force densities than existing permanent magnet – bulk designs, giving it potential to be used as a compact magnetic bearing. A system was created to magnetize bulks using a pulsed magnetic field down to 10 K and then measure levitation force. In proving the concept of the proposed design, the highest levitation forces ever reported between two superconducting bulks were measured, including a levitation force of 500 N between a 1.7 T magnetized YBCO bulk and a coaxial $MgB_{2}$ bulk tube. The biggest factor limiting the use of magnetized bulks in applications is magnetizing them in the first place. Using a pulsed magnetic field is most practical but generates excessive heat dissipation leading to a loss of flux in conventional bulk superconductors, which are 100% superconductor. Although multi-pulse techniques help maximise the trapped field, the poor thermal properties of bulk (RE)BCO are a limiting factor. New composite superconducting structures are reported which can overcome these problems by using high thermal conductivity materials, the motivation for which came from finite element modelling of the critical state coupled with heat transfer. In particular, composite structures created by cutting and stacking 12 mm wide (RE)BCO superconducting tape are shown experimentally to have exceptional field trapping ability due to superior thermal and mechanical properties compared to existing bulks. Up to 2 T was trapped in a stack of commercially available tape produced by SuperPower Inc. in the first reported pulsed magnetization of such a stack. Over 7 T was trapped between two stacks using field cooling at 4.2 K, the highest field yet trapped in such a sample.

No description available.

Interest In the vertical fault problem for electromagnetic fields has been recently revived by the papers of I. d'Erceville and G. Kunetz (1962) and D. Rankin (1962). In the derivation of his equations Rankin used d'Erceville1s theory which contains some fallacious assumptions. These have been pointed out by J.T. Weaver (1962) and also in this thesis. This thesis follows the lines of mathematical attack first employed by d'Erceville and Kunetz, and later developed by Weaver, in applying the theory of integral transforms to the partial differential equations satisfied by land and sea conductors. The problem of both a vertical fault and also a sloping fault, i.e. 0 < α < 90° where α is the angle of dip of the fault are considered. The results in the general case are Inconclusive, no solution has been found and no solution is suggested. The case of α = 90° has proved to be equally indeterminate, but a solution has been suggested, which, although it has not been proved rigourously, does not appear to violate any physical principles and also seems to represent the field equations on the surface of the land and the sea. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

A planetary nebula (PN) consists of material, mainly gas, that has been ejected from a star on the asymptotic giant branch of its life cycle. This material emits electromagnetic radiation due to photoionization and recombination, collisional and radiative excitation or free-free radiation. The envelope of material moves outwards from the central star and may take one of a variety of shapes. These shapes are believed to be sculpted by the stellar wind, magnetic fields and interactions with a binary companion. However, within a time scale of as little as 10 000 years the nebula fades from view and merges with the interstellar medium.Similar variations in the shape of planetary nebulae (PNe) can be seen in both the Galactic Bulge and Disc and in the Magellanic Clouds. It is therefore reasonable to assume that the shaping process is universal. By classifying PNe by morphology and relating those shapes to other nebular properties we have attempted to derive information about that shaping process.We have used photometric narrowband observations of a sample of PNe listed in the Strasbourg-ESO Catalogue of Galactic Planetary Nebulae to investigate the relationship between PN morphology and the other PN characteristics. The high resolution images were made using ESO's New Technology Telescope and the Hubble Space Telescope. The information we could obtain directly from the observations was augmented by information in the literature in order to address that question. The observations were used to classify the morphologies of 154 PNe, to estimate the sizes of 138 of those nebulae that we considered to lie within the Galactic Bulge, to determine the orientations of 130 of those Bulge nebulae and to derive photometric fluxes for the 69 PNe which had observations of standard stars made during the same night. Information on central star binarity, nebular abundances and radial and expansion velocity was obtained from the literature.Our photometrically derived PNe line fluxes were used to verify 59 H-beta and 69 [OIII] catalogued values (which were obtained using spectroscopy). We found sufficient discrepancy between the values for 9 PNe to merit a further check taking place.We found no distinguishing relationship between PN morphology and any of PN size, radial velocity, or angular location within the Bulge. The abundances of He and O, and the N/O ratio, are generally lower in bipolar nebulae than in those nebulae with no apparent internal structure. We are unable to come to any conclusion as to a relationship between PN morphology and stellar metallicity.Given the short lifespan of PNe and the age of the Bulge it appears that almost all PNe in the Bulge must be associated with low mass stars. The high ratio of bipolar PNe we found in our Bulge sample suggests that, at least within the Bulge, bipolar nebulae are not necessarily associated with high mass stars. Our results show that unlike the orientations of other types of PNe the orientations of the bipolar nebulae in the Bulge are not randomly distributed. Measured to a line tip to tip along the lobes they peak and have their mean approximately along the Galactic Plane. This suggests that the bipolar PNe originate in a different environment from other morphological types, perhaps related to binary separation. However, we find that bipolarity does not imply common-envelope evolution. If the hypothesis that bipolar nebulae are formed in binary star systems is correct, binary systems in the Galactic Bulge have angular momentum vectors that are preferentially aligned along the Galactic Plane. As the orientation appears to be unrelated to lobe size and hence nebular age, the alignment implies that the non-random nature of the angular momentum vectors originated at the time the Bulge stellar population formed. We suggest that it is due to the direction and strength of the ambient magnetic fields.

L'augmentation du nombre de fonctions électriques disponibles dans les systèmes embarqués amène de nouvelles contraintes d'encombrement et de masse de leurs alimentations. Pour adresser ces problèmes, la miniaturisation et l'intégration des convertisseurs statiques sont donc des thématiques importantes de recherche qui aboutissent à de nombreuses évolutions technologiques et structurelles dont l'apparition de convertisseurs statiques à fréquence de fonctionnement élevée permettant la réduction des éléments passifs du convertisseurs.Ces avancées s'accompagnent cependant d'une augmentation des niveaux de perturbations électromagnétiques générés par le système. Afin de les diminuer, l'insertion de filtres CEM dans le système est nécessaire. Leurs performances sont fortement liées au contrôle de leurs éléments parasites. Les modèles développés jusqu'à présent concernent pour la plupart les effets conduits et l'évaluation de l'impact des phénomènes rayonnés est souvent ignoré ou au mieux basé sur des modèles simplistes. Un des objectifs de cette thèse est donc d'apporter un degré de complexification plus élevé des modèles de rayonnement des composants magnétiques utilisés dans les filtres CEM, tant par une approche par modélisation numérique que par la mise en oeuvre d'un modèle analytique.Dans un premier temps, une étude poussée du rayonnement magnétique de composants simples, les inductances toriques de mode différentiel, a été réalisée. Cette étude a débouché sur la mise en évidence des paramètres critiques déterminant la topologie du champ magnétique rayonné dans l'environnement proche du composant. Le résultat majeur de cette étude est l'importance de la répartition du bobinage autour du circuit magnétique sur le champ magnétique rayonné. De nouveaux modèles ont été proposés pour permettre la prédiction des champs proches rayonnés pour une gamme de fréquence inférieure à la résonance propre du composant.Par la suite, un modèle analytique fin du rayonnement magnétique des inductances de mode commun a été proposé. Ce modèle permet de déterminer \emph{a priori} le rayonnement magnétique proche du composant. Les études menées par la suite ont permis de relier les effets observés en rayonné au phénomènes conduits qui apparaissent dans ces composants notamment pour expliquer certains effets de transfert de mode (commun/différentiel).Dans une dernière partie, une étude de ces composants en susceptibilité électromagnétique (EM) a été menée. Elle a permis de rendre compte de l'influence d'une onde incidente de champ magnétique sur les composants étudiés et de valider les modèles proposés via une approche basée sur la réciprocité EM: la direction privilégiée de rayonnement est aussi celle de couplage facile pour un champ magnétique externe. / The number of electronic devices in embedded systems is constantly increasing and their contribution to volume and weight is a major concern. In order to solve these issues, a large research effort is devoted to volume reduction and power converters' integration. This lead to constant technological evolution including the appearance of high frequency power electronic converters allowing the reduction of the volume of passive components.However, due to the increase of operating frequencies and the minimization of inter-components distances, the electromagnetic radiations generated by these systems become more important. In order to decrease this interference, EMI filters are often necessary. Their performances are often related to the value of parasitic elements in the filter which must therefore be controlled. Nonetheless most of the existing models focus on conducted electromagnetic interference (EMI) and the impact of radiated phenomena is often ignored or greatly simplified. This work will therefore focus on developing highly accurate radiation models for magnetic components commonly used in EMI filters using both numeric and analytic tools.First, the magnetic fields radiated by differential mode (MD) toroidal coils, which belong to the basic magnetic components, will be thoroughly studied. This study highlighted the critical parameters determining the near-field topology. The main result is the discovery of the impact of the winding's layout around the magnetic core on the radiated magnetic field. New models have been developed in order to predict the radiated near field.Then, an accurate analytic model of the the magnetic radiation of common-mode (CM) chokes has been developed. It allows the prediction of the magnetic near-field. The application of the model lead to the correlation between radiated phenomena and conducted effects existing in these components. The importance of the winding on CM to DM mode coupling has therefore been highlighted.Finally, the electromagnetic (EM) susceptibility of these components has been studied. This work describes the influence of an external magnetic field on the components and validates the radiation models developed using the principle of EM reciprocity. It has been shown that the easy directions are the same for both the radiated and the coupled phenomena.

Nesta tese, investigamos a discrepância existente entre o número de galáxias satéli-tes da Via Láctea que é previsto e aquele que é observado, questão conhecida como ``problema da falta de satélites\'\' (PFS). Este problema pode ser reformulado em termos de um desacordo entre a função de luminosidades das galáxias satélites (FLS) que é estimada a partir de dados observacionais e a FLS predita por modelos numéricos de formação de galáxias. Nós revisamos tanto propriedades observacionais da população de satélites quanto a teoria associada à modelagem da formação de galáxias e estruturas. Para abordar o PFS, estudamos diferentes soluções possíveis. Nós desenvolvemos uma modificação simples ao potencial do inflaton usual e mostramos que esta leva a uma redução no número de halos de matéria escura de pequena massa. Nós usamos, então, um modelo semi-analítico de formação de galáxias para confirmar que supressões similares do espectro de potências de pequena escala produzem uma FLS com a forma correta. Em uma outra direção, nós discutimos outros mecanismos astrofísicos capazes de reduzir o número de galáxias pequenas, especificamente: os ventos gerados por explosões de supernovas e o aquecimento do meio intergalático durante a reionização do Universo. Finalmente, nós estudamos como um campo magnético primordial pode influenciar a formação de galáxias de pequena massa. Para isso, nós inicialmente mostramos que a pressão devida a um campo magnético leva a uma alteração significativa na massa de filtragem, levando a uma importante supressão na acresção de gás por galáxias de baixa massa. Introduzindo estas modifi-cações em um modelo numérico de formação de galáxias, mostramos que, para valo-res realistas de intensidade de campo, a pressão devido ao campo magnético leva a um bom acordo entre a FLS prevista e observada. / In this thesis we investigate the discrepancy between the predicted and observed number of satellite galaxies in the Milky Way, known as ``the missing satellites problem\'\' (MSP). This problem can be translated into the disagreement between the satellite luminosity function (SLF), which is estimated from the observational (particularly the SDSS) data and the SLF predicted by numerical models of galaxy formation. We review both the observational properties of the satellite population and the essentials of galaxy and structure formation modelling. To tackle the MSP, we study different possible solutions. We develop a small modification to the usual chaotic inflaton potential and show that it leads to a reduction in the number of small mass haloes. We use a semi-analytic model of galaxy formation to confirm that suppressions of the small scale power spectrum can produce a SLF with the correct shape. In a different direction, we discuss other astrophysical mechanisms that can reduce the number of small mass galaxies, namely: the outflows generated by supernovae explosions and the heating of the intergalactic medium during the reionization of the Universe. Finally, we study how a primordial magnetic field can influence the formation of small mass galaxies. We first find that small primordial magnetic field significantly change the filtering mass, leading to an important suppression in the gas accretion by small mass haloes. ( The filtering mass is the mass for which the baryon accretion is reduced to approximately 1/2 its normal value.) Introducing these modifications in the galaxy formation model, we show that for realistic field strengths, the pressure due to the magnetic field can result in a good match between the observed SLF and the model predictions.

Neste trabalho investigamos os efeitos de choques (induzidos por supernovas) e de turbulência magneto-hidrodinâmica no processo de formação estelar. Primeiramente, considerando o impacto de um remanescente de supernova (RSN) com uma nuvem neutra magnetizada derivamos analiticamente um conjunto de condições através das quais estas interações podem levar à formação de estruturas densas capazes de tornarem-se gravitacionalmente instáveis e formar estrelas. Usando estas condições, construímos diagramas do raio do RSN, $R_$, versus a densidade inicial da nuvem, $n_c$, os quais delimitam um domínio no espaço paramétrico onde a formação estelar é permitida. Estes diagramas foram testados através de simulações numéricas magneto-hidrodinâmicas tridimensionais (3D MHD) onde seguimos a evolução espaço-temporal da interação de um RSN com uma nuvem auto-gravitante. Verificamos que a análise numérica está de acordo com os resultados previstos pelos diagramas. Observamos ainda que a presença de um campo magnético fraco, $\\sim 1 \\; \\mu$G, inicialmente homogêneo e perpendicular à velocidade de impacto do RSN, resulta em uma pequena diminuição da região permitida para formação estelar nos diagramas quando comparado a diagramas para nuvens não magnetizadas. Já um campo magnético mais intenso ($\\sim 10\\;\\mu$G) causa um encolhimento significativo nestas, como esperado. Embora derivados de considerações analíticas simples estes diagramas fornecem uma ferramenta útil para identificar locais onde a formação estelar pode ter sido induzida pelo impacto de uma onda de choque de SN. Aplicações a algumas regiões de nossa Galáxia (como a Grande Concha de CO na direção de Escorpião e a Nuvem Periférica 2 na direção da constelação de Cassiopeia) mostram que a formação estelar nestes locais pode ter sido induzida por uma onda de choque de um RSN em passado recente, quando se consideram valores específicos para as condições iniciais das nuvens impactadas.%, para valores específicos de raio do RSN e uma faixa de densidades iniciais possíveis para estas nuvens. Avaliamos também a eficiência de formação estelar efetiva para estas interações e encontramos que esta é geralmente menor do que os valores observados para a nossa Galáxia (sfe $\\sim$ 0.01$-$0.3). Este resultado é consistente com outros trabalhos da literatura e também sugere que este mecanismo, embora poderoso para induzir a formação de estruturas, turbulência supersônica e eventualmente formação estelar local, não parece ser suficiente para induzir a formação estelar global em galáxia normais, nem mesmo quando o campo magnético é desprezado. Além do estudo acima, exploramos ainda a formação estelar considerando a injeção prévia de turbulência (por um mecanismo físico arbitrário) em nuvens magnetizadas. Para uma nuvem ou glóbulo de nuvem molecular formar estrelas deve haver transporte de fluxo magnético das regiões internas mais densas para as regiões externas menos densas da nuvem, de outra forma o colapso poderá ser impedido pela força magnética. Consideramos aqui um novo mecanismo. Reconexão magnética rápida, a qual ocorre em presença de turbulência, pode induzir um processo de difusão eficiente dos campos magnéticos. Neste trabalho investigamos esse processo por meio de simulações numéricas 3D MHD e suas implicações para a formação estelar, estendendo um estudo prévio realizado para nuvens de simetria cilíndrica e sem auto-gravidade (Santos-Lima et al. 2010). Aqui consideramos nuvens mais realistas com potenciais gravitacionais esféricos (devido a estrelas embebidas) e também levando em conta os efeitos da auto-gravidade do gás. Determinamos, pela primeira vez, quais as condições em que o transporte do campo magnético devido à difusão por reconexão turbulenta leva uma nuvem inicialmente subcrítica a tornar-se super-crítica e capaz de colapsar para formar estrelas. Nossos resultados indicam que a formação de um núcleo supercrítico é resultado de uma complexa interação entre gravidade, auto-gravidade, intensidade do campo magnético e turbulência aproximadamente trans-sônica e trans-Alfvénica. Em particular, a auto-gravidade favorece a difusão do campo magnético por reconexão turbulenta e, como resultado, seu desacoplamento do gás colapsante torna-se mais eficiente do que quando apenas um campo gravitacional externo está presente. Demonstramos que a difusão por reconexão turbulenta é capaz de remover fluxo magnético da maior parte das nuvens investigadas, porém somente uma minoria desenvolve núcleos aproximadamente críticos ou super-críticos, o que é consistente com as observações. A formação destes é restrita ao seguinte intervalo de condições iniciais para as nuvens: razão pressão térmica-pressão magnética, $\\beta \\sim 1$ a $3$, razões entre a energia turbulenta e a energia magnética $E_/E_\\sim 1.62$ a $2.96$, e densidades $50 < n < 140$ cm$^$, quando consideramos massas estelares M$_{\\star}\\sim 25$M$_{\\odot}$, implicando uma massa total da nuvem (gás + estrelas) M$_\\lesssim 120$M$_{\\odot}$. / In this work, we have investigated the effects of shocks (induced by supernovae) and magnetohydrodynamical turbulence in the process of star formation. Considering first, the impact of a supernova remnant (SNR) with a neutral magnetized cloud we derived analytically a set of conditions through which these interactions can lead to the formation of dense structures able to become gravitationally unstable and form stars. Using these conditions, we have built diagrams of the SNR radius, $R_{SNR}$, versus the initial cloud density, $n_c$, that constrain a domain in the parameter space where star formation is allowed. These diagrams have been also tested by means of three-dimensional magneto-hydrodynamical (3D MHD) numerical simulations where the space-time evolution of a SNR interacting with a self-gravitating cloud is followed. We find that the numerical analysis is in agreement with the results predicted by the diagrams. We have also found that the effects of a weak homogeneous magnetic field ($\\sim 1 \\; \\mu$G) approximately perpendicular to the impact velocity of the SNR results only a small decrease of the allowed zone for star formation in the diagrams when compared with the diagrams with non-magnetized clouds. A larger magnetic field ($\\sim 10\\;\\mu$G) on the other hand, causes a significant shrinking of the star formation zone, as one should expect. Although derived from simple analytical considerations, these diagrams provide a useful tool for identifying sites where star formation could be triggered by the impact of a SN blast wave. Applications of them to a few regions of our own Galaxy (e.g., the large CO shell in the direction of Scorpious, and the Edge Cloud 2 in the direction of the Cassiopeia constellation) have revealed that star formation in those sites could have been triggered by shock waves from SNRs in a recent past, when considering specific values of the SNR radius and the initial conditions in the neutral clouds. We have also evaluated the effective star formation efficiency for this sort of interaction and found that it is generally smaller than the observed values in our Galaxy (sfe $\\sim$ 0.01$-$0.3). This result is consistent with previous work in the literature and also suggests that the mechanism presently investigated, though very powerful to drive structure formation, supersonic turbulence and eventually, local star formation, does not seem to be sufficient to drive $global$ star formation in normal star forming galaxies, not even when the magnetic field is neglected. Besides the study above, we have also explored star formation considering a priori injection of turbulence (by an arbitrary physical mechanism) in magnetized clouds. For a molecular cloud clump to form stars some transport of magnetic flux may be required from the denser, inner regions to the outer regions of the cloud, otherwise this can prevent the gravitational collapse. We have considered here a new mechanism. Fast magnetic reconnection which takes place in the presence of turbulence can induce a process of reconnection diffusion of the magnetic field. In this work, we have investigated this process by means of 3D MHD numerical simulations considering its implications on star formation. We have extended a previous study which considered clouds with cylindrical geometry and no self-gravity (Santos-Lima et al. 2010). Here, we considered more realistic clouds with spherical gravitational potentials (from embedded stars) and also accounted for the effects of the gas self-gravity. We demonstrated that reconnection diffusion takes place. We have also, for the first time, determined the conditions under which reconnection diffusion is efficient enough to make an initially subcritical cloud clump to become supercritical and collapse. Our results indicate that the formation of a supercritical core is regulated by a complex interplay between gravity, self-gravity, magnetic field strength and nearly transonic and trans-Alfvénic turbulence. In particular, self-gravity helps reconnection diffusion and, as a result, the magnetic field decoupling from the collapsing gas becomes more efficient than in the case when only an external gravitational field is present. We have demonstrated that reconnection diffusion is able to remove magnetic flux from most of the collapsing clumps analysed, but only a few of them develop nearly critical or supercritical cores, which is consistent with the observations. Their formation is restricted to a range of initial conditions for the clouds as follows: thermal to magnetic pressure ratios $\\beta \\sim$ 1 to 3, turbulent to magnetic energy ratios $E_{turb}/E_{mag}\\sim 1.62$ to $2.96$, and densities $50 < n < 140$ cm$^{-3}$, when considering stellar masses M$_{\\star}\\sim 25$M$_{\\odot}$, implying total (gas+stellar) masses M$_{tot} \\lesssim 120$M$_{\\odot}$.