A evolução do lítio em estrelas do tipo-solar através do diagrama HR

Important advances have been made along the last decade in the study of the lithium behavior in solar-type stars. Among the most important discoveries what attracts attention is that the distribution of lithium abundance in the late F-type giant stars tends to be discontinuous, at the same time of a sudden decline in rotation and a gradual decline according to the temperature for giant red stars of such spectral type. Other studies have also shown that synchronized binary systems with evolved components seem to keep more of their original lithium than the unsynchronized systems. evertheless, the connection between rotation and lithium abundance as well as the role of tidal effects on lithium dilution seem to be more complicated matters, depending on mass, metallicity and age. This work brings an unprecedented study about the behavior of lithium abundance in solartype evolved stars based on an unique sample of 1067 subgiant, giant and supergiant stars, 236 of them presenting spectroscopic binary characteristics, with precise lithium abundance and projected rotational speed. Now the lithium-rotation connection for single and binary evolved stars is analyzed taking into account the role of mass and stellar age

Evolução da atividade cromosférica, abundância de lítio e rotação das estrelas análogas e gêmeas solares

The study of solar-type stars also includes the familiar solar analogs and twins. These objects have been one of the major research subjects in astrophysics nowadays. A direct comparison of solar activity with chromospheric activity indices for a set of stars very similar to the Sun (twins and analogs) provides an excellent opportunity to study the evolution of stellar activity on timescales of the order of the lifetime on the main sequence. This work deals with the relationship between the abundance of lithium, chromospheric activity, X-ray emission and rotation period in terms of stellar ages. We explore the influence of stellar evolution in the global properties of the stars and the aspects linked to its coronal, chromospheric and magnetic activity. Our main objective is to probe the law of decay of each of these parameters based on a sample of stars classified as well-connected as analogs stars and solar twins.

Uma análise teórica da evolução da rotação estelar

In the past 50 years, large efforts have been made toward the understanding of the stellar evolution. In the observational context, large sets of precise measurements of projected rotational velocity were produced, in particular by the Natal and Geneva groups. From these data, it is now possible to establish the behavior of stellar rotation from the turnoff to the red giant branch. In addition, these data have shown the role of tidal effects on stellar rotation in close binary systems. Nevertheless, relatively little attention has been paid to theoretical studies on the evolution of rotation along the HR Diagram, a topic itself directly associated to the evolution of the stars. Basically, there are two reasons for such a fact, (i) spherical symmetry is not assumed, what leads to a substantial increase in the numerical complexity of equations and (ii) non rotating models have been very successful in explaining relevant observational data, including the mass-luminosity relation and chemical abundances. In spite of these facts, it is clear that considerable work remains to be done on the role of rotation in the later stages of the evolution, where clear disagreements arise from confrontations between theoretical predictions and observations. In the present work we study the evolutionary behavior of stellar rotation along the HR Diagram, taking into account constraint conditions issued from recent observational survey of rotational velocity carried out with high precision procedures and new evolutionary codes

Sobre a natureza dos processos físicos de aquecimento da atmosfera de estrelas do tipo solar

In the present work, we have studied the nature of the physical processes of the coronal heating, considering as basis significant samples of single and binary evolved stars, that have been achieved with the ROSAT satellite. In a total of 191 simple stars were studied, classified in the literature as giants with spectral type F, G and K. The results were compared with those obtained from 106 evolved stars of spectral type F, G and K, which belong to the spectroscopic binary systems. Accurate measurements on rotation and information about binarity were obtained from De Medeiros s catalog. We have analysed the behavior of the coronal activity in function of diverse stellar parameters. With the purpose to better clarify the profile of the stars evolution, the HR diagram was built for the two samples of stars, the single and the binary ones. The evolved traces added in the diagram were obtained from the Toulouse-Geneve code, Nascimento et al. (2000). The stars were segregated in this diagram not only in range of rotational speed but also in range of X-ray flux. Our analysis shows clearly that the single stars and the binary ones have coronal activity controlled by physical process independent on the rotation. Non magnetic processes seem to be strongly influencing the coronal heating. For the binary stars, we have also studied the behavior of the coronal emission as a function of orbital parameters, such as period and eccentricity, in which it was revealed the existence of a discontinuity in the emission of X-rays around an orbital period of 100 days. The study helped to conclude that circular orbits of the binary stars are presented as a necessary property for the existence of a higher level ofX-rays emission, suggesting that the effect of the gravitational tide has an important role in the coronal activity level. When applied the Kolmogorov-Smirnov test (KS test ) for the Vsini and FX parameters to the samples of single and binary stars, we could evidence very relevant aspects for the understanding of the mechanisms inherent to the coronal activity. For the Vsini parameter, the differences between the single stars and the binary ones for rotation over 6.3 km/s were really remarkable. We believe, therefore, that the existence of gravitational tide is, at least, one of the factors that most contribute for this behavior. About the X-rays flux, the KS test showed that the behavior of the single and the binary stars, regarding the coronal activity, comes from the same origin

Parâmetros físico-químicos de estrelas nos campos de exoplanetas do satélite corot

A rotação estelar é um dos mais importantes observáveis da evolução estelar. Neste sentido, o satélite CoRoT representa uma oportunidade única de medir os períodos rotacionais para uma amostra de estrelas estatisticamente robusta, oferecendo dados absolutamente necessários para o estudo da rotação e seu papel na evolução estelar. Para conseguir isto, um passo fundamental é a caracterização física e química das estrelas observadas pelo CoRoT, especificamente devido ao fato de que o cálculo de períodos rotacionais confiáveis é um trabalho difícil sem a ajuda dos parâmetros estelares. Desta forma, foi elaborado um importante seguimento observacional das estrelas nos campos do CoRoT do anticentro LRa01 e do centro LRc01, permitindo a correta identificação dos períodos que reflitam a modulação rotacional. Nesta tese de doutorado são apresentados os resultados de tal seguimento. Parâmetros físicos e químicos, tais como temperatura efetiva Teff , gravidade superficial log(g), velocidade de microturbulência Vmic, abundância de ferro [Fe/H], velocidade de rotação projetada Vsin(i), e abundância de lítio A(Li) são apresentados para uma amostra de 116 estrelas dos campos CoRoT. Elas se encontram em diferentes estágios evolutivos, desde a sequência principal (SP) até o ramo das gigantes vermelhas (GV). As observações foram feitas utilizando os espectrógrafos UVES (VLT) e HYDRA (CTIO). Para a derivação de tais parâmetros foram utilizados o programa TurboSpectrum e os modelos de atmosfera de MARCS. Paralelamente, velocidades rotacionais Vsin(i) foram obtidas a partir do ajuste dos perfis observados e sintéticos das linhas de ferro e por meio de uma calibração de função de correlação cruzada (CCF). Períodos rotacionais Prot para 77 estrelas da amostra foram obtidos a partir das curvas de luz do satélite CoRoT. Extensas tabelas destes parâmetros e seus respectivos erros são apresentadas. Foram encontradas diferenças nas distribuições de Teff , [Fe/H] e estágios evolutivos entre os diferentes campos do CoRoT, indicando possíveis efeitos de seleção na amostra, assim como a existência de diferentes populações estelares do disco Galáctico. Por outro lado, o comportamento rotacional e as abundâncias de lítio não apresentam diferenças entre estrelas de parâmetros físicos similares, mas que pertencem a diferentes campos do CoRoT. A partir da análise de temperaturas, foi encontrada uma maior extinção por avermelhamento para estrelas do CoRoT localizadas no campo LRc01, assim como um gradiente deste valor em função da distância. Os resultados mostram que as abundâncias de lítio, as velocidades de rotação e os períodos rotacionais apresentam o mesmo comportamento descrito na literatura. Por outro lado, é apresentada pela primeira vez a relação que existe entre o lítio e o período de rotação em diferentes estágios evolutivos, mostrando, tal como era esperado, que ambas as grandezas possuem uma anticorrelação. Também é apresentada a evolução simultânea da rotação e do lítio, e foram calculadas relações que permitem obter valores médios de A(Li) como função da temperatura efetiva e do período rotacional. Os dados apresentados nesta tese de doutorado representam um importante ponto de partida para serem utilizados como uma amostra de calibração para diferentes programas no contexto da missão do satélite CoRoT, uma vez que a lista de estrelas aqui analisadas são parte das mais brilhantes que compõem o campo Exo do CoRoT

A evolução da rotação estelar na vizinhança solar

Different studies point for an rotation age link following a α tα relationship. The value of the α -parameter has a strong role on the evolutionary behaviour of rotation, because it indicates how strong is the spindown once stars evolve. The well known Skumanich s relation α t −1/2, which is consistent with simple theories of angular momentum loss from rotating stars with magnetic fields and winds, is one of the best accepted. Nevertheless, several studies show clearly that such a relation cannot hold for stars much younger or much older than the Pleiades (100 Mega years) without leading to velocities much greater or much lower than those presently observed. The present study aims at improving this picture on the basis of an enlarged analyses taking into account the role of mass and metallicity on the rotation age relation, based on an unprecedented sample of about 14 000 stars in the solar neighbourhood. From this new approach we show that the α parameter it depends strongly on the stellar age and, by consequence, on the metallicity. In addition, one observes a strong dependence of the referred parameter on the single or binary status of the stars

Um estudo da abundância de lítio, rotação, atividade cromosférica e magnetismo das estrelas análogas e gêmeas solares

The study physical process that control the stellar evolution is strength influenced by several stellar parameters, like as rotational velocity, convective envelope mass deepening, and magnetic field intensity. In this study we analyzed the interconnection of some stellar parameters, as Lithium abundance A(Li), chromospheric activity and magnetic field intensity as well as the variation of these parameters as a function of age, rotational velocity, and the convective envelope mass deepening for a selected sample of solar analogs and twins stars. In particular, we analyzed the convective envelope mass deepening and the dispersion of lithium abundance for these stars. We also studied the evolution of rotation in subgiants stars, because its belong to the following evolutionary stage of solar analogs, and twins stars. For this analyze, we compute evolutionary models with the TGEC code to derive the evolutionary stage, as well as the convective envelope mass deepening, and derive more precisely the stellar mass, and age for this 118 stars. Our Investigation shows a considerable dispersion of lithium abundance for the solar analogs stars. We also realize that this dispersion is not by the convective zone deep, in this way we observed which the scattering of A(Li) can not be explained by classical theories of mixing in the convective zone. In conclusion we have that are necessary extra-mixing process to explain this decrease of Lithium abundance in solar analogs and twins stars. We analyzed the subgiant stars because this are the subsequent evolutionary stage after the solar analogs and twins stars. For this analysis, we compute the rotational period for 30 subgiants stars observed by Co- RoT satellite. For this task we apply two different methods: Lomb-Scargle algorithm, and the Plavchan Periodogram. We apply the TGEC code we compute models with internal distribution of angular momentum to confront the predict results with the models, and the observational results. With this analyze, we showed which solid body rotation models are incompatible with the physical interpretation of observational results. As a result of our study we still concluded that the magnetic field, convective envelope mass deepening, and internal redistribution of angular momentum are essential to explain the evolution of low-mass stars, and its observational characteristics. Based on population synthesis simulation, we concluded that the solar neighborhood presents a considerable quantity of solar twins when compared with the discovered set nowadays. Altogether we foresee the existence around 400 solar analogs in the solar neighborhood (distance of 100 pc). We also study the angular momentum of solar analogs and twins, in this study we concluded that added angular momentum from a Jupiter type planet, putted in the Jupiter position, is not enough to explain the angular momentum predicted by Kraft law (Kraft 1970)

Rotação diferencial em estrelas do tipo solar

Stellar differential rotation is an important key to understand hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors as well as for a better treatment of tides in close binary and star-planet systems. The space-borne high-precision photometry with MOST, CoRoT, and Kepler has provided large and homogeneous datasets. This allows, for the first time, the study of differential rotation statistically robust samples covering almost all stages of stellar evolution. In this sense, we introduce a method to measure a lower limit to the amplitude of surface differential rotation from high-precision evenly sampled photometric time series such as those obtained by space-borne telescopes. It is designed for application to main-sequence late-type stars whose optical flux modulation is dominated by starspots. An autocorrelation of the time series is used to select stars that allow an accurate determination of spot rotation periods. A simple two-spot model is applied together with a Bayesian Information Criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty are obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov Chain (hereafter MCMC) approach. We apply our method to the Sun and eight other stars for which previous spot modelling has been performed to compare our results with previous ones. The selected stars are of spectral type F, G and K. Among the main results of this work, We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite to a successful measurement of differential rotation through spot modelling. For a proper MCMC analysis, it is necessary to take into account the strong correlations among different parameters that exists in spot modelling. For the planethosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation. We confirm that the Sun as a star in the optical passband is not suitable for a measurement of the differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison with more sophisticated procedures used until now in the study of stellar differential rotation

Estudo sistemático de estrelas variáveis na era dos grandes surveys

The interest in the systematic analysis of astronomical time series data, as well as development in astronomical instrumentation and automation over the past two decades has given rise to several questions of how to analyze and synthesize the growing amount of data. These data have led to many discoveries in the areas of modern astronomy asteroseismology, exoplanets and stellar evolution. However, treatment methods and data analysis have failed to follow the development of the instruments themselves, although much effort has been done. In present thesis, we propose new methods of data analysis and two catalogs of the variable stars that allowed the study of rotational modulation and stellar variability. Were analyzed the photometric databases fromtwo distinctmissions: CoRoT (Convection Rotation and planetary Transits) and WFCAM (Wide Field Camera). Furthermore the present work describes several methods for the analysis of photometric data besides propose and refine selection techniques of data using indices of variability. Preliminary results show that variability indices have an efficiency greater than the indices most often used in the literature. An efficient selection of variable stars is essential to improve the efficiency of all subsequent steps. Fromthese analyses were obtained two catalogs; first, fromtheWFCAMdatabase we achieve a catalog with 319 variable stars observed in the photometric bands Y ZJHK. These stars show periods ranging between ∼ 0, 2 to ∼ 560 days whose the variability signatures present RR-Lyrae, Cepheids , LPVs, cataclysmic variables, among many others. Second, from the CoRoT database we selected 4, 206 stars with typical signatures of rotationalmodulation, using a supervised process. These stars show periods ranging between ∼ 0, 33 to ∼ 92 days, amplitude variability between ∼ 0, 001 to ∼ 0, 5 mag, color index (J - H) between ∼ 0, 0 to ∼ 1, 4 mag and spectral type CoRoT FGKM. The WFCAM variable stars catalog is being used to compose a database of light curves to be used as template in an automatic classifier for variable stars observed by the project VVV (Visible and Infrared Survey Telescope for Astronomy) moreover it are a fundamental start point to study different scientific cases. For example, a set of 12 young stars who are in a star formation region and the study of RR Lyrae-whose properties are not well established in the infrared. Based on CoRoT results we were able to show, for the first time, the rotational modulation evolution for an wide homogeneous sample of field stars. The results are inagreement with those expected by the stellar evolution theory. Furthermore, we identified 4 solar-type stars ( with color indices, spectral type, luminosity class and rotation period close to the Sun) besides 400 M-giant stars that we have a special interest to forthcoming studies. From the solar-type stars we can describe the future and past of the Sun while properties of M-stars are not well known. Our results allow concluded that there is a high dependence of the color-period diagram with the reddening in which increase the uncertainties of the age-period realized by previous works using CoRoT data. This thesis provides a large data-set for different scientific works, such as; magnetic activity, cataclysmic variables, brown dwarfs, RR-Lyrae, solar analogous, giant stars, among others. For instance, these data will allow us to study the relationship of magnetic activitywith stellar evolution. Besides these aspects, this thesis presents an improved classification for a significant number of stars in the CoRoT database and introduces a new set of tools that can be used to improve the entire process of the photometric databases analysis

Aglomerado estelar M67: processos de diluição e a evolução do Momentum Angular

Galactic stellar clusters have a great variety of physical properties that make valuable probes of stellar and galactic chemical evolution. Current studies show a discrepancy between the standard evolutionary models and observations, mainly considering the level of mixing and convective dilution of light elements, as well as to the evolution of the angular momentum. In order to better settle some of these properties, we present a detailed spectroscopic analysis of 28 evolved stars, from the turn-off to the RGB, belonging to the stellar open cluster M67. The observations were performed using UVES+FLAMES at VLT/UT2. We determined stellar parameters and metallicity from LTE analysis of Fe I and Fe II lines between 420 1100 nm. The Li abundance was obtained using the line at 6707.78 ˚A, for the whole sample of stars. The Li abundances of evolved stars of M67 present a gradual decreasing when decreasing the effective temperature. The Li dilution factor for giant stars of M67 with Teff ∼ 4350K is at least 2300 times greater than that predicted by standard theory for single field giant stars. The Li abundance as a function of rotation exhibits a good correlation for evolved stars of M67, with a much smaller dispersion than the field evolved stars. The mass and the age seem to be some of the parameters that influence this connection. We discovered a Li-rich subgiant star in M67 (S1242). It is member of a spectroscopic binary system with a high eccentricity. Its Li abundance is 2.7, the highest Li content ever measured for an evolved star in M67. Two possibilities could explain this anomalous Li content: (i) preservation of the Li at the post turn off stage due to tidal effects, or (ii) an efficient dredge-up of Li, hidden below the convective zone by atomic diffusion occurring in the post turn off stage. We also study the evolution of the angular momentum for the evolved stars in M67. The results are in agreement with previous studies dedicated to evolved stars of this cluster, where stars in the same region of the CM-diagram have quite similar rotations, but with values that indicate an extra breaking along the main sequence. Finally, we analize the distributions of the average rotational velocity and of the average Li abundance as a function of age. With relation to the average Li abundances, stars in clusters and field stars present the same type of exponencial decay law t−β. Such decay is observed for ages lesser than 2 Gyr. From this age, is observed that the average Li abundance remain constant, differently of the one observed in the rotation age connection, where the average rotational velocity decreases slowly with age

Lítio e rotação nas estrelas análogas solares: análise teórica das observações

The projected rotational velocity together with lithium abundance and the onset of the dilution by the deepening in mass of the convective envelope provide a key tool to investigate the so far poorly understood processes at work in stellar interiors of solar-analog stars. To investigate the link between abundances, convection and rotational velocities in solar-analog G dwarf stars, we study a bona fide sample of 118 selected solar-analog G dwarf stars presenting measured lithium abundances, rotational velocities, and fundamental parameters together with computed evolutionary tracks (Toulouse-Geneva code) for a range of stellar masses around 1 M and metallicity consistent with the solar-analog range. The aim of this work is to build up an evolution of lithium and rotation as a function of stellar age, mass, effective temperature, and convection. We analyze the evolutionary status of the sample of 118 solar-analog G dwarf in the HR diagram based on Hipparcos data and using a grid of stellar models in the effective temperature and mass range of the solar-analog stars. We discuss the deepening (in mass) of the convective envelope and the influence on the Li abundances and projected rotational velocities. We determined the stellar mass and the mass of the convective envelope for a bona fide sample of 118 selected solar-analog G dwarf and checked the evolutionary link between the rotational velocity, lithium abundance, and the deepening of the convective envelope. Fast rotators (vsini 6 km s��1) are also stars with high Li content. Slow rotators present a wide range of values of log n(Li). Our results shed new light on the lithium and rotational behavior in G dwarf stars. We confirmed the presence of a large Li abundance spread among the solar-analog stars and concluded that the solar twins probably share a similar mixing history with the Sun

Investigando o campo magnético das estrelas análogas e gêmeas solares através da espectropolarimetria

This study proposes an observing program focused on the investigation of the stellar magnetism and dynamo evolution in cool active solar-like stars. More mainly in the solar analogs and twins. Observations of stars of our base were carried out with two spectropolarimeter (ESPaDOnS@CFHT and NARVAL@TBL). The analyse of stars in stage different allows an understanding of the dependence of magnetic activity on basic stellar parameters such as rotation, mass, age and depth of the convection zone. This study provides measures necessary for testing dynamo theories. The 65 targets for this project are solar type stars with mass spanning from 0:9 M=Mfi 1:075 solar masses and at different evolutionary stages. Our two main science objectives were, (i) To determine how the magnetic field evolved from the ZAMS to the TO (turn off) for stars with 0:9 M=Mfi 1:075; (ii) To determine the impact of convective depth and rotation on magnetic of cool stars of solar type. The main result from this study was the characterization of the dependence of magnetic field intensity as function of age, Rossby number and the convective zone deepening. This context, the availability of ESPaDOnS and NARVAL opens an exceptional possibility to study the magnetic properties of Sun-like stars by means of spectropolarimetric observations

Sobre a composição química em estrelas evoluídas do aglomerado aberto M67

The Galaxy open clusters have a wide variety of physical properties that make them valuable laboratories for studies of stellar and chemical evolution of the Galaxy. In order to better settle these properties we investigate the abundances of a large number of chemical elements in a sample of 27 evolved stars of the open cluster M67 with different evolutionary stages (turn-off, subgiant and giant stars). For such a study we used high-resolution spectra (R 47 000) and high S/N obtained with UVES+FLAMES at VLT/UT2, covering the wavelength interval 4200-10 600 Å. Our spectral analysis is based on the MARCS models of atmosphere and Turbospectrum spectroscopic tool. The oxygen abundances were determined from the [O I] line at 6300 Å. In addition, we have also computed abundances of Si I, Na I, Mg I, Al I, Ca I, Ti I, Co I, Ni I, Zr I, La II and Cr I. The abundances investigated in this work, combined with their stellar parameters, offers an opportunity to determine the level of mixing and convective dilution of evolved stars in M67. Based on the obtained parameters, the abundances of these seem to follow a similar trend to the curve of solar abundances. Additionally, following strategies of other studies have investigated the relative abundances as a function of effective temperature and metallicity, where it was possible to observe an abundance of Na, Al and Si to the stars in the field of giants. A large dispersion from star to star, is observed in the ratios [X / Fe] for the Co, Zr and La, and the absence of Zr and La, in the stars of the turn-off. Comparisons made between our results and other studies in the literature show that values of abundances are in agreement and close to the limits of the errors

Análise do processo de aprendizagem e alfabetização científica sobre a evolução dos veterbrados em um museu de ciências

Os museus como centros de ciências, enquanto espaços de educação não formal podem, por meio da participação ativa do público, promover a compreensão da ciência ao aguçar a curiosidade do indivíduo e estimular o prazer pela descoberta. Ação desenvolvida como intervenção acadêmica, social e cultural associada ao PIBID/UFRN/Biologia, tem como objetivo avaliar o uso de espaço de ensino não formal, na aprendizagem de conceitos, promovendo a alfabetização científica através de uma exposição em um museu de ciências e morfológicas. A visitação foi realizada no Museu de Ciências Morfológicas da UFRN, com alunos do 1º ano do ensino médio da escola Estadual Lourdes Guilherme, sendo aplicados questionários de pré e pós-visita sobre a Evolução dos Vertebrados, com intuito de analisar a contribuição do museu na aprendizagem destes conteúdos. A porcentagem de acertos no questionário pré-visita variou entre 8 e 68% em relação ao conhecimento geral dos alunos quanto à evolução dos vertebrados, enquanto no pós-visita essa variação foi de 16 a 90%. Com base nesses primeiros resultados verificamos o quanto os museus interativos de ciência se apresentam como um espaço educativo complementar à educação formal, possibilitando a ampliação e a melhoria do conhecimento científico de estudantes. Isso demonstra que o uso de espaços não formais contribui para a aprendizagem significativa, além de promover a alfabetização científica destes alunos ao gerar a compreensão da ciência e aguçar a curiosidade dos mesmos para o prazer da descoberta.

Política de promoção da exportação : um olhar sobre a evolução da cultura de melão do Rio Grande do Norte

Some sectors in Brazil are earning notoriety in the international market, configuring itself in dynamic areas for the Country. The most typical case is the agribusiness. Rio Grande do Norte state has important role, because 90% of the output of the melon exported by Brazil is produced at Assu/Mossoró. The present work planned to verify the evolution of the culture of the melon produced at Assu/Mossoró area, from 1990 to 2003. Through descriptive research, utilizing the case study and documentary analysis of secondary data this work showed the evolution of the area reaped of melon in the pole Assu/Mossoró, the quantity produced of melon and of the value of the output of the melon between 1990 and 2003. The research verified that all of the factors studied show growth during the analyzed period, showing up the importance of the agribusiness for the region. However the analysis shows the vulnerability of the sector concerning external macroeconomics factors, such as the exchange rates. Showing the importance and/or dependence of the producers for public actions to development of the culture, that might be on areas like infrastructure, economics or taxes