In this thesis, an assessment is made of the value of optical CMDs as a useful diagnostic of the accretion properties of young stars. An analysis has been made of the phenomena that we observe and their effect on the position of stars in the CMD. Limitations and potential biases have been identified and evaluated. Variability causes some luminosity spread at a given colour in optical CMDs. A detailed characterisation of variability has been performed which places strong constraints on the magnitudes and the timescales on which the variability is seen. On timescales 15 minutes, almost no variability is detected (at levels greater than ≈ 0.2%) in the i band for a sample of ≈ 700 disc-bearing young stellar objects (YSOs). This suggests that the variability predicted by some accretion shock models is either very weak or not present. On hours to days timescales the optical variability in most stars is well described by a simple power law. The amplitude of the variability, a ∝ f−k, where f is the frequency of the variability in days. Disc-bearing and discless YSOs exhibit median values of k of 0.85 ± 0.02 and 0.95 ± 0.03 respectively, the uncertainity being the error on the median. The power law is valid up to a certain timescale (tmax) at which point the variability amplitude does not increase any further. tmax is found to be 1.50 ± 0.07 days and 1.41 ± 0.10 days for disc-bearing and discless stars respectively. Disc-bearing stars show greater variability amplitudes than the discless stars. However, it is notable that the variability timescale and power spectrum exponent are remarkably similar. This implies that the amplitude of the variability is driven by the physics of the underlying process, but that the timescales are instead driven by geometric effects. For disc-bearing stars, the highest amplitude variables are the accreting stars, which often appear to vary in the CMD along lines that correspond to changes in accretion luminosity. Four disc-bearing stars (approximately 0.5% of the disc-bearing sample) in Cep OB3b show extreme variability on timescales of years. Three (possible EXor candidates), show long-timescale changes that have a dramatic effect on their CMD position. However their small numbers mean that the overall impact on the CMDs of young associations is small. Variability on timescales of the rotational period and shorter adds uncertainty to age estimates of individual stars that are calculated by comparison with PMS models. Having provided a detailed description of variability and its impact on the CMD, it is clear that there are further significant mechanisms that affect the positions of YSOs in the CMD. I show that the spread in luminosity seen in the Orion Nebula Cluster and NGC 2264 could not be explained by accretion at rates of M ̇ ≥ 5 × 10−4 M⊙ yr−1 occurring within the protostellar phase of YSO evolution. Thus it appears that CMDs are not a useful diagnostic for study of the accretion histories of YSOs. The wavelength dependence of the extinction by dust within the inner regions of YSO discs is shown to differ from that seen in the ISM. Typically the wavelength dependence of the extinction is given by RV ≈5-8, compared with the value of RV ≈3.1 typical of the ISM. The interpretation is that grain growth has occurred. The location of this material within the ‘snow line’ implies that grains have coalesced rather than simply gaining an ice mantle. This is evidence for the beginning of planet formation. The effect of the high value of RV on the CMD is to add additional uncertainty of 0.1 mag to photometric measurements that have been corrected for the effects of extinction. Accretion luminosity is shown to be the dominant signal in the luminosity spread seen in CMDs of young associations. Stars which exhibit excess flux in the U band or Hα are displaced in CMD space. The accretion vector is shown to be a significant blueward shift in colour accompa- nied by a modest brightening in the g, g − i CMD. Accretion results in a luminosity spread as stars are displaced blueward below the PMS locus. This effect is not seen in non-accreting disc-bearing stars. Examination of the underlying excess luminosity spectrum for 15 accreting stars shows that the colour of the emission excess is not consistent across the sample. Thus to quantify the effect of accretion luminosity on CMD positions for individual stars, moderate resolution spectra are required with a large range in wavelength. This accretion luminosity may systematically bias estimates of PMS ages. A simple mitigation is to exclude accreting stars from age analysis. U band and Hα flux excesses are shown to vary independently by ≈ 1 dex on timescales shorter than the rotation period of the star. The relation between U band flux excess and veiling at 7000Å also appears to be variable. This implies that single epoch measurements of these parameters will add an uncertainty of ≈ 1 dex on accretion rates derived from them. Accretion rates derived from either U or Hα excess should be calculated from a mean of several photometric measurements, separated by significant fractions of the rotation period of the star. In most stars, the veiling at 7000Å is shown not to be a good measure for the calculation of the accretion rate. Despite providing a detailed characterisation of phenomena that influence the positions of YSOs in the CMD, there exists some residual luminosity spread at a given Teff that cannot be explained by variability on any timescale, extinction uncertainties or accretion luminosity. This residual spread should provide an opportunity to study an as-yet uncharacterised aspect of young stars.

We present new models for two low-mass X-ray binaries (LMXB), 4U 1822-371 and V1408 Aql (= 4U 1957+115). The eclipsing LMXB 4U 1822-371 is the prototypical accretion disk corona (ADC) system. We have obtained new time-resolved UV spectroscopy of 4U 1822-371 with the Advanced Camera for Surveys/Solar Blind Channel on the Hubble Space Telescope and new V- and J- band photometry with the 1.3-m SMARTS telescope at Cerro Tololo Inter-American Observatory. We use the new data to construct the UV/optical spectral energy distribution of 4U 1822-371 and its orbital light curve in the UV, V , and J bands. We derive an improved ephemeris for the optical eclipses and confirm that the orbital period is changing rapidly, indicating extremely high rates of mass flow in the system; and we show that the accretion disk in the system has a strong wind with projected radial velocities up to 4400 km s⁻¹. We show that the disk has a vertically extended, optically thick component at optical wavelengths. This component extends almost to the edge of the disk and has a height equal to ~0.5 of the disk radius. As it has a low brightness temperature, we identify it as the optically thick base of the disk wind, not as the optical counterpart of the ADC. Like previous models of 4U 1822-371, ours needs a tall obscuring wall near the edge of the accretion disk, but we interpret the wall as a layer of cooler material at the base of the disk wind, not as a tall, luminous disk rim. V1408 Aql is a black hole candidate. We have obtained new optical photometry of this system in 2008 and 2009 with the Argos photometer on the 2.1-m Otto Struve telescope and optical spectra with the low resolution spectrometer on the Hobby Eberly telescope. From the data we derive an improved optical orbital ephemeris and a new geometric model for the system. The model uses only a simple thin disk without the need for a warped disk or a large disk rim. The orbital variation is produced by the changing aspect of the irradiated secondary star with orbital phase. The new model leaves the orbital inclination unconstrained and allows for inclinations as low as 20 degrees. The spectra is largely featureless continuum with He II and occasionally H[alpha] emission lines, and an absorption line from Na D. The lines are highly variable in strength and wavelength, but the variations do not correlate with orbital phase. / text

Jatos e discos de acreção associados a objetos galácticos e extragalácticos tais como, microquasares (i.e., buracos negros de massa estelar presentes em alguns sistemas binários estelares), núcleos ativos de galáxias (NAGs) e objetos estelares jovens (OEJs), frequentemente exibem eventos de ejeção de matéria quase periódicos que podem fornecer importantes informações sobre os processos físicos que ocorrem nas suas regiões mais internas. Entre essas classes de objetos, os microquasares com emissão transiente em raios-X vêm sendo identificados em nossa Galáxia desde a última década, e tal como os NAGs e quasares distantes, alguns desses sistemas também produzem jatos colimados com velocidades aparentemente superluminais, não deixando dúvidas de que se tratam de um gás ejetado com velocidades relativísticas. Um exemplo amplamente observado em comprimentos de onda do rádio aos raios-X é o microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), que foi o primeiro objeto galáctico a exibir evidências de um jato com movimento aparentemente superluminal (Mirabel e Rodríguez, 1998, 1994). Um modelo para explicar a origem dessas ejeções superluminais, bem como a emissão rádio sincrotrônica em flares não muito diferentes dos que ocorrem na coroa solar, foi desenvolvido por de Gouveia Dal Pino e Lazarian (2005), onde é invocado um processo de reconexão magnética violenta entre as linhas de campo magnético que se erguem do disco de acreção e as linhas da magnetosfera da fonte central. Em episódios de acreção onde a razão entre a pressão efetiva do disco e a pressão magnética diminui para valores menores ou da ordem de 1 e as taxas de acreção se aproximam da taxa crítica de Eddington, a reconexão pode tornar-se violenta e libera grandes quantidades de energia magnética em pouco tempo. Parte dessa energia aquece o gás, tanto da coroa quanto do disco, e parte acelera as partículas a velocidades relativísticas por um processo de Fermi de primeira ordem, pela primeira vez estudado em zonas de reconexão magnética por esses autores, produzindo um espectro sincrotrônico de lei de potência com índice espectral comparável às observações. Neste trabalho realizamos um estudo complementar, iniciado por Piovezan (2009), no qual generalizamos o modelo acima descrito para o caso dos NAGs. Nesse estudo, constatamos que a atividade de reconexão magnética na região coronal, na base de lançamento do jato, pode explicar a origem das ejeções relativísticas, dos microquasares aos NAGs de baixa luminosidade (tais como galáxias Seyfert e LINERS). A potência liberada em eventos de reconexão magnética em função das massas dos buracos negros dessas fontes, de 5 massas solares a 10^10 massas solares, obedece a uma correlação que se mantém por todo esse intervalo, abrangendo 10^9 ordens de magnitude. Essa correlação implica em uma dependência quase linear (em um diagrama log-log), aproximadamente independente das características físicas locais dos discos de acreção dessas fontes. Além do mais, ela é compatível com o chamado plano fundamental, obtido empiricamente, que correlaciona a emissão rádio e raios-X dos microquasares e NAGs às massas dos seus buracos negros (veja Merloni et al., 2003). Assim, o modelo de de Gouveia Dal Pino e Lazarian (2005), oferece uma interpretação física simples para a existência dessa correlação empírica, como devida à atividade magnética coronal nessas fontes. Já os quasares e NAGs mais luminosos não satisfazem à mesma correlação, possivelmente porque a densidade ao redor da região coronal nessas fontes é tão alta que mascara a emissão devida à atividade magnética. A emissão rádio nesses casos deve-se, possivelmente, a regiões mais externas do jato supersônico, onde ele já expandiu o suficiente para tornar-se opticamente fino e visível, e onde os elétrons relativísticos são possivelmente produzidos em choques (veja também de Gouveia Dal Pino et al., 2010a,b). Paralelamente, investigamos a formação de eventos de reconexão magnética através de simulações magnetohidrodinâmicas axissimétricas (2.5D-MHD), da interação entre o campo magnético poloidal ancorado no disco de acreção viscoso (satisfazendo ao modelo padrão de Shakura e Sunyaev, 1973) e a magnetosfera dipolar da fonte central em rotação. Para esse fim, consideramos condições iniciais semelhantes às dos OEJs. Nos testes preliminares aqui realizados, a reconexão magnética das linhas ocorre em presença de uma resistividade numérica, que não é intensa o bastante para determinar um processo de reconexão a taxas da ordem da velocidade de Alfvén, ou seja, ela é essencialmente lenta. Ainda assim, pudemos identificar alguns dos efeitos previstos pelo modelo de reconexão magnética rápida aqui estudado. Por exemplo, verificamos que a frequência e a intensidade com que eventos de reconexão magnética podem ocorrer é sensível tanto à topologia inicial do campo magnético do sistema quanto às taxas de acreção do disco (como previsto pelo modelo de de Gouveia Dal Pino e Lazarian, 2005), de modo que tais eventos ocorrem de forma mais eficiente em regimes de alta taxa de acreção. Finalmente, além da investigação sobre o desenvolvimento de eventos de reconexão magnética, pudemos também examinar a partir das simulações a formação natural de funis de acreção, os quais são colunas de acreção que conduzem gás do disco para a superfície da fonte central através das linhas do campo magnético. Os resultados desse estudo foram comparados com as observações de funis de acreção de objetos estelares jovens. / Jets and accretion disks associated with galactic and extragalactic objects such as microquasars (i.e., stellar-mass black holes occurring in some binary stellar systems), active galactic nuclei (AGNs) and young stellar objects (YSOs), often exhibit quasi-periodic ejections of matter that may offer important clues about the physical processes that occur in their inner regions. Among these classes of objects, microquasars with transient emission in X-rays have been identified in our Galaxy since the last decade and like AGNs and distant quasars, some of them also produce collimated jets with apparent superluminal speeds, leaving no doubt that we are also dealing with ejected gas with relativistic velocities. One example widely investigated from radio wavelengths to X-rays is the microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), which was the first Galactic object to show evidence of a jet with apparent superluminal motion (Mirabel e Rodríguez, 1998, 1994). A model to explain the origin of the superluminal ejections and the synchrotron radio emission in flares which are not very different from those occurring in the solar corona, was developed by de Gouveia Dal Pino e Lazarian (2005), where they invoked a process of violent magnetic reconnection between the magnetic field lines that arise from the accretion disk and the lines of the magnetosphere of the central source. In accretion episodes where the ratio between the effective disk pressure and magnetic pressure decreases to values smaller than the unity and the accretion rate approaches the critical Eddington rate, the reconnection may become violent and releases large amounts of magnetic energy in a short time. Part of this energy heats the coronal and the disk gas and part accelerates particles to relativistic velocities through a first-order Fermi-like process, which was investigated for the first time in magnetic reconnection by these authors and results a synchrotron radio power-law spectrum that is compatible to the observations. In the present work we conducted a complementary study, initiated by Piovezan (2009), which generalize the model described above for the case of AGNs. We found that the activity due to magnetic reconnection in the coronal region, at the base of the launching jet, can explain the origin of relativistic ejections from microquasars to low luminous AGNs (LLAGNs, such as Seyfert galaxies and LINERs). The power released by magnetic reconnection events as a function of the black hole masses of these sources, between 5 solar mass and 10^10 solar mass, obeys a correlation that is maintained throughout this interval, spanning 10^9 orders of magnitude. This correlation implies an almost linear dependence (in a log-log diagram), which is approximately independent of the physical properties of the accretion disks of these sources. Moreover, it is compatible with the so-called fundamental plan obtained empirically, which correlates the radio and X-rays emission of microquasars and AGNs with the masses of their black holes (see Merloni et al., 2003). Thus, the model of de Gouveia Dal Pino e Lazarian (2005) provides a simple physical interpretation for the existence of this empirical correlation as due to coronal magnetic activity in these sources. More luminous AGNs and quasars do not seem to obey the same correlation, possibly because the density around the coronal region in these sources is so high that it \"masks\" the emission due to the magnetic activity. The radio emission in these cases is possibly due regions further out of the supersonic jet, where it has already expanded enough to become optically thin and visible and where the relativistic electrons are probably accelerated in shocks (see also de Gouveia Dal Pino et al., 2010a,b). In addition, we investigated the development of magnetic reconnection events through axisymmetric magnetohydrodynamic simulations (2.5D-MHD) of the interaction between the poloidal magnetic field that arises from the viscous accretion disk (which satisfies the standard model of Shakura e Sunyaev, 1973) and the dipolar magnetosphere of the rotating central source. To this aim, we considered initial conditions which are compatible to those of YSOs. In the preliminary tests conducted here, magnetic reconnection occurs in the presence of numerical resistivity only, which is not intense enough to determine a process of reconnection with rates of the order of the Alfvén speed, i.e., it is essentially slow. Nevertheless, we were able to identify some of the effects predicted by the model of fast magnetic reconnection studied here. For example, we found that the frequency and strength with which events of magnetic reconnection can occur is sensitive to both the initial topology of the magnetic field of the system and the accretion disk rates (as predicted by the model of de Gouveia Dal Pino e Lazarian, 2005), so that such events occur more efficiently under high accretion rates. Finally, besides the investigation of the development of magnetic reconnection events, we could also examine in our numerical studies the natural formation of funnel flows which are accretion columns that transport gas from the accretion disk to the surface of the central source along the magnetic field lines. The results of these studies were compared with the observations of funnel flows in young stellar objects.

This thesis focuses on the evolution of zonal flows in self-gravitating accretion discs and their resulting effect on disc stability; it also studies the process of disc gravito-turbulence, with particular emphasis given to the way the turbulent state is able to extract energy from the background flow and sustain itself by means of a feedback. Chapters 1 and 2 provide an overview of systems involving accretion discs and a theoretical introduction to the theory of accretion discs, along with potential methods of angular momentum transport to explain the observed accretion rates. To address the issue of the gravito-turbulence self-sustenance, a compressible non-linear spectral code (dubbed CASPER) was developed from scratch in C; its equations and specifications are laid out in Chapter 3. In Chapter 4 an ideal (no viscosities or cooling) linear stability analysis to non-axisymmetric perturbations is carried out when a zonal flow is present in the flow. This yields two instabilities: a Kelvin-Helmholtz instability (active only if the zonal flow wavelength is sufficiently small) and one driven by self-gravity. A stability analysis of the zonal flow itself is carried out in Chapter 5 by means of an axisymmetric linear analysis, using non-ideal conditions. This considers instability due to both density wave modes (which give rise to overstability) and slow modes (which result in thermal or viscous instability) and, thanks a different perturbation wavelength regime, represents an extension to the classical theory of thermal and viscous instabilities. The slow mode instability is found to be aided by high Prandtl numbers and adiabatic index γ values, while quenched by fast cooling. The overstability is likewise stabilised by fast cooling, and occurs in a non-self-gravitational regime only if γ ≲ 1.305. Lastly, Chapter 6 illustrates the results of the non-linear simulations carried out using the CASPER code. Here the system settles into a state of gravito-turbulence, which appears to be linked to a spontaneously-developing zonal flow. Results show that this zonal flow is driven by the slow mode instability discussed in Chapter 5, and that the presence of zonal flows triggers a non-axisymmetric instability, as seen in Chapter 4. The role of the latter is to constrain the zonal flow amplitude, with the resulting zonal flow disruption providing a generation of shearing waves which permits the self-sustenance of the turbulent state.

No description available.

Blazars, a subclass of active galactic nuclei with powerful relativistic plasma jets, are among the most luminous and violently variable objects in the universe. They emit radiation across the entire electromagnetic spectrum, and often change in brightness over the course of hours or days. Different emission mechanisms are necessary in order to explain the observed flux in different frequency ranges. In the ultraviolet-optical- infrared regime these include components that arise from: 1) polarized synchrotron radiation emanating from a powerful parsec-scale jet flowing from near the central accreting black hole, 2) a multi-temperature accretion disk emitting thermal radia- tion, and 3) an optically thick dusty torus located several parsecs from the central engine that absorbs and re-emits, at infrared wavelengths, radiation originating in the accretion disk. The goal of this study is to determine the relative importance of these spectral components in the spectra of blazars. I use data from the Spitzer Space Telescope in order to search for the presence of the dusty torus surrounding four blazars, as well as to determine its luminosity and temperature. In two of the observed sources, 1222+216 and CTA102, I determine that the torus can be modeled as a 1200 K blackbody emitting at nearly 10 46 erg s −1 . Furthermore, I determine the relative variability of the accretion disk of a sample of blazars by using spec- tropolarimetry observations to separate the optical-UV spectrum into a polarized viiicomponent, consisting of radiation described by a power-law F ν ∝ ν −α , and an ac- cretion disk which consists of a thin disk described by the power-law F disk ∝ ν 1/3 plus a hot-spot of variable temperature. The spectra of several blazars are explained by a version of this model in which the thin disk component is held constant, while the blackbody varies on timescales of approximately years resulting with a flux of the blackbody component comparable to the power-law disk component. I find that variations in the emission from the hot-spot occurs approximately within 100 days of γ-ray variations.

Doctor of Philosophy / We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B < 8G. For a significant subset of these strengths (200mG < B < 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 AU for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc, than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B > 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B < 2 G. For strong fields, perturbations exhibit a kink at the height where x-ray ionisation becomes active. Finally, for R = 5 AU (10 AU), unstable modes exist for B < 800 mG (B < 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 mG < B < 500 mG (2 mG < B < 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B < 100 mG (B < 10 mG). Unstable modes grow even at the midplane for B > 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs.

Astrophysikalische Jets sind ausgedehnte, kollimierte Massenausflüsse von verschiedenen astronomischen Objekten. Zeitabhängige magnetohydrodynamische (MHD) Simulationen der Jet-Entwicklung müssen den Akrretionsprozess in der Scheibe berücksichtigen, da der Jet aus der Scheibenmaterie gespeist wird. Allerdings ist die simultane Berechnung der Entwicklung von Scheibe und Jet schwierig, da die charakteristischen Zeitskalen unterschiedlich sind. Selbstähnliche Modelle zeigten, daß eine Beschreibung der Jetentstehung aus einer Akkretionsscheibe durch rein magnetische Prozesse möglich ist. / In this thesis the magnetohydrodynamic jet formation and the effects of magnetic diffusion on the formation of axisymmetric protostellar jets have been investigated in three different simulation sets. The time-dependent numerical simulations have been performed, using the magnetohydrodynamic ZEUS-3D code.

Wind farms are nowadays more often constructed in alpine terrain than earlier due to theprofitable wind resource as well as, often, less conflicting interests than in more denselypopulated areas. The cold climate poses a relatively new challenge to the wind power industrysince icing of the wind turbine blades and sensors may induce losses in production, increasethe wear and tear of the components, leading to a shortening of structural life time as well as itdecreases the availability and hence reducing the economical profitability for the owner.This study focuses on modelling of ice accretion on a vertically mounted cylinder,dimensioned to correspond to an IceMonitor, and comparing the results with measured iceload on a similar instrument during the winter of 2009/2010. The modelling is carried outwith both a statistical approach using multiple linear regression and a physical approach usingmodel for ice accretion. Ice load was also modelled for the period 1989-2009 using the ERAinterimre-analysis data set in order to compare the winter 09/10 with a longer referenceseries. Modelled ice loads for four winters between 2005 and 2009 were compared withproduction data to investigate a possible connection between ice load and production losses.The results showed that the statistical approach was unable in its current form toreproduce and predict measured ice loads and the method was deemed unsuitable. Thephysical model shows more promising results, although with problems in modelling rapid iceaccretion and ice shedding events.No clear connection between measured production losses and modelled ice loads wasfound when analyzing available data. Uncertainties in input data correction as well asimportance of ice density are possible sources of error.Due to confidentiality of some of the data, the measurement sites used in this thesis aredenoted site A, site B and site C.

Results from several studies are presented which detail explorations of the physical and spectral properties of low luminosity active galactic nuclei. An initial Sagittarius A* general relativistic magnetohydrodynamic simulation and Monte Carlo radiation transport model suggests accretion rate changes as the dominant flaring method. A similar study on M87 introduces new methods to the Monte Carlo model for increased consistency in highly energetic sources. Again, accretion rate variation seems most appropriate to explain spectral transients. To more closely resolve the methods of particle energization in active galactic nuclei accretion disks, a series of localized shearing box simulations explores the effect of numerical resolution on the development of current sheets. A particular focus on numerically describing converged current sheet formation will provide new methods for consideration of turbulence in accretion disks.