We present a range of steady-state photoionization simulations, corresponding to different assumed shell geometries and compositions, of the unseen postulated rapidly expanding outer shell to the Crab Nebula. The properties of the shell are constrained by the mass that must lie within it, and by limits to the intensities of hydrogen recombination lines. In all cases the photoionization models predict very strong emission from high ionization lines that will not be emitted by the Crab’s filaments, alleviating problems with detecting these lines in the presence of light scattered from brighter parts of the Crab. The NIR [Ne VI] λ 7.652 mm line is a particularly good case; it should be dramatically brighter than the optical lines commonly used in searches. The C IV λ1549Å doublet is predicted to be the strongest absorption line from the shell, which is in agreement with HST observations. We show that the cooling timescale for the outer shell is much longer than the age of the Crab, due to the low density. This means that the temperature of the shell will actually “remember” its initial conditions. However, the recombination time is much shorter than the age of the Crab, so the predicted level of ionization should approximate the real ionization. In any case, it is clear that IR observations present the best opportunity to detect the outer shell and so guide future models that will constrain early events in the original explosion. Infrared observations have discovered a variety of objects, including filaments in the Crab Nebula and cool-core clusters of galaxies, where the H2 1-0 S(1) line is stronger than the infrared H I lines. A variety of processes could be responsible for this emission. Although many complete shock or PDR calculations of H2 emission have been published, we know of no previous simple calculation that shows the emission spectrum and level populations of thermally excited low-density H2. We present a range of purely thermal collisional simulations, corresponding to constant gas kinetic temperature at different densities. We consider the cases where the collisions affecting H2 are predominantly with atomic or molecular hydrogen. The resulting level population (often called “excitation”) diagrams show that excitation temperatures are sometimes lower than the gas kinetic temperature when the density is too low for the level populations to go to LTE. The atomic case goes to LTE at much lower densities than the molecular case due to larger collision rates. At low densities for the v=1 and 2 vibrational manifolds level populations are quasi-thermal, which could be misinterpreted as showing the gas is in LTE at high density. At low densities for the molecular case the level population diagrams are discontinuous between v=0 and 1 vibrational manifolds and between v=2, J=0, 1 and other higher J levels within the same vibrational manifold. These jumps could be used as density diagnostics. We show how much the H2 mass would be underestimated using the H2 1-0 S(1) line strength if the density is below that required for LTE. We give diagnostic diagrams showing level populations over a range of density and temperature. The density where the level populations are given by a Boltzmann distribution relative to the total molecular abundance (required to get the correct H2 mass), is shown for various cases. We discuss the implications of these results for the interpretation of H2 observations of the Crab Nebula and filaments in cool-core clusters of galaxies.

L'instabilité de Vishniac est invoquée pour expliquer la fragmentation et la filamentation de la coquille fine de matière choquée présente dans les restes de supernova radiatifs. Toutefois l'implication et les conséquences de ce processus spécifique sur la morphologie complexe des restes de supernova ne sont pas entièrement démontrées. Nous avons réalisé des simulations numériques 2D d'une onde de souffle perturbée qui se propage dans un milieu ambiant homogène afin de mieux comprendre le mécanisme de l'instabilité de Vishniac. Le code hydrodynamique HYDRO-MUSCL 2D a été utilisé afin de déclencher la perturbation de la coquille fine dans les géométries plan-parallèle et sphérique. Dans ce travail, je montrerai que nous avons obtenu la surstabilité de Vishniac (" Vishniac overstability ") comme prédit par l'analyse théorique. Ce processus repose sur une oscillation d'amplitude et de période temporelle croissante des grandeurs fluides et spatiales. Nous avons testé l'effet de paramètres spécifiques sur la variation de masse d'une région donnée dans le cadre d'une étude paramétrique que nous avons réalisée sur le supercalculateur Titane. Nous avons trouvé que la perturbation est atténuée après quelques oscillations de la variation de masse pour tous les jeux de paramètres. Ainsi nous concluons que dans notre modèle, l'instabilité de Vishniac ne permet pas la fragmentation de la coquille fine à cause d'effets qui ne sont pas pris en compte par l'analyse théorique.

<p>Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data.</p><p>Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images.</p><p>The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.</p>

Multi-wavelength observations of mature supernova remnants (SNRs), especially with recent advances in gamma-ray astronomy, make it possible to constrain energy distribution of energetic particles within these remnants. In consideration of the SNR origin of Galactic cosmic rays and physics related to particle acceleration and radiative processes, we use a simple one-zone model to fit the nonthermal emission spectra of three shell-type SNRs located within 2 degrees on the sky: RX J1713.7-3946, CTB 37B, and CTB 37A. Although radio images of these three sources all show a shell (or half-shell) structure, their radio, X-ray, and gamma-ray spectra are quite different, offering an ideal case to explore evolution of energetic particle distribution in SNRs. Our spectral fitting shows that (1) the particle distribution becomes harder with aging of these SNRs, implying a continuous acceleration process, and the particle distributions of CTB 37A and CTB 37B in the GeV range are harder than the hardest distribution that can be produced at a shock via the linear diffusive shock particle acceleration process, so spatial transport may play a role; (2) the energy loss timescale of electrons at the high-energy cutoff due to synchrotron radiation appears to be always a bit (within a factor of a few) shorter than the age of the corresponding remnant, which also requires continuous particle acceleration; (3) double power-law distributions are needed to fit the spectra of CTB 37B and CTB 37A, which may be attributed to shock interaction with molecular clouds.

Galaxies, and clusters of galaxies, can act as gravitational lenses and magnify the light of objects behind them. The effect enables observations of very distant supernovae, that otherwise would be too faint to be detected by existing telescopes, and allows studies of the frequency and properties of these rare phenomena when the universe was young. Under the right circumstances, multiple images of the lensed supernovae can be observed, and due to the variable nature of the objects, the difference between the arrival times of the images can be measured. Since the images have taken different paths through space before reaching us, the time-differences are sensitive to the expansion rate of the universe. One class of supernovae, Type Ia, are of particular interest to detect. Their well known brightness can be used to determine the magnification, which can be used to understand the lensing systems. In this thesis, galaxy clusters are used as gravitational telescopes to search for lensed supernovae at high redshift. Ground-based, near-infrared and optical search campaigns are described of the massive clusters Abell 1689 and 370, which are among the most powerful gravitational telescopes known. The search resulted in the discovery of five photometrically classified, core-collapse supernovae at redshifts of 0.671&lt;z&lt;1.703 with significant magnification from the cluster. Owing to the power of the lensing cluster, the volumetric core-collapse supernova rates for 0.4 ≤ z &lt; 2.9 were calculated, and found to be in good agreement with previous estimates and predictions from cosmic star formation history. During the survey, two Type Ia supernovae in A1689 cluster members were also discovered, which allowed the Type Ia explosion rate in galaxy clusters to be estimated. Furthermore, the expectations of finding lensed supernovae at high redshift in simulated search campaigns that can be conducted with upcoming ground- and space-based telescopes, are discussed. Magnification from a galaxy lens also allows for detailed studies of the supernova properties at high redshift that otherwise would not be possible. Spectroscopic observations of lensed high-redshift supernovae Type Ia are of special interest since they can be used to test for evolution of the standard candle nature of these objects. If systematic redshift-dependent properties are found, their utility for future surveys could be challenged. In the thesis it is shown that the strongly lensed and very distant supernova Type Ia PS1-10afx at z=1.4, does not deviate from the well-studied nearby and intermediate populations of normal supernovae Type Ia. In a different study, the discovery of the first resolved multiply-imaged gravitationally lensed supernova Type Ia is also reported. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.</p>

Supernovae (SNe) are energetic explosions that signal the end of a star's life. These events and the supernova remnants (SNRs) they leave behind play a central role in stellar feedback by adding energy and momentum and metals to the interstellar medium (ISM). Emission associated with these feedback processes, especially atomic and molecular line emission as well as thermal and nonthermal continuum emission is known to be enhanced in regions of high density, such as dense circumstellar matter (CSM) around SNe and molecular clouds (MCs). In this thesis, I begin with a brief overview of the physics of SN shocks in Chapter 1, focusing on a foundation for studying pan-chromatic signatures of interactions between SNe and dense environments. In Chapter 2, I examine an unusual SN with signatures of CSM interaction in the form of narrow lines of hydrogen (Type IIn) and thermal continuum emission. This SN appears to belong to a class of Type Ia SNe that shares spectroscopic features with Type IIn SNe. I discuss the difficulties of decomposing spectra in a regime where interaction occurs between SN ejecta and CSM, potentially confusing the underlying SN type. This is followed by a discussion of rebrightening that occurred at late-time in 𝐵 and 𝑉 band photometry of this SN, possibly associated with clumpy or dense CSM at large distances from the progenitor. In Chapter 3, I examine synchrotron emission from Cassiopeia A, observed in the 𝐾ₛ band over multiple epochs. The synchrotron emission is generally diffuse over the remnant, but there is one location in the southwest portion of the remnant where it appears to be enhanced and entrained as knots of emission in the SNR ejecta. I evaluate whether the 𝐾ₛ band knots are dominated by synchrotron emission by comparing them to other infrared and radio imaging that is known to be dominated by synchrotron emission. Concluding that they are likely synchrotron-emitting knots, I measure the magnetic field strength and electron density required for their evolution over the ~ 10 yr baseline they were observed and find 𝐵 ≈ 1.3-5.8 mG and 𝑛ₑ≈ 1,000-15,000 cm⁻³. The magnetic field strengths appear enhanced beyond values required by the adiabatic strong shock limit, arguing in favor of other forms of magnetic field amplification in the shock. In Chapter 4, I again discuss Cassiopeia A and interaction between the remnant and nearby MCs as seen at mid-infrared and millimeter wavelengths. I report detection of a SNR-MC interaction and analyze its signatures in broadened molecular lines. I extend this analysis in Chapter 5 to a large survey for SNR-MC interactions in the ¹²CO 𝐽=2-1 line. Although broadened ¹²CO 𝐽=2-1 line emission should be detectable toward virtually all SNR-MC interactions, I find relatively few examples; therefore, the number of interactions is low. This result favors mechanisms other than supernova feedback as the basic trigger for star formation. In addition, I find no significant association between TeV gamma-ray sources and MC interactions, contrary to predictions that SNR-MC interfaces are the primary venues for cosmic ray acceleration. I end this dissertation in Chapter 6 with a brief summary of my results and two extensions of this work: examining the late-time radio light curves of CSM-interacting SNe for signatures of radio synchrotron emission and dense or clumpy CSM at large distances from the progenitor and re-observing SNR-MC interactions in ¹²CO 𝐽=3-2 in order to verify the presence of shock-heated molecular gas and perform a census on the densities and temperatures of post-shock molecular gas.

The study of Supernova Remnants (SNRs) is fundamental to understanding the chemical enrichment and magnetism in galaxies, including our own Milky Way. In an effort to understand the connection between the morphology of SNRs and the Galactic Magnetic Field (GMF), we have examined the radio images of all known SNRs in our Galaxy and compiled a large sample that have an axisymmetric morphology, which we define to mean SNRs with a bilateral or barrel-shaped morphology, in addition to one-sided shells. We selected the cleanest examples and model each of these at their appropriate Galactic position using two GMF models, one of which includes a vertical halo component, and another that is oriented entirely parallel to the plane. Since the magnitude and relative orientation of the magnetic field changes with distance from the Sun, we analyze a range of distances, from 0.5 to 10 kpc in each case. Using a physically motivated model of an SNR expanding into an ambient GMF that includes a vertical halo component, we find it is possible to reproduce observed morphologies of many SNRs in our sample. These results strongly support the presence of an off-plane, vertical component to the GMF, and the importance of the Galactic field on SNR morphology. Our approach also provides a potentially new method for determining distances to SNRs, or conversely, distances to features in the large-scale GMF if SNR distances are known. The mechanism for acceleration of cosmic rays in SNRs is another outstanding question in the field. To investigate this, the same sample of axisymmetric SNRs was again modelled, but this time using two competing, and physically motivated, Cosmic Ray Electron (CRE) acceleration cases: quasi-perpendicular and quasi-parallel. We find that the quasi-perpendicular CRE acceleration case is much more consistent with the data than the quasi-parallel CRE acceleration case, with G327.6+14.6 (SN1006) being a notable exception. We propose that SN1006 may be an example of a case where both quasi-parallel and quasi-perpendicular acceleration is simultaneously at play in a single SNR. / October 2016

We report a discovery of shocked gas from the supernova remnant (SNR) G357.7+0.3. Our millimeter and submillimeter observations reveal broad molecular lines of CO(2-1), CO(3-2), CO(4-3), (CO)-C-13 (2-1), and (CO)-C-13 (3-2), HCO+, and HCN using the Heinrich Hertz Submillimeter Telescope, the Arizona 12 m Telescope, APEX, and the MOPRA Telescope. The widths of the broad lines are 15-30 km s(-1), and the detection of such broad lines is unambiguous, dynamic evidence showing that the SNR G357.7+0.3 is interacting with molecular clouds. The broad lines appear in extended regions (>4'.5 x 5'). We also present the detection of shocked H-2 emission in the mid-infrared but lacking ionic lines using Spitzer/IRS observations to map a few-arcminute area. The H2 excitation diagram shows a best fit with a two-temperature local thermal equilibrium model with the temperatures of similar to 200 and 660 K. We observed [C II] at 158 mu m and high-J CO(11-10) with the German Receiver for Astronomy at Terahertz Frequencies (GREAT) on the Stratospheric Observatory for Infrared Astronomy. The GREAT spectrum of [C II], a 3 sigma detection, shows a broad line profile with a width of 15.7 km(-1) that is similar to those of broad CO molecular lines. The line width of [C II] implies that ionic lines can come from a low-velocity C-shock. Comparison of H2 emission with shock models shows that a combination of two C-shock models is favored over a combination of C- and J-shocks or a single shock. We estimate the CO density, column density, and temperature using a RADEX model. The best-fit model with n(H-2) = 1.7 x 10(4) cm(-3), N(CO) = 5.6 x 10(16) cm(-2), and T = 75 K can reproduce the observed millimeter CO brightnesses.

We examine a diffuse emission region near the center of SNR 0509-67.5 to determine its nature. Within this diffuse region we observe a point-like source that is bright in the near-IR, but is not visible in the B and V bands. We consider an emission line observed at 6766 angstrom and the possibilities that it is Ly alpha, H alpha, and [O II] lambda 3727. We examine the spectral energy distribution (SED) of the source, comprised of Hubble Space Telescope B, V, I, J, and H bands in addition to Spitzer/IRAC 3.6, 4.5, 5.8, and 8 mu m bands. The peak of the SED is consistent with a background galaxy at z approximate to 0.8 +/- 0.2 and a possible Balmer jump places the galaxy at z approximate to 0.9 +/- 0.3. These SED considerations support the emission line's identification as [O II] lambda 3727. We conclude that the diffuse source in SNR 0509-67.5 is a background galaxy at z approximate to 0.82. Furthermore, we identify the point-like source superposed near the center of the galaxy as its central bulge. Finally, we find no evidence for a surviving companion star, indicating a double-degenerate origin for SNR 0509-67.5.

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$_{\\odot}$.