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S Mathis - One of the best experts on this subject based on the ideXlab platform.
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Horizontal shear instabilities in rotating Stellar Radiation zones
'EDP Sciences', 2021Co-Authors: Junho Park, Vincent Prat, S Mathis, Lisa BugnetAbstract:Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in Stellar Radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in Stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating Stellar Radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component $ \tilde{f} $ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as $ \tilde{f} $ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as $ 0 < f < 1+\tilde{f}^{2}/N^{2} $, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ < 180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in Stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in Stellar Radiation zones
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horizontal shear instabilities in rotating Stellar Radiation zones i inflectional and inertial instabilities and the effects of thermal diffusion
Astronomy and Astrophysics, 2020Co-Authors: Junho Park, V Prat, S MathisAbstract:Rotational mixing, the key process in Stellar evolution, transports angular momentum and chemical elements in Stellar radiative zones. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities in the context of Stellar radiative zones. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. As a first step, we consider a polar $f$-plane where the gravity and rotation vector are aligned. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. The three-dimensional inflectional instability is destabilized by stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum $\sqrt{f(1-f)}$ in the inviscid limit as the vertical wavenumber goes to infinity, where $f$ is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a self-similarity in both the inflectional and inertial instabilities based on the rescaled parameter $PeN^2$ with the Peclet number $Pe$ and the Brunt-Vaisala frequency $N$.
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Anisotropic turbulent transport in stably stratified rotating Stellar Radiation zones
Astronomy and Astrophysics - A&A, 2018Co-Authors: S Mathis, V Prat, Louis Amard, C Charbonnel, A Palacios, N Lagarde, P EggenbergerAbstract:Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from Stellar Radiation zones over the whole Hertzsprung–Russell diagram. Turbulent transport in differentially rotating, stably stratified Stellar Radiation zones should be carefully modelled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. So far only phenomenological prescriptions have been proposed for the transport in the horizontal direction. This, however, constitutes a cornerstone in current theoretical formalisms for Stellar hydrodynamics in evolution codes. We aim to improve its modelling. We derived a new theoretical prescription for the anisotropy of the turbulent transport in Radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implemented this framework in the Stellar evolution code STAREVOL and quantified its impact on the rotational and structural evolution of solar metallicity low-mass stars from the pre-main-sequence to the red giant branch. The anisotropy of the turbulent transport scales as N4τ2/(2Ω2), N and Ω being the buoyancy and rotation frequencies respectively and τ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. Hence the models computed with the new formalism still build up too steep internal rotation gradients compared to helioseismic and asteroseismic constraints. As a consequence, a complementary transport mechanism such as internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along Stellar evolution. The new prescription links for the first time the anisotropy of the turbulent transport in Radiation zones to their stratification and rotation. This constitutes important theoretical progress and demonstrates how turbulent closure models should be improved to get firm conclusions on the potential importance of other processes that transport angular momentum and chemicals inside stars along their evolution.
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anisotropic turbulent transport in stably stratified rotating Stellar Radiation zones
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: S Mathis, V Prat, Louis Amard, C Charbonnel, A Palacios, N Lagarde, P EggenbergerAbstract:Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from Stellar Radiation zones over the whole Hertzsprung-Russell diagram. Turbulent transport in differentially rotating stably stratified Stellar Radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a cornerstone in current theoretical formalisms for Stellar hydrodynamics in evolution codes. We derive a new theoretical prescription for the anisotropy of the turbulent transport in Radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implement this framework in the Stellar evolution code STAREVOL and quantify its impact on the rotational and structural evolution of low-mass stars from the pre-main-sequence to the red giant branch. The anisotropy of the turbulent transport scales as $N^4\tau^2/\left(2\Omega^2\right)$, $N$ and $\Omega$ being the buoyancy and rotation frequencies respectively and $\tau$ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. As a consequence, a complementary transport mechanism like internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along Stellar evolution.
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the coupling between internal waves and shear induced turbulence in Stellar Radiation zones the critical layer
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Lucie Alvan, S Mathis, T DecressinAbstract:Internal gravity waves (hereafter IGWs) are known as one of the candidates for explaining the angular velocity profile in the Sun and in solar-type main-sequence and evolved stars, due to their role in the transport of angular momentum. Our bringing concerns critical layers, a process poorly explored in Stellar physics, defined as the location where the local relative frequency of a given wave to the rotational frequency of the fluid tends to zero (i.e that corresponds to co-rotation resonances). IGW propagate through stably-stratified radiative regions, where they extract or deposit angular momentum through two processes: radiative and viscous dampings and critical layers. Our goal is to obtain a complete picture of the effects of this latters. First, we expose a mathematical resolution of the equation of propagation for IGWs in adiabatic and non-adiabatic cases near critical layers. Then, the use of a dynamical Stellar evolution code, which treats the secular transport of angular momentum, allows us to apply these results to the case of a solar-like star.The analysis reveals two cases depending on the value of the Richardson number at critical layers: a stable one, where IGWs are attenuated as they pass through a critical level, and an unstable turbulent case where they can be reflected/transmitted by the critical level with a coefficient larger than one. Such over-reflection/transmission can have strong implications on our vision of angular momentum transport in Stellar interiors. This paper highlights the existence of two regimes defining the interaction between an IGW and a critical layer. An application exposes the effect of the first regime, showing a strengthening of the damping of the wave. Moreover, this work opens new ways concerning the coupling between IGWs and shear instabilities in Stellar interiors.
N De Brye - One of the best experts on this subject based on the ideXlab platform.
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low frequency internal waves in magnetized rotating Stellar Radiation zones ii angular momentum transport with a toroidal field
Astronomy and Astrophysics, 2012Co-Authors: S Mathis, N De BryeAbstract:Context. With the progress of observational constraints on dynamical processes in stars, it becomes necessary to understand the angular momentum and the rotation profile history. In this context, internal waves constitute an efficient transport mechanism over long distances in Stellar Radiation zones. Indeed, they could be one of the mechanisms responsible for the quasi-flat rotation profile of the solar radiative region up to 0.2 R� . Aims. Angular momentum transport induced by internal waves depends on the properties of their excitation regions and of their dissipation during propagation. Then, the bottom of convective envelopes (the top of convective cores, respectively) are differentially rotating magnetic layers while Radiation zones may host fossil magnetic fields. It is therefore necessary to understand the modification of internal wave mechanisms by both rotation and magnetic fields. Methods. We continue our previous work by proceeding step by step. We analytically built a complete formalism that treats the angular momentum transport by internal waves while taking into account both the Coriolis acceleration and the Lorentz force in a non-perturbative way for an axisymmetric toroidal field. We assumed a uniform Alfven frequency and a weak differential rotation to isolate the transport properties as a function of the Rossby and Elsasser numbers. Results. We examined the different possible approximations to describe low-frequency internal waves modified by the Coriolis acceleration and the Lorentz force in a deep spherical shell. The complete structure of these waves, which become magneto-gravitoinertial waves, is given assuming the quasi-linear approximation first in the adiabatic case and then in the dissipative one. Vertical and equatorial trapping phenomena appear that favor retrograde waves. The efficiency of the induced transport as a function of the Rossby and Elsasser numbers is then obtained. Conclusions. A complete study of the transport of angular momentum induced by magneto-gravito-inertial waves in Stellar radiative regions is achieved for an axisymmetric toroidal magnetic field for a uniform Alfven frequency and a weak differential rotation. General differential rotation, complex azimuthal magnetic fields, and poloidal and mixed fields will be examined in follow-up studies.
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low frequency internal waves in magnetized rotating Stellar Radiation zones i wave structure modification by a toroidal field
Astronomy and Astrophysics, 2011Co-Authors: S Mathis, N De BryeAbstract:Context. The study of helioseismology, asteroseismology, and powerful ground-based instrumentation dedicated to Stellar physics is developing strongly (cf. CoRoT, KEPLER, and ESPaDOnS). This generates tight constraints on the Stellar internal structure and dynamical processes. In this context, it is thus necessary to go beyond the non-rotating and the non-magnetic picture of Stellar interiors, particularly for large-scale transport mechanisms and waves. Aims. We focus on low-frequency internal waves in magnetic, rotating, stably stratified Stellar Radiation zones. For frequencies, which can be close to the Alfven and the inertial frequencies, we go beyond the non-magnetic and non-rotating description of wave dynamics with taking the Coriolis acceleration and the Lorentz force into account. Then, we have to couple wave dynamics with fossil magnetic fields, which must have mixed configurations (both poloidal and toroidal) to survive in Stellar Radiation zones. Methods. We chose to study such coupling step by step, first with purely toroidal fields and then with purely poloidal fields, to unravel their modification by each corresponding component of a realistic mixed-field. Thus, we analytically built a complete formalism, which describes both effects of the Coriolis acceleration and of the Lorentz force in a non-perturbative way in the case of an axisymmetric toroidal field. We consider here the case where both Alfven frequency and angular velocity are chosen to be uniform, to isolate wave properties. Results. The different approximations possible for low-frequency internal waves in this model are examined and discussed. In this way, the traditional approximation used to describe the dynamics of low-frequency regular elliptic gravito-inertial waves in the purely hydrodynamical case is generalized to the magnetic one. The complete structure of internal waves, which become magneto-gravitoinertial waves, is then derived and compared to the non-magnetic case. The asymptotic behaviour of such waves is obtained. Conclusions. A global study of magneto-gravito-inertial waves in Stellar Radiation zones is achieved in the case of an axisymmetric toroidal magnetic field. In the near future, consequences for angular momentum transport and the case of general differential rotation and azimuthal magnetic field have to be studied. Moreover, the same methodology must be applied to the case of poloidal fields, and the hyperbolic regime has to be carefully studied.
Leonid L Kitchatinov - One of the best experts on this subject based on the ideXlab platform.
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the effective magnetic prandtl number in magnetized and differentially rotating Stellar Radiation zones
arXiv: Solar and Stellar Astrophysics, 2014Co-Authors: G Ruediger, M Schultz, Leonid L KitchatinovAbstract:With application to inner Stellar radiative zones, a linear theory is used to analyze the instability of a dipole-parity toroidal background field, in the presence of density stratification, differential rotation, and realistically small Prandtl numbers. The physical parameters are the normalized latitudinal shear $a$ and the normalized field amplitude $b$. Only the solutions for the wavelengths with the maximal growth rates are considered. If these scales are combined to the radial values of velocity, one finds that the (very small) radial velocity only depends slightly on $a$ and $b$, so that it can be used as the free parameter of the eigenvalue system. The resulting instability-generated tensors of magnetic diffusivity and eddy viscosity are highly anisotropic. The eddy diffusivity in latitudinal direction exceeds the eddy diffusivity in radial direction by orders of magnitude. Its latitudinal profile shows a strong concentration toward the poles which is also true for the effective viscosity which has been calculated via the angular momentum transport of the instability pattern. The resulting effective magnetic Prandtl number reaches values of $O(10^2)$, so that the differential rotation decays much faster than the toroidal background field, which is {the} necessary condition to explain the observed slow rotation of the early red-giant and sub-giant cores by means of magnetic instabilities.
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baroclinic instability in Stellar Radiation zones
The Astrophysical Journal, 2014Co-Authors: Leonid L KitchatinovAbstract:Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar Radiation zones with baroclinic stratification can be unstable. Instabilities in Radiation zones are of crucial importance for angular momentum transport, mixing of chemical species, and, possibly, for magnetic field generation. This paper performs linear analysis of baroclinic instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation nonuniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of baroclinic instability. The instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of Stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic instability onsets at a very small differential rotation of below 1%. The characteristic time of instability growth is about 1000 rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from baroclinic instability in differentially rotating Radiation zones is therefore possible.
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baroclinic instability in Stellar Radiation zones
arXiv: Solar and Stellar Astrophysics, 2014Co-Authors: Leonid L KitchatinovAbstract:Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar Radiation zones with baroclinic stratification can be unstable. Instabilities in Radiation zones are of crucial importance for angular momentum transport, mixing of chemical species and, possibly, for magnetic field generation. This paper performs linear analysis of baroclinic instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation non-uniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of baroclinic instability. The instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of Stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic instability onsets at a very small differential rotation of below 1%. The characteristic time of instability growth is about one thousand rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from baroclinic instability in differentially rotating Radiation zones is, therefore, possible.
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baroclinic instability in differentially rotating stars
Astronomy Letters, 2013Co-Authors: Leonid L KitchatinovAbstract:A linear analysis of baroclinic instability in a Stellar Radiation zone with radial differential rotation is performed. The instability sets in at a very small rotation inhomogeneity, ΔΩ ∼ 10−3Ω. There are two families of unstable disturbances corresponding to Rossby waves and internal gravity waves. The instability is dynamical: its growth time is several thousand rotation periods but is short compared to the Stellar evolution time. A decrease in thermal conductivity amplifies the instability. Unstable disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from the instability is possible.
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helicity and dynamo action in magnetized Stellar Radiation zones
arXiv: Solar and Stellar Astrophysics, 2011Co-Authors: G Ruediger, Leonid L Kitchatinov, Detlef ElstnerAbstract:Helicity and \alpha effect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in Stellar Radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the \alpha effect by the most rapidly growing mode has the same sign as the current helicity of the background field. The \alpha effect is found as too small to drive an \alpha^{2} dynamo but the excitation conditions for an \alpha\Omega dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own \alpha effect by the magnetic instability then problems with its sign do not arise. For all cases, however, the \alpha effect shows an extremely strong concentration to the poles so that a possible \alpha\Omega dynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in Stellar Radiation zones on the basis of the current-driven instability of toroidal fields.
V Urpin - One of the best experts on this subject based on the ideXlab platform.
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rotational suppression of the tayler instability in Stellar Radiation zones
Monthly Notices of the Royal Astronomical Society, 2013Co-Authors: Alfio Bonanno, V UrpinAbstract:The study of the magnetic field in Stellar Radiation zones is an important topic in modern astrophysics because the magnetic field can play an important role in several transport phenomena such as mixing and angular momentum transport. We consider the influence of rotation on stability of a predominantly toroidal magnetic field in the Radiation zone. We find that the effect of rotation on the stability depends on the magnetic configuration of the basic state. If the toroidal field increases sufficiently rapidly with the spherical radius, the instability cannot be suppressed entirely even by a very fast rotation although the strength of the instability can be significantly reduced. On the other hand, if the field increases slowly enough with the radius or decreases, the instability has a threshold and can be completely suppressed in rapidly rotating stars. We find that in the regions where the instability is entirely suppressed a particular type of magnetohydrodynamic waves may exist which are marginally stable.
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stability of the toroidal magnetic field in Stellar Radiation zones
The Astrophysical Journal, 2012Co-Authors: Alfio Bonanno, V UrpinAbstract:The stability of the magnetic field in Radiation zones is of crucial importance for mixing, angular momentum transport, etc. We consider the stability properties of a star containing a predominant toroidal field in spherical geometry by means of a linear stability in the Boussinesq approximation taking into account the effect of thermal conductivity. We calculate the growth rate of instability and analyze in detail the effects of stable stratification and heat transport. We argue that the stabilizing influence of gravity can never entirely suppress the instability caused by electric currents in Radiation zones. However, the stable stratification can essentially decrease the growth rate of instability
J Szulagyi - One of the best experts on this subject based on the ideXlab platform.
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observational constraints on the Stellar Radiation field impinging on transitional disk atmospheres
The Astrophysical Journal, 2012Co-Authors: J Szulagyi, Ilaria Pascucci, Peter Abraham, Daniel Apai, J Bouwman, A MoorAbstract:Mid-infrared atomic and ionic line ratios measured in spectra of pre-main-sequence stars are sensitive indicators of the hardness of the Radiation field impinging on the disk surface. We present a low-resolution Spitzer IRS search for [Ar II] at 6.98 μm, [Ne II] at 12.81 μm, and [Ne III] 15.55 μm lines in 56 transitional disks. These objects, characterized by reduced near-infrared but strong far-infrared excess emission, are ideal targets to set constraints on the Stellar Radiation field onto the disk, because their spectra are not contaminated by shock emission from jets/outflows or by molecular emission lines. After demonstrating that we can detect [Ne II] lines and recover their fluxes from the low-resolution spectra, here we report the first detections of [Ar II] lines toward protoplanetary disks. We did not detect [Ne III] emission in any of our sources. Our [Ne II]/[Ne III] line flux ratios combined with literature data suggest that a soft-EUV or X-ray spectrum produces these gas lines. Furthermore, the [Ar II]/[Ne II] line flux ratios point to a soft X-ray and/or soft-EUV Stellar spectrum as the ionization source of the [Ar II] and [Ne II] emitting layer of the disk. If the soft X-ray component dominates over the EUV, then we would expect larger photoevaporation rates and, hence, a reduction of the time available to form planets.
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observational constraints on the Stellar Radiation field impinging on transitional disk atmospheres
arXiv: Earth and Planetary Astrophysics, 2012Co-Authors: J Szulagyi, Ilaria Pascucci, Peter Abraham, Daniel Apai, J Bouwman, A MoorAbstract:Mid-infrared atomic and ionic line ratios measured in spectra of pre-main sequence stars are sensitive indicators of the hardness of the Radiation field impinging on the disk surface. We present a low-resolution Spitzer IRS search for [Ar II] at 6.98 $\mu$m, [Ne II] at 12.81 $\mu$m, and [Ne III] 15.55 $\mu$m lines in 56 transitional disks. These objects, characterized by reduced near-infrared but strong far-infrared excess emission, are ideal targets to set constraints on the Stellar Radiation field onto the disk because their spectra are not contaminated by shock emission from jets/outflows or by molecular emission lines. After demonstrating that we can detect [Ne II] lines and recover their fluxes from the low-resolution spectra, here we report the first detections of [Ar II] lines towards protoplanetary disks. We did not detect [Ne III] emission in any of our sources. Our [Ne II]/[Ne III] line flux ratios combined with literature data suggest that a soft-EUV or X-ray spectrum produces these gas lines. Furthermore, the [Ar II]/[Ne II] line flux ratios point to a soft X-ray and/or soft-EUV Stellar spectrum as the ionization source of the [Ar II] and [Ne II] emitting layer of the disk. If the soft X-ray component dominates over the EUV than we would expect larger photoevaporation rates hence a reduction of the time available to form planets.
