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For comparison. equivalent results with £j.,=106€ and Oy.=0.5 are plotted by means of symbols in Fig. 2..
For comparison, equivalent results with $\xi_\ion{He}{i} = 10\%$ and $\delta_{\rm He} = 0.5$ are plotted by means of symbols in Fig. \ref{fig:mhdwaves}.
We see that for realistic values of One. Its role is almost irrelevant. meaning that the presence of can be neglected.
We see that for realistic values of $\delta_{\rm He}$ , its role is almost irrelevant, meaning that the presence of can be neglected.
It is worth mentioning that we have repeated these calculations for other values of fij and similar results have been obtained.
It is worth mentioning that we have repeated these calculations for other values of $\mutilde_{\rm H}$ and similar results have been obtained.
Next. we study the thermal mode.
Next, we study the thermal mode.
Since it is a purely damped. non-propagating disturbance (We= 0) we only plot the damping time. rp. as a function of & for jjj=0.8 and dye=0.ἱ (Fig. 3)).
Since it is a purely damped, non-propagating disturbance $\omega_{\rm R} = 0$ ), we only plot the damping time, $\td$, as a function of $k$ for $\mutilde_{\rm H} = 0.8$ and $\delta_{\rm He}=0.1$ (Fig. \ref{fig:therm}) ).
We can see that the effect of helium is different in two ranges of &.
We can see that the effect of helium is different in two ranges of $k$.
For &>107 m. thermal conduction is the dominant damping mechanism.
For $k \gtrsim 10^{-4}$ $^{-1}$, thermal conduction is the dominant damping mechanism.
So. the larger the amount of helium. the smaller rp because of the enhanced thermal conduction by neutral helium atoms.
So, the larger the amount of helium, the smaller $\td$ because of the enhanced thermal conduction by neutral helium atoms.
On the other hand. radiative losses are more relevant for k€1077 m.
On the other hand, radiative losses are more relevant for $k \lesssim 10^{-4}$ $^{-1}$.
In this region. the thermal mode damping time grows as the helium abundance increases.
In this region, the thermal mode damping time grows as the helium abundance increases.
Since these variations of the damping time are very small. we have to conclude again that the damping time obtained in the absence of helium does not significantly change when helium is taken into account.
Since these variations of the damping time are very small, we have to conclude again that the damping time obtained in the absence of helium does not significantly change when helium is taken into account.
Computations with other values of /tj and oy. do not modify this statement.
Computations with other values of $\mutilde_{\rm H}$ and $\delta_{\rm He}$ do not modify this statement.
We can estimate the effect of a magnetic structure. say a slab ora cylinder. which would act as a waveguide.
We can estimate the effect of a magnetic structure, say a slab ora cylinder, which would act as a waveguide.
To do so. weset the wavenumber component in the perpendicular direction to magnetic field lines to a fixed value. k-L= 2/2. with La typical length-scale in the perpendicular
To do so, weset the wavenumber component in the perpendicular direction to magnetic field lines to a fixed value, $k_z L = \pi/2$ , with $L$ a typical length-scale in the perpendicular
2003).
.
. They are generally based on the detinition of fossil groups from Jonesetal.2003).. i.e. groups with a minimum X-ray luminosity of Lx70.251077) "erg las well as minimum magnitude difference of two between the first and second ranked galaxies. within half the projected radius that encloses an overdensity of 200 times the mean density of the universe (ους).
They are generally based on the definition of fossil groups from \citet{b65}, i.e. groups with a minimum X-ray luminosity of $L_{\rm X,bol} \approx 0.25 \times 10^{42} h^{-2}$ erg $^{-1}$, as well as minimum magnitude difference of two between the first and second ranked galaxies, within half the projected radius that encloses an overdensity of 200 times the mean density of the universe $R_{200}$ ).
For an NFW profile (Navarro.Frenk 1996). this is roughly equivalent to /7?555. the radius enclosing an overdensity of SOO times the mean (for NFW haloes of the ypropriate concentration. {έτος~0.59 Royo)
For an NFW profile \citep{b123}, , this is roughly equivalent to $R_{500}$, the radius enclosing an overdensity of 500 times the mean (for NFW haloes of the appropriate concentration, $R_{500} \sim 0.59 \times R_{200}$ ).
A few of these fossil groups have been the subject of detailed investigations (Khosroshahi.Jones&Ponman2004:Yoshiokaetal.Sunetal. 2006).
A few of these fossil groups have been the subject of detailed investigations \citep{b75,b185,b165,b167,b45,b100,b80}.
. While most previous studies have focused on X-ray properties of fossils. there is also emerging evidence that the galaxy properties in fossils are different from those in non-fossils (Khosroshahi.Ponman&Jones 2006).
While most previous studies have focused on X-ray properties of fossils, there is also emerging evidence that the galaxy properties in fossils are different from those in non-fossils \citep{b82}.
. For instance the isophotal shapes of the central fossil galaxies appear to be non-boxy. suggesting that they may have formed in gas rich mergers.
For instance the isophotal shapes of the central fossil galaxies appear to be non-boxy, suggesting that they may have formed in gas rich mergers.
Various observational and theoretical studies have suggested a significant fraction of galaxy groups to be fossils (Vikhlininetal.1999:Jones 2006).. though often the criteria used to detine fossils in theoretical work are not easy to relate to observational studies.
Various observational and theoretical studies have suggested a significant fraction of galaxy groups to be fossils \citep{b170,b65,b50,b115,b147}, though often the criteria used to define fossils in theoretical work are not easy to relate to observational studies.
Fossils may represent extreme examples of a continuum of group properties — they are consistently found to be outliers in the usual scaling relations involving optical. X-ray and dynamical properties (Khosroshahi.Ponman&Jones2007).
Fossils may represent extreme examples of a continuum of group properties – they are consistently found to be outliers in the usual scaling relations involving optical, X-ray and dynamical properties \citep{b85}.
. While fossils fall on the L-T relation of non-fossil groups and clusters. they appear to be both hotter and more X-ray luminous than non-fossils of the same mass.
While fossils fall on the L-T relation of non-fossil groups and clusters, they appear to be both hotter and more X-ray luminous than non-fossils of the same mass.
Cooler fossil groups also show lower entropy than their non-fossil counterparts.
Cooler fossil groups also show lower entropy than their non-fossil counterparts.
According to Khosroshahi.Pon-man&Jones (2007). the haloes of fossil groups appear to be more concentrated than those of non-fossil systems. for a given mass. which suggests that fossils have an early formation epoch.
According to \citet{b85}, the haloes of fossil groups appear to be more concentrated than those of non-fossil systems, for a given mass, which suggests that fossils have an early formation epoch.
As such. we have much to learn from them. and the investigation of objects with similar properties in cosmological simulations can provide important insights into the physical processes that underly the scaling relations.
As such, we have much to learn from them, and the investigation of objects with similar properties in cosmological simulations can provide important insights into the physical processes that underly the scaling relations.
It can also reveal limitations in the numerical simulations. related to the treatment of physical effects like pre-heating. feedback and merging. which are difficult to model.
It can also reveal limitations in the numerical simulations, related to the treatment of physical effects like pre-heating, feedback and merging, which are difficult to model.
It is thus important to study the formation and evolution of these systems in the cosmological N-Body simulations which have become essential tools for studying formation of large scale structure in the Universe.
It is thus important to study the formation and evolution of these systems in the cosmological N-Body simulations which have become essential tools for studying formation of large scale structure in the Universe.
In this paper we use the Millennium simulation (Springeletal.2005) together with the semi-analytic models (Crotonetal.2006) of galaxy formation within dark matter haloes and the Millennium gas simulation (Pearceetal.20073.. to identify fossil groups. study their properties in the simulations and make a comparison to the observations.
In this paper we use the Millennium simulation \citep{b160} together with the semi-analytic models \citep{b40} of galaxy formation within dark matter haloes and the Millennium gas simulation \citep{b128}, to identify fossil groups, study their properties in the simulations and make a comparison to the observations.
We begin with a brief discussion in 322 of the Millennium Simulation. and the implemented semi-analytic galaxy catalogues and gas simulations.
We begin with a brief discussion in 2 of the Millennium Simulation, and the implemented semi-analytic galaxy catalogues and gas simulations.
In $33 we discuss our method of identifying andX-rav fossil groups from these catalogues.
In 3 we discuss our method of identifying and fossil groups from these catalogues.
In S44. we discuss the various properties of these fossil groups. their abundance in the local Universe and the evolution of simulated X-ray fossils with time.
In 4, we discuss the various properties of these fossil groups, their abundance in the local Universe and the evolution of simulated X-ray fossils with time.
Finally. in $55. we summarize the implications of our results in terms of the evolution of fossil groups in the context of multiwavelength observations.
Finally, in 5, we summarize the implications of our results in terms of the evolution of fossil groups in the context of multiwavelength observations.
Throughout the paper we adopt {ο=100/ kms + ¢ for the Hubble constant.
Throughout the paper we adopt $H_{0} = 100 \,h$ km $^{-1}$ $^{-1}$ for the Hubble constant.
In order to extract fossil groups in the Millennium simulation. using observational selection criteria. we require a simulation suite that includes the baryonic physics of hot gas and galaxies. as well as a high resolution dark matter framework and a sufficient spatial volume to limit the effects of cosmic variance.
In order to extract fossil groups in the Millennium simulation, using observational selection criteria, we require a simulation suite that includes the baryonic physics of hot gas and galaxies, as well as a high resolution dark matter framework and a sufficient spatial volume to limit the effects of cosmic variance.
For this study we use the dark matter Millennium Simulation (Springeletal.2005).. a 10-billion particle model of a comoving volume of side 5005.+ Mpc. on top of which a publicly available semi-analytic galaxy model (Crotonetal.2006). has been constructed.
For this study we use the dark matter Millennium Simulation \citep{b160}, a 10-billion particle model of a comoving volume of side $h^{-1}$ Mpc, on top of which a publicly available semi-analytic galaxy model \citep{b40} has been constructed.
For the hot gas we have repeated the Millennium simulation with a lower resolution simulation including gas physics utilising the same volume. phases and amplitudes as the original dark-matter-only model.
For the hot gas we have repeated the Millennium simulation with a lower resolution simulation including gas physics utilising the same volume, phases and amplitudes as the original dark-matter-only model.
This run accurately reproduces the structural framework of the Millennium Simulation (Pearceetal.20073.
This run accurately reproduces the structural framework of the Millennium Simulation \citep{b128}.
. Below we summarize the main characteristics of the above simulations.
Below we summarize the main characteristics of the above simulations.
The Millennium Simulation is based on a Cold) Dark Matter cosmological model of structure formation. with a Dark Energy field A.
The Millennium Simulation is based on a Cold Dark Matter cosmological model of structure formation, with a Dark Energy field $\Lambda$.
The basic assumptions are those of an inflationary universe. dominated by dark matter particles. leading to a bottom-up hierarchy of structure formation. via collapsing and merging of small dense haloes at high redshifts. into the large virialised systems such as groups and clusters that contain the galaxies that we observe today.
The basic assumptions are those of an inflationary universe, dominated by dark matter particles, leading to a bottom-up hierarchy of structure formation, via collapsing and merging of small dense haloes at high redshifts, into the large virialised systems such as groups and clusters that contain the galaxies that we observe today.
The simulation was performed using the publiclyavailable parallel TreePM code Gadget? (Springeletal. 2001). achieving a 3D dynamic range of 10" by evolving 2160* particles of individual mass 8.6.1075.+ M.. within a co-moving periodic box of side 500.+ Mpc. and employing a gravitational softening of Sf! kpc. from redshift >=127 to he present day.
The simulation was performed using the publiclyavailable parallel TreePM code Gadget2 \citep{b155}, achieving a 3D dynamic range of $10^5$ by evolving $^3$ particles of individual mass $8.6\times10^{8}h^{-1}$ $_{\odot}$, within a co-moving periodic box of side $h^{-1}$ Mpc, and employing a gravitational softening of $h^{-1}$ kpc, from redshift $z=127$ to the present day.
The cosmological parameters for the Millennium Simulation were: (34.=0.75.0,,0.25.0),0.045.0)i3.nΞ ]. and oy=0.9. where the Hubble constant is characterised as 100kms.‘Alpe+. These cosmological xrameters are consistent with recent combined analysis from data (Spergeletal.2003) and the 2dF galaxy redshift survey (Collessetal.2001). although the value for ax is a little ligher than would perhaps have been desirable in retrospect.
The cosmological parameters for the Millennium Simulation were: $\Omega_\Lambda = 0.75, \Omega_M = 0.25, \Omega_b = 0.045, h = 0.73, n = 1$ , and $\sigma_8 = 0.9$, where the Hubble constant is characterised as $100 \,h \,{\rm km s^{-1} Mpc^{-1}}.$ These cosmological parameters are consistent with recent combined analysis from data \citep{b146} and the 2dF galaxy redshift survey \citep{b31}, although the value for $\sigma_8$ is a little higher than would perhaps have been desirable in retrospect.
The derived dark matter halo catalogues include haloes down o a resolution limit of 20 particles. which yields a minimum xilo mass of 10775.! M..
The derived dark matter halo catalogues include haloes down to a resolution limit of 20 particles, which yields a minimum halo mass of $\times 10^{10}h^{-1}$ $_{\odot}$.
Haloes in the simulation are ound using a friends-of-friends (FOF) group. finder. tuned. to extract haloes with overdensities of at least 200 relative to the critical density.
Haloes in the simulation are found using a friends-of-friends (FOF) group finder, tuned to extract haloes with overdensities of at least 200 relative to the critical density.
Within a FOF halo. substructures or subhaloes are identified using the SUBFIND algorithm developed by Springelal. (2001). and the treatment of the orbital decay of satellites is deseribed in the next section.
Within a FOF halo, substructures or subhaloes are identified using the SUBFIND algorithm developed by \citet{b155}, and the treatment of the orbital decay of satellites is described in the next section.
During the Millennium Simulation. 64 time-slices of the locations and. velocities of all the particleswere stored. spread approximately logarithmically in time between +=127 and += 0.
During the Millennium Simulation, 64 time-slices of the locations and velocities of all the particleswere stored, spread approximately logarithmically in time between $z=127$ and $z=0$ .
From these time-slices. merger trees are built by combining the tables of all haloes found at any given output time. a process which enables us to trace the growth of haloes and their subhaloes through time within the simulation.
From these time-slices, merger trees are built by combining the tables of all haloes found at any given output time, a process which enables us to trace the growth of haloes and their subhaloes through time within the simulation.
with sz,=1—sz+97 for szxlors: =-(s2+52-1) otherwise.
with $s_{w}^{2}={1-s^{2}_{u}+s^{2}_{v}}$ for $s^{2}_{u}+s^{2}_{v}\le1$ or $s_{w}^{2}=- ({s^{2}_{u}+s^{2}_{v}-1})$ otherwise.
Complex values of s, lead to exponentially decaying (evanescent) electric fields that are typically not measurable far from the scatterer.
Complex values of $s_{w}$ lead to exponentially decaying (evanescent) electric fields that are typically not measurable far from the scatterer.
The other (homogeneous) waves are those measured by a distant observer.
The other (homogeneous) waves are those measured by a distant observer.
If one further uses the Fourier transform of the scattering potential. (s)=(ffdane"Fu. one can write the scattered electric field üs where we assume a geometry where w=0 is the ground-plane below the ionosphere where 7=1. and that w>O is in the direction of the zenith or the phase reference center (see below).
If one further uses the Fourier transform of the scattering potential, $\tilde{\Phi}(\vc{s}) = \iiint \Phi(\vc{u}) e^{-2 \pi i \vc{s} \cdot \vc{u}} d^{3}\vc{u},$ one can write the scattered electric field as where we assume a geometry where $w=0$ is the ground-plane below the ionosphere where $n=1$, and that $w>0$ is in the direction of the zenith or the phase reference center (see below).
The interferometer is placed in a plane defined at a constant way=zui.
The interferometer is placed in a plane defined at a constant $w_{\rm ant} = z_{\rm ant}/\lambda$.
Typically one ean assume Wyn.=0.
Typically one can assume $w_{\rm ant}=0$.
Thence. one finds a relation between the Fourter transform of the observed electric field in the plane of the interferometer at Wan, and the Fourter transform of the scattering potential with E'?(s,.5.)=ITVeWandedaddy.
Thence, one finds a relation between the Fourier transform of the observed electric field in the plane of the interferometer at $w_{\rm ant}$ and the Fourier transform of the scattering potential with $ \tilde{E}^{(s)}(s_{u}, s_{v}) = \iint E_{1}^{(s)}(u,v,w_{\rm ant}) e^{ + 2 \pi i (s_{u} u + s_{v} v)} du dv$.
This can be regarded as the Fourier Ea.transform of a two-dimensional slice through a three-dimensional scattered electric field.
This can be regarded as the Fourier transform of a two-dimensional slice through a three-dimensional scattered electric field.
In this paper we do not treat the case of an interferometer with varying Way.
In this paper we do not treat the case of an interferometer with varying $w_{\rm ant}$.
A planar array is an reasonable assumption for relatively compact kkm-seale) interferometers. but breaks down on large scales where the curvature of the Earth can not be neglected2009).
A planar array is an reasonable assumption for relatively compact km-scale) interferometers, but breaks down on large scales where the curvature of the Earth can not be neglected.
. For a planar array. however. the w-term due to the array can be neglected for small integration times unstantaneous sampling of the electric field in à plane). in contrast to visibilities from very different time frames where the array has rotated over a substantial angle compared to the phase center (only a linear east-west array does not suffer from the w-term).
For a planar array, however, the $w$ -term due to the array can be neglected for small integration times instantaneous sampling of the electric field in a plane), in contrast to visibilities from very different time frames where the array has rotated over a substantial angle compared to the phase center (only a linear east-west array does not suffer from the $w$ -term).
The physical interpretation of Eqn.(8)) is the following: Every point of the two-dimensional Fourier transform of the scattered electric fieldin the plane of an interferometer probes a single three-dimensional mode of the scattering potential tthe scattering medium) for a single point source.
The physical interpretation of \ref{eqn:scattered_field}) ) is the following: Every point of the two-dimensional Fourier transform of the scattered electric field in the plane of an interferometer probes a single three-dimensional mode of the scattering potential the scattering medium) for a single point source.
In the presence of N point sources. all in different directions. every point of the two-diminsional Fourier transform of the scattered electric field in the plane of an interferometer probes the sum of N independent three-dimensional modes of the scattering potential.
In the presence of $N$ point sources, all in different directions, every point of the two-diminsional Fourier transform of the scattered electric field in the plane of an interferometer probes the sum of $N$ independent three-dimensional modes of the scattering potential.
In Section5 we show how to unravel this information.
In Section 5 we show how to unravel this information.
In radio interferometry one does not analyze the electric field itself.
In radio interferometry one does not analyze the electric field itself.
In that case. Eqn.(8)) would directly yield the three-dimensional structure of the ionosphere (per integration time) because the phase information of the Fourier transform of the electron density of the tonosphere is fully retained in the phase information of the scattered electric field.
In that case, \ref{eqn:scattered_field}) ) would directly yield the three-dimensional structure of the ionosphere (per integration time) because the phase information of the Fourier transform of the electron density of the ionosphere is fully retained in the phase information of the scattered electric field.
In reality. only the cross-correlations of the electric field. measured at different antennae pairs. are stored tthe complex visibilities) and the phase information. of thetonospherie density fluctuationsis lost.
In reality, only the cross-correlations of the electric field, measured at different antennae pairs, are stored the complex visibilities) and the phase information of the ionospheric density fluctuations is lost.
In the following. we assume that the total electric field from the entire sky tthe antenna sensitivity is directionally independent) ismeasured over the infinite interferometer plane with w2Wane.
In the following, we assume that the total electric field from the entire sky the antenna sensitivity is directionally independent) ismeasured over the infinite interferometer plane with $w=w_{\rm ant}$.
Visibilities are sampled from the cross-correlation of the electric field E(u)=A+Eu) with its complex conjugate. Vibb=«ΕΕια+b», with b. being the baseline between two points (antennae) in plane of the interferometer.
Visibilities are sampled from the cross-correlation of the electric field $E(\vc{u}) = E^{(i)}(\vc{u}) + E^{(s)}(\vc{u})$ with its complex conjugate, $V(\vc{b})\equiv \langle E(\vc{u}) E^{*}(\vc{u} + \vc{b}) \rangle_{\rm t}$ with $\vc{b}$ being the baseline between two points (antennae) in plane of the interferometer.
The averaging 1s assumed to be over time.
The averaging is assumed to be over time.
The Fourier transform of the visibilities forms the incident intensity from the sky. as follows from the van Cittert-Zernike theorem2009).
The Fourier transform of the visibilities forms the incident intensity from the sky, as follows from the van Cittert-Zernike theorem.
. The same intensity is also the product of the Fourier transform of the electric field with its complex conjugate.
The same intensity is also the product of the Fourier transform of the electric field with its complex conjugate.
A bit of algebra shows that the cross-correlation between the incident and scattered fields depends on the imaginarypart of the zero-mode. 4X0). of the ionosphere. and consequently is equal to zero.
A bit of algebra shows that the cross-correlation between the incident and scattered fields depends on the imaginary part of the zero-mode, $\tilde{\Phi}(0)$, of the ionosphere, and consequently is equal to zero.
The multiplication of the Fourier transform of the scattered electric field with its complex conjugate therefore provides the complete scattered intensity where the dependence on Wan --
The multiplication of the Fourier transform of the scattered electric field with its complex conjugate therefore provides the complete scattered intensity where the dependence on $w_{\rm ant}$ disappears.
Using Eqn.(8)). we find the following result This equation is exact for phase-coherent point sources to first order Born approximation.
Using \ref{eqn:scattered_field}) ), we find the following result This equation is exact for phase-coherent point sources to first order Born approximation.
However. the sky is an incoherent emitterfields).
However, the sky is an incoherent emitter.
. Hence. the cross-terms with 2zi depend on the electric field coming from incoherent point sources and vanish. such that we are left with where we dropped the subscript.
Hence, the cross-terms with $n\neq m$ depend on the electric field coming from incoherent point sources and vanish, such that we are left with where we dropped the subscript.
This equation forms the basis for further discussions in the paper.
This equation forms the basis for further discussions in the paper.
The above equation is only correct for an interferometer and an electric field measured ina plane.
The above equation is only correct for an interferometer and an electric field measured in a plane.
In three dimensions. one would no longer be able to use simple Fourier transforms (see below). because 5, depends explicitly on s», and ον.
In three dimensions, one would no longer be able to use simple Fourier transforms (see below), because $s_{w}$ depends explicitly on $s_{u}$ and $s_{v}$.
To understand the physical interpretation of the above equation. one might suppose a point source in the zenith (or equivalently in the phase center) emitting a plane wave in the absence of the tonosphere.
To understand the physical interpretation of the above equation, one might suppose a point source in the zenith (or equivalently in the phase center) emitting a plane wave in the absence of the ionosphere.
Because the phase of the electric field 1s the same at each antenna (by construction). its Fourter transform yields a complex delta function in the zenith with a time-varying phase.
Because the phase of the electric field is the same at each antenna (by construction), its Fourier transform yields a complex delta function in the zenith with a time-varying phase.
Multiplied with its complex conjugate. this recovers the point source intensity.
Multiplied with its complex conjugate, this recovers the point source intensity.
If a two-dimensional thin phase-screen is placed in between the source and the array. exhibiting a single wave-mode in electron density perpendicular to the zenith or phase reference center direction. then part of the electric field amplitude will be modulated such that its phases show to first order the imprint of this ionospheric wave-mode description).
If a two-dimensional thin phase-screen is placed in between the source and the array, exhibiting a single wave-mode in electron density perpendicular to the zenith or phase reference center direction, then part of the electric field amplitude will be modulated such that its phases show to first order the imprint of this ionospheric wave-mode .
. The modulated phase aa single wave over the array) can be interpreted as being identical in. the weak scattering limit to the modulated phase of a point source offset from the zenith in the direction of the ionospheric wave- by a distance set by the phase-frequency over the array.
The modulated phase a single wave over the array) can be interpreted as being identical in the weak scattering limit to the modulated phase of a point source offset from the zenith in the direction of the ionospheric wave-vector by a distance set by the phase-frequency over the array.
Hence. squared.
Hence, .
The sum of all speckles create à halo of scattered emission around the point source. when not corrected forthrough phase calibration.
The sum of all speckles create a halo of scattered emission around the point source, when not corrected forthrough phase calibration.
First we investigate the effects of outer truncation.
First we investigate the effects of outer truncation.
Convolved synthetic maps for the emission in [OI]. 6300 for some numerical models and run (500.1000.0.5) are given in Fig. 6..
Convolved synthetic maps for the emission in [OI] $\lambda$ 6300 for some numerical models and run (500,1000,0.5) are given in Fig. \ref{Fig_emissmaps_outertrunc}.
Truncation leads to collimation of the emission region with respect to the model ADO without any truncation.
Truncation leads to collimation of the emission region with respect to the model ADO without any truncation.
Agam we extracted the jet width from emission maps like these.
Again we extracted the jet width from emission maps like these.
The resulting widths derived from the synthetic [OI] images and sealed to AU are presented in Fig. 7..
The resulting widths derived from the synthetic [OI] images and scaled to AU are presented in Fig. \ref{jet_widths_modelSC}.
We found similarities in. behavior in the truncated. models to the untruncated model ADO.
We found similarities in behavior in the truncated models to the untruncated model ADO.
The jet widths show again no dependency on the density. as described for model ADO in the previous section.
The jet widths show again no dependency on the density, as described for model ADO in the previous section.
Surprisingly. in. models SCla-c. SC2 and SC4 the runs (500.600.0.2) and (500.1000.0.5) and also (500.1000.0.8) lead to almost similar physical Jet widths.
Surprisingly, in models SC1a-c, SC2 and SC4 the runs (500,600,0.2) and (500,1000,0.5) and also (500,1000,0.8) lead to almost similar physical jet widths.
The first two also almost coincide in models SCId-e. As in model ADO. also in the truncated models the run (500.600.0.5) has the smallest jet widths (after the first bump).
The first two also almost coincide in models SC1d-e. As in model ADO, also in the truncated models the run (500,600,0.5) has the smallest jet widths (after the first bump).
In principle. we can reproduce even smaller values than the observed ones.
In principle, we can reproduce even smaller values than the observed ones.
In paper I we also performed numerical simulations. in which we truncated the analytical solution in the interior. Le. at an inner truncation radius.
In paper I we also performed numerical simulations, in which we truncated the analytical solution in the interior, i.e. at an inner truncation radius.
The physical picture behind. this scenario is a stellar magnetosphere truncating the jet-emitting disk.
The physical picture behind this scenario is a stellar magnetosphere truncating the jet-emitting disk.
We showed that inner truncation leads to a decrease of the jet radius and compression of the material in the inner region.
We showed that inner truncation leads to a decrease of the jet radius and compression of the material in the inner region.
Unfortunately. only one run met our scaling requirements (Sect. 3.1)):
Unfortunately, only one run met our scaling requirements (Sect. \ref{sec_norm}) ):
model SC3 and run (---. 100. 0.2).
model SC3 and run $\cdots$, 100, 0.2).