ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
⇂⊳∖↥∩∖∖↽⋯⋯⇂≺↵2i 2EE 24: ⋅ ⋅ frequencies⋅ are oeiven⋅ by we.fis7 Ὀίωτ-,een>οαπ)τε0ο-⇁(ωρα/aAστ—kheie.12 where wy7=ck> ancl =í(k-.b)/p.	The fast and slow mode frequencies are given by $\omega^2_{f,s} =.5(\omega_b^2+\omega_s^2) \pm 0.5 \left( (\omega_b^2+\omega_s^2)^2 - 4\omega_s^2 \omega_a^2 \right)^{1/2}$ where $\omega_s^2=c_s^2k^2$ and $\omega_a^2=(\kvec \cdot \bvec)^2/\rho$.
We7g- evolvedH the waves for one. period.	We evolved the waves for one period.
TheJ results for the" fast andwy slow waves are shown in figures 3. aud. L. respectively.	The results for the fast and slow waves are shown in figures \ref{fig:fast} and \ref{fig:slow}, respectively.
The slow wave is subject to substantial diffusion as compared to the [ast wave siuce its [requency isso uch lower for these extreme values of 5».	The slow wave is subject to substantial diffusion as compared to the fast wave since its frequency isso much lower for these extreme values of $\beta$.
These 1d tests of the code involve a shock tube along the x-axis. as in fig.2a.b of ?..	These 1d tests of the code involve a shock tube along the x-axis, as in fig.2a,b of \citet{1998ApJ...509..244R}.
We used continuous boundary coucditious aud 1021 grkl points for both tests.	We used continuous boundary conditions and 1024 grid points for both tests.
The initial conditions for lig.5 are (p.ey.cy.t:.pb,by.b.)=(1.10.0.0.20.5/νax.5/V15.0) for the left side and (1.10.0.0.1.5/VIm.15.0) for the right side.	The initial conditions for \ref{fig:shock1} are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)= (1,10,0,0,20,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the left side and $(1,-10,0,0,1,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the right side.
The code is run for a time 0.08L.	The code is run for a time $0.08 L$.
The result agrees well with ποσα of ?..	The result agrees well with fig.2a of \citet{1998ApJ...509..244R}.
The following features cau be seen.	The following features can be seen.
The steep discontinulties atorQoL aud ar0.82 are fast shock frouts where the incoming flow couverts its kinetic energy into thermal energy aid compresses the trausverse field b,.	The steep discontinuities at $x\sim 0.1$ and $x\sim 0.85$ are fast shock fronts where the incoming flow converts its kinetic energy into thermal energy and compresses the transverse field $b_y$.
As new matter [alls on. this shock is regenerated and maintains it’s steep profile as it moves outward.	As new matter falls on, this shock is regenerated and maintains it's steep profile as it moves outward.
At ic~0.6 and pc90.2 are a slow shock aud W.slow rarefaction. respectively.	At $x\simeq 0.6$ and $x \simeq 0.5$ are a slow shock and slow rarefaction, respectively.
The slow shock again compresses the fluicl but decreases the transverse field.	The slow shock again compresses the fluid but decreases the transverse field.
At ar20.55 the two phases of the initial gas configuration with different eutropies form a contact discontinuity.	At $x\simeq 0.55$ the two phases of the initial gas configuration with different entropies form a contact discontinuity.
Pressure. magnetic fiekl auc velocity are continuous while density aud thermal enerey experience a discontinuity.	Pressure, magnetic field and velocity are continuous while density and thermal energy experience a discontinuity.
This discontuity moves rightward across the grid. aud the TVD advection of such discoutinuities results in some smeariug or diffusion of the structure.	This discontuity moves rightward across the grid, and the TVD advection of such discontinuities results in some smearing or diffusion of the structure.
No pliysical mechauisma steepeus this contact. discontiuuitv once it sinears. aud a slow numerical diffusion is visible in this. aud all generic TVD codes which do uot introduce explicit contact steepeners.	No physical mechanism steepens this contact discontinuity once it smears, and a slow numerical diffusion is visible in this, and all generic TVD codes which do not introduce explicit contact steepeners.
There are no significant oscillations.	There are no significant oscillations.
Both our aud ?"s solution have a slight overshoot in some variables in the first postshock cell. but this effect does uot persist onto subsequent cells.	Both our and \citet{1998ApJ...509..244R}' 's solution have a slight overshoot in some variables in the first postshock cell, but this effect does not persist onto subsequent cells.
The initial couditiou for Ge.6 has velocity and maguetic field components in all directions. aud hence exhibits additional structures such asrotational discontinuities.	The initial condition for \ref{fig:shock2} has velocity and magnetic field components in all directions, and hence exhibits additional structures such asrotational discontinuities.
The values are (p.ty.espbby.b.) = (1.08.1.2.0.01.0.5.0.05.ήνE.3.6/V/Ex.2/Ix) on the left side and (1.0.0.0.1.2//Ez.L/v/E.VDc) ou tlie right hand side.	The values are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)$ = $(1.08,1.2,0.01,0.5, 0.95,2/\sqrt{4\pi},3.6/\sqrt{4\pi},2/\sqrt{4\pi})$ on the left side and $(1,0,0,0,1,2/\sqrt{4\pi},4/\sqrt{4\pi},2/\sqrt{4\pi})$ on the right hand side.
The code is run for a time 0.2L.	The code is run for a time $0.2 L$.
The results again agreewith ?..	The results again agreewith \citet{1998ApJ...509..244R}.
The following features may be seen: fast shocksator20.3 aud 0.9. rotational discontiuuity at ο220.53 right uext to a slow shock at ο2 0.55. contact. discontiuulty at or2 0.6. slow shock aud. rotational discontinuity at 0.68 and 0.70 respectively.	The following features may be seen: fast shocksat$x\simeq 0.3$ and $0.9$ , rotational discontinuity at $x\simeq 0.53$ right next to a slow shock at $x \simeq 0.55$ , contact discontinuity at $x \simeq 0.6$ , slow shock and rotational discontinuity at $0.68$ and $0.70$ respectively.
Excluding those clusters whose position angles suller [rom large uncertainties. we end up with a smaller subsample of 13 clusters and redetermined (he number Iraction distribution as a funetion of ó.	Excluding those clusters whose position angles suffer from large uncertainties, we end up with a smaller subsample of $13$ clusters and redetermined the number fraction distribution as a function of $\phi$ .
Figure 4. plots the results.	Figure \ref{fig:compare2} plots the results.
As it can be seen. the distribution has a hieher peak at (he second bin but süll deviates significantly from (he numerical result. based on a ACDAL cosmology and the semi-analvtie galaxy formation model.	As it can be seen, the distribution has a higher peak at the second bin but still deviates significantly from the numerical result based on a $\Lambda$ CDM cosmology and the semi-analytic galaxy formation model.
The recaleulation of V for this case rejects the hypothesis that the observational result. [rom the 13 clusters is consistent with the numerical result is rejected at the 95%. confidence level.	The recalculation of $\chi^{2}$ for this case rejects the hypothesis that the observational result from the $13$ clusters is consistent with the numerical result is rejected at the $95\%$ confidence level.
lt is worth mentioning the differences in the redshill range between the numerical ancl observational data used for the above comparison: The munerical result has been obtained al 2=0 while the observational results have been drawn [rom the galaxy. clusters al 0.3.	It is worth mentioning the differences in the redshift range between the numerical and observational data used for the above comparison: The numerical result has been obtained at $z=0$ while the observational results have been drawn from the galaxy clusters at $0.1<z<0.3$ .
This difference in the redshift range. however. would even worsen the disagreement between the munerical and the observational result for the following5 reason.	This difference in the redshift range, however, would even worsen the disagreement between the numerical and the observational result for the following reason.
As mentioned in 82 and as shown by N-bocly simulations (e.g..Dailin&Steinmetz2005:etal.AltayAltavetal.2006:2006;Lee&KangΊναπο 2006).. 0the correlationsrrelations between the major axes of[dark dark matter and satellite galaxy distributions tend to be stronger at higher redshifts.	As mentioned in 2 and as shown by N-body simulations \citep[e.g.,][]{BS05,bailin-etal05,atlay-etal06,LK06}, the correlations between the major axes of dark matter and satellite galaxy distributions tend to be stronger at higher redshifts.
In other words. the predicted strength of the correlations used lor the comparison with the observational result is underestimated.	In other words, the predicted strength of the correlations used for the comparison with the observational result is underestimated.
One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analvsis of Oeurietal.(2010) only those bright galaxies with mag222 al r-band are used unlike in the numerical analvsis.	One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analysis of \citet{Oguri-etal10} only those bright galaxies with $mag > 22$ at r-band are used unlike in the numerical analysis.
Recall. however. that we used the Iuminositv-weighted ealaxv distributions in the numerical analysis to determine the major axes. which should minimize (he expected selection bias.	Recall, however, that we used the luminosity-weighted galaxy distributions in the numerical analysis to determine the major axes, which should minimize the expected selection bias.
Another difference lies in the values of the cosmological parameters used for the Run simulations.	Another difference lies in the values of the cosmological parameters used for the mili-Millennium Run simulations.
Especially. the value of σς chosen by the Millennium Run simulation has been known to be higher than the WALAP value (IxXomatsuetal.2010).	Especially, the value of $\sigma_{8}$ chosen by the Millennium Run simulation has been known to be higher than the WMAP value \citep{wmap7}.
. The correlations between dark matter and satellite galaxy distributions in (riaxial clusters. however. are unlike to be significantly affected by the initial cosmological conditions. since il represents a nonlinear observable rather than a linear one.	The correlations between dark matter and satellite galaxy distributions in triaxial clusters, however, are unlike to be significantly affected by the initial cosmological conditions, since it represents a nonlinear observable rather than a linear one.
Now that we have found (the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy. clusters to be inconsistent with the numerical prediction based on a ACDMcosmology and (he semi-analvtic galaxy. lormation model. we	Now that we have found the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy clusters to be inconsistent with the numerical prediction based on a $\Lambda$ CDMcosmology and the semi-analytic galaxy formation model, we
We detected 7 min continuum emission towards each of the three observed sources.	We detected 7 mm continuum emission towards each of the three observed sources.
The position. flux densities. and angular size of the detected radio sources are given in Table 2..	The position, flux densities, and angular size of the detected radio sources are given in Table \ref{tbl-obspar}.
In what follows we present the results of our continuum observations and discuss the nature of the detected. sources in each of the regions. imdividuallv.	In what follows we present the results of our continuum observations and discuss the nature of the detected sources in each of the regions, individually.
For the derivation of plivsical parameters we used (he distances given by Sridharan et al. (	For the derivation of physical parameters we used the distances given by Sridharan et al. (
2002) and listecl in Table 3.	2002) and listed in Table 3.
Figure \| shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044.	Figure \ref{fig-18470maps} shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044.
The emission arises from two distinct compact sources separated by ((labelecd A and D).	The emission arises from two distinct compact sources separated by (labeled A and B).
Both sources were also detected at 3.6 em and 6.0 em wavelengths.	Both sources were also detected at 3.6 cm and 6.0 cm wavelengths.
A contour map of the 3.6 em emission is shown in the lower panel of Fig. 1..	A contour map of the 3.6 cm emission is shown in the lower panel of Fig. \ref{fig-18470maps}.
Component A is associated with a massive dust core detected at 350 and 450 jim by Williams et al. (	Component A is associated with a massive dust core detected at 850 and 450 $\mu$ m by Williams et al. (
2004) and at 1200 jan by Deuther et al. (	2004) and at 1200 $\mu$ m by Beuther et al. (
20028).	2002a).
At 1.2 mm the core has major and minor axis of 1T and12”.. respectivelv. implving a core radius. estimated [rom the geometric mean of the axis. of 0.29 pe (assuming a distance of 8.2 kpc).	At 1.2 mm the core has major and minor axis of 17 and, respectively, implying a core radius, estimated from the geometric mean of the axis, of 0.29 pc (assuming a distance of 8.2 kpc).
The mass of the core determined [rom the 850. jan observations is 720AL.	The mass of the core determined from the 850 $\mu$ m observations is 720.
.. The peak position of the core is marked with a cross in Fig. 1..	The peak position of the core is marked with a cross in Fig. \ref{fig-18470maps}.
The spectral index of the emission between 5.0 ancl 43.4 Giz are —0.1250.1 ancl —O0.140.1 for the east (A) ancl west (D) components. respectively. indicating that the emission in this frequency range is optically thin thermal emission.	The spectral index of the emission between 5.0 and 43.4 GHz are $-0.1\pm0.1$ and $-0.1\pm0.1$ for the east (A) and west (B) components, respectively, indicating that the emission in this frequency range is optically thin thermal emission.
We conclude (hat the emission from these two objects is [ree-free emission from ionized gas.	We conclude that the emission from these two objects is free-free emission from ionized gas.
Table 3. lists the distance [col. (	Table \ref{tbl-derived} lists the distance [col. (
2)]. the derived parameters of the regions of ionized gas: diameter [col. (	2)], the derived parameters of the regions of ionized gas: diameter [col. (
3)]. emission measure (col. (	3)], emission measure [col. (
4)]. and electron density \|col. (	4)], and electron density [col. (
5)]. the minimum number of ionizing photons required to maintain the ionization of the nebula [col. (	5)], the minimum number of ionizing photons required to maintain the ionization of the nebula [col. (
6)]. and inferred spectral type of the exciting star icol. (	6)], and inferred spectral type of the exciting star [col. (
0)].	7)].
They were caleulated following the formulation of Mezger and Henderson (1967). assuming that the gas has constant electron density and an electron temperature of 107 Ix. The regions of ionized eas have radii of 0.021 and 0.029 pc. in the range of those of UC ILL regions. and densities of 4.3x10% and 2.5x10* . much lower than those of UC I] regions.	They were calculated following the formulation of Mezger and Henderson (1967), assuming that the gas has constant electron density and an electron temperature of $10^4$ K. The regions of ionized gas have radii of 0.021 and 0.029 pc, in the range of those of UC HII regions, and densities of $4.3\times10^3$ and $2.5\times10^3$ $^{-3}$, much lower than those of UC HII regions.
We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions. and have already reached pressure ecquilibrium with the dense ambient gas (e.e.. De Pree. guez. Goss 1995; Xie et al.	We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions, and have already reached pressure equilibrium with the dense ambient gas (e.g., De Pree, guez, Goss 1995; Xie et al.
1996).	1996).
The equilibrium radius is given by (see Garay Lizano	The equilibrium radius is given by (see Garay Lizano
where R 6 are the cylindrical radius and polar angle, respectively, is the characteristic width of thejet sheath, no and bo are wiethe density and field strength scaling (and are to the question of the RM asymmetry), β is the ultimatelyvelocity and unimportantαι and o; are the velocity and magnetic field pitch angles, respectively.	where $R$ $\phi$ are the cylindrical radius and polar angle, respectively, $w_{\rm jet}$ is the characteristic width of thejet sheath, $n_0$ and $b_0$ are the density and field strength scaling (and are ultimately unimportant to the question of the $\RM$ asymmetry), $\beta$ is the velocity and $\alpha_u$ and $\alpha_b$ are the velocity and magnetic field pitch angles, respectively.
Finally, we define the angle between the line of sight and the jet axis to be O, i.e. ke2cosO, =cosó and ke= Th	Finally, we define the angle between the line of sight and the jet axis to be $\Theta$, i.e. $ \hat{k}^z = \cos\Theta $, $ \hat{k}^R = \sin\Theta \cos\phi $ and $ \hat{k}^\phi = -\sin\Theta\sin\phi/R $.
us, O=0° and ©=90° sinOcorrespond to lines of sight —sinOsing/R.along and orthogonal to the jet axis, respectively.	Thus, $\Theta=0^\circ$ and $\Theta=90^\circ$ correspond to lines of sight along and orthogonal to the jet axis, respectively.
For a variety of values for these we compute the RM as defined in (6)) as a function parameters,of transverse position, thereby constructing Equationprofiles across the jet.	For a variety of values for these parameters, we compute the $\RM$ as defined in Equation \ref{eq:RM}) ) as a function of transverse position, thereby constructing profiles across the jet.
The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the RM across the jet.	The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the $\RM$ across the jet.
In the limit of a static jet, where the plasma is at rest in the observer frame, the RM profile is shown in Figure 1 for a variety of magnetic pitch angles, as viewed from ©=60°.	In the limit of a static jet, where the plasma is at rest in the observer frame, the $\RM$ profile is shown in Figure \ref{fig:static} for a variety of magnetic pitch angles, as viewed from $\Theta=60^\circ$.
For purely toroidal magnetic fields (a,=90°, blue), the RM profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the decrease in theelectron	For purely toroidal magnetic fields $\alpha_b=90^\circ$, blue), the $\RM$ profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the precipitous decrease in theelectron density.
In contrast, for magnetic precipitousfields nearly parallel to the jet density.(αν= 0°, red) the background density variation is clearly imprinted in the RM profile.	In contrast, for magnetic fields nearly parallel to the jet $\alpha_b=0^\circ$ , red) the background density variation is clearly imprinted in the $\RM$ profile.
Due solely to geometry, the degree to which this occurs upon O, with the deviations at small O and αρ. depend	Due solely to geometry, the degree to which this occurs depends upon $\Theta$, with the largest deviations at small $\Theta$ and $\alpha_b$.
sHowever, the absolute variationlargest in the RM across the jet in this case is considerably reduced, and in the limit of a,=0? vanishes completely.	However, the absolute variation in the $\RM$ across the jet in this case is considerably reduced, and in the limit of $\alpha_b=0^\circ$ vanishes completely.
More importantly, polarization maps of jets typically imply Rb?/b?>1 (2)..	More importantly, polarization maps of jets typically imply $R b^\phi/b^z\gtrsim 1$ \citep{Lyut-Pari-Gabu:05}.
Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static	Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static counterparts.
In this case the of the motion for counterparts.the RM profiles, apart from primarythe drastic consequencereduction in the net RM, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind.	In this case the primary consequence of the motion for the $\RM$ profiles, apart from the drastic reduction in the net $\RM$, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind.
This is seen explicitly for an extreme case in Figure 2,, in which the RM profiles are nearly identical to those for the static jet though rotated 180°.	This is seen explicitly for an extreme case in Figure \ref{fig:vertical}, in which the $\RM$ profiles are nearly identical to those for the static jet though rotated $180^\circ$.
Most importantly, the sense of the RM gradient does not reverse as a consequence of the bulktion?.	Most importantly, the sense of the $\RM$ gradient does not reverse as a consequence of the bulk.
. The RM profiles do not significantly differ from the case shown for y>3, and for smaller velocities become even more degenerate in αν.	The $\RM$ profiles do not significantly differ from the case shown for $\gamma>3$, and for smaller velocities become even more degenerate in $\alpha_b$ .
Therefore, generally, within the context of symmetric models, magnetic fields with moderate pitch axiallyangles are incapablejet of producing strong asymmetric features in the RM profiles, though o; and jet Lorentz factor do play a substantial role in determining the absolute RM.	Therefore, generally, within the context of axially symmetric jet models, magnetic fields with moderate pitch angles are incapable of producing strong asymmetric features in the $\RM$ profiles, though $\alpha_b$ and jet Lorentz factor do play a substantial role in determining the absolute $\RM$.
In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in RM profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the RM gradient.	In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in $\RM$ profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the $\RM$ gradient.
As seen in Figure 3,, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as 30°.	As seen in Figure \ref{fig:helical}, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as $30^\circ$.
Generic of relativistic helical motion is the noticeable bow in the RM	Generic of relativistic helical motion is the noticeable bow in the $\RM$ profiles.
This feature is only weakly dependent upon ué and present profiles.for oy,230? for u>1.	This feature is only weakly dependent upon $u^z$ and present for $\alpha_u\gtrsim30^\circ$ for $u^z\gtrsim1$.
Unlike similar features for non- jets, this occurs for a wide range of absolute rotation measures.	Unlike similar features for non-rotating jets, this occurs for a wide range of absolute rotation measures.
When the revolving plasma in the jet sheath is approaching almost directly, ie. 9 is within an angle y! of É, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure 3)).	When the revolving plasma in the jet sheath is approaching almost directly, i.e., $\bmath{\beta}$ is within an angle $\gamma^{-1}$ of $\bmath{\hat{k}}$, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure \ref{fig:helical}) ).
As a result, the RM evolves rapidly with a,.	As a result, the $\RM$ evolves rapidly with $\alpha_u$ .
At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute RM, andfor a, very close to O, complex RM profiles.	At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute $\RM$ , andfor $\alpha_u$ very close to $\Theta$ , complex $\RM$ profiles.
However,for all but the slowestjets, this is restricted to such a small regime in viewing angle that it is relatively unlikely to be observed in practice.	However,for all but the slowestjets, this is restricted to such a small regime in viewing angle that it is relatively unlikely to be observed in practice.
A much	A much
At the solar surface it is ¢@=0.3 and f=0.5 (Howard et al. 1983)).	At the solar surface it is $a\simeq 0.3$ and $f\simeq 0.5$ (Howard et al. \cite{HAB83}) ).
The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. 1999)).	The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. \cite{CDG99}) ).
The amplitude a(1—f) of the cos?4 term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction f of cost6 contribution drops to practically zero near the base (cf.	The amplitude $a(1-f)$ of the $\cos^2\theta$ term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction $f$ of $\cos^4\theta$ contribution drops to practically zero near the base (cf.
Fig.	Fig.
10 of Charbonneau et al. 1999)).	10 of Charbonneau et al. \cite{CDG99}) ).
The stratification. 1s characterized by the buoyancy frequency N. where g is the gravity. cp is the specific heat at constant pressure. and s is the specific entropy.	The stratification is characterized by the buoyancy frequency $N$, where $g$ is the gravity, $c_\mathrm{p}$ is the specific heat at constant pressure, and $s$ is the specific entropy.

⇂⊳∖↥∩∖∖↽⋯⋯⇂≺↵2i 2EE 24: ⋅ ⋅ frequencies⋅ are oeiven⋅ by we.fis7 Ὀίωτ-,een>οαπ)τε0ο-⇁(ωρα/aAστ—kheie.12 where wy7=ck> ancl =í(k-.b)/p.

The fast and slow mode frequencies are given by $\omega^2_{f,s} =.5(\omega_b^2+\omega_s^2) \pm 0.5 \left( (\omega_b^2+\omega_s^2)^2 - 4\omega_s^2 \omega_a^2 \right)^{1/2}$ where $\omega_s^2=c_s^2k^2$ and $\omega_a^2=(\kvec \cdot \bvec)^2/\rho$.

We7g- evolvedH the waves for one. period.

We evolved the waves for one period.

TheJ results for the" fast andwy slow waves are shown in figures 3. aud. L. respectively.

The results for the fast and slow waves are shown in figures \ref{fig:fast} and \ref{fig:slow}, respectively.

The slow wave is subject to substantial diffusion as compared to the [ast wave siuce its [requency isso uch lower for these extreme values of 5».

The slow wave is subject to substantial diffusion as compared to the fast wave since its frequency isso much lower for these extreme values of $\beta$.

These 1d tests of the code involve a shock tube along the x-axis. as in fig.2a.b of ?..

These 1d tests of the code involve a shock tube along the x-axis, as in fig.2a,b of \citet{1998ApJ...509..244R}.

We used continuous boundary coucditious aud 1021 grkl points for both tests.

We used continuous boundary conditions and 1024 grid points for both tests.

The initial conditions for lig.5 are (p.ey.cy.t:.pb,by.b.)=(1.10.0.0.20.5/νax.5/V15.0) for the left side and (1.10.0.0.1.5/VIm.15.0) for the right side.

The initial conditions for \ref{fig:shock1} are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)= (1,10,0,0,20,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the left side and $(1,-10,0,0,1,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the right side.

The code is run for a time 0.08L.

The code is run for a time $0.08 L$.

The result agrees well with ποσα of ?..

The result agrees well with fig.2a of \citet{1998ApJ...509..244R}.

The following features cau be seen.

The following features can be seen.

The steep discontinulties atorQoL aud ar0.82 are fast shock frouts where the incoming flow couverts its kinetic energy into thermal energy aid compresses the trausverse field b,.

The steep discontinuities at $x\sim 0.1$ and $x\sim 0.85$ are fast shock fronts where the incoming flow converts its kinetic energy into thermal energy and compresses the transverse field $b_y$.

As new matter [alls on. this shock is regenerated and maintains it’s steep profile as it moves outward.

As new matter falls on, this shock is regenerated and maintains it's steep profile as it moves outward.

At ic~0.6 and pc90.2 are a slow shock aud W.slow rarefaction. respectively.

At $x\simeq 0.6$ and $x \simeq 0.5$ are a slow shock and slow rarefaction, respectively.

The slow shock again compresses the fluicl but decreases the transverse field.

The slow shock again compresses the fluid but decreases the transverse field.

At ar20.55 the two phases of the initial gas configuration with different eutropies form a contact discontinuity.

At $x\simeq 0.55$ the two phases of the initial gas configuration with different entropies form a contact discontinuity.

Pressure. magnetic fiekl auc velocity are continuous while density aud thermal enerey experience a discontinuity.

Pressure, magnetic field and velocity are continuous while density and thermal energy experience a discontinuity.

This discontuity moves rightward across the grid. aud the TVD advection of such discoutinuities results in some smeariug or diffusion of the structure.

This discontuity moves rightward across the grid, and the TVD advection of such discontinuities results in some smearing or diffusion of the structure.

No pliysical mechauisma steepeus this contact. discontiuuitv once it sinears. aud a slow numerical diffusion is visible in this. aud all generic TVD codes which do uot introduce explicit contact steepeners.

No physical mechanism steepens this contact discontinuity once it smears, and a slow numerical diffusion is visible in this, and all generic TVD codes which do not introduce explicit contact steepeners.

There are no significant oscillations.

Both our aud ?"s solution have a slight overshoot in some variables in the first postshock cell. but this effect does uot persist onto subsequent cells.

Both our and \citet{1998ApJ...509..244R}' 's solution have a slight overshoot in some variables in the first postshock cell, but this effect does not persist onto subsequent cells.

The initial couditiou for Ge.6 has velocity and maguetic field components in all directions. aud hence exhibits additional structures such asrotational discontinuities.

The initial condition for \ref{fig:shock2} has velocity and magnetic field components in all directions, and hence exhibits additional structures such asrotational discontinuities.

The values are (p.ty.espbby.b.) = (1.08.1.2.0.01.0.5.0.05.ήνE.3.6/V/Ex.2/Ix) on the left side and (1.0.0.0.1.2//Ez.L/v/E.VDc) ou tlie right hand side.

The values are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)$ = $(1.08,1.2,0.01,0.5, 0.95,2/\sqrt{4\pi},3.6/\sqrt{4\pi},2/\sqrt{4\pi})$ on the left side and $(1,0,0,0,1,2/\sqrt{4\pi},4/\sqrt{4\pi},2/\sqrt{4\pi})$ on the right hand side.

The code is run for a time 0.2L.

The code is run for a time $0.2 L$.

The results again agreewith ?..

The results again agreewith \citet{1998ApJ...509..244R}.

The following features may be seen: fast shocksator20.3 aud 0.9. rotational discontiuuity at ο220.53 right uext to a slow shock at ο2 0.55. contact. discontiuulty at or2 0.6. slow shock aud. rotational discontinuity at 0.68 and 0.70 respectively.

The following features may be seen: fast shocksat$x\simeq 0.3$ and $0.9$ , rotational discontinuity at $x\simeq 0.53$ right next to a slow shock at $x \simeq 0.55$ , contact discontinuity at $x \simeq 0.6$ , slow shock and rotational discontinuity at $0.68$ and $0.70$ respectively.

Excluding those clusters whose position angles suller [rom large uncertainties. we end up with a smaller subsample of 13 clusters and redetermined (he number Iraction distribution as a funetion of ó.

Excluding those clusters whose position angles suffer from large uncertainties, we end up with a smaller subsample of $13$ clusters and redetermined the number fraction distribution as a function of $\phi$ .

Figure 4. plots the results.

Figure \ref{fig:compare2} plots the results.

As it can be seen. the distribution has a hieher peak at (he second bin but süll deviates significantly from (he numerical result. based on a ACDAL cosmology and the semi-analvtie galaxy formation model.

As it can be seen, the distribution has a higher peak at the second bin but still deviates significantly from the numerical result based on a $\Lambda$ CDM cosmology and the semi-analytic galaxy formation model.

The recaleulation of V for this case rejects the hypothesis that the observational result. [rom the 13 clusters is consistent with the numerical result is rejected at the 95%. confidence level.

The recalculation of $\chi^{2}$ for this case rejects the hypothesis that the observational result from the $13$ clusters is consistent with the numerical result is rejected at the $95\%$ confidence level.

lt is worth mentioning the differences in the redshill range between the numerical ancl observational data used for the above comparison: The munerical result has been obtained al 2=0 while the observational results have been drawn [rom the galaxy. clusters al 0.3.

It is worth mentioning the differences in the redshift range between the numerical and observational data used for the above comparison: The numerical result has been obtained at $z=0$ while the observational results have been drawn from the galaxy clusters at $0.1<z<0.3$ .

This difference in the redshift range. however. would even worsen the disagreement between the munerical and the observational result for the following5 reason.

This difference in the redshift range, however, would even worsen the disagreement between the numerical and the observational result for the following reason.

As mentioned in 82 and as shown by N-bocly simulations (e.g..Dailin&Steinmetz2005:etal.AltayAltavetal.2006:2006;Lee&KangΊναπο 2006).. 0the correlationsrrelations between the major axes of[dark dark matter and satellite galaxy distributions tend to be stronger at higher redshifts.

As mentioned in 2 and as shown by N-body simulations \citep[e.g.,][]{BS05,bailin-etal05,atlay-etal06,LK06}, the correlations between the major axes of dark matter and satellite galaxy distributions tend to be stronger at higher redshifts.

In other words. the predicted strength of the correlations used lor the comparison with the observational result is underestimated.

In other words, the predicted strength of the correlations used for the comparison with the observational result is underestimated.

One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analvsis of Oeurietal.(2010) only those bright galaxies with mag222 al r-band are used unlike in the numerical analvsis.

One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analysis of \citet{Oguri-etal10} only those bright galaxies with $mag > 22$ at r-band are used unlike in the numerical analysis.

Recall. however. that we used the Iuminositv-weighted ealaxv distributions in the numerical analysis to determine the major axes. which should minimize (he expected selection bias.

Recall, however, that we used the luminosity-weighted galaxy distributions in the numerical analysis to determine the major axes, which should minimize the expected selection bias.

Another difference lies in the values of the cosmological parameters used for the Run simulations.

Another difference lies in the values of the cosmological parameters used for the mili-Millennium Run simulations.

Especially. the value of σς chosen by the Millennium Run simulation has been known to be higher than the WALAP value (IxXomatsuetal.2010).

Especially, the value of $\sigma_{8}$ chosen by the Millennium Run simulation has been known to be higher than the WMAP value \citep{wmap7}.

. The correlations between dark matter and satellite galaxy distributions in (riaxial clusters. however. are unlike to be significantly affected by the initial cosmological conditions. since il represents a nonlinear observable rather than a linear one.

The correlations between dark matter and satellite galaxy distributions in triaxial clusters, however, are unlike to be significantly affected by the initial cosmological conditions, since it represents a nonlinear observable rather than a linear one.

Now that we have found (the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy. clusters to be inconsistent with the numerical prediction based on a ACDMcosmology and (he semi-analvtic galaxy. lormation model. we

Now that we have found the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy clusters to be inconsistent with the numerical prediction based on a $\Lambda$ CDMcosmology and the semi-analytic galaxy formation model, we

We detected 7 min continuum emission towards each of the three observed sources.

We detected 7 mm continuum emission towards each of the three observed sources.

The position. flux densities. and angular size of the detected radio sources are given in Table 2..

The position, flux densities, and angular size of the detected radio sources are given in Table \ref{tbl-obspar}.

In what follows we present the results of our continuum observations and discuss the nature of the detected. sources in each of the regions. imdividuallv.

In what follows we present the results of our continuum observations and discuss the nature of the detected sources in each of the regions, individually.

For the derivation of plivsical parameters we used (he distances given by Sridharan et al. (

For the derivation of physical parameters we used the distances given by Sridharan et al. (

2002) and listecl in Table 3.

2002) and listed in Table 3.

Figure | shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044.

Figure \ref{fig-18470maps} shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044.

The emission arises from two distinct compact sources separated by ((labelecd A and D).

The emission arises from two distinct compact sources separated by (labeled A and B).

Both sources were also detected at 3.6 em and 6.0 em wavelengths.

Both sources were also detected at 3.6 cm and 6.0 cm wavelengths.

A contour map of the 3.6 em emission is shown in the lower panel of Fig. 1..

A contour map of the 3.6 cm emission is shown in the lower panel of Fig. \ref{fig-18470maps}.

Component A is associated with a massive dust core detected at 350 and 450 jim by Williams et al. (

Component A is associated with a massive dust core detected at 850 and 450 $\mu$ m by Williams et al. (

2004) and at 1200 jan by Deuther et al. (

2004) and at 1200 $\mu$ m by Beuther et al. (

20028).

2002a).

At 1.2 mm the core has major and minor axis of 1T and12”.. respectivelv. implving a core radius. estimated [rom the geometric mean of the axis. of 0.29 pe (assuming a distance of 8.2 kpc).

At 1.2 mm the core has major and minor axis of 17 and, respectively, implying a core radius, estimated from the geometric mean of the axis, of 0.29 pc (assuming a distance of 8.2 kpc).

The mass of the core determined [rom the 850. jan observations is 720AL.

The mass of the core determined from the 850 $\mu$ m observations is 720.

.. The peak position of the core is marked with a cross in Fig. 1..

The peak position of the core is marked with a cross in Fig. \ref{fig-18470maps}.

The spectral index of the emission between 5.0 ancl 43.4 Giz are —0.1250.1 ancl —O0.140.1 for the east (A) ancl west (D) components. respectively. indicating that the emission in this frequency range is optically thin thermal emission.

The spectral index of the emission between 5.0 and 43.4 GHz are $-0.1\pm0.1$ and $-0.1\pm0.1$ for the east (A) and west (B) components, respectively, indicating that the emission in this frequency range is optically thin thermal emission.

We conclude (hat the emission from these two objects is [ree-free emission from ionized gas.

We conclude that the emission from these two objects is free-free emission from ionized gas.

Table 3. lists the distance [col. (

Table \ref{tbl-derived} lists the distance [col. (

2)]. the derived parameters of the regions of ionized gas: diameter [col. (

2)], the derived parameters of the regions of ionized gas: diameter [col. (

3)]. emission measure (col. (

3)], emission measure [col. (

4)]. and electron density |col. (

4)], and electron density [col. (

5)]. the minimum number of ionizing photons required to maintain the ionization of the nebula [col. (

5)], the minimum number of ionizing photons required to maintain the ionization of the nebula [col. (

6)]. and inferred spectral type of the exciting star icol. (

6)], and inferred spectral type of the exciting star [col. (

0)].

7)].

They were caleulated following the formulation of Mezger and Henderson (1967). assuming that the gas has constant electron density and an electron temperature of 107 Ix. The regions of ionized eas have radii of 0.021 and 0.029 pc. in the range of those of UC ILL regions. and densities of 4.3x10% and 2.5x10* . much lower than those of UC I] regions.

They were calculated following the formulation of Mezger and Henderson (1967), assuming that the gas has constant electron density and an electron temperature of $10^4$ K. The regions of ionized gas have radii of 0.021 and 0.029 pc, in the range of those of UC HII regions, and densities of $4.3\times10^3$ and $2.5\times10^3$ $^{-3}$, much lower than those of UC HII regions.

We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions. and have already reached pressure ecquilibrium with the dense ambient gas (e.e.. De Pree. guez. Goss 1995; Xie et al.

We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions, and have already reached pressure equilibrium with the dense ambient gas (e.g., De Pree, guez, Goss 1995; Xie et al.

1996).

The equilibrium radius is given by (see Garay Lizano

where R 6 are the cylindrical radius and polar angle, respectively, is the characteristic width of thejet sheath, no and bo are wiethe density and field strength scaling (and are to the question of the RM asymmetry), β is the ultimatelyvelocity and unimportantαι and o; are the velocity and magnetic field pitch angles, respectively.

where $R$ $\phi$ are the cylindrical radius and polar angle, respectively, $w_{\rm jet}$ is the characteristic width of thejet sheath, $n_0$ and $b_0$ are the density and field strength scaling (and are ultimately unimportant to the question of the $\RM$ asymmetry), $\beta$ is the velocity and $\alpha_u$ and $\alpha_b$ are the velocity and magnetic field pitch angles, respectively.

Finally, we define the angle between the line of sight and the jet axis to be O, i.e. ke2cosO, =cosó and ke= Th

Finally, we define the angle between the line of sight and the jet axis to be $\Theta$, i.e. $ \hat{k}^z = \cos\Theta $, $ \hat{k}^R = \sin\Theta \cos\phi $ and $ \hat{k}^\phi = -\sin\Theta\sin\phi/R $.

us, O=0° and ©=90° sinOcorrespond to lines of sight —sinOsing/R.along and orthogonal to the jet axis, respectively.

Thus, $\Theta=0^\circ$ and $\Theta=90^\circ$ correspond to lines of sight along and orthogonal to the jet axis, respectively.

For a variety of values for these we compute the RM as defined in (6)) as a function parameters,of transverse position, thereby constructing Equationprofiles across the jet.

For a variety of values for these parameters, we compute the $\RM$ as defined in Equation \ref{eq:RM}) ) as a function of transverse position, thereby constructing profiles across the jet.

The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the RM across the jet.

The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the $\RM$ across the jet.

In the limit of a static jet, where the plasma is at rest in the observer frame, the RM profile is shown in Figure 1 for a variety of magnetic pitch angles, as viewed from ©=60°.

In the limit of a static jet, where the plasma is at rest in the observer frame, the $\RM$ profile is shown in Figure \ref{fig:static} for a variety of magnetic pitch angles, as viewed from $\Theta=60^\circ$.

For purely toroidal magnetic fields (a,=90°, blue), the RM profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the decrease in theelectron

For purely toroidal magnetic fields $\alpha_b=90^\circ$, blue), the $\RM$ profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the precipitous decrease in theelectron density.

In contrast, for magnetic precipitousfields nearly parallel to the jet density.(αν= 0°, red) the background density variation is clearly imprinted in the RM profile.

In contrast, for magnetic fields nearly parallel to the jet $\alpha_b=0^\circ$ , red) the background density variation is clearly imprinted in the $\RM$ profile.

Due solely to geometry, the degree to which this occurs upon O, with the deviations at small O and αρ. depend

Due solely to geometry, the degree to which this occurs depends upon $\Theta$, with the largest deviations at small $\Theta$ and $\alpha_b$.

sHowever, the absolute variationlargest in the RM across the jet in this case is considerably reduced, and in the limit of a,=0? vanishes completely.

However, the absolute variation in the $\RM$ across the jet in this case is considerably reduced, and in the limit of $\alpha_b=0^\circ$ vanishes completely.

More importantly, polarization maps of jets typically imply Rb?/b?>1 (2)..

More importantly, polarization maps of jets typically imply $R b^\phi/b^z\gtrsim 1$ \citep{Lyut-Pari-Gabu:05}.

Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static

Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static counterparts.

In this case the of the motion for counterparts.the RM profiles, apart from primarythe drastic consequencereduction in the net RM, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind.

In this case the primary consequence of the motion for the $\RM$ profiles, apart from the drastic reduction in the net $\RM$, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind.

This is seen explicitly for an extreme case in Figure 2,, in which the RM profiles are nearly identical to those for the static jet though rotated 180°.

This is seen explicitly for an extreme case in Figure \ref{fig:vertical}, in which the $\RM$ profiles are nearly identical to those for the static jet though rotated $180^\circ$.

Most importantly, the sense of the RM gradient does not reverse as a consequence of the bulktion?.

Most importantly, the sense of the $\RM$ gradient does not reverse as a consequence of the bulk.

. The RM profiles do not significantly differ from the case shown for y>3, and for smaller velocities become even more degenerate in αν.

The $\RM$ profiles do not significantly differ from the case shown for $\gamma>3$, and for smaller velocities become even more degenerate in $\alpha_b$ .

Therefore, generally, within the context of symmetric models, magnetic fields with moderate pitch axiallyangles are incapablejet of producing strong asymmetric features in the RM profiles, though o; and jet Lorentz factor do play a substantial role in determining the absolute RM.

Therefore, generally, within the context of axially symmetric jet models, magnetic fields with moderate pitch angles are incapable of producing strong asymmetric features in the $\RM$ profiles, though $\alpha_b$ and jet Lorentz factor do play a substantial role in determining the absolute $\RM$.

In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in RM profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the RM gradient.

In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in $\RM$ profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the $\RM$ gradient.

As seen in Figure 3,, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as 30°.

As seen in Figure \ref{fig:helical}, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as $30^\circ$.

Generic of relativistic helical motion is the noticeable bow in the RM

Generic of relativistic helical motion is the noticeable bow in the $\RM$ profiles.

This feature is only weakly dependent upon ué and present profiles.for oy,230? for u>1.

This feature is only weakly dependent upon $u^z$ and present for $\alpha_u\gtrsim30^\circ$ for $u^z\gtrsim1$.

Unlike similar features for non- jets, this occurs for a wide range of absolute rotation measures.

Unlike similar features for non-rotating jets, this occurs for a wide range of absolute rotation measures.

When the revolving plasma in the jet sheath is approaching almost directly, ie. 9 is within an angle y! of É, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure 3)).

When the revolving plasma in the jet sheath is approaching almost directly, i.e., $\bmath{\beta}$ is within an angle $\gamma^{-1}$ of $\bmath{\hat{k}}$, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure \ref{fig:helical}) ).

As a result, the RM evolves rapidly with a,.

As a result, the $\RM$ evolves rapidly with $\alpha_u$ .

At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute RM, andfor a, very close to O, complex RM profiles.

At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute $\RM$ , andfor $\alpha_u$ very close to $\Theta$ , complex $\RM$ profiles.

However,for all but the slowestjets, this is restricted to such a small regime in viewing angle that it is relatively unlikely to be observed in practice.

A much

At the solar surface it is ¢@=0.3 and f=0.5 (Howard et al. 1983)).

At the solar surface it is $a\simeq 0.3$ and $f\simeq 0.5$ (Howard et al. \cite{HAB83}) ).

The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. 1999)).

The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. \cite{CDG99}) ).

The amplitude a(1—f) of the cos?4 term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction f of cost6 contribution drops to practically zero near the base (cf.

The amplitude $a(1-f)$ of the $\cos^2\theta$ term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction $f$ of $\cos^4\theta$ contribution drops to practically zero near the base (cf.

Fig.

10 of Charbonneau et al. 1999)).

10 of Charbonneau et al. \cite{CDG99}) ).

The stratification. 1s characterized by the buoyancy frequency N. where g is the gravity. cp is the specific heat at constant pressure. and s is the specific entropy.

The stratification is characterized by the buoyancy frequency $N$, where $g$ is the gravity, $c_\mathrm{p}$ is the specific heat at constant pressure, and $s$ is the specific entropy.