source
stringlengths 1
2.05k
⌀ | target
stringlengths 1
11.7k
|
|---|---|
Both H»O and CO» ice absorptions towards HV Tau should originate in both the disk and foreground clouds. since the depths of the absorption bands are larger than the continuum flux of the HV Tau C. Towards HK Tau. the depth of the H»O absorption is comparable to the continuum flux of HK Tau B; if the H:O absorption originates in the disk around HK Tau B. the HO ice column density is ~3x10/5 em. which is comparable to the value obtained by Terada et al. (2007)). | Both $_2$ O and $_2$ ice absorptions towards HV Tau should originate in both the disk and foreground clouds, since the depths of the absorption bands are larger than the continuum flux of the HV Tau C. Towards HK Tau, the depth of the $_2$ O absorption is comparable to the continuum flux of HK Tau B; if the $_2$ O absorption originates in the disk around HK Tau B, the $_2$ O ice column density is $\sim 3 \times 10^{18}$ $^{-2}$, which is comparable to the value obtained by Terada et al. \cite{terada07}) ). |
The CO: absorption. on the other hand. is deeper than the continuum flux of HK Tau B. and thus should originate at least partially in the foreground clouds. | The $_2$ absorption, on the other hand, is deeper than the continuum flux of HK Tau B, and thus should originate at least partially in the foreground clouds. |
We also detected shallow H3O ice bands towards UY Aur. which again originate in the foreground component. since the inclination of the disk is ~42 degrees. | We also detected shallow $_2$ O ice bands towards UY Aur, which again originate in the foreground component, since the inclination of the disk is $\sim 42$ degrees. |
If the H:O absorptions towards HV Tau and HK Tau originated in the foreground clouds. the estimated HO ice column densities would be smaller than the HO ice column densities in the edge-on disks obtained by Terada et al. (2007)) | If the $_2$ O absorptions towards HV Tau and HK Tau originated in the foreground clouds, the estimated $_2$ O ice column densities would be smaller than the $_2$ O ice column densities in the edge-on disks obtained by Terada et al. \cite{terada07}) ) |
by about an order of magnitude: the HO ice column density would be 3.31xΤΟΙΣ επι for HK Tau B. and (2.69—4.20)x emo? for HV Tau C. Our observations thus support the argument of Terada et al (2007)) that the disk component overwhelms the foreground component towards HK Tau B and HV Tau C. We have observed ice absorption bands at 2.5—5 jm towards eight low-mass YSOs: three class 0-I protostellar cores with edge-on geometry. two edge-on class HI objects. two multiple | by about an order of magnitude; the $_2$ O ice column density would be $3.31 \times 10^{18}$ $^{-2}$ for HK Tau B, and $(2.69-4.20) \times 10^{18}$ $^{-2}$ for HV Tau C. Our observations thus support the argument of Terada et al \cite{terada07}) ) that the disk component overwhelms the foreground component towards HK Tau B and HV Tau C. We have observed ice absorption bands at $2.5-5$ $\mu$ m towards eight low-mass YSOs: three class 0-I protostellar cores with edge-on geometry, two edge-on class II objects, two multiple |
constructed preliminary O6 diagrams. | constructed preliminary $O-C$ diagrams. |
Then. the average period values (22.) over the century were determined. and used in order to obtain a symmetrical form of the diagrams. | Then, the average period values $P_{\mathrm{a}}$ ) over the century were determined and used in order to obtain a symmetrical form of the diagrams. |
If it was necessary. several trials were done to find the best period. which gave the most reasonable ο)6 plot. | If it was necessary, several trials were done to find the best period, which gave the most reasonable $O-C$ plot. |
Phis was especially the case. if significant abrupt and irregular period variations occurred. | This was especially the case, if significant abrupt and irregular period variations occurred. |
I£the O| Cis fitted by a polynomial then it can be readily seen that the period. variation can be eliminated. if the times of the observations are transformed according to the equation The time-transformed data can be coherently phased with the period. £2. | If the $O-C$ is fitted by a polynomial then it can be readily seen that the period variation can be eliminated, if the times of the observations are transformed according to the equation The time-transformed data can be coherently phased with the period, $P_{\mathrm{a}}$. |
For some of the variables with strong period variations. the zero-point corrections of the different data sets. had slightly incorrect’ values because of the smearing of the folded. light curves. | For some of the variables with strong period variations, the zero-point corrections of the different data sets had slightly incorrect values because of the smearing of the folded light curves. |
In such cases. we used the linie-transformed. light curves to derive refined. values for the corrected. magnitudes. | In such cases, we used the time-transformed light curves to derive refined values for the corrected magnitudes. |
In summary. thefollowing steps were applied: where mu. fü. m4. £4 and me. £o» refer to the magnitudes and times of the original observations: the zero-poin corrected. time-transformec data: and the refined. point corrected. time-transformed data. | In summary, thefollowing steps were applied: where $m_0$, $t_0$, $m_1$, $t_1$ and $m_2$, $t_2$ refer to the magnitudes and times of the original observations; the zero-point corrected, time-transformed data; and the refined, zero-point corrected, time-transformed data. |
All the obervations usec in. the analysis anc the magnitude-zero-point ancl time-translormed cata are given in electronic form as Supporting Information (Table S44) and can be downloaded from the url: M5. | All the obervations used in the analysis and the magnitude-zero-point and time-transformed data are given in electronic form as Supporting Information (Table S4) and can be downloaded from the url: . |
Table4. gives a sample of the data. | Table \ref{all} gives a sample of the data. |
Ixeplerian rotation. | Keplerian rotation. |
In the unperturbed disc. pressure and density are related by à polvtropic law. which is à reasonably good approximation for optically thick dises (see e.g. LOOS). | In the unperturbed disc, pressure and density are related by a polytropic law, which is a reasonably good approximation for optically thick discs (see e.g., LO98). |
This allows us to consider the specific features of the dynamics for subadiabatic. adiabatie ancl superacdiabatic vertical stratifications by simply varving the polvtropic index. | This allows us to consider the specific features of the dynamics for subadiabatic, adiabatic and superadiabatic vertical stratifications by simply varying the polytropic index. |
As a first step towards understanding the effects of self-gravitv on the perturbation modes. we restrict ourselves to axiswnunetric perturbations only. | As a first step towards understanding the effects of self-gravity on the perturbation modes, we restrict ourselves to axisymmetric perturbations only. |
The linear results obtained bere will form the basis for studying the non-linear development of gravitational instability in the local shearing box approximation that allows much higher numerical resolution than global clise mocels can alford. | The linear results obtained here will form the basis for studying the non-linear development of gravitational instability in the local shearing box approximation that allows much higher numerical resolution than global disc models can afford. |
The paper is organized as follows. | The paper is organized as follows. |
The physical model and basic equations are introduced. in Section 2. | The physical model and basic equations are introduced in Section 2. |
The classification of vertical modes in the absence of sell-gravity is performed in Section 3. | The classification of vertical modes in the absence of self-gravity is performed in Section 3. |
Elfects of self-gravity on all normal mocles are analysed in Section 4. | Effects of self-gravity on all normal modes are analysed in Section 4. |
In Section 5. we focus on the properties of gravitational instability in 3D. Comparison between the criteria of gravitational instability in 3D and 2D is mace in Section 6. | In Section 5, we focus on the properties of gravitational instability in 3D. Comparison between the criteria of gravitational instability in 3D and 2D is made in Section 6. |
Summary and discussions are given in Section 7. | Summary and discussions are given in Section 7. |
1n order to study the dynamics of three-cimensional modes in gaseous seli-gravitating discs. following LP. WP. LO98. we adopt a local shearing box approximation (?).. | In order to study the dynamics of three-dimensional modes in gaseous self-gravitating discs, following LP, KP, LO98, we adopt a local shearing box approximation \citep{GLB65b}. |
In the shearing box model. the disc dynamics is studied. in a local Cartesian reference. frame rotating with the angular velocity. of disc rotation at some fiducial radius from the central star. so that. curvature ellects. due to. evlindrical ecometry of the disc are ignored. | In the shearing box model, the disc dynamics is studied in a local Cartesian reference frame rotating with the angular velocity of disc rotation at some fiducial radius from the central star, so that curvature effects due to cylindrical geometry of the disc are ignored. |
In this coordinate frame. the unperturbed. dillerential rotation of the disce manifests itself as a parallel azimuthal flow with a constant velocity shear in the radial direction. | In this coordinate frame, the unperturbed differential rotation of the disc manifests itself as a parallel azimuthal flow with a constant velocity shear in the radial direction. |
A Coriolis force is included to take into account the ellects of coordinate [frame rotation. | A Coriolis force is included to take into account the effects of coordinate frame rotation. |
The vertical component of the gravity force of the central object is also present. | The vertical component of the gravity force of the central object is also present. |
As a result. we can write down the three-climensional shearing box equations and the equation of conservation of entropy This set of equations is supplemented with Poisson's equation to take care of dise sell-egravity llere ue=(petty.tte) is the velocity in. the local frame. p.p.c are. respectively, the pressure. density and the gravitational potential of the disc gas. | As a result, we can write down the three-dimensional shearing box equations and the equation of conservation of entropy This set of equations is supplemented with Poisson's equation to take care of disc self-gravity Here ${\bf u}=(u_x,u_y,u_z)$ is the velocity in the local frame, $p,
\rho, \psi$ are, respectively, the pressure, density and the gravitational potential of the disc gas. |
© is the angular velocity. of the local reference. framerotation as a whole. ανμες sre. respectively. the radial. azimuthal ancl vertical coordinates. Z is the unit vector along the vertical direction and ddl=0/00|uV is the total time derivative. | $\Omega$ is the angular velocity of the local reference framerotation as a whole, $x,y,z$ are, respectively, the radial, azimuthal and vertical coordinates, ${\bf \hat{z}}$ is the unit vector along the vertical direction and $d/dt=\partial/\partial t+{\bf u}\cdot \nabla$ is the total time derivative. |
The shear parameter is q=1.5 for the Ixeplerian rotation considered in this paper. | The shear parameter is $q=1.5$ for the Keplerian rotation considered in this paper. |
The adiabatic index. or the ratio of specific heats. 4;=L4 as typical of a disc composed. of molecular hydrogen: we adopt this value throughout the paper. | The adiabatic index, or the ratio of specific heats, $\gamma=1.4$ as typical of a disc composed of molecular hydrogen; we adopt this value throughout the paper. |
Equations (1-4) have an equilibrium solution that is stationary and axisvmametric. | Equations (1-4) have an equilibrium solution that is stationary and axisymmetric. |
In this unperturbed state. the velocity field represents. as noted above. à parallel azimuthal How. uo. with a constant radial shear q: In the shearing box. the equilibrium density po. pressure po and gravitational potential cu depend only on the vertical coordinate and satisfv the hyerostatic relation As in LP. WP and RPL. pressure ancl density in the unpoerturbed cise are related by à polvtropie relationship of the form where A is the polvtropic constant and. 50 is the xiblvtropic index. | In this unperturbed state, the velocity field represents, as noted above, a parallel azimuthal flow, ${\bf
u_{0}}$, with a constant radial shear $q$: In the shearing box, the equilibrium density $\rho_0$, pressure $p_0$ and gravitational potential $\psi_0$ depend only on the vertical $z-$ coordinate and satisfy the hydrostatic relation As in LP, KP and RPL, pressure and density in the unperturbed disc are related by a polytropic relationship of the form where $K$ is the polytropic constant and $s>0$ is the polytropic index. |
The Brunt-Vàiisallà [requencey.1 squaredI is defined. as where e?=5pofpo is the adiabatie sound. speed squared. | The Brunt-Väiisällä frequency squared is defined as where $c_{s}^2=\gamma p_0/\rho_0$ is the adiabatic sound speed squared. |
161|1/s«5 (subacliabatie thermal stratification). then ANS>0 all along the height and the equilibrium. vertical structure of the disc is convectively stable. | If $1+1/s<\gamma$ (subadiabatic thermal stratification), then $N_0^2>0$ all along the height and the equilibrium vertical structure of the disc is convectively stable. |
In the opposite case l1|l/s~ (superadiabatie thermal stratification). No«0 everywhere and this corresponds to a convectively unstable equilibrium. | In the opposite case $1+1/s>\gamma$ (superadiabatic thermal stratification), $N_0^2<0$ everywhere and this corresponds to a convectively unstable equilibrium. |
For 1|l/s=+ (adiabatie thermal stratification). No=0 and all the motions/mocles due to buovaney. disappear. | For $1+1/s=\gamma$ (adiabatic thermal stratification), $N_0^2=0$ and all the motions/modes due to buoyancy disappear. |
Later we will consider these three regimics separately. | Later we will consider these three regimes separately. |
To determine the vertical structure. we need to solve equations (5-6) subject to the boundary. condition that the pressure vanish at the free surface of the disc. | To determine the vertical structure, we need to solve equations (5-6) subject to the boundary condition that the pressure vanish at the free surface of the disc. |
Because we have a polvtropic model. it is convenient to work with the pseudo-enthalpy The disc structure is also symmetric with respect to the midplane. z—0. and. as a consequence. it follows from. equations (5-7)5-in that the derivative of wy at the midplane vanishes (Le. dires/dz(0)= 0). | Because we have a polytropic model, it is convenient to work with the pseudo-enthalpy The disc structure is also symmetric with respect to the midplane, $z=0$, and, as a consequence, it follows from equations (5-7) that the derivative of $w_0$ at the midplane vanishes (i.e., $dw_0/dz(0)=0$ ). |
Decause of this reflection svnunetry. we consider only the upper half of the disc. >i0. | Because of this reflection symmetry, we consider only the upper half of the disc, $z\geq 0$. |
At the surface of the disc wy= O. similar to the pressure. | At the surface of the disc $w_0=0$ , similar to the pressure. |
“This allows us to determine the equilibrium vertical structure of the disc. | This allows us to determine the equilibrium vertical structure of the disc. |
Phe non-dimensional variables being used throughout the paper are: | The non-dimensional variables being used throughout the paper are: |
Cravitationallv bound stellar clusters are the onlv known class of systems that. to the Hinit of our precision. eoncrally consist of stars of tlie same age (forsomeno-2007:Alackeyetal. 2008). | Gravitationally bound stellar clusters are the only known class of systems that, to the limit of our precision, generally consist of stars of the same age \citep[for some notable exceptions see][]{villanova, piotto, mackey08}. |
.. As such they plav a ceutral role in the development of our uuderstaudiug of stellar evolution (cf.Sandage1953) anc of the ανασα] evolution of stellar systems (cf.Nine1966). | As such they play a central role in the development of our understanding of stellar evolution \citep[cf.][]{sandage}
and of the dynamical evolution of stellar systems \citep[cf.][]{king}. |
. Ποπονα, there is one siguifcant shortcomime of the sample of Allkv Wav clusters as a testhed of models they are almost exclusively old. | However, there is one significant shortcoming of the sample of Milky Way clusters as a testbed of models — they are almost exclusively old. |
While argunieuts continue reearding the exact spread iu the ages of Milkv Wav elobular clusters. the consensus is that they are mostly older than 10 Cyr (Salaris&Weiss2002). | While arguments continue regarding the exact spread in the ages of Milky Way globular clusters, the consensus is that they are mostly older than 10 Gyr \citep{salaris}. |
. Fortunately. the stellar clusters in other local galaxies do not suffer the same cluster senility. | Fortunately, the stellar clusters in other local galaxies do not suffer the same cluster senility. |
For vich aud vouug clusters in the Local Croup. there exist age estimates based on the analysis of stellar color-magnitude diagrams (Pietrzvuski& Udal-Ixoch 2010). | For rich and young clusters in the Local Group, there exist age estimates based on the analysis of stellar color-magnitude diagrams \citep{p99, mackey04, glatt10}. |
. ILowever. the sample of clusters with such ueasureinents and correspondiug size. nass and other structural measurements is niodest iu comparison to ιο total number of nearby clusters. | However, the sample of clusters with such measurements and corresponding size, mass and other structural measurements is modest in comparison to the total number of nearby clusters. |
The Magellanic Clouds alone contain several thousand clusters. | The Magellanic Clouds alone contain several thousand clusters. |
There are two complementary approaches to the study of jese clusters. | There are two complementary approaches to the study of these clusters. |
One can construct a high-quality. resolution sample of observations. usually uxiug sed data; of a limuted muuber of clusters (Alackev&Cüliiore2003a.b:Cdattetal. 2009).. | One can construct a high-quality, high-resolution sample of observations, usually using space-based data, of a limited number of clusters \citep{mackey03a, mackey03b, glatt}. |
These data produce he highest fidelity measurements of the structural xuanmeters and ages. | These data produce the highest fidelity measurements of the structural parameters and ages. |
Alternatively, one can iueasure hese parameters more crudely. usually usimg erounud-owed data. but for a significautlv larger sample of clusters. | Alternatively, one can measure these parameters more crudely, usually using ground-based data, but for a significantly larger sample of clusters. |
Because of our involvement iu the \lagellanic Clouds Photometric Survey2001).. we have adopted the second approach. | Because of our involvement in the Magellanic Clouds Photometric Survey, we have adopted the second approach. |
We have previously preseuted catalogs of stellar clusters iu the Small Alagellanic Cloud that quantified the structure (ll&Zavitskv2006) and age (Rafelski&Zaritsky2005) for ~ 200 clusters. | We have previously presented catalogs of stellar clusters in the Small Magellanic Cloud that quantified the structure \citep{hz} and age \citep{rz} for $\sim$ 200 clusters. |
Here we preseut the analogous catalog of structural properties for 1066 clusters in the Large. Magellanic Cloud and compare those to the structural properties of the cluster populations of the SAIC. | Here we present the analogous catalog of structural properties for 1066 clusters in the Large Magellanic Cloud and compare those to the structural properties of the cluster populations of the SMC. |
We adopt an LAC distance of 50 kpe when converting to plivsical units. | We adopt an LMC distance of 50 kpc when converting to physical units. |
We briefly review the data and iodel fitting procedure in 822 and 3. and discuss clusters properties iu Lt. | We briefly review the data and model fitting procedure in 2 and 3, and discuss clusters properties in 4. |
The origimal C. B. V. aud £ band images. from which the photometric stellar catalog was coustiucted. conie from drift seans obtained with the Caveat Circle Camera (Zaritskyetal.1996) mounted on the Swope lii telescope at the Las Campanas| Observatory in Chile for the Magellanic Clouds Photometric Survey (Zartskyetal. 1997). | The original $U$, $B$, $V$ , and $I$ band images, from which the photometric stellar catalog was constructed, come from drift scans obtained with the Great Circle Camera \citep{zsb} mounted on the Swope 1m telescope at the Las Campanas Observatory in Chile for the Magellanic Clouds Photometric Survey \citep{zht}. |
. Tn sunuuary. these images have a pixel scale of 0.7 arcsec 5. exposure times raneine from about [ to 5 imunutes. and typical secing of 1.5 arcsec. | In summary, these images have a pixel scale of 0.7 arcsec $^{-1}$, exposure times ranging from about 4 to 5 minutes, and typical seeing of 1.5 arcsec. |
We obtained these data primarily to recover the star formation history of the Alaecllanic Clouds aud that work is described by Ihuris&Zaritsky(2001.2009). | We obtained these data primarily to recover the star formation history of the Magellanic Clouds and that work is described by \cite{hz1,hz2}. |
. To detect the candidate clusters presented here. we use the LMC photometric catalog (Zaritskyetal.2001). and search for overdcusitics in that stellar distribution. as we did when studving the clusters of the Small Magellanic Cloud (hl&Zavritsky2006) aud a portion of the LAIC (Zavitskyetal.1997). | To detect the candidate clusters presented here, we use the LMC photometric catalog \citep{lmc} and search for overdensities in that stellar distribution, as we did when studying the clusters of the Small Magellanic Cloud \citep{hz} and a portion of the LMC \citep{zht}. |
.. To search for clusters. we first biu he stellar deusitv. for stars with V.«20.5. in units of 10 aresee pixels. | To search for clusters, we first bin the stellar density, for stars with $V < 20.5$, in units of 10 arcsec pixels. |
Then. we produce a s1»othed. versiou of the stellar deusitv ou the skv using a median filter en pixels across. | Then, we produce a smoothed version of the stellar density on the sky using a median filter ten pixels across. |
By subtracting the latter from the ormoer. localizedconcentrations are highlighted. | By subtracting the latter from the former, localizedconcentrations are highlighted. |
We use SExtractor (Bertin&Arnouts1996). to identify objects. requiring 5 contiguous pixels that are above a τσ local hresholc. | We use SExtractor \citep{bertin} to identify objects, requiring 5 contiguous pixels that are above a $\sigma$ local threshold. |
computation was terminated when the bow was 90% of the wav to the domain's Lar edge. as bv (hen significant dissipation and disruption of the jet had occurred. | computation was terminated when the bow was $\sim 90$ of the way to the domain's far edge, as by then significant dissipation and disruption of the jet had occurred. |
Renders in planes parallel to the inflow plane reveal a small influence of the boundary on structures close to the edge of (he computational domain. | Renders in planes parallel to the inflow plane reveal a small influence of the boundary on structures close to the edge of the computational domain. |
However. there is no evidence that the limited lateral extent of the computational domain influences the spine of the flow. which is (hat structure of most significance (o us. | However, there is no evidence that the limited lateral extent of the computational domain influences the spine of the flow, which is that structure of most significance to us. |
Figure 12. shows a sequence of slices in the plane ο=0 al ecqually-spacecl intervals during the evolution. using schlieren plots of laboratory frame density. | Figure \ref{precA} shows a sequence of slices in the plane $x=0$ at equally-spaced intervals during the evolution, using schlieren plots of laboratory frame density. |
Superlicial inspection ol the final slice suggests that to a significant extent. the jet has retained its integrity. ancl is driving a bow not dissimilar to that seen in the unprecessed case. | Superficial inspection of the final slice suggests that to a significant extent, the jet has retained its integrity, and is driving a bow not dissimilar to that seen in the unprecessed case. |
In particular. on average the bow is advancing al e0.41. which is ~63% the speed with which it advanced in (he unprecessed case. suggesting a relatively undiminished jet thrust. | In particular, on average the bow is advancing at $v\sim 0.41$, which is $\sim
63$ the speed with which it advanced in the unprecessed case, suggesting a relatively undiminished jet thrust. |
However. Figure 13 shows [rom left to right. a schlieren render of (he pressure there are dramatic variations of pressure along the jets path. suggestive of significant dissipation: a linear render of the pressure (clominated by the leading bow) with 3-velocity vectors superposed — evidently the jets momentum has been shared with a broad sheath of material: and finally. the Lorentz factor showing that despite precession. (he jet does retain ils integrity. for almost 50 but thereafter the flow speed drops dramatically. | However, Figure \ref{precB} shows from left to right, a schlieren render of the pressure – there are dramatic variations of pressure along the jet's path, suggestive of significant dissipation; a linear render of the pressure (dominated by the leading bow) with 3-velocity vectors superposed – evidently the jet's momentum has been shared with a broad sheath of material; and finally, the Lorentz factor – showing that despite precession, the jet does retain its integrity for almost $50$ jet-radii, but thereafter the flow speed drops dramatically. |
The asvnunetric bow is being driven forward by a flow in which the pressure maintains a high enthalpy. and which is to some extent locussed onto a small area al the bow's apex. | The asymmetric bow is being driven forward by a flow in which the pressure maintains a high enthalpy, and which is to some extent focussed onto a small area at the bow's apex. |
Figure 14 quantifies this. showing the run of rest [rame densitv. pressure. Lorentz factor and momentum flux (or discharge). F=5?(e+p)v?+p. along the spine of the flow. | Figure \ref{precC} quantifies this, showing the run of rest frame density, pressure, Lorentz factor and momentum flux (or `discharge'), ${\cal
F}=\gamma^2\left(e+p\right) v_z^2+p$, along the spine of the flow. |
This spine was defined by computing weighted. average c and y values in a series of planes 2 =constant. within a evlinder of diameter 6 jet-radii aligned with the jet inflow (to exclude complex structures near to (the edge of the computational domain). | This spine was defined by computing weighted, average $x$ and $y$ values in a series of planes $z=$ constant, within a cylinder of diameter $6$ jet-radii aligned with the jet inflow (to exclude complex structures near to the edge of the computational domain). |
Using the Lorentz factor as a weighting function produced a locus barely disünguishable from that [ound using the momentum [lux as a weighting function. leading us (to the conclusion (hat (his approach indeed picks out a physically sienilicant core flow. | Using the Lorentz factor as a weighting function produced a locus barely distinguishable from that found using the momentum flux as a weighting function, leading us to the conclusion that this approach indeed picks out a physically significant core flow. |
The quantities plotted in Figure 14. are spatial averages within evlindrical pills of one jet radius. aligned locally with the spine. | The quantities plotted in Figure \ref{precC} are spatial averages within cylindrical pills of one jet radius, aligned locally with the spine. |
Increasing the radius of these sampling volumes decreased the average Lorentz factor and momentum fhix. but did not change the character of (he variation of these quantities along the spine. | Increasing the radius of these sampling volumes decreased the average Lorentz factor and momentum flux, but did not change the character of the variation of these quantities along the spine. |
Bevond 50 jet-radii the Lorentz factor falls well below its initial value ancl the local flow direction becomes more chaotic. | Beyond $50$ jet-radii the Lorentz factor falls well below its initial value and the local flow direction becomes more chaotic. |
Indeed. the orientation of the velocity vectors within the jet. relative to the local jet direction — defined by the locus of the spine is a quantitv of fundamental importance. | Indeed, the orientation of the velocity vectors within the jet, relative to the local jet `direction' – defined by the locus of the spine – is a quantity of fundamental importance. |
Is the flow locally parallel to the jet boundary. with little momentum imparted to the jets | Is the flow locally parallel to the jet boundary, with little momentum imparted to the jet's |
The products of à 47. aud ct with the Associated Legendre polynomials can be replaced with expressions containing only Associated Leseudre polynomials of the same azimuthal order. i. using the recursion relation where Ay’ is given by eq. | The products of $x$ , $x^2$ , and $x^4$ with the Associated Legendre polynomials can be replaced with expressions containing only Associated Legendre polynomials of the same azimuthal order, $m$, using the recursion relation where $A_\ell^m$ is given by eq. |
AG and Eq. | A6 and Eq. |
| À9 then reduces to (after droppingc» the primes) in Eq. | A9 then reduces to (after dropping the primes) A common factor in Eq. |
A12 is of the form D" (tan o The donuiuant terms on the RIIS of Eq. | A12 is of the form The dominant terms on the RHS of Eq. |
A12 are those for the direct rotation of the R7" cocticicuts. | A12 are those for the direct rotation of the $R_\ell^m$ coefficients. |
These ternis are best handledanalyticallyby taking where | These terms are best handledanalyticallyby taking where |
likely clue to the detailed structure of the ambient eas and shock front in each sector. | likely due to the detailed structure of the ambient gas and shock front in each sector. |
The temperature profiles for the position angles of 135 s6 and SG225. drawn from Vie. 10.. | The temperature profiles for the position angles of $-135-86$ and $86-225$, drawn from Fig. \ref{fig:kTFeNS}, |
are shown in the lower panels of Fig. | are shown in the lower panels of Fig. |
15. We have approximated. the ambient temperature profile as a linear fit to the plotted data range. excluding the bins within the ~40 arcsec thick shock. | \ref{fig:vert} We have approximated the ambient temperature profile as a linear fit to the plotted data range, excluding the bins within the $\sim40$ arcsec thick shock. |
Under this assumption. we observe that both the northern and southern projected temperature profiles contain at least four bins (between 130r170 arcsec) that appear hotter (5 per cent) than expected. | Under this assumption, we observe that both the northern and southern projected temperature profiles contain at least four bins (between $130\approxlt r\approxlt 170$ arcsec) that appear hotter $\sim5$ per cent) than expected. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.