Astronomy & Astrophysics

All Figures

$\begin{figure} \par\epsfig{file=fig1.eps,height=5.9cm,angle=0}\end{figure}$ Figure 1: Numerical measurement of the Coulomb logarithm (left) and of the satellite energy loss by dynamical friction (right) for run A₁ (characterized by $M_{\rm s}/M = 0.1$ , $R_{\rm s}/R = 0.1$ , $t_{\rm fall}/t_{\rm cr} = 48.125$ ). The quantities are plotted against a Lagrangian radial coordinate in the same format as in the paper by Bontekoe & van Albada (1987).
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In the text

$\begin{figure} { \epsfig{file=fig2a.eps,height=5.55cm,angle=0}\hspace*{1mm} \eps... ...{1mm} \epsfig{file=fig2f.eps,height=5.55cm,angle=0}\vspace*{1mm} } \end{figure}$ Figure 2: Six frames describing the equatorial density response $\rho _1 = \rho - \rho _0$ of the galaxy to the infalling satellite for run A₁. The density wakes are portrayed at time $t/t_{\rm cr} = {\bf a)}$ 38.5, b) 39.875, c) 41.25, d) 42.625, e) 44, and f) 53.625. The white circle denotes the location of the satellite.
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In the text

$\begin{figure} { \epsfig{file=fig3a.eps,height=5.1cm,angle=0}\epsfig{file=fig3b.... ...height=5.1cm,angle=0}\epsfig{file=fig3f.eps,height=5.1cm,angle=0} } \end{figure}$ Figure 3: For each frame of Fig. 2 we illustrate in detail the monopole (l=0) and the dipole (l=1) contributions to the density wake in the galaxy (the various curves represent the coefficients A₁₀, A₁₁, A₀₀, and B₁₁ defined in the text; see Sect. 4.3).
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In the text

$\begin{figure} { \epsfig{file=fig4.eps,height=5.2cm,angle=0} } \end{figure}$ Figure 4: For run A₁ we plot the mean azimuthal velocity of the galaxy measured on the equatorial plane at three different times; the rotation induced by the angular momentum exchange with the infalling satellite is approximately that of a solid body. As usual, time is measured in units of $t_{\rm cr}$ .
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In the text

$\begin{figure} { \epsfig{file=fig5.eps,height=6.2cm,angle=0} } \end{figure}$ Figure 5: For run A₁ we plot two othogonal equatorial cuts of the anisotropy distribution generated in the galaxy by the infalling satellite at time $t = 53.625~t_{\rm cr}$ , after the satellite has reached the center.
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In the text

$\begin{figure} { \epsfig{file=fig6.eps,width=8.8cm,angle=0} } \end{figure}$ Figure 6: The curves illustrate the orbital decay process for the satellite for three different runs (A₆, A₈, and A₉, labeled as 1, 2, and 3 respectively) characterized by different spatial size of the infalling satellite ( $R_{\rm s} = 0.1,~0.05,~0.025~R$ ; $M_{\rm s}/M = 0.05$ ).
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In the text

$\begin{figure} { \epsfig{file=fig7a.eps,height=6cm,angle=0}\psfig{file=fig7b.eps,height=6cm,angle=0} } \end{figure}$ Figure 7: Left: The density distribution change induced in the galaxy by the infall of the satellite (run A₁). The thick upper curve (1) represents the initial distribution, while the thin lower curve (2) is associated with the final state. Right: Orbital decay for run A₁ (cf. Fig. 2) as in Fig. 6.
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In the text

$\begin{figure} \mbox{ \epsfig{file=fig13_a.eps,height=5.3cm,angle=0}\hspace*{5mm... ...mm}\epsfig{file=fig13_d.eps,height=5.2cm,angle=0}\hspace*{5.5mm} } \end{figure}$ Figure 8: The fall of a shell of fragments towards the galaxy center, for the case of $N_{\rm f } = 20$ (left frame on the top, run BS₁) and for $N_{\rm f} = 100$ (right frame on the top, run BS₂). For comparison, the left frame at the bottom describes the time evolution of a collisionless shell (a run with $N_{\rm f} = 5 \times 10^4$ ). Displayed lines represent 5, 15, 25, 35, 45, 55, 65, 75, 85, and 95% of the shell mass. The right frame at the bottom displays, for run BS₂, the correlation between single particle energy at time $t = 14~ t_{\rm cr}$ and energy at time $t = 118 ~t_{\rm cr}$ , showing the effects of scattering associated with dynamical friction; units for energy are those indicated in Sect. 4.1.
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In the text

$\begin{figure} \mbox{ \epsfig{file=fig14_a.eps,height=5.7cm,angle=0}\epsfig{file=fig14_b.eps,height=5.7cm,angle=0} } \end{figure}$ Figure 9: The development of pressure anisotropy in the galaxy as a result of the interaction with a shell of fragments dragged in towards the galaxy center, for the case of $N_{\rm f } = 20$ (left frame, run BS₁) and for $N_{\rm f} = 100$ (right frame, run BS₂). The dashed curves represent the evolving value of K_T/2, where $K_{\rm T}$ is the total kinetic energy associated with the star motions in the tangential directions; the solid curve represents the evolving value of $K_{\rm r}$ , the total kinetic energy associated with the star motions in the radial direction.
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In the text

$\begin{figure} { \epsfig{file=fig15.eps,height=7cm,angle=0} }\end{figure}$ Figure 10: The change in density profile for the galaxy as a result of the interaction with a shell of fragments dragged in towards the galaxy center, for the case of $N_{\rm f } = 20$ (run BS₁). The thicker curve (1) represents the initial density profile, the thinner (2) gives the final profile.
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In the text

$\begin{figure} {\hspace*{7mm}\epsfig{file=fig16_a.eps,height=5cm,angle=0}\epsfig... ...e=0}\epsfig{file=fig16_d.eps,height=55mm,width=77mm,angle=0} }\par\end{figure}$ Figure 11: The effects of dynamical friction on a shell of fragments created out of the initial distribution function (case III of Sect. 3). The lower frames show the general decay of orbits of the fragments for the case $N_{\rm f } = 20$ (run BT₃) and $N_{\rm f} = 100$ (run BT₄); displayed lines represent 5, 15, 25, 35, 45, 55, 65, 75, 85, and 95% of the shell mass. For the two runs, the upper frames show the corresponding effect of circularization of orbits; here the histograms record the number of fragments (crosses represent initial conditions, open circles the conditions at the end of the run) with orbit aspect ratio above $R_{\rm min}/R_{\rm max}$ , where $R_{\rm min}$ and $R_{\rm max}$ are consecutive minimum and maximum radii attained by a fragment along its orbit.
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In the text

$\begin{figure} {\epsfig{file=fig17a.eps,height=5.2cm,angle=0}\epsfig{file=fig17b.eps,height=5.2cm,angle=0} } \end{figure}$ Figure 12: The energies associated with the system of minisatellites (left frame) and measurement of the Coulomb logarithm $<\ln(\lambda)>~ = \sum_{j=1}^{j=N_{\rm f}} \ln(\lambda)/N_{\rm f}$ (right frame) (run BS₂).
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In the text

$\begin{figure} \par\epsfig{file=fig1.eps,height=5.9cm,angle=0}\end{figure}$	Figure 1: Numerical measurement of the Coulomb logarithm (left) and of the satellite energy loss by dynamical friction (right) for run A₁ (characterized by $M_{\rm s}/M = 0.1$ , $R_{\rm s}/R = 0.1$ , $t_{\rm fall}/t_{\rm cr} = 48.125$ ). The quantities are plotted against a Lagrangian radial coordinate in the same format as in the paper by Bontekoe & van Albada (1987).
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$\begin{figure} { \epsfig{file=fig2a.eps,height=5.55cm,angle=0}\hspace{1mm} \eps... ...{1mm} \epsfig{file=fig2f.eps,height=5.55cm,angle=0}\vspace{1mm} } \end{figure}$	Figure 2: Six frames describing the equatorial density response $\rho _1 = \rho - \rho _0$ of the galaxy to the infalling satellite for run A₁. The density wakes are portrayed at time $t/t_{\rm cr} = {\bf a)}$ 38.5, b) 39.875, c) 41.25, d) 42.625, e) 44, and f) 53.625. The white circle denotes the location of the satellite.
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$\begin{figure} { \epsfig{file=fig3a.eps,height=5.1cm,angle=0}\epsfig{file=fig3b.... ...height=5.1cm,angle=0}\epsfig{file=fig3f.eps,height=5.1cm,angle=0} } \end{figure}$	Figure 3: For each frame of Fig. 2 we illustrate in detail the monopole (l=0) and the dipole (l=1) contributions to the density wake in the galaxy (the various curves represent the coefficients A₁₀, A₁₁, A₀₀, and B₁₁ defined in the text; see Sect. 4.3).
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$\begin{figure} { \epsfig{file=fig4.eps,height=5.2cm,angle=0} } \end{figure}$	Figure 4: For run A₁ we plot the mean azimuthal velocity of the galaxy measured on the equatorial plane at three different times; the rotation induced by the angular momentum exchange with the infalling satellite is approximately that of a solid body. As usual, time is measured in units of $t_{\rm cr}$ .
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$\begin{figure} { \epsfig{file=fig5.eps,height=6.2cm,angle=0} } \end{figure}$	Figure 5: For run A₁ we plot two othogonal equatorial cuts of the anisotropy distribution generated in the galaxy by the infalling satellite at time $t = 53.625~t_{\rm cr}$ , after the satellite has reached the center.
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$\begin{figure} { \epsfig{file=fig6.eps,width=8.8cm,angle=0} } \end{figure}$	Figure 6: The curves illustrate the orbital decay process for the satellite for three different runs (A₆, A₈, and A₉, labeled as 1, 2, and 3 respectively) characterized by different spatial size of the infalling satellite ( $R_{\rm s} = 0.1,~0.05,~0.025~R$ ; $M_{\rm s}/M = 0.05$ ).
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$\begin{figure} { \epsfig{file=fig7a.eps,height=6cm,angle=0}\psfig{file=fig7b.eps,height=6cm,angle=0} } \end{figure}$	Figure 7: Left: The density distribution change induced in the galaxy by the infall of the satellite (run A₁). The thick upper curve (1) represents the initial distribution, while the thin lower curve (2) is associated with the final state. Right: Orbital decay for run A₁ (cf. Fig. 2) as in Fig. 6.
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$\begin{figure} { \epsfig{file=fig15.eps,height=7cm,angle=0} }\end{figure}$	Figure 10: The change in density profile for the galaxy as a result of the interaction with a shell of fragments dragged in towards the galaxy center, for the case of $N_{\rm f } = 20$ (run BS₁). The thicker curve (1) represents the initial density profile, the thinner (2) gives the final profile.
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$\begin{figure} {\epsfig{file=fig17a.eps,height=5.2cm,angle=0}\epsfig{file=fig17b.eps,height=5.2cm,angle=0} } \end{figure}$	Figure 12: The energies associated with the system of minisatellites (left frame) and measurement of the Coulomb logarithm $<\ln(\lambda)>~ = \sum_{j=1}^{j=N_{\rm f}} \ln(\lambda)/N_{\rm f}$ (right frame) (run BS₂).
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