Differences

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--- tests:discs:mockread1d [2014/11/03 08:53] – created kawata
+++ tests:discs:mockread1d [2022/10/24 12:26] (current) – external edit 127.0.0.1
@@ Line 28: / Line 28: @@
 <latex>
-$\sigma_z^2(z) = \frac{1}{\nu(z)} \int_0^z \nu(z') K_z(z') dz' + \frac{C}{\nu(z)}$
+$\sigma_z^2(z) = \frac{1}{\nu(z)} \int_0^z \nu(z') K_z(z') dz' + \frac{\sigma_z^2(0)\nu(0)}{\nu(z)}$
 </latex>
-where <latex>$C$</latex> is a constant that sets the velocity dispersion at <latex>$z = 0$</latex>. However, we do not use this. Instead, we use the distribution function:
+where <latex>$\sigma_z^2(0) = -\frac{1}{\nu(0)} \int_0^\infty \nu(z') K_z(z') dz'$</latex> sets the velocity dispersion at <latex>$z = 0$</latex>. However, we do not use this. Instead, we use the distribution function:
 <latex>
@@ Line 51: / Line 51: @@
 </latex>
-We set up several models by drawing stars from the above distribution function. These are detailed in the following table. For completeness I list also the normalisation constant for the Jeans equation solution <latex>$C$</latex>, though this is not required when using the full distribution function method.
+We set up several models by drawing stars from the above distribution function. These are detailed in the following table.
 ^ Model ^ Parameters ^ Data files ^ Plots ^
-| Simple | <latex>z_0 = 0.4\,{\rm kpc}</latex>; <latex>K = 1500</latex>; <latex>F = 267.65</latex>; <latex>C = 22.85^2</latex>; <latex>D = 0.18</latex>; <latex>n_* = 10^4</latex>; <latex>\Delta z_{\rm bin} = 0.05\,{\rm kpc}</latex>| {{:data:simplenu_sigz_bin.dat}} {{:data:simplenu_sigz.dat}} {{:data:simplenu_sigz_raw.dat}} | {{:data:simple.png?200}} |
+| Simple | <latex>z_0 = 0.4\,{\rm kpc}</latex>; <latex>K = 1500</latex>; <latex>F = 267.65</latex>; <latex>D = 0.18</latex>; <latex>n_* = 10^4</latex>; <latex>\Delta z_{\rm bin} = 0.05\,{\rm kpc}</latex>| {{:data:simplenu_sigz_bin.dat}} {{:data:simplenu_sigz.dat}} {{:data:simplenu_sigz_raw.dat}} | {{:data:simple.png?200}} |
 | Simplelow | As Simple, above, but with <latex>n_* = 10^3</latex> | {{:data:simplelownu_sigz_bin.dat}} {{:data:simplelownu_sigz.dat}} {{:data:simplelownu_sigz_raw.dat}} | |
-| Simple2 | <latex>z_0 = 0.9\,{\rm kpc}</latex> and <latex>C = 38.978^2</latex>; otherwise as Simple, above| {{:data:simple2nu_sigz_bin.dat}} {{:data:simple2nu_sigz.dat}} {{:data:simple2nu_sigz_raw.dat}} | {{:data:simple2.png?200}} |
+| Simple2 | <latex>z_0 = 0.9\,{\rm kpc}</latex>; otherwise as Simple, above| {{:data:simple2nu_sigz_bin.dat}} {{:data:simple2nu_sigz.dat}} {{:data:simple2nu_sigz_raw.dat}} | {{:data:simple2.png?200}} |
-| High | As Simple2, above, but with <latex>z_0 = 0.65\,{\rm kpc}</latex>; <latex>C = 31.734946^2</latex>; data cut on 2 < z < 4 kpc; just ~500 stars; and <latex>\Delta z = 0.25\,{\rm kpc}</latex> | {{:data:highnu_sigz_bin.dat}} {{:data:highnu_sigz.dat}} {{:data:highnu_sigz_raw.dat}} | {{:data:high.png?200}} |
+| High | As Simple2, above, but with <latex>z_0 = 0.65\,{\rm kpc}</latex>; data cut on 2 < z < 4 kpc; just ~500 stars; and <latex>\Delta z = 0.25\,{\rm kpc}</latex> | {{:data:highnu_sigz_bin.dat}} {{:data:highnu_sigz.dat}} {{:data:highnu_sigz_raw.dat}} | {{:data:high.png?200}} |
 where <latex>n_*</latex> is the number of stars, and <latex>\Delta z_{\rm bin}</latex> is the bin size (for the binned data).