===== Tidally stripped models =====

For these models, we set up a spherical two component (stars/dark matter) "dwarf-like" galaxy that we throw at a host Milky Way-like galaxy on a range of orbits. The initial conditions and modelling follows similarly to [[http://adsabs.harvard.edu/abs/2006MNRAS.367..387R|Read et al. 2006]]. The initial dwarf **before infall** has a Dehnen profile for both the stars and the dark matter: 

<latex>
\rho = \frac{M(3-\alpha)}{4\pi a^3}\frac{1}{(r/a)^\alpha(1+r/a)^{4-\alpha}}
</latex>

With parameters: 

^ <latex>M_*</latex> ^ <latex>a_*</latex> ^ <latex>\alpha_*</latex> ^ <latex>M_{\rm dm}</latex> ^ <latex>a_{\rm dm}</latex> ^ <latex>\alpha_{\rm dm}</latex> ^ 
| <latex>10^6\,{\rm M}_\odot</latex> | <latex>0.3\,{\rm kpc}</latex> | 0.01 | <latex>10^9\,{\rm M}_\odot</latex> | <latex>2\,{\rm kpc}</latex> | 0.99 |

This was then put on a range of orbits of increasing ellipticity in a Miyamoto-Nagai-Log potential: 

<latex>
\Phi = \Phi_M + \Phi_L
</latex>

<latex>
\Phi_M(R,z) = -\frac{GM_{\rm disk}}{\sqrt{R^2 + (a+\sqrt{b^2+z^2})^2}}
</latex>

<latex>
\Phi_L(R,z) = \frac{v_0^2}{2}\ln\left(R_c^2 + R^2 + \frac{z^2}{q_0^2}\right) + {\rm const.} 
</latex>

with: 

<latex>
M_{\rm disk} = 5 \times 10^{10}\,{\rm M}_\odot 
</latex>;
<latex>
v_0 = 220\,{\rm km/s} 
</latex>;
<latex>
r_t = 8\,{\rm kpc}
</latex>;
<latex>
a = 4\,{\rm kpc}
</latex>;
<latex>
b = 0.5\,{\rm kpc}
</latex>;
<latex>
q_0 = 1.0 
</latex>

Four orbits were chosen as follows; each aligned at 40 degrees to the x-z plane; each evolved for 5 Gyrs using a version of the [[http://www.mpa-garching.mpg.de/gadget/|Gadget2]] code.

^ Orbit ^ x(kpc) ^ y(kpc) ^ z(kpc) ^ vx(km/s) ^ vy(km/s) ^ vz(km/s) ^ [peri,apo](kpc) ^ 
| Orbit1 (Circular; <latex>1.0 \times v_c</latex>) | 76.604251 | 0.21981924 | -64.278601 | -0.38536909 | 219.81886 | 0.32415738 | [~100,100] | 
| Orbit2 (Elliptical; <latex>0.75 \times v_c</latex>) | 76.604251 | 0.16486443 | -64.278601 | -0.38536936 | 164.86415 | 0.32415761 | [56,100] | 
| Orbit3 (Very Elliptical; <latex>0.5 \times v_c</latex>) | 76.604251 | 0.10990962 | -64.278601 | -0.38536956 | 109.90943 | 0.32415778 | [29,100] |
| Orbit4 (Very Very Elliptical; <latex>0.25 \times v_c</latex>) | 76.604251 | 0.054954810 | -64.278601 | -0.38536968 | 54.954715	| 0.32415788 | [11,100] | 

Density projections of the final stellar distribution are as follows (left to right :: Orbit1 -> Orbit4): 

| {{:tests:orbit1.png}} | {{:tests:orbit2.png}} | {{:tests:orbit3.png}} | {{:tests:orbit4.png}} |


The following give data files for each. These include .txt files of **all** stars for the final disrupted satellite centred on the origin. This amounts to three data sets if using only projected data (i.e. one along each of the x,y,z projections). In addition, the raw Gadget data files are included. These have not been centred. PyNbody python tools for loading and manipulating these Gadget data can be found [[https://github.com/pynbody/pynbody|here]]. Units for each file are as follows: 

  * .txt files :: x(kpc),y(kpc),z(kpc),vx(km/s),vy(km/s),vz(km/s).
  * _err.txt files :: The same as above but assuming 2km/s Gaussian velocity errors. 
  * .dat files (Gadget) :: <latex>L = {\rm kpc}</latex>, <latex>M = 2.33\times 10^5\,{\rm M}_\odot</latex>, <latex>V = {\rm km/s}</latex>.
  * Files are numbered by the sampling e.g. _10000 is 10,000 stars and by the random draw from the full distribution e.g. _10000_0. **As with the spherical mocks, you should model by default including the 2km/s errors and using the _0 then _1, _2, _3 files in order**. (i.e. if you can only afford to run a single tidal mock for each orbit, then you should run the _10000_0_err file projected along the z-axis.)

^ Orbit ^ Data files ^ 
| Orbit1 | {{:tests:orbit1.dat}} {{:data:orbit1.tar}} | 
| Orbit2 | {{:tests:orbit2.dat}} {{:data:orbit2.tar}} | 
| Orbit3 | {{:tests:orbit3.dat}} {{:data:orbit3.tar}} | 
| Orbit4 | {{:tests:orbit4.dat}} {{:data:orbit4.tar}} |