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Fitting stream with varying RAR (theta_0, W_0) and disk parameters. #5
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@ankrut @Charly-Arguelles @danielcarpintero , here the results. The varying parameters in the fit are theta_0, d_theta (=W_0-theta_0) plus the thin and thick disk parameters (Please note that I use the same factors for both disks). The disk parameters are the total mass, the r-scale and the z-scale.
The a priori bounds for those parameters (theta_0, d_theta, alpha, scale, scaleb) are: In the second case I obtained: Both cases are compatible between them and also in agreement with the case with fixed barions (alpha=1, scale=1, scaleb=1). |
How do you compute chi^2 in these experiments?
El mié, 2 mar 2022 a las 16:04, martinmestre ***@***.***>)
escribió:
… @ankrut <https://github.com/ankrut> @Charly-Arguelles
<https://github.com/Charly-Arguelles> @danielcarpintero
<https://github.com/danielcarpintero> , here the results.
The varying parameters in the fit are theta_0, d_theta (=W_0-theta_0) plus
the thin and thick disk parameters (Please note that I use the same factors
for both disks). The disk parameters are the total mass, the r-scale and
the z-scale.
def pot_model(ener_f, theta_0, W_0, beta_0, alpha, scale, scaleb):
"""Potential model including barions and dark matter halo."""
# Set barionic potentials
M_gal = 2.32e7 # Msun
bulge = pot.Plummer(460.0*M_gal, 0.3)
thin = pot.MiyamotoNagai(1700.0*M_gal*alpha, 5.3*scale, 0.25*scaleb)
thick = pot.MiyamotoNagai(1700.0*M_gal*alpha, 2.6*scale, 0.8*scaleb)
# Set halo potential
param = np.array([ener_f, theta_0, W_0, beta_0])
halo = pot.RAR(param)
return bulge, thin, thick, halo
The a priori bounds for those parameters (theta_0, d_theta, alpha, scale,
scaleb) are:
# bounds = ((34, 39), (25, 30), (0.85, 1.15), (0.9, 1.1), (0.9, 1.1))
I made two runs with a rather large number of iterations-population equal
to 40-40 and 100-100, respectively.
In the first case I obtained:
theta_0, d_theta, alpha, scale, scaleb =
3.642214195068059013e+01,
2.758970214272743249e+01
1.089703158216322576e+00
1.033675113036105708e+00
9.062517097351714401e-01
In the second case I obtained:
3.626724510339099083e+01
2.747475602895485736e+01
1.148997022079204511e+00
1.063196394644405185e+00
9.072897756291734561e-01
Both cases are compatible between them and also in agreement with the case
with fixed barions (alpha=1, scale=1, scaleb=1).
The chi^2 reduces a bit to 27 in this two cases with varying disk. In the
case of fixed disk, the chi^2 is 29. This slight difference is not
noticeable from the plots. Please notice that in this case I am using
beta_0=1.25e-5 while in the original fits I used 1.2e-5.
Here is a plot of the rotation curve for the second case,
[image: rotation_curve_beta0_1 25e-5]
<https://user-images.githubusercontent.com/58749264/156430375-774527c5-8a6f-496a-a89f-8a00786af3d2.png>
in order to compare with the plots in the previous issue.
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Excellent @martinmestre @ankrut , @danielcarpintero , as we were discussing today with Martin (from what he figured it out), by defining a NEW likelihood, where we add the \Chi² with the Vrot data (e.g. Sofue+ 2020), to the already used \Chi² of the stream data, it would be very interesting to see the new result of maximization of this new Likelihood, because now we may obtain a considerably better fit to the V_rot , while still providing a good fit to the stream. As Daniel asks, it would be nice if you can write down how you are planning to define the Lieklihhods (either in the original case, as in the new one) |
Like this:
It is a discrete sum of the differences between the Ibata polynomials and our orbits, for the five observables: position in sky (only Phi_2 because Phi_1 is the independent variable here), distance, proper motion and radia velocity, all added together. Likke an L_2 norm between functions. |
Dear @Charly-Arguelles @danielcarpintero @ankrut :
I quote from the previous issue:
I will do some fits varying the barions as follows:
15% for central values of the masses and 10% for characteristic scales, according to the first paragraph of section 3.1.2 of this paper
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