Simulating observations

This notebook shows how to use the Simulator class to easily generate synthetic observation datasets, with: * how to set up the observed environment (using the distributions implemented in infobs.sampling) * how to simulate noise-free observations of the considered environment (using the IdealInstrument class) * how to simulate realistic IRAM-30m observations of the considered environment (using the IRAM30mEMIR class) * how to modify the noise model (eg, adding a beam dilution or changing the integration time)

[1]:

import os
import sys

sys.path.insert(0, os.path.join(".."))

from infobs import Simulator
from infobs.instruments import IdealInstrument, IRAM30mEMIR
from infobs.sampling import Constant, LogUniform

Settings

[2]:

lines = ["13c_o_j1__j0", "13c_o_j2__j1", "13c_o_j3__j2"]

n_samples = 5
linewidth = 10  # km/s
obstime = 1  # Minutes

Samplers

[3]:

samplers = {
    "Av": LogUniform(1, 25),
    "G0": LogUniform(1e1, 1e3),
    "Pth": LogUniform(1e5, 5e6),
    "angle": Constant(0.0),
}

Warning: Sampler intervals should be included in the emulator’s range of validity, i.e., - \(A_v^{\text{max}} \in \left[1,\,40\right]\), - \(G_0 \in \left[1,\,10^5\right]\), - \(P_{\text{th}} \in \left[10^5,\,10^9\right]\), - \(\alpha \in \left[0,\,60\right]\).

The chosen sampler corresponds roughly to the range of values within the horsehead pillar. Note that here a loguniform distribution is used while in practice the distributions are more sophisticated (see sampling.ipynb example notebook).

What’s more, here the sampler chosen for the angle \(\alpha\) is constant at 0, meaning that the PDR is assumed to be always observed face-on.

Ideal instrument

[4]:

ideal = IdealInstrument()
simulator = Simulator(ideal)

simulator.simulate(n_samples, samplers, lines, obstime)

[4]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 7.198038 570.499386 3.693990e+06 0.0 1.0 14.992116 28.134336 23.984704
1 4.608825 92.881820 1.439909e+05 0.0 1.0 9.052731 11.887270 4.681478
2 6.942497 185.331395 4.777970e+05 0.0 1.0 15.412903 22.866178 13.715204
3 1.895651 481.791933 4.189151e+06 0.0 1.0 0.251140 0.841297 1.259055
4 21.184942 145.542715 3.520733e+05 0.0 1.0 36.264065 36.262805 21.246866

IRAM 30m EMIR

[5]:

emir = IRAM30mEMIR(linewidth)
simulator = Simulator(emir)

simulator.simulate(n_samples, samplers, lines, obstime)

[5]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 2.847111 21.085553 3.552803e+06 0.0 1.0 6.829083 11.925423 -9.174312
1 3.040641 16.727384 8.808243e+05 0.0 1.0 2.466090 6.999750 -10.259963
2 1.317259 33.406536 2.265809e+06 0.0 1.0 -0.783804 2.974079 39.529699
3 21.889157 71.478694 2.314246e+06 0.0 1.0 39.421040 37.358304 39.375572
4 2.190706 77.452951 3.691687e+06 0.0 1.0 0.682725 4.190670 -8.518081

Changing integration time

[6]:

simulator.simulate(n_samples, samplers, lines, 10 * obstime)

[6]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 4.229869 26.681007 220630.823769 0.0 1.0 10.577816 12.412982 2.017352
1 3.789195 189.533693 452559.587539 0.0 1.0 5.869740 10.598447 2.437343
2 1.144148 29.433223 224806.036917 0.0 1.0 0.186957 0.247534 -2.231751
3 16.926389 354.780451 434166.693873 0.0 1.0 33.717319 35.881103 26.869483
4 1.325555 25.320594 919837.041967 0.0 1.0 0.222746 1.394906 -1.255470

Adding a scaling parameter \(\kappa\)

The \(\kappa\) scaling parameter is used to integrated beam dilution (\(\kappa < 1\)) and geometry uncertainty (\(\kappa > 1\)). It is always positive.

[7]:

kappa_sampler = LogUniform(0.1**0.5, 10**0.5)

simulator.simulate(n_samples, samplers, lines, 10 * obstime, kappa=kappa_sampler)

[7]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 23.686477 843.422009 2.270589e+06 0.0 3.010717 138.534038 185.767947 132.078238
1 8.109191 167.207760 2.507045e+06 0.0 0.936190 16.987200 29.694781 27.264040
2 3.464913 12.616020 1.996795e+05 0.0 0.331824 2.827064 3.422085 2.893635
3 2.655290 371.130520 5.962335e+05 0.0 2.264428 2.478202 4.637277 0.899065
4 15.686875 17.287925 1.365352e+05 0.0 2.532635 78.114017 84.804080 24.215629

Seeding

Using seeding, one can generate random yet reproducible datasets.

[8]:

simulator.simulate(n_samples, samplers, lines, obstime, kappa=kappa_sampler)

[8]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 1.762621 36.670826 1.627096e+06 0.0 2.901282 3.242177 12.028595 29.372548
1 20.872742 10.365981 1.112904e+06 0.0 0.340715 12.526270 11.554773 21.952827
2 1.796031 188.980283 2.047123e+06 0.0 0.867330 -1.521585 -7.372223 -7.909411
3 5.246656 56.475428 2.092535e+06 0.0 1.617773 20.820918 35.449467 16.807344
4 17.537479 443.548195 4.297136e+06 0.0 2.551548 93.187963 118.875414 64.150959 
[9]:

simulator.simulate(n_samples, samplers, lines, obstime, kappa=kappa_sampler, seed=0)

[9]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 5.850707 195.788972 2.213691e+06 0.0 0.386482 7.773508 7.470687 11.525396
1 9.995208 75.019544 7.917291e+05 0.0 0.331298 5.980112 3.396069 19.040374
2 6.960285 607.499607 9.227641e+05 0.0 2.150898 33.660216 47.636578 78.493467
3 5.777155 845.912653 3.737326e+06 0.0 1.897391 15.426901 35.160349 27.747462
4 3.910605 58.463261 1.320347e+05 0.0 2.344294 21.657290 25.216067 11.163777 
[10]:

simulator.simulate(n_samples, samplers, lines, obstime, kappa=kappa_sampler, seed=0)

[10]:
Av G0 Pth angle kappa 13c_o_j1__j0 13c_o_j2__j1 13c_o_j3__j2
0 5.850707 195.788972 2.213691e+06 0.0 0.386482 7.773508 7.470687 11.525396
1 9.995208 75.019544 7.917291e+05 0.0 0.331298 5.980112 3.396069 19.040374
2 6.960285 607.499607 9.227641e+05 0.0 2.150898 33.660216 47.636578 78.493467
3 5.777155 845.912653 3.737326e+06 0.0 1.897391 15.426901 35.160349 27.747462
4 3.910605 58.463261 1.320347e+05 0.0 2.344294 21.657290 25.216067 11.163777