Two Clusters

Using the SOXS Python interface, this example shows how to generate photons from two thermal spectra and two \(\beta\)-model spatial distributions, as an approximation of two galaxy clusters.

import matplotlib

matplotlib.rc("font", size=18)
import soxs

Generate Spectral Models

We want to generate thermal spectra, so we first create a spectral generator using the ApecGenerator class:

emin = 0.05  # keV
emax = 20.0  # keV
nbins = 20000
agen = soxs.ApecGenerator(emin, emax, nbins)

Next, we’ll generate the two thermal spectra. We’ll set the APEC norm for each to 1, and renormalize them later:

kT1 = 6.0
abund1 = 0.3
redshift1 = 0.05
norm1 = 1.0
spec1 = agen.get_spectrum(kT1, abund1, redshift1, norm1)

kT2 = 4.0
abund2 = 0.4
redshift2 = 0.1
norm2 = 1.0
spec2 = agen.get_spectrum(kT2, abund2, redshift2, norm2)

Now, re-normalize the spectra using energy fluxes between 0.5-2.0 keV:

flux1 = 1.0e-13  # erg/s/cm**2
flux2 = 5.0e-14  # erg/s/cm**2
emin = 0.5  # keV
emax = 2.0  # keV
spec1.rescale_flux(flux1, emin=0.5, emax=2.0, flux_type="energy")
spec2.rescale_flux(flux2, emin=0.5, emax=2.0, flux_type="energy")

We’ll also apply foreground galactic absorption to each spectrum:

n_H = 0.04  # 10^20 atoms/cm^2
spec1.apply_foreground_absorption(n_H)
spec2.apply_foreground_absorption(n_H)

spec1 and spec2 are Spectrum objects. Let’s have a look at the spectra:

fig, ax = spec1.plot(
    xmin=0.1,
    xmax=20.0,
    ymin=1.0e-8,
    ymax=1.0e-3,
    label="$\mathrm{kT\ =\ 6\ keV,\ Z\ =\ 0.3\ Z_\odot,\ z\ =\ 0.05}$",
)
spec2.plot(
    label="$\mathrm{kT\ =\ 4\ keV,\ Z\ =\ 0.4\ Z_\odot,\ z\ =\ 0.1}$", fig=fig, ax=ax
)
ax.legend()

<matplotlib.legend.Legend at 0x136eb42d0>

Generate Spatial Models

Now what we want to do is associate spatial distributions with these spectra. Each cluster will be represented using a \(\beta\)-model. For that, we use the BetaModel class. For fun, we’ll give the second BetaModel an ellipticity and tilt it by 45 degrees (a bit extreme, but it demonstrates the functionality nicely):

# Parameters for the clusters
r_c1 = 30.0  # in arcsec
r_c2 = 20.0  # in arcsec
beta1 = 2.0 / 3.0
beta2 = 1.0

# Center of the field of view
ra0 = 30.0  # degrees
dec0 = 45.0  # degrees

# Space the clusters roughly a few arcminutes apart on the sky.
# They're at different redshifts, so one is behind the other.
dx = 3.0 / 60.0  # degrees
ra1 = ra0 - 0.5 * dx
dec1 = dec0 - 0.5 * dx
ra2 = ra0 + 0.5 * dx
dec2 = dec0 + 0.5 * dx

# Now actually create the models
pos1 = soxs.BetaModel(ra1, dec1, r_c1, beta1, ellipticity=0.5, theta=45.0)
pos2 = soxs.BetaModel(ra2, dec2, r_c2, beta2)

Create SIMPUT files

Now, what we want to do is generate energies and positions from these models. We want to create a large sample that we’ll draw from when we run the instrument simulator, so we choose a large exposure time and a large collecting area (should be bigger than the maximum of the ARF). To do this, we use the from_models() method of the SimputPhotonList class to make instances of the latter:

t_exp = (500.0, "ks")
area = (3.0, "m**2")
cluster_phlist1 = soxs.SimputPhotonList.from_models(
    "cluster1", spec1, pos1, t_exp, area
)
cluster_phlist2 = soxs.SimputPhotonList.from_models(
    "cluster2", spec2, pos2, t_exp, area
)

soxs : [INFO     ] 2023-09-15 12:57:51,511 Creating 1539357 energies from this spectrum.
soxs : [INFO     ] 2023-09-15 12:57:51,654 Finished creating energies.
soxs : [INFO     ] 2023-09-15 12:57:52,056 Creating 725799 energies from this spectrum.
soxs : [INFO     ] 2023-09-15 12:57:52,120 Finished creating energies.

We can quickly show the positions using the plot() method of the SimputPhotonList instances. For simplicity, we’ll only show every 100th event using the stride argument, and restrict ourselves to a roughly \(20'\times~20'\) field of view.

fig, ax = cluster_phlist1.plot(
    [30.0, 45.0], 6.0, marker=".", stride=100, label="Cluster 1"
)
cluster_phlist2.plot(
    [30.0, 45.0], 6.0, marker=".", stride=100, fig=fig, ax=ax, label="Cluster 2"
)
ax.legend()

<matplotlib.legend.Legend at 0x137124650>

Now that we have the positions and the energies of the photons in the SimputPhotonLists, we can write them to a SIMPUT catalog, using the SimputCatalog class. Each cluster will have its own photon list, but be part of the same SIMPUT catalog:

# Create the SIMPUT catalog "sim_cat" from the photon lists "cluster1" and "cluster2"
sim_cat = soxs.SimputCatalog.from_source(
    "clusters_simput.fits", cluster_phlist1, overwrite=True
)
sim_cat.append(cluster_phlist2)

soxs : [INFO     ] 2023-09-15 12:57:53,010 Appending source 'cluster1' to clusters_simput.fits.
soxs : [INFO     ] 2023-09-15 12:57:53,078 Appending source 'cluster2' to clusters_simput.fits.

Simulate an Observation

Finally, we can use the instrument simulator to simulate the two clusters by ingesting the SIMPUT file, setting an output file "evt.fits", setting an exposure time of 50 ks (less than the one we used to generate the source), the "lynx_hdxi" instrument, and the pointing direction of (RA, Dec) = (30.,45.) degrees.

soxs.instrument_simulator(
    "clusters_simput.fits",
    "evt.fits",
    (50.0, "ks"),
    "lynx_hdxi",
    [30.0, 45.0],
    overwrite=True,
)

soxs : [INFO     ] 2023-09-15 12:57:53,094 Making observation of source in evt.fits.
soxs : [INFO     ] 2023-09-15 12:57:53,193 Detecting events from source cluster1.
soxs : [INFO     ] 2023-09-15 12:57:53,194 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:57:53,230 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:57:53,241 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:57:53,259 74336 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:57:53,281 Detecting events from source cluster2.
soxs : [INFO     ] 2023-09-15 12:57:53,282 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:57:53,300 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:57:53,305 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:57:53,312 38357 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:57:53,315 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2023-09-15 12:57:53,863 Adding background events.
soxs : [INFO     ] 2023-09-15 12:57:53,923 Adding in point-source background.
soxs : [INFO     ] 2023-09-15 12:57:56,462 Detecting events from source ptsrc_bkgnd.
soxs : [INFO     ] 2023-09-15 12:57:56,462 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:57:56,729 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:57:56,918 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:57:57,154 1361548 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:57:57,194 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2023-09-15 12:57:58,814 Generated 1361548 photons from the point-source background.
soxs : [INFO     ] 2023-09-15 12:57:58,814 Adding in astrophysical foreground.

soxs : [INFO     ] 2023-09-15 12:58:10,450 Adding in instrumental background.
soxs : [INFO     ] 2023-09-15 12:58:10,735 Making 8541663 events from the galactic foreground.
soxs : [INFO     ] 2023-09-15 12:58:10,736 Making 101614 events from the instrumental background.
soxs : [INFO     ] 2023-09-15 12:58:11,312 Writing events to file evt.fits.
soxs : [INFO     ] 2023-09-15 12:58:12,109 Observation complete.

We can use the write_image() function in SOXS to bin the events into an image and write them to a file, restricting the energies between 0.5 and 2.0 keV:

soxs.write_image("evt.fits", "img.fits", emin=0.5, emax=2.0, overwrite=True)

Now we show the resulting image:

fig, ax = soxs.plot_image(
    "img.fits", stretch="log", cmap="viridis", vmin=0.1, vmax=10.0, width=0.1
)

Alternative Way to Generate the SIMPUT Catalog

In the above example, we generated the SIMPUT catalog for the observation of the two clusters using SimputPhotonLists, which in previous versions was the only option available in SOXS. It is also possible to use two SimputSpectrum objects, which is another type of SIMPUT source that consists of a spectrum and (optionally) an image. The image is used by SOXS to serve as a model to generate photon positions on the sky. If no image is included, then the source is simply a point source.

In this case of course, the clusters are two extended sources, so we can use the from_models method in a similar way as we did above, but in this case we have to supply the width and the resolution (nx) of the image that we want to associate with the spectrum:

width = 10.0  # arcmin by default
nx = 1024  # resolution of image
cluster_spec1 = soxs.SimputSpectrum.from_models("cluster1", spec1, pos1, width, nx)
cluster_spec2 = soxs.SimputSpectrum.from_models("cluster2", spec2, pos2, width, nx)

Then we create the SIMPUT catalog in essentially the same way as before:

# Create the SIMPUT catalog "sim_cat" from the spectra "cluster1" and "cluster2" in the same way
sim_cat2 = soxs.SimputCatalog.from_source(
    "clusters2_simput.fits", cluster_spec1, overwrite=True
)
sim_cat2.append(cluster_spec2)

soxs : [INFO     ] 2023-09-15 12:58:19,290 Appending source 'cluster1' to clusters2_simput.fits.
soxs : [INFO     ] 2023-09-15 12:58:19,336 Appending source 'cluster2' to clusters2_simput.fits.

Run the instrument_simulator:

soxs.instrument_simulator(
    "clusters2_simput.fits",
    "evt2.fits",
    (50.0, "ks"),
    "lynx_hdxi",
    [30.0, 45.0],
    overwrite=True,
)

soxs : [INFO     ] 2023-09-15 12:58:19,349 Making observation of source in evt2.fits.
soxs : [INFO     ] 2023-09-15 12:58:19,442 Detecting events from source cluster1.
soxs : [INFO     ] 2023-09-15 12:58:19,443 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:58:19,504 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:58:19,516 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:58:19,536 80780 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:58:19,553 Detecting events from source cluster2.
soxs : [INFO     ] 2023-09-15 12:58:19,553 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:58:19,590 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:58:19,596 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:58:19,604 39485 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:58:19,606 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2023-09-15 12:58:20,151 Adding background events.
soxs : [INFO     ] 2023-09-15 12:58:20,210 Adding in point-source background.
soxs : [INFO     ] 2023-09-15 12:58:22,793 Detecting events from source ptsrc_bkgnd.
soxs : [INFO     ] 2023-09-15 12:58:22,793 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2023-09-15 12:58:23,044 Pixeling events.
soxs : [INFO     ] 2023-09-15 12:58:23,223 Scattering events with a image-based PSF.
soxs : [INFO     ] 2023-09-15 12:58:23,495 1216147 events were detected from the source.
soxs : [INFO     ] 2023-09-15 12:58:23,533 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2023-09-15 12:58:25,108 Generated 1216147 photons from the point-source background.
soxs : [INFO     ] 2023-09-15 12:58:25,109 Adding in astrophysical foreground.

soxs : [INFO     ] 2023-09-15 12:58:36,550 Adding in instrumental background.
soxs : [INFO     ] 2023-09-15 12:58:36,839 Making 8541873 events from the galactic foreground.
soxs : [INFO     ] 2023-09-15 12:58:36,839 Making 102364 events from the instrumental background.
soxs : [INFO     ] 2023-09-15 12:58:37,416 Writing events to file evt2.fits.
soxs : [INFO     ] 2023-09-15 12:58:38,559 Observation complete.

and make an image:

soxs.write_image("evt2.fits", "img2.fits", emin=0.5, emax=2.0, overwrite=True)
fig, ax = soxs.plot_image(
    "img2.fits", stretch="log", cmap="viridis", vmin=0.1, vmax=10.0, width=0.1
)

We used the same models, so the resulting images are the same except that different random numbers were used.