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()

<>:6: SyntaxWarning: invalid escape sequence '\m'
<>:9: SyntaxWarning: invalid escape sequence '\m'
<>:6: SyntaxWarning: invalid escape sequence '\m'
<>:9: SyntaxWarning: invalid escape sequence '\m'
/var/folders/6n/s0lf9frd7zq68c7dhlr090y4c91lh9/T/ipykernel_61107/1595130315.py:6: SyntaxWarning: invalid escape sequence '\m'
  label="$\mathrm{kT\ =\ 6\ keV,\ Z\ =\ 0.3\ Z_\odot,\ z\ =\ 0.05}$",
/var/folders/6n/s0lf9frd7zq68c7dhlr090y4c91lh9/T/ipykernel_61107/1595130315.py:9: SyntaxWarning: invalid escape sequence '\m'
  label="$\mathrm{kT\ =\ 4\ keV,\ Z\ =\ 0.4\ Z_\odot,\ z\ =\ 0.1}$", fig=fig, ax=ax

<matplotlib.legend.Legend at 0x162a2fec0>

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     ] 2024-06-19 16:04:02,147 Creating 1538585 energies from this spectrum.
soxs : [INFO     ] 2024-06-19 16:04:02,279 Finished creating energies.
soxs : [INFO     ] 2024-06-19 16:04:02,608 Creating 728323 energies from this spectrum.
soxs : [INFO     ] 2024-06-19 16:04:02,667 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 0x162c1ecf0>

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     ] 2024-06-19 16:04:03,541 Appending source 'cluster1' to clusters_simput.fits.
soxs : [INFO     ] 2024-06-19 16:04:03,600 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     ] 2024-06-19 16:04:03,617 Making observation of source in evt.fits.
soxs : [INFO     ] 2024-06-19 16:04:03,736 Detecting events from source cluster1.
soxs : [INFO     ] 2024-06-19 16:04:03,737 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:03,774 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:03,784 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:03,793 74937 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:03,810 Detecting events from source cluster2.
soxs : [INFO     ] 2024-06-19 16:04:03,810 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:03,827 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:03,831 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:03,836 38400 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:03,838 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-06-19 16:04:04,439 Adding background events.
soxs : [INFO     ] 2024-06-19 16:04:04,509 Adding in point-source background.
soxs : [INFO     ] 2024-06-19 16:04:07,291 Detecting events from source ptsrc_bkgnd.
soxs : [INFO     ] 2024-06-19 16:04:07,291 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:07,610 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:07,832 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:08,003 1559155 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:08,048 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-06-19 16:04:10,098 Generated 1559155 photons from the point-source background.
soxs : [INFO     ] 2024-06-19 16:04:10,099 Adding in astrophysical foreground.

soxs : [INFO     ] 2024-06-19 16:04:21,421 Adding in instrumental background.
soxs : [INFO     ] 2024-06-19 16:04:21,700 Making 8543155 events from the galactic foreground.
soxs : [INFO     ] 2024-06-19 16:04:21,701 Making 131229 events from the instrumental background.
soxs : [INFO     ] 2024-06-19 16:04:22,273 Writing events to file evt.fits.
soxs : [INFO     ] 2024-06-19 16:04:23,073 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     ] 2024-06-19 16:04:30,702 Appending source 'cluster1' to clusters2_simput.fits.
soxs : [INFO     ] 2024-06-19 16:04:30,745 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     ] 2024-06-19 16:04:30,758 Making observation of source in evt2.fits.
soxs : [INFO     ] 2024-06-19 16:04:30,860 Detecting events from source cluster1.
soxs : [INFO     ] 2024-06-19 16:04:30,861 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:30,903 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:30,912 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:30,920 76492 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:30,927 Detecting events from source cluster2.
soxs : [INFO     ] 2024-06-19 16:04:30,928 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:30,955 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:30,960 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:30,965 38266 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:30,966 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-06-19 16:04:31,535 Adding background events.
soxs : [INFO     ] 2024-06-19 16:04:31,605 Adding in point-source background.
soxs : [INFO     ] 2024-06-19 16:04:33,662 Detecting events from source ptsrc_bkgnd.
soxs : [INFO     ] 2024-06-19 16:04:33,662 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.
soxs : [INFO     ] 2024-06-19 16:04:33,859 Pixeling events.
soxs : [INFO     ] 2024-06-19 16:04:34,000 Scattering events with a image-based PSF.
soxs : [INFO     ] 2024-06-19 16:04:34,107 980257 events were detected from the source.
soxs : [INFO     ] 2024-06-19 16:04:34,137 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-06-19 16:04:35,599 Generated 980257 photons from the point-source background.
soxs : [INFO     ] 2024-06-19 16:04:35,600 Adding in astrophysical foreground.

soxs : [INFO     ] 2024-06-19 16:04:47,036 Adding in instrumental background.
soxs : [INFO     ] 2024-06-19 16:04:47,298 Making 8538460 events from the galactic foreground.
soxs : [INFO     ] 2024-06-19 16:04:47,298 Making 130469 events from the instrumental background.
soxs : [INFO     ] 2024-06-19 16:04:47,866 Writing events to file evt2.fits.
soxs : [INFO     ] 2024-06-19 16:04:48,613 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.