# 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.

[1]:

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:

[2]:

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:

[3]:

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

[4]:

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:

[5]:

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:

[6]:

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:

[7]:

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_81413/1595130315.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_81413/1595130315.py:9: SyntaxWarning: invalid escape sequence '\m'
label="$\mathrm{kT\ =\ 4\ keV,\ Z\ =\ 0.4\ Z_\odot,\ z\ =\ 0.1}$", fig=fig, ax=ax

[7]:

<matplotlib.legend.Legend at 0x169361730>


## 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):

[8]:

# 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:

[9]:

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     ] 2024-05-02 19:41:33,687 Creating 1539319 energies from this spectrum.

soxs : [INFO     ] 2024-05-02 19:41:33,824 Finished creating energies.

soxs : [INFO     ] 2024-05-02 19:41:34,169 Creating 727267 energies from this spectrum.

soxs : [INFO     ] 2024-05-02 19:41:34,230 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.

[10]:

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()

[10]:

<matplotlib.legend.Legend at 0x169fca810>


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:

[11]:

# 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     ] 2024-05-02 19:41:35,142 Appending source 'cluster1' to clusters_simput.fits.

soxs : [INFO     ] 2024-05-02 19:41:35,228 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.

[12]:

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

soxs : [INFO     ] 2024-05-02 19:41:35,245 Making observation of source in evt.fits.

soxs : [INFO     ] 2024-05-02 19:41:35,366 Detecting events from source cluster1.

soxs : [INFO     ] 2024-05-02 19:41:35,366 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:41:35,405 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:41:35,415 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:41:35,427 74327 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:41:35,444 Detecting events from source cluster2.

soxs : [INFO     ] 2024-05-02 19:41:35,444 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:41:35,463 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:41:35,468 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:41:35,473 38612 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:41:35,475 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-05-02 19:41:36,094 Adding background events.

soxs : [INFO     ] 2024-05-02 19:41:36,163 Adding in point-source background.

soxs : [INFO     ] 2024-05-02 19:41:39,603 Detecting events from source ptsrc_bkgnd.

soxs : [INFO     ] 2024-05-02 19:41:39,604 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:41:40,029 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:41:40,277 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:41:40,503 1945042 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:41:40,578 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-05-02 19:41:43,100 Generated 1945042 photons from the point-source background.

soxs : [INFO     ] 2024-05-02 19:41:43,101 Adding in astrophysical foreground.

soxs : [INFO     ] 2024-05-02 19:41:54,555 Adding in instrumental background.

soxs : [INFO     ] 2024-05-02 19:41:54,899 Making 8539803 events from the galactic foreground.

soxs : [INFO     ] 2024-05-02 19:41:54,900 Making 100756 events from the instrumental background.

soxs : [INFO     ] 2024-05-02 19:41:55,944 Writing events to file evt.fits.

soxs : [INFO     ] 2024-05-02 19:41:57,918 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:

[13]:

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


Now we show the resulting image:

[14]:

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:

[15]:

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:

[16]:

# 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     ] 2024-05-02 19:42:09,136 Appending source 'cluster1' to clusters2_simput.fits.

soxs : [INFO     ] 2024-05-02 19:42:09,184 Appending source 'cluster2' to clusters2_simput.fits.


Run the instrument_simulator:

[17]:

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

soxs : [INFO     ] 2024-05-02 19:42:09,200 Making observation of source in evt2.fits.

soxs : [INFO     ] 2024-05-02 19:42:09,295 Detecting events from source cluster1.

soxs : [INFO     ] 2024-05-02 19:42:09,296 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:42:09,337 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:42:09,346 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:42:09,362 75732 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:42:09,374 Detecting events from source cluster2.

soxs : [INFO     ] 2024-05-02 19:42:09,374 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:42:09,402 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:42:09,408 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:42:09,413 38202 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:42:09,415 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-05-02 19:42:09,995 Adding background events.

soxs : [INFO     ] 2024-05-02 19:42:10,065 Adding in point-source background.

soxs : [INFO     ] 2024-05-02 19:42:12,487 Detecting events from source ptsrc_bkgnd.

soxs : [INFO     ] 2024-05-02 19:42:12,488 Applying energy-dependent effective area from xrs_hdxi_3x10.arf.

soxs : [INFO     ] 2024-05-02 19:42:12,732 Pixeling events.

soxs : [INFO     ] 2024-05-02 19:42:12,900 Scattering events with a image-based PSF.

soxs : [INFO     ] 2024-05-02 19:42:13,035 1162983 events were detected from the source.

soxs : [INFO     ] 2024-05-02 19:42:13,072 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2024-05-02 19:42:14,736 Generated 1162983 photons from the point-source background.

soxs : [INFO     ] 2024-05-02 19:42:14,737 Adding in astrophysical foreground.

soxs : [INFO     ] 2024-05-02 19:42:26,085 Adding in instrumental background.

soxs : [INFO     ] 2024-05-02 19:42:26,388 Making 8538280 events from the galactic foreground.

soxs : [INFO     ] 2024-05-02 19:42:26,388 Making 101241 events from the instrumental background.

soxs : [INFO     ] 2024-05-02 19:42:26,944 Writing events to file evt2.fits.

soxs : [INFO     ] 2024-05-02 19:42:28,299 Observation complete.


and make an image:

[18]:

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.