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_36165/1595130315.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_36165/1595130315.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 0x1299327b0>

../_images/cookbook_Two_Clusters_14_2.png

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     ] 2025-02-18 14:04:37,061 Creating 1540111 energies from this spectrum.
soxs : [INFO     ] 2025-02-18 14:04:37,137 Finished creating energies.
soxs : [INFO     ] 2025-02-18 14:04:37,475 Creating 729759 energies from this spectrum.
soxs : [INFO     ] 2025-02-18 14:04:37,509 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 0x12ff32e90>

../_images/cookbook_Two_Clusters_22_1.png

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     ] 2025-02-18 14:04:38,142 Appending source 'cluster1' to clusters_simput.fits.
soxs : [INFO     ] 2025-02-18 14:04:38,203 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     ] 2025-02-18 14:04:38,304 Simulating events from 2 sources using instrument lynx_hdxi for 50 ks.
soxs : [INFO     ] 2025-02-18 14:04:38,420 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2025-02-18 14:04:38,965 Detected 113392 events in total.
soxs : [INFO     ] 2025-02-18 14:04:38,966 Adding background events.
soxs : [INFO     ] 2025-02-18 14:04:39,027 Adding in point-source background.
soxs : [INFO     ] 2025-02-18 14:04:43,675 Simulating events from 1 sources using instrument lynx_hdxi for 50 ks.
soxs : [INFO     ] 2025-02-18 14:04:45,078 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2025-02-18 14:04:46,475 Detected 940894 events in total.
soxs : [INFO     ] 2025-02-18 14:04:46,483 Generated 940894 photons from the point-source background.
soxs : [INFO     ] 2025-02-18 14:04:46,483 Adding in astrophysical foreground.

soxs : [INFO     ] 2025-02-18 14:04:56,897 Adding in instrumental background.
soxs : [INFO     ] 2025-02-18 14:04:57,194 Making 8435447 events from the galactic foreground.
soxs : [INFO     ] 2025-02-18 14:04:57,197 Making 130679 events from the instrumental background.
soxs : [INFO     ] 2025-02-18 14:04:58,609 Observation complete.
soxs : [INFO     ] 2025-02-18 14:04:58,610 Writing events to file evt.fits.

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
)

../_images/cookbook_Two_Clusters_31_0.png

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     ] 2025-02-18 14:05:07,668 Appending source 'cluster1' to clusters2_simput.fits.
soxs : [INFO     ] 2025-02-18 14:05:07,706 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     ] 2025-02-18 14:05:07,807 Simulating events from 2 sources using instrument lynx_hdxi for 50 ks.
soxs : [INFO     ] 2025-02-18 14:05:07,907 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2025-02-18 14:05:08,431 Detected 114717 events in total.
soxs : [INFO     ] 2025-02-18 14:05:08,432 Adding background events.
soxs : [INFO     ] 2025-02-18 14:05:08,487 Adding in point-source background.
soxs : [INFO     ] 2025-02-18 14:05:13,075 Simulating events from 1 sources using instrument lynx_hdxi for 50 ks.
soxs : [INFO     ] 2025-02-18 14:05:14,296 Scattering energies with RMF xrs_hdxi.rmf.

soxs : [INFO     ] 2025-02-18 14:05:15,622 Detected 910014 events in total.
soxs : [INFO     ] 2025-02-18 14:05:15,630 Generated 910014 photons from the point-source background.
soxs : [INFO     ] 2025-02-18 14:05:15,631 Adding in astrophysical foreground.

soxs : [INFO     ] 2025-02-18 14:05:25,873 Adding in instrumental background.
soxs : [INFO     ] 2025-02-18 14:05:26,152 Making 8429791 events from the galactic foreground.
soxs : [INFO     ] 2025-02-18 14:05:26,153 Making 131113 events from the instrumental background.
soxs : [INFO     ] 2025-02-18 14:05:27,066 Observation complete.
soxs : [INFO     ] 2025-02-18 14:05:27,109 Writing events to file evt2.fits.

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
)

../_images/cookbook_Two_Clusters_40_0.png

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