Line Emission

This example shows how to create a line emission model. It uses a galaxy cluster from a Gadget SPH cosmological dataset, and will create a thermal model out of the gas particles and will use the dark matter particles to add line emission to the spectrum, assuming that the emission comes from some decay process of the dark matter.

First, we load the modules:

[1]:
%matplotlib inline
import matplotlib

matplotlib.rc("font", size=18, family="serif")
import yt
import matplotlib.pyplot as plt
from yt.units import mp
import pyxsim

As in the Advanced Thermal Emission example, we’ll set up a hot gas filter:

[2]:
# Note that the units of all numbers in this function are CGS
def hot_gas(pfilter, data):
    pfilter1 = data[pfilter.filtered_type, "density"] < 5e-25
    pfilter2 = data[pfilter.filtered_type, "temperature"] > 3481355.78432401
    pfilter3 = data[pfilter.filtered_type, "temperature"] < 4.5e8
    return (pfilter1) & (pfilter2) & (pfilter3)


yt.add_particle_filter(
    "hot_gas",
    function=hot_gas,
    filtered_type="gas",
    requires=["density", "temperature"],
)

The dataset used here does not have a field for the electron number density, which is required to construct the emission measure field. Because we’ll only be using the hot gas, we can create a ("gas","El_number_density") field which assumes complete ionization (while taking into account the H and He mass fractions vary from particle to particle). This is not strictly true for all of the "gas" type particles, but since we’ll be using the "hot_gas" type it should be sufficiently accurate for our purposes. We’ll define the field here and add it.

[3]:
def _El_number_density(field, data):
    mueinv = data["gas", "H_fraction"] + 0.5 * (1.0 - data["gas", "He_fraction"])
    return data["gas", "density"] * mueinv / (1.0 * mp)


yt.add_field(
    ("gas", "El_number_density"),
    _El_number_density,
    units="cm**-3",
    sampling_type="local",
)

and we load the dataset in yt:

[4]:
ds = yt.load("snapshot_033/snap_033.0.hdf5")
ds.add_particle_filter("hot_gas")
yt : [INFO     ] 2024-10-07 13:46:15,247 Parameters: current_time              = 4.343952725460923e+17 s
yt : [INFO     ] 2024-10-07 13:46:15,247 Parameters: domain_dimensions         = [1 1 1]
yt : [INFO     ] 2024-10-07 13:46:15,248 Parameters: domain_left_edge          = [0. 0. 0.]
yt : [INFO     ] 2024-10-07 13:46:15,248 Parameters: domain_right_edge         = [25. 25. 25.]
yt : [INFO     ] 2024-10-07 13:46:15,248 Parameters: cosmological_simulation   = 1
yt : [INFO     ] 2024-10-07 13:46:15,248 Parameters: current_redshift          = -4.811891664902035e-05
yt : [INFO     ] 2024-10-07 13:46:15,249 Parameters: omega_lambda              = 0.762
yt : [INFO     ] 2024-10-07 13:46:15,249 Parameters: omega_matter              = 0.238
yt : [INFO     ] 2024-10-07 13:46:15,249 Parameters: omega_radiation           = 0.0
yt : [INFO     ] 2024-10-07 13:46:15,249 Parameters: hubble_constant           = 0.73
yt : [INFO     ] 2024-10-07 13:46:15,334 Allocating for 4.194e+06 particles
Loading particle index: 100%|███████████████████████████████████████████████████████████████████████████████████| 12/12 [00:00<00:00, 614.45it/s]
[4]:
True

To get a sense of what the cluster looks like, let’s take a slice through the density and temperature:

[5]:
slc = yt.SlicePlot(
    ds,
    "z",
    [("gas", "density"), ("gas", "temperature")],
    center="max",
    width=(3.0, "Mpc"),
)
slc.show()
yt : [INFO     ] 2024-10-07 13:46:16,393 max value is 7.22543e-22 at 9.1760425567626953 12.2128591537475586 9.3898868560791016
yt : [INFO     ] 2024-10-07 13:46:16,477 xlim = 8.081095 10.270990
yt : [INFO     ] 2024-10-07 13:46:16,477 ylim = 11.117912 13.307806
yt : [INFO     ] 2024-10-07 13:46:16,479 xlim = 8.081095 10.270990
yt : [INFO     ] 2024-10-07 13:46:16,479 ylim = 11.117912 13.307806
yt : [INFO     ] 2024-10-07 13:46:16,480 Making a fixed resolution buffer of (('gas', 'temperature')) 800 by 800
yt : [INFO     ] 2024-10-07 13:46:17,246 Making a fixed resolution buffer of (('gas', 'density')) 800 by 800


Now set up a sphere centered on the maximum density in the dataset:

[6]:
sp = ds.sphere("max", (1.0, "Mpc"))
yt : [INFO     ] 2024-10-07 13:46:18,684 max value is 7.22543e-22 at 9.1760425567626953 12.2128591537475586 9.3898868560791016

and create a thermal source model:

[7]:
thermal_model = pyxsim.CIESourceModel("apec", 0.2, 11.0, 10000, ("gas", "metallicity"))
pyxsim : [INFO     ] 2024-10-07 13:46:18,973 kT_min = 0.025 keV
pyxsim : [INFO     ] 2024-10-07 13:46:18,974 kT_max = 64 keV

Now we’ll set up a line emission field for the dark matter particles. We won’t try to replicate a specific model, but will simply assume that the emission is proportional to the dark matter mass. Note that this field is a particle field.

[8]:
norm = yt.YTQuantity(100.0, "g**-1*s**-1")


def _dm_emission(field, data):
    return data["PartType1", "particle_mass"] * norm


ds.add_field(
    ("PartType1", "dm_emission"),
    function=_dm_emission,
    sampling_type="particle",
    units="photons/s",
    force_override=True,
)

Now we can set up the LineSourceModel object. The first argument is the line center energy in keV, and the second is the field we just created, that sets up the line amplitude. There is another parameter, sigma, for adding in broadening of the line, but in this case we’ll rely on the velocities of the dark matter particles themselves to produce the line broadening.

[9]:
line_model = pyxsim.LineSourceModel(3.5, ("PartType1", "dm_emission"))

Now set up the parameters for generating the photons:

[10]:
exp_time = (300.0, "ks")  # exposure time
area = (1000.0, "cm**2")  # collecting area
redshift = 0.05

and actually generate the photons:

[11]:
ntp, ntc = pyxsim.make_photons(
    "therm_photons.h5", sp, redshift, area, exp_time, thermal_model
)
nlp, nlc = pyxsim.make_photons(
    "line_photons.h5", sp, redshift, area, exp_time, line_model
)
pyxsim : [INFO     ] 2024-10-07 13:46:18,991 Cosmology: h = 0.73, omega_matter = 0.238, omega_lambda = 0.762
pyxsim : [INFO     ] 2024-10-07 13:46:18,992 Using emission measure field '('gas', 'emission_measure')'.
pyxsim : [INFO     ] 2024-10-07 13:46:18,992 Using temperature field '('gas', 'temperature')'.
pyxsim : [INFO     ] 2024-10-07 13:47:06,316 Finished generating photons.
pyxsim : [INFO     ] 2024-10-07 13:47:06,318 Number of photons generated: 1533243
pyxsim : [INFO     ] 2024-10-07 13:47:06,318 Number of cells with photons: 34430
pyxsim : [INFO     ] 2024-10-07 13:47:06,337 Cosmology: h = 0.73, omega_matter = 0.238, omega_lambda = 0.762
pyxsim : [INFO     ] 2024-10-07 13:47:06,739 Finished generating photons.
pyxsim : [INFO     ] 2024-10-07 13:47:06,740 Number of photons generated: 400
pyxsim : [INFO     ] 2024-10-07 13:47:06,740 Number of cells with photons: 399

Next, project the photons for the total set and the line set by itself:

[12]:
nte = pyxsim.project_photons(
    "therm_photons.h5",
    "therm_events.h5",
    "y",
    (30.0, 45.0),
    absorb_model="wabs",
    nH=0.02,
)
nle = pyxsim.project_photons(
    "line_photons.h5", "line_events.h5", "y", (30.0, 45.0), absorb_model="wabs", nH=0.02
)
pyxsim : [INFO     ] 2024-10-07 13:47:06,751 Foreground galactic absorption: using the wabs model and nH = 0.02.
pyxsim : [INFO     ] 2024-10-07 13:47:07,265 Detected 1165581 events.
pyxsim : [INFO     ] 2024-10-07 13:47:07,268 Foreground galactic absorption: using the wabs model and nH = 0.02.
pyxsim : [INFO     ] 2024-10-07 13:47:07,283 Detected 399 events.

Write the raw, unconvolved spectra to disk:

[13]:
et = pyxsim.EventList("therm_events.h5")
el = pyxsim.EventList("line_events.h5")
et.write_spectrum("therm_spec.fits", 0.1, 10.0, 5000, overwrite=True)
el.write_spectrum("line_spec.fits", 0.1, 10.0, 5000, overwrite=True)

Now let’s plot up both spectra. We see that we have a thermal spectrum with the addition of a line at 3.5 keV (in real life such a line would not be so prominent, but it makes the example easier to see):

[14]:
import astropy.io.fits as pyfits

f1 = pyfits.open("therm_spec.fits")
f2 = pyfits.open("line_spec.fits")
fig = plt.figure(figsize=(9, 7))
ax = fig.add_subplot(111)
ax.loglog(
    f1["SPECTRUM"].data["ENERGY"],
    f1["SPECTRUM"].data["COUNTS"] + f2["SPECTRUM"].data["COUNTS"],
)
ax.loglog(f2["SPECTRUM"].data["ENERGY"], f2["SPECTRUM"].data["COUNTS"])
ax.set_xlim(0.2, 10)
ax.set_ylim(1, 3.0e4)
ax.set_xlabel("E (keV)")
ax.set_ylabel("counts/bin")
[14]:
Text(0, 0.5, 'counts/bin')
../_images/cookbook_Line_Emission_28_1.png

Let’s zoom into the region surrounding the line, seeing that it has some broadening due to the random velocities of the dark matter particles:

[15]:
ax.set_xscale("linear")
ax.set_xlim(3, 3.7)
ax.set_ylim(1.0, 3.0e2)
fig
[15]:
../_images/cookbook_Line_Emission_30_0.png