# Thermal Sources¶

X-ray emission from thermal sources in pyXSIM can be generated from models which assume collisional ionization is dominant (whether in equilibrium or not) or a combination of collisional and photoionization processes are relevant. In the former case, the emission is a function of temperature $$T$$ and metallicity $$Z$$, and is proportional to the density squared:

$\varepsilon(E) = n_en_H\Lambda(T, Z; E)$

In the case where photoionization is important, the emission is directly dependent on the number density of hydrogen:

$\varepsilon(E) = n_en_H\Lambda(n_H, T, Z; E)$

In either case, the metallicity $$Z$$ may be a single value encompassing all metals or a vector corresponding to a list of individual elements. Since generating spectra and/or fluxes from each particle or cell would be prohibitively expensive, the emission is first binned into a 1-D or 2-D table (depending on whether or not the spectrum itself is density-dependent or only dependent on the temperature), and for each bin a spectrum or flux is calculated. For each cell or particle, the spectrum or flux is then linearly interpolated from this table. The accuracy of this method is sufficient for most purposes.

Warning

Thermal source models at minimum require a temperature field and a density field. In addition, some information regarding the number densities of hydrogen and free electrons need to be provided, so that a field for the emission measure $$n_en_HdV$$ can be constructed. This requires the ("gas","H_nuclei_density") (total number density of all species of hydrogen) and ("gas","El_number_density") (number density of free electrons) fields to be present in your dataset, which should be the case if your simulation keeps track of individual species. If they are not, and you only have a ("gas","density") field, you may assume full ionization by loading your dataset like this: ds = yt.load(filename, default_species_fields="ionized").

Three types of thermal source models are available, which will be described in turn below.

## Thermal Sources in Collisional Ionization Equilbrium (CIE)¶

The CIESourceModel class simulates thermal emission under the assumption of collisional ionization equilibrium (CIE). By default, setting up a CIESourceModel object requires the following arguments:

• model: The specific CIE model to use. Options are "apec", "spex", "mekal", or "cloudy".

• emin: The minimum energy for the spectrum in keV.

• emax: The maximum energy for the spectrum in keV.

• nbins: The number of bins in the spectrum.

• Zmet: The metallicity. Either a floating-point number for a constant metallicity, or the name of a yt field for a spatially-varying metallicity.

Exactly what abundances are set by the Zmet parameter depends on the model used:

• "apec" and "spex": Includes C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni (He fixed at abundance table value, Li, Be, B, F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, Zn fixed at solar).

• "mekal": Includes C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni (He fixed at abundance table value, other elements not modeled)

• "cloudy": He fixed at abundance table value, all higher elements up Zn to included.

Creating a default instance is rather simple:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 11.0, 10000, 0.3)


However, this model is very customizable. There are a number of other optional parameters which can be set:

• binscale: The scale of the energy binning: “linear” or “log”. Default: “linear”

• temperature_field: The yt field to use as the temperature. Must have dimensions of temperature. The default is ("gas", "temperature").

• emission_measure_field: The yt field to use as the emission measure. Must have dimensions of number density or per-volume. The default is ("gas", "emission_measure").

• h_fraction: The hydrogen mass fraction. If a float, assumes a constant mass fraction of hydrogen throughout. If a string or tuple of strings, is taken to be the name of the hydrogen fraction field from yt. Defaults to the appropriate value for the chosen abundance table.

• kT_min: The minimum temperature in units of keV. Default is 0.025.

• kT_max: The maximum temperature in units of keV. Default is 64.0.

• max_density: The maximum mass density of the cells or particles to use when generating photons. If a float, the units are assumed to be g/cm**3. can also be a YTQuantity or a float, string tuple such as (5.0e-25, "g/cm**3") Default: None, meaning no maximum density.

• method: The method used to generate the photon energies from the spectrum. Either "invert_cdf", which inverts the cumulative distribution function of the spectrum, or "accept_reject", which uses the acceptance-rejection method on the spectrum. The first method should be sufficient for most cases.

• thermal_broad: A boolean specifying whether or not the spectral lines should be thermally broadened. Only available for the "apec" and "spex" models. Default: True

• model_root: A path specifying where the model files are stored. If not provided, a default location known to pyXSIM is used.

• model_vers: The version identifier string for the model files, e.g. “2.0.2”. The default depends on the model used. Currently only implemented for the "apec", "spex", or "cloudy" models.

• var_elem: Optionally used to specify the abundances of specific elements, whether via floating-point numbers or yt fields. A dictionary of elements and values should be specified. See Variable Abundances below for more details.

• nolines: If set to True, the photons for this source will be generated assuming no emission lines. Only available for the "apec" and "spex" models. Default: False

• abund_table: The solar abundance table assumed for the different elements. See the discussion in Changing the Solar Abundance Table below for more details. Default: "angr"

• prng: A pseudo-random number generator. Typically will only be specified if you have a reason to generate the same set of random numbers, such as for a test or a comparison. Default is the numpy.random module, but a RandomState object or an integer seed can also be used.

### Changing the Solar Abundance Table¶

The abundance parameters discussed so far assume abundance of a particular element or a number of elements relative to the Solar value. Underlying this are the values of the Solar abundances themselves. It is possible to change the Solar abundance table in pyXSIM via the optional abund_table argument to CIESourceModel. By default, pyXSIM assumes the Anders & Grevesse 1989 abundances corresponding to a setting of "angr" for this parameter, but it is possible to use other tables of solar abundances. tables included which can be used are:

The Solar abundance table can be changed like this:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000,
("gas","metallicity"),
prng=25, abund_table='lodd')


Alternatively, one can supply their own abundance table by providing a NumPy array, list, or tuple of abundances 30 elements in length corresponding to the Solar abundances relative to hydrogen in the order of H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn. An example:

my_abund = np.array([1.00E+00, 8.51E-02, 1.12E-11, 2.40E-11, 5.01E-10,
2.69E-04, 6.76E-05, 4.90E-04, 3.63E-08, 8.51E-05,
1.74E-06, 3.98E-05, 2.82E-06, 3.24E-05, 2.57E-07,
1.32E-05, 3.16E-07, 2.51E-06, 1.07E-07, 2.19E-06,
1.41E-09, 8.91E-08, 8.51E-09, 4.37E-07, 2.69E-07,
3.16E-05, 9.77E-08, 1.66E-06, 1.55E-08, 3.63E-08])

thermal_model = pyxsim.CIESourceModel("spex", 0.1, 20.0, 10000,
prng=25, abund_table=my_abund)


Note

Currently the solar abundance table cannot be changed for the "cloudy" model. It is set to "feld".

### Variable Abundances¶

As noted above, by default CIESourceModel assumes all abundances besides H, He, and perhaps some trace elements are set by the single value or yt field provided by the Zmet parameter. However, more fine-grained control is possible. CIESourceModel accepts a var_elem optional argument to specify which elements should be allowed to vary freely. The syntax is the same as for Zmet, in that each element set can be a single floating-point value or a yt field name corresponding to a field in the dataset. var_elem should be a dictionary of key, value pairs where the key is the standard abbreviation for the element and the value is the single number or field name:

# Setting abundances by yt field names
Zmet = ("gas", "metallicity")
var_elem = {"O": ("gas", "O_fraction"), "Ca": ("gas","Ca_fraction")}
source_model = pyxsim.CIESourceModel("cloudy", 0.05, 50.0, 10000, Zmet, var_elem=var_elem)

# Setting abundances by numbers
Zmet = 0.3
var_elem = {"O": 0.4, "Ca": 0.5}
source_model = pyxsim.CIESourceModel("mekal", 0.05, 50.0, 10000, Zmet, var_elem=var_elem)


Whatever elements are not specified here are assumed to be set as normal, whether they are H, He, trace elements, or metals covered by the Zmet parameter. The abundances that you can specify in var_elem depend on the model being used:

• "apec" and "spex": Can vary any element He and higher up to Zn

• "mekal": Can vary He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni

• "cloudy": Can vary C, N, O, Ne, Fe, S, Si, Ca, and Mg

### Examples¶

Here, we will show several examples of constructing CIESourceModel objects.

An example where we use the default parameters, and a constant metallicity:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000, 0.5)


An example where we use a metallicity field and change the temperature field:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000,
("gas", "metallicity"),
temperature_field=("hot_gas","temperature")


An example where we change the limits of the temperature, and use the MeKaL model:

thermal_model = pyxsim.CIESourceModel("mekal", 0.1, 20.0, 10000, 0.3,
kT_min=0.1, kT_max=100.)


An example where we turn off thermal broadening of spectral lines, specify a directory to find the model files, and specify the model version:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000, 0.3,
model_root="/Users/jzuhone/data",
model_vers="3.0.3")


An example where we specify a random number generator and use the Cloudy model:

thermal_model = pyxsim.CIESourceModel("cloudy", 0.1, 20.0, 10000, 0.3,
prng=25)


Turning off line emission for the "apec" model:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000, 0.3,
prng=25, nolines=True)


## Non-Equilibrium Ionization¶

pyXSIM has support for emission from plasmas in a non-equilibrium ionization state in the NEISourceModel. In this case, it is assumed that the NEI calculation for the various ionization states has been carried out in your simulation code, so that you have fields available for each element and ionization state that you want to generate emission from.

To use NEISourceModel, one must first create a dictionary mapping elements in their different ionization states to the corresponding fields in your dataset as seen from yt, or single floating-point values. The ionization states in the keys of this dictionary are given in the "{elem}^{ion}" format, where ion=0 is neutral, ion=1 is singly ionized, and so on.

Here is an example from a FLASH dataset:

# The dict mapping ionization states of different elements to different
# yt fields
var_elem = {"H^1": ("flash", "h   "),
"He^0": ("flash", "he  "),
"He^1": ("flash", "he1 "),
"He^2": ("flash", "he2 "),
"O^0": ("flash", "o   "),
"O^1": ("flash", "o1  "),
"O^2": ("flash", "o2  "),
"O^3": ("flash", "o3  "),
"O^4": ("flash", "o4  "),
"O^5": ("flash", "o5  "),
"O^6": ("flash", "o6  "),
"O^7": ("flash", "o7  "),
"O^8": ("flash", "o8  ")
}


Unlike the CIESourceModel, for the NEISourceModel source all elements and ionizations must be specified in the var_elem dictionary, which is now required. There is no separate Zmet which can be set. The required arguments are:

• emin: The minimum energy for the spectrum in keV.

• emax: The maximum energy for the spectrum in keV.

• nbins: The number of bins in the spectrum.

• var_elem: Used to specify the abundances of specific elements, whether via floating-point numbers or yt fields. A dictionary of elements and values should be specified.

All other optional keyword arguments are the same as in the CIESourceModel, see above for details. The NEISourceModel is currently only compatible with the "apec" emission model. An example invocation is:

source_model = pyxsim.NEISourceModel(0.3, 1.7, 1000, var_elem)


Note that no other elements will be modeled except those which are specified in var_elem.

## IGM Source Model¶

The IGMSourceModel is a source model for a thermal plasma including photoionization and resonant scattering from the CXB, based on Khabibullin & Churazov 2019 and Churazov et al. 2001. Because of the included effects of photoionization and resonant scattering, this model is dependent on the hydrogen number density in an explicit way, aside from the normalization.

This model is appropriate for simulation emission from low-density, high-temperature plasmas such as the warm-hot intergalactic medium (WHIM) and the outskirts of the circumgalactic medium (CGM). The densities and temperatures involved are $$n_H \sim 10^{-7} - 10^{-4} \rm{cm}^{-3}$$ and $$T \sim 10^5 - 10^7$$ K. For resonant scattering, it is assumed that a fraction of CXB photons are scattering off of heavy ions, enhancing line emission.

For temperatures higher than $$kT \sim 1.09$$ keV, the emission is essentially density-independent (aside from the normalization) and a Cloudy-based CIE model is used to compute the spectrum. This model assumes the abundance tables from Feldman 1992 ("feld") and currently cannot be changed to another.

The arguments for IGMSourceModel are very similar to CIESourceModel. Required arguments are:

• emin: The minimum energy for the spectrum in keV.

• emax: The maximum energy for the spectrum in keV.

• nbins: The number of bins in the spectrum.

• Zmet: The metallicity. Either a floating-point number for a constant metallicity, or the name of a yt field for a spatially-varying metallicity.

For the IGMSourceModel, He is fixed at abundance table value, and all higher elements up Zn to included in Zmet. Optional arguments are:

• binscale: The scale of the energy binning: “linear” or “log”. Default: “linear”

• resonant_scattering: Whether or not to include the effects of resonant scattering from CXB photons. Default: False

• cxb_factor: The fraction of the CXB photons that are resonant scattered to enhance the lines. Default: 0.5

• nh_field: The yt field to use as the number density of hydrogen. Must have number density dimensions. The default is ("gas", "H_nuclei_density").

• temperature_field: The yt field to use as the temperature. Must have dimensions of temperature. The default is ("gas", "temperature").

• emission_measure_field: The yt field to use as the emission measure. Must have dimensions of number density or per-volume. The default is ("gas", "emission_measure").

• h_fraction: The hydrogen mass fraction. If a float, assumes a constant mass fraction of hydrogen throughout. If a string or tuple of strings, is taken to be the name of the hydrogen fraction field from yt. Defaults to the appropriate value for the Feldman abundance table.

• kT_min: The minimum temperature in units of keV. Default is 0.00431.

• kT_max: The maximum temperature in units of keV. Default is 64.0.

• max_density: The maximum mass density of the cells or particles to use when generating photons. If a float, the units are assumed to be g/cm**3. can also be a YTQuantity or a float, string tuple such as (5.0e-25, "g/cm**3") Default: None, meaning no maximum density.

• method: The method used to generate the photon energies from the spectrum. Either "invert_cdf", which inverts the cumulative distribution function of the spectrum, or "accept_reject", which uses the acceptance-rejection method on the spectrum. The first method should be sufficient for most cases.

• var_elem: Optionally used to specify the abundances of specific elements, whether via floating-point numbers or yt fields. A dictionary of elements and values should be specified. See Variable Abundances below for more details.

• model_vers: The version of the IGM tables to use in the calculations. Options are: “4_lo”: Tables computed from Cloudy using a continuum resolution of 0.1 with a range of 0.05 to 10 keV. “4_hi”: Tables computed from Cloudy using enhanced continuum resolution of 0.025 with a range of 0.05 to 10 keV. Excellent energy resolution, but may be expensive to evaluate. Default: “4_lo”

• prng: A pseudo-random number generator. Typically will only be specified if you have a reason to generate the same set of random numbers, such as for a test or a comparison. Default is the numpy.random module, but a RandomState object or an integer seed can also be used.

### Examples¶

A simple invocation of the IGM model using a single metallicity field, and log-spaced energy binning:

source_model = pyxsim.IGMSourceModel(0.1, 5.0, 1000,
("gas","metallicity"), binscale="log")


Turning on resonant scattering, assuming 30% of the CXB photons are scattered:

source_model = pyxsim.IGMSourceModel(0.1, 5.0, 1000,
("gas","metallicity"),
resonant_scattering=True,
cxb_factor=0.3,
binscale="log")


Specifying the abundances of C, N, and Fe separately:

var_elem = {"C": ("gas", "C_fraction"),
"N": ("gas", "N_fraction"),
"Fe": ("gas", "Fe_fraction")}

source_model = pyxsim.IGMSourceModel(0.1, 5.0, 1000,
("gas","metallicity"),
resonant_scattering=True,
cxb_factor=0.3,
binscale="log",
var_elem=var_elem)


## Filtering Out Non-X-ray Emitting Gas¶

In simulations where may gas phases are present, there may be a significant amount of thermal gas that is not expected to be emitting in X-rays. For any of the thermal source models detailed above, there are various ways to ensure that this gas is not operated on in pyXSIM.

### pyXSIM-based Filtering¶

The first is to make use of the kT_min and kT_max keyword arguments:

thermal_model = pyxsim.CIESourceModel("apec", 0.1, 20.0, 10000,
("gas","metallicity"),
kT_min=0.1,
kT_max=50.0,
prng=25, abund_table='lodd')


where both kT_min and kT_max are in units of keV. It may also be useful to specify a maximum density above which no emission should be calculated with the max_density keyword argument:

source_model = pyxsim.IGMSourceModel(0.1, 5.0, 1000,
("gas","metallicity"),
max_density=(5.0e-25, "g/cm**3"),
binscale="log")


### yt-based Filtering¶

If you want more detailed control over which cells or particles may get used, then you need to use one of various methods in yt for dataset filtering.

#### AMR cell-based Filtering¶

For example, if your dataset is AMR cell-based, then the use of a yt cut region is recommended. In this case, we exclude all gas above $$T = 3 \times 10^5 \rm{K}$$, below $$\rho = 5 \times 10^{-25}~\rm{g}~\rm{cm}^{-3}$$, and include no gas with star formation.

# this example takes a box region and makes cuts on density, temperature, and star
# formation rate

c = ds.find_min(("gas", "gravitational_potential")) # center of box
w = ds.quan(1.0, "Mpc") # width of box
le = c-0.5*w # left edge of box
re = c+0.5*w # right edge of box
box = ds.box(le, re) # create the box

# chain these conditions together
hot_box = box.include_above(("gas", "temperature"), 3e5, "K")
hot_diffuse_box = hot_box.include_below(("gas", "density"), 5e-25), "g/cm**3")
xray_box = hot_diffuse_box.include_equal(("gas", "star_formation_rate"), 0.0), "Msun/yr")


This is a new data container exactly like a sphere or box object that can be used to create photons, make fields, etc.

#### Particle-based Filtering¶

In the case of particle data (including particle-ish data like Arepo Voronoi cells), it makes most sense to use a yt particle filter. This creates a new particle type that can be used in analysis in the same way as regular particle types.

Here is an example of instantiating a particle filter for an Arepo dataset. In this case, we exclude all gas above $$T = 3 \times 10^5 \rm{K}$$, below $$\rho = 5 \times 10^{-25}~\rm{g}~\rm{cm}^{-3}$$, and include no gas with star formation.

# define hot gas filter
def hot_gas(pfilter, data):
pfilter1 = data[pfilter.filtered_type, "temperature"] > 3.0e5
pfilter2 = data["PartType0", "StarFormationRate"] == 0.0
pfilter3 = data[pfilter.filtered_type, "density"] < 5e-25
return pfilter1 & pfilter2 & pfilter3
# add the filter to yt itself

Note that for this dataset the "gas" and "PartType0" field types are the same.