API Reference

`pipeline`

This module contains the class `pipeline`.

class echo21.pipeline.pipeline(cosmo=None, astro=None, sfrd=None, grid_on=False, path='echo21_outputs/')

This is the main class you would first interact with. It brings together all the functionalities of the code.

To run a simulation you need to specify three inputs – cosmological parameters, astrophysical parameter, and star formation related parameters. They are supplied through arguments, cosmo, astro, and sfrd, respectively. The notation for the parameters is as follows. All of these need to be dictionaries. For example:

cosmo = {'Ho':67.4, 'Om_m':0.315, 'Om_b':0.049, 'sig8':0.811, 'ns':0.965, 'Tcmbo':2.725, 'Yp':0.245},
astro = {'fLy':1, 'sLy' : 2.64, 'fX':1, 'wX':1.5, 'fesc':0.01},
sfrd = {'type':'phy', 'hmf':'press74', 'mdef':'fof', 'Tmin_vir':1e4}

Arguments

cosmo: dict

Dictionary of cosmological parameters. They are:

Hofloat, optional: Hubble parameter today in units of \(\mathrm{km\,s^{-1}\,Mpc^{-1}}\). Default value 67.4.
Om_mfloat, optional: Relative matter density. Default value 0.315.
Om_bfloat, optional: Relative baryon density. Default value 0.049.
sig8float, optional: Amplitude of density fluctuations. Default value 0.811.
nsfloat, optional: Spectral index of the primordial scalar spectrum. Default value 0.965.
Tcmbofloat, optional: CMB temperature today in kelvin. Default value 2.725.
Ypfloat, optional: Primordial helium fraction by mass. Default value 0.245.

astro: dict

Dictionary of cosmological parameters. They are:

fLyfloat, optional: \(f_{\mathrm{Ly}}\), a dimensionless parameter which controls the emissivity of the Lyman series photons. Default value 1.0.
sLyfloat, optional: \(s\), spectral index of Lyman series SED, when expressed as \(\epsilon\propto E^{-s}\). \(\epsilon\) is energy emitted per unit energy range and per unit volume. Default value 2.64.
fXfloat, optional: \(f_{\mathrm{X}}\), a dimensionless parameter which controls the emissivity of the X-ray photons. Default value 1.0.
wXfloat, optional: \(w\), spectral index of X-ray SED, when expressed as \(\epsilon\propto E^{-w}\). \(\epsilon\) is energy emitted per unit energy range and per unit volume. Default value 1.5.
fescfloat, optional: \(f_{\mathrm{esc}}\), a dimensionless parameter which controls the escape fraction of the ionizing photons. Default value 0.01.

sfrddict

This should be a dictionary containing all the details of SFRD.

typestr, optional

Available types are ‘phy’ (default), ‘semi-emp’, and ‘emp’, for a physically-motivated, semi-empirical, and an empiricaly-motivated SFRD, respectively.

hmfstr, optional

HMF model to use. Default value press74. Other commonly used HMFs are

sheth99 (for Sheth & Tormen 1999)
tinker08 (for Tinker et al 2008)

For the full list see colossus page.

mdef: str, optional: Definition for halo mass. Default is fof. For most HMFs such as Press-Schechter or Sheth-Tormen, friends-of-friends (fof) algorithm is used. For Tinker08, it is an integer times mean matter density (<int>m). See the colossus documentation for definition page
Tmin_virfloat, optional: Minimum virial temperature (in units of kelvin) for star formation. Default value 1e4.
t_starfloat, optional: Star formation timescale in units of the Hubble time. Default value 0.5. (This is only relevant for the semi-empirical SFRD model.)
afloat, optional: Power law index for the SFRD in the empirical model. Default value 0.257. (This is only relevant for the empirical SFRD model.)

grid_on: bool

Whether to generate a grid of parameter combinations. Default is False, i.e., parameters are varied one at a time. In this case all varied parameters should have the same number of values. If True, then all possible combinations of the parameters will be generated.

Methods

run_simulation(): This is the main function which runs the ECHO21 simulation and saves the outputs.

`config`

This module contains class `config`.

class echo21.config.config(params=None, dm_model='CDM')

A configuration object for a particular model which gives access to all the model parameters, such as \(H_0\).

Arguments

params: dict: A dictionary containing all the cosmological and astrophysical parameters.
dm_modelstr: DM type - ‘CDM’ (default) or ‘IDM’

`funcs`

This module contains class `funcs`

class echo21.funcs.funcs(config)

funcs is a wrapper around the function_container and thus, provides a common point of access to all the functions in the container.

Arguments

configconfig: A configuration object for a particular model which gives access to all the model parameters, such as \(H_0\).

class echo21.function_container.basic.basic(config)

Class of all the basic \(\Lambda\) CDM-cosmology-related functions, such as Hubble function, CMB temperature, etc.

Methods

mu(xe)

The average baryon mass.

Arguments

xefloat: Electron fraction, dimensionless

Returns

\(\mu\), dimensionless

xHe()

Ratio of helium number density to hydrogen number density

Arguments

No arguments required.

Returns

float: \(n_{\mathrm{He}}/n_{\mathrm{H}}\)

Tcmb(Z)

CMB temperature at a given redshift

Arguments

Zfloat: \(1+z\)

Returns

float: CMB temperature at the given redshift in kelvin

rho_crit()

Critical density of the Universe today

Arguments

No arguments required.

Returns

float: Critical density today, \(\rho_{\mathrm{crit}}=\frac{3H_0^2}{8\pi G_{\mathrm{N}}}\) in units of \(\mathrm{kg}\,\mathrm{m}^{-3}\)

nH(Z)

Hydrogen number density (proper).

Arguments

Zfloat: \(1+z\)

Returns

float: Proper hydrogen number density at given redshift in units of \(\mathrm{m}^{-3}\)

Hubble(Z)

Hubble factor in SI units.

Arguments

Zfloat: \(1+z\)

Returns

float: Hubble parameter at a given redshift in units of \(\mathrm{s}^{-1}\).

class echo21.function_container.recomb.recomb(config, basic)

Class of all the recombination-physics-related functions.

Methods

alpha(T)

\(\alpha_{\mathrm{B}}=\alpha_{\mathrm{B}}(T)\)

The effective case-B recombination coefficient for hydrogen. See Eq. (70) from Seager et al (2000).

Arguments

Tfloat: Temperature in units of kelvin.

Returns

float: The effective case-B recombination coefficient for hydrogen \((\mathrm{m}^3\mathrm{s}^{-1})\).

beta(T)

\(\beta=\beta(T)\)

The total photoionization rate. See description below Eq. (71) from Seager et al (2000). Relation between \(\alpha_{\mathrm{B}}\) and \(\beta\):

\(\beta=\alpha_{\mathrm{B}}\left(\frac{2\pi m_{\mathrm{e}}k_{\mathrm{B}}T}{h_{\mathrm{P}}^2}\right)^{3/2}\exp\left(-\frac{B_2}{k_{\mathrm{B}}T}\right)\)

Arguments

Tfloat: Temperature in units of kelvin.

Returns

float: The total photoionization rate in \((\mathrm{s}^{-1})\).

Krr(Z)

Redshifting rate appearing in the Peebles’ ‘C’ factor

Arguments

Zfloat: 1+z

Returns

float: Redshifting rate in units of \(\mathrm{m^3s}\)

Peebles_C(Z, xe, T)

\(C_{\mathrm{P}}\)

Arguments

Zfloat: 1 + redshift, dimensionless
xefloat: Electron fraction, dimensionless
Tkfloat: Temperature in units of kelvin.

Returns

float: Peebles ‘C’ factor appearing in Eq. (71) from Seager et al (2000), dimensionless.

Saha_xe(Z, T)

Electron fraction predicted by the Saha’s equation. This is important to initialize the differential equation for \(x_{\mathrm{e}}\). At high redshift such as \(z=1500\), Saha’s equation gives accurate estimate of \(x_{\mathrm{e}}\).

Arguments

Zfloat: 1 + redshift, dimensionless
Tfloat: Temperature in units of kelvin

Returns

float: Electron fraction predicted by Saha’s equation. Dimensionless.

class echo21.function_container.halo.halo(config, basic)

Class of all the functions related to star formation - HMF, minimum halo mass, collapse fraction, and SFRD.

Methods

dndlnM(M, Z)

The halo mass function (HMF) in the form of \(\mathrm{d}n/\mathrm{d\,ln}M\). Note the natural logarithm.

Arguments

Mfloat: The desired halo mass at which you want to evaluate HMF. Input M in units of solar mass.
Zfloat: 1 + redshift, dimensionless.

Returns

float: HMF, \(\mathrm{d}n/\mathrm{d\,ln}M=M\mathrm{d}n/\mathrm{d}M\), in units of \(\mathrm{cMpc}^{-3}\), where ‘cMpc’ represents comoving mega parsec.

dndM(M, Z)

The halo mass function (HMF) in a different form, i.e., \(\mathrm{d}n/\mathrm{d}M\).

Arguments

Mfloat: The desired halo mass at which you want to evaluate HMF. Input M in units of solar mass (\(\mathrm{M}_{\odot}\)).
Zfloat: \(1+z\), dimensionless.

Returns

float: HMF in a different form, \(\mathrm{d}n/\mathrm{d}M\), in units of \(\mathrm{cMpc}^{-3}\mathrm{M}_{\odot}^{-1}\), where ‘cMpc’ represents comoving mega parsec and \(\mathrm{M}_{\odot}\) represents the solar mass.

m_min(Z)

The minimum halo mass for which star formation is possible.

Arguments

Zfloat: \(1+z\), dimensionless. It can be a single number or an array.

Returns

float: The mass returned is in units of \(\mathrm{M}_{\odot}/h\).

f_coll(Z)

Collapse fraction – fraction of total matter that collapsed into the haloes. See definition below. \(F_{\mathrm{coll}}=\frac{1}{\bar{\rho}^0_{\mathrm{m}}}\int_{M_{\mathrm{min}}}^{\infty} M\frac{\mathrm{d}n}{\mathrm{d} M}\,\mathrm{d} M\,,\)

Arguments

Zfloat: \(1+z\), dimensionless. Can be a single quantity or an array.

Returns

float: Collapse fraction. Single number or an array accordingly as Z is single number or an array.

dfcoll_dz(Z): Redshift derivative of the collapse fraction, i.e., \(\mathrm{d}F_{\mathrm{coll}}/\mathrm{d}z\)

sfrd(Z)

This function returns the comoving star formation rate density (SFRD, \(\dot{\rho}_{\star}\)).

Arguments

Zfloat: \(1+z\), dimensionless. Can be a single quantity or an array.

Returns

float: Comoving SFRD in units of \(\mathrm{kgs^{-1}m^{-3}}\). Single number or an array accordingly as Z is single number or an array. To convert to solar mass per year per cubic Mpc, use the factor Msolar_by_Mpc3_year_to_kg_by_m3_sec available in the module const.

class echo21.function_container.heating.heating(config, basic, halo, lya)

Class of all the standard heating terms (Compton, Ly-\(\alpha\), X-ray). Exotic heating terms, such as those for IDM live, in their own module. Also, note that the return value is in the form of

\(\frac{2q}{3n_{\mathrm{b}}k_{\mathrm{B}}H}\),

where \(q, n_{\mathrm{b}}, k_{\mathrm{B}}\), and \(H\) are the volumetric heating rate, baryon number density, Boltzman constant, and Hubble factor, respectively.

Within this class I have also included the ionization rate due to X-ray photons.

Methods

Ecomp(Z, xe, Tk)

See Eq.(2.32) from Mittal et al (2022), JCAP. (However, there is a typo in that equation; numerator has an \(x_{\mathrm{e}}\) missing.)

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature.

Returns

float: Compton heating. Units kelvin.

Elya(Z, xe, Tk)

Ly-\(\alpha\) heating rate. For details see Mittal & Kulkarni (2021) or the ECHO21 paper Mittal et al (2025)

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature.

Returns

float: Net heating by the Lyman series photons. Units kelvin.

Ex(Z, xe)

We use the parametric approach for X-ray heating as in Furlanetto (2006). We adopt the \(L_{\mathrm{X}}/\mathrm{SFR}\) relation from Lehmer et al. (2024).

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.

Returns

float: Net heating by the X-ray photons. Units kelvin.

Gamma_x(Z, xe)

Ionization (of bulk IGM) rate due to X-ray photons.

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.

Returns

float: Ionization due to X-ray photons in units of \(\mathrm{s}^{-1}\).

class echo21.function_container.hyfi.hyfi(config, basic, lyman_alpha)

Class of all the functions related to the computation of 21-cm signal. These are \(\kappa_{\mathrm{HH}}, \kappa_{\mathrm{eH}}, x_{\mathrm{k}}, x_{\mathrm{Ly}}, T_{\mathrm{s}}\) and \(T_{21}\).

Methods

kHH(Tk)

Volumetric spin flip rate for hydrogen-hydrogen collision. This fitting function and the next one is available from Pritchard & Loeb (2012).

Arguments

Tkfloat: Gas kinetic temperature.

Returns

float: \(k_{\mathrm{HH}}\) in units of \(\mathrm{m^3s^{-1}}\).

keH(Tk)

Volumetric spin flip rate for electron-hydrogen collision.

Arguments

Tkfloat: Gas kinetic temperature.

Returns

float: \(k_{\mathrm{eH}}\) in units of \(\mathrm{m^3s^{-1}}\).

kpH(Tk)

Volumetric spin flip rate for electron-proton collision. Fit taken from Mittal et al. (2022).

Arguments

Tkfloat: Gas kinetic temperature.

Returns

float: \(k_{\mathrm{pH}}\) in units of \(\mathrm{m^3s^{-1}}\).

col_coup(Z, xe, Tk)

Collisional coupling.

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature.

Returns

float: \(x_{\mathrm{k}}\), dimensionless.

lya_coup(Z, xe, Tk)

Ly-\(\alpha\) coupling or the Wouthuysen–Field coupling.

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature.

Returns

float: \(x_{\mathrm{Ly}}\), dimensionless.

spin_temp(Z, xe, Tk)

Spin temperature.

Arguments

Zfloat: \(1+z\), dimensionless.
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature.

Returns

float: \(T_{\mathrm{s}}\), K.

twentyone_cm(Z, xHI, Ts)

The global (sky-averaged) 21-cm signal.

Arguments

Zfloat: \(1+z\), dimensionless.
xHIfloat: Two-zone-model-averaged neutral hydrogen fraction.
Tsfloat: Spin temperature (K).

Returns

float: \(T_{21}\), mK.

class echo21.function_container.lyman_alpha.lyman_alpha(config, basic, halo)

Class of all the functions required to construct the specific intensity of the Ly-\(\alpha\) photons.

Methods

phi_Ly(E)

Spectral energy distribution (SED) of Lyman series photons in units of number of photons per unit frequency per stellar baryon.

Arguments

Efloat: Energy in eV.

Returns

float: SED in dimensions \(\mathrm{Hz^{-1}}\).

eps_Ly(Z, E)

Emissivity of Lyman series photons in units of number of photons per unit frequency per unit comoving volume per unit time. Construction:

\(\epsilon_{\mathrm{Ly}}=\frac{1}{m_{\mathrm{b}}}\phi_{\mathrm{Ly}}\dot{\rho}_{\star}\)

Arguments

Zfloat: 1+z
Efloat: Energy in eV.

Returns

float: Emissivity in dimensions \(\mathrm{m^{-3}Hz^{-1}s^{-1}}\).

lya_spec_inten(Z)

Specific intensity of Ly-\(\alpha\) photons, \(J_{\mathrm{Ly}}\), due to continuum and injected photons.

Arguments

Zfloat: \(1 + z\), dimensionless. Can be array.

Returns

float: Specific intensity in terms of number per unit time per unit area per unit frequency per unit solid angle (\(\mathrm{m^{-2}s^{-1}Hz^{-1}sr^{-1}}\)). Two values are returned, namely intensity due to continuum and injected photons, respectively.

class echo21.function_container.eor.eor(config, basic, halo)

Class of all the functions related to reionization - clumping factor, CMB optical depth, analytical equation that governs the reionization, and the ODE solver.

Methods

clumping_factor(Z)

Clumping factor for the ionization of hydrogen. From Shull et al. (2012).

Arguments

Zfloat: \(1+z\)

cmb_tau(Z)

Compute the Thomson-scattering optical depth up to a given redshift.

Arguments

Zfloat: \(1+z\) to which you want to calculate \(\tau_{\mathrm{e}}\).

Returns

float: \(\tau_{\mathrm{e}}\) (dimensionless).

dQdlna(Z, QHii)

Analytical equation of reionization (Madau et al 1999).

Arguments

Zfloat: \(1+z\)
QHiifloat: The volume filling factor of the ionized regions.

Returns

float: \(\mathrm{d}Q/\mathrm{d}\ln(a)\)

solve_dQdlna()

Solves the reionization equation.

Returns

float array: QHii for the cosmic dawn redshifts, Z_CD.

class echo21.function_container.idm.idm(config, basic)

A class of all the functions related to interacting dark matter model.

Methods

u_t(xe, Tk, Tx)

The characteristic thermal sound speed of the DM-baryon fluid.

Arguments

xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature (K).
Txfloat: DM temperature (K).

Returns

float: \(u_{\mathrm{th}} (\mathrm{m\,s^{-1}})\).

r_t(xe, Tk, Tx, v_bx)

Ratio of relative velocity of DM and baryons to the characteristic thermal sound speed.

Arguments

xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature (K).
Txfloat: DM temperature (K).
v_bxfloat: Relative velocity of DM and baryons (m/s).

Returns

float: \(v_{\mathrm{b}\chi}/u_{\mathrm{th}}\), dimensionless.

Drag(Z, xe, Tk, Tx, v_bx)

Drag due to DM baryon interaction.

Arguments

Zfloat: 1+z
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature (K).
Txfloat: DM temperature (K).
v_bxfloat: Relative velocity of DM and baryons (m/s).

Returns

float: \(D (\mathrm{m\,s^{-2}})\).

mu_bx(xe)

Reduced mass for DM-baryon system.

Arguments

xefloat: Electron fraction.

Returns

float: \(\mu_{\mathrm{b}\chi} (\mathrm{kg})\)

Ex2b(Z, xe, Tk, Tx, v_bx)

This corresponds to the heat that flows into the baryonic system from the DM.

Arguments

Zfloat: 1+z
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature (K).
Txfloat: DM temperature (K).
v_bxfloat: Relative velocity of DM and baryons \((\mathrm{m\,s^{-1}})\).

Returns

float: \(\dot{Q}_{\mathrm{k}} (\mathrm{K})\).

Eb2x(Z, xe, Tk, Tx, v_bx)

This corresponds to the heat that flows into the DM from baryons.

Arguments

Zfloat: 1+z
xefloat: Electron fraction.
Tkfloat: Gas kinetic temperature (K).
Txfloat: DM temperature (K).
v_bxfloat: Relative velocity of DM and baryons (m/s).

Returns

float: \(\dot{Q}_{\chi}\) (K).

class echo21.function_container.ivp.ivp(config, basic, recomb, halo, idm, heating)

Class of all the functions required to solve the initial value problem of bulk of IGM. EoR related functions are in the class eor.

Methods

initial_conditions()

Initial conditions for the IGM equations at \(z=1500\). For CDM, we need electron fraction and gas kinetic temperature. For IDM, we also need DM temperature and relative velocity of DM and baryons.

Also, note that for gas temperature it is a transformed variable. Instead of \(T_{\mathrm{k}}\) we evolve \(y = \ln(T_{\mathrm{k}}/T_{\gamma})\). At \(z=1500\), \(T_{\mathrm{k}}=T_{\gamma}\) so the initial value is \(y=0\).

For IDM case instead of velocity we have \(\ln(v_{\mathrm{b}\chi})\).

Arguments

Zfloat: 1 + z, dimensionless.

Returns

tuple: Initial conditions. For CDM, the tuple is (xe_init, yT_init). For IDM, the tuple is (xe_init, yT_init, Tx_init, ln_vbx_init).

igm_solver(Z_solver, *initial_conditions, eqns_func)

This function solves the coupled IGM differential equations. In case of CDM it is just electron fraction and gas temperature. When IDM is involed DM temperature and relative DM-baryon velocity is also solved.

Arguments

Z_solver: array: Redshift array (decreasing) over which to solve. Use Z_DA for dark ages, Z_CD for cosmic dawn, or Z_default for the full range.
initial_conditions: tuple: Initial conditions for the ODE solver. For CDM, the tuple is (xe_init, yT_init). For IDM, the tuple is (xe_init, yT_init, Tx_init, ln_vbx_init). For DA the second variable is yT but for CD-EoR it is Tk. Use initial_conditions() to get the initial conditions when the starting redshift is \(z=1500\).
eqns_func: callable: The RHS function to pass to the ODE solver. Either dark ages or cosmic dawn.

Returns

array: \(x_{\mathrm{e}}\), \(y=\ln(T_{\mathrm{k}}/T_{\gamma})\) or \(T_{\mathrm{k}}\), \(T_{\chi}\), \(\ln v_{\mathrm{b}\chi}\)

class echo21.function_container.uvlf.uvlf(config, basic, halo)

Class of all the functions relevant to galaxy surveys, such as luminosity functions and galaxy count for given limiting magnitude. If you use this module please consider citing Mittal & Kulkarni (2022)

However, note that there are some differences in the implementation of the UV LF and galaxy count functions in this module and the ones I used previously. The main difference is in the star formation rate. Previously,

\(\dot{M}_{\star} = f_{\star} \dot{M}_{\star0} \left(\frac{M}{10^{10}M_{\odot}}\right)^{a} \left(\frac{1+z}{7}\right)^{b}\) ,

whereas in this module, we have used

\(\dot{M}_{\star} = f_{\star} \frac{\Omega_b}{\Omega_m} \frac{M}{t_{\star}H(z)^{-1}}\)

Accordingly, the following calculations are relevant only for semi-empirical star formation models.

Methods

dLUV_dM(Z)

Rate of change of luminosity w.r.t. halo mass. (For our assumed constant star formation efficiency, this is independent of halo mass.)

Arguments

Zfloat: \(1+z\)

Returns

float: \(\left(\frac{\partial L}{\partial M}\right)_{z}\) in units of \(\mathrm{W Hz^{-1}M_{\odot}^{-1}}\)

luminosity(M, Z)

Compute the UV luminosity for given halo mass and redshift.

Arguments

Mfloat: The desired halo mass at which you want to evaluate absolute magnitude. Input M in units of solar mass.
Zfloat: \(1+z\)

Returns

float: UV luminosity in units of W/Hz.

halomass_to_absmag(M, Z)

Absolute AB magnitude.

Arguments

Mfloat: The desired halo mass at which you want to evaluate absolute magnitude. Input M in units of solar mass.
Zfloat: \(1+z\)

Returns

float: Absolute AB magnitude (Oke 1974)

absmag_to_halomass(MUV, Z)

Compute the halo mass which produces the given absolute magnitude at the given redshift.

Arguments

MUVfloat: Absolute AB magnitude (Oke 1974)
Zfloat: \(1+z\)

Returns

float: Halo mass in units of solar mass.

appmag_to_halomass(mUV, Z)

Compute the halo mass which produces the given apparent magnitude at the given redshift.

Arguments

mUVfloat: Apparent AB magnitude (Oke 1974)
Zfloat: \(1+z\)

Returns

float: Halo mass in units of solar mass.

lum_func(MUV, Z)

For given absolute magnitude and redshift, get UV luminosity function (LF). LF is defined as \(\mathrm{d}\Phi/\mathrm{d}M_{\mathrm{UV}}\), which represents number density (comoving) per unit absolute AB magnitude. Important note: valid only when star formation efficiency is a constant.

Arguments

MUVfloat or array_like: Absolute AB magnitude.
Zfloat or array_like: \(1+z\)

Returns

float or ndarray: Luminosity function in units of \(\mathrm{cMpc}^{-3}\), where ‘cMpc’ represents comoving mega parsec. Shape is (len(MUV), len(Z)) when both inputs are arrays; 1-D when one is scalar; scalar when both are scalar.

dNdz(mUV, Z, area=1.0)

Gradient of the number of galaxies seen at a given redshift and a limiting apparent magnitude of the survey and the survey area.

Arguments

mUVfloat: Apparent AB magnitude (Oke 1974) for for the faintest object the survey can see.
Zfloat: \(1+z\) (>1); this can be an array as well
areafloat, optional: Survey area in sq. deg.; default is 1.0.

Returns

float: \(\left(\frac{\mathrm{d}N}{\mathrm{d}z}\right)_{z}\); dimensionless

num_gal(mUV, Z1, Z2, area=1.0)

Cumulative number of galaxies brighter than the limiting apparent magnitude between a redshift range.

Arguments

mUVfloat: Apparent AB magnitude (Oke 1974) for for the faintest object the survey can see.
Z1float: \(1+z_1\), lower value defining the redshift range (>1)
Z2float: \(1+z_2\), upper value defining the redshift range (>Z1)
areafloat, optional: Survey area in sq. deg.; default is 1.0.

Returns

float: \(\int_{z1}^{z2} \left(\frac{\mathrm{d}N}{\mathrm{d}z}\right)_{z'} \mathrm{d}z'\); dimensionless

`utils`

This module contains non-physics functions.

echo21.utils.load_pipeline(filename)

To load the class object pipeline.

Arguments

filenamestr: Full path to the output directory (output_<YYYYMMDD-HHMMSS>) which contains the pickle file pipeline.pkl.

Returns

class: echo21.pipeline

echo21.utils.load_results(filename, Z_eval=None)

Read the output and return a dictionary of parameters, redshifts, global signal, etc. If you do not provide any redshift, the quantities are returned at their default redshift(s).

Arguments

filenamestr: Full path to the output directory (output_<YYYYMMDD-HHMMSS>) which contains the pipeline.pkl file and HDF5 file echo21_output.h5.
Z_eval: array, optional: array of \(1+z\) values; can be in decreasing as well as increasing order. Default = None

Returns

dict: params (pandas dataframe), MUV (numpy array), xe (numpy array), Q_Hii (numpy array), Tk (numpy array), Ts (numpy array), T21 (numpy array), xHI (numpy array), tau (numpy array), UVLF (numpy array). Also one_plus_z_cd (numpy array), and one_plus_z (numpy array) too if the run is not astro-only. Neither is included if Z_eval is given, since you already have those redshifts.

API Reference

pipeline

This module contains the class pipeline.

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config

This module contains class config.

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funcs

This module contains class funcs

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`pipeline`

This module contains the class `pipeline`.

`config`

This module contains class `config`.

`funcs`

This module contains class `funcs`

`utils`