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Temperature

temperature

GhirardiniModel

Bases: Module

Universal temperature profile as defined in Ghirardini 2018+ in the X-COP cluster sample

Source code in src/temperature.py 
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class GhirardiniModel(hk.Module):
    """
    Universal temperature profile as defined in Ghirardini 2018+ in the X-COP cluster sample
    """

    def __init__(self):
        super(GhirardiniModel, self).__init__()
        self.cosmo = LambdaCDM(H0 = 70, Om0 = 0.3, Ode0= 0.7)


    def __call__(self, r, z = 0.1):
        r"""Compute the temperature function for a given radius.

        $$\dfrac{T(x)}{T_{500}} = T_0 \dfrac{\frac{T_\mathrm{min}}{T_0} + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}}{1 + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}} \frac{1}{(1 + (\frac{x}{r_t})^2)^{\frac{c}{2}}}$$

        Parameters:
            r (jnp.array): Radius at which to compute the temperature, in kpc
            z (float): Redshift of cluster
        Returns:
            (jnp.array): Temperature function evaluated at the given radius in keV
        """


        M500 = 0.7 #(x10^15 Msun)
        Ez   = self.cosmo.efunc(z)
        h_70 = 0.7

        T500 = 8.85 * (M500*h_70)**(2./3.) * Ez**(2./3.)
        T0 = 1.09
        rcool = jnp.exp(-4.4)
        rt = 0.45
        TmT0 = 0.66
        acool = 1.33
        c2 = 0.3

        R500 = 1309. #[kpc]
        x = r/R500

        term1 = (TmT0 + (x / rcool) ** acool)
        term2 = (1 + (x / rcool) ** acool) * (1 + (x / rt) ** 2) ** c2

        T = T500 * T0 * term1 / term2

        #Clip the values to the [1-7] keV range (otherwise the T-Z interpolation does not work.)
        return T #jnp.clip(T, 1., 7.)

__call__(r, z=0.1)

Compute the temperature function for a given radius.

\[\dfrac{T(x)}{T_{500}} = T_0 \dfrac{\frac{T_\mathrm{min}}{T_0} + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}}{1 + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}} \frac{1}{(1 + (\frac{x}{r_t})^2)^{\frac{c}{2}}}\]

Parameters:

Name Type Description Default
r array

Radius at which to compute the temperature, in kpc

 required
z float

Redshift of cluster

 0.1

Returns: (jnp.array): Temperature function evaluated at the given radius in keV

Source code in src/temperature.py 
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def __call__(self, r, z = 0.1):
    r"""Compute the temperature function for a given radius.

    $$\dfrac{T(x)}{T_{500}} = T_0 \dfrac{\frac{T_\mathrm{min}}{T_0} + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}}{1 + (\frac{x}{r_\mathrm{cool}})^{a_\mathrm{cool}}} \frac{1}{(1 + (\frac{x}{r_t})^2)^{\frac{c}{2}}}$$

    Parameters:
        r (jnp.array): Radius at which to compute the temperature, in kpc
        z (float): Redshift of cluster
    Returns:
        (jnp.array): Temperature function evaluated at the given radius in keV
    """


    M500 = 0.7 #(x10^15 Msun)
    Ez   = self.cosmo.efunc(z)
    h_70 = 0.7

    T500 = 8.85 * (M500*h_70)**(2./3.) * Ez**(2./3.)
    T0 = 1.09
    rcool = jnp.exp(-4.4)
    rt = 0.45
    TmT0 = 0.66
    acool = 1.33
    c2 = 0.3

    R500 = 1309. #[kpc]
    x = r/R500

    term1 = (TmT0 + (x / rcool) ** acool)
    term2 = (1 + (x / rcool) ** acool) * (1 + (x / rt) ** 2) ** c2

    T = T500 * T0 * term1 / term2

    #Clip the values to the [1-7] keV range (otherwise the T-Z interpolation does not work.)
    return T #jnp.clip(T, 1., 7.)