Cauchy

# Parameters
func_name = "Cauchy"
wide_energy_range = True
x_scale = "linear"
y_scale = "linear"
linear_range = True

Description

func.display()

• description: The Cauchy distribution
• formula: $ K \frac{1}{ \gamma \pi} \left[ \frac{\gamma^2}{(x-x_0)^2 + \gamma^2} \right] $
• parameters:
  • K:
    • value: 1.0
    • desc: Integral between -inf and +inf. Fix this to 1 to obtain a Cauchy distribution
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • x0:
    • value: 0.0
    • desc: Central value
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • gamma:
    • value: 1.0
    • desc: standard deviation
    • min_value: 1e-12
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True

Shape

The shape of the function.

If this is not a photon model but a prior or linear function then ignore the units as these docs are auto-generated

fig, ax = plt.subplots()


ax.plot(energy_grid, func(energy_grid), color=blue)

ax.set_xlabel("energy (keV)")
ax.set_ylabel("photon flux")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

F\(_{\nu}\)

The F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid * func(energy_grid), red)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"energy flux (F$_{\nu}$)")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

\(\nu\)F\(_{\nu}\)

The \(\nu\)F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid**2 * func(energy_grid), color=green)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"$\nu$F$_{\nu}$")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)