Broken powerlaw

[3]:

# Parameters
func_name = "Broken_powerlaw"
wide_energy_range = True
x_scale = "log"
y_scale = "log"
linear_range = False

Description

[5]:

func.display()
  • description: A broken power law function
  • formula: $ f(x)= K~\begin{cases}\left( \frac{x}{x_{b}} \right)^{\alpha} & x < x_{b} \\ \left( \frac{x}{x_{b}} \right)^{\beta} & x \ge x_{b} \end{cases} $
  • parameters:
    • K:
      • value: 1.0
      • desc: Normalization (differential flux at x_b)
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: True
      • delta: 0.1
      • free: True
    • xb:
      • value: 10.0
      • desc: Break point
      • min_value: 1.0
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 1.0
      • free: True
    • alpha:
      • value: -1.5
      • desc: Index before the break xb
      • min_value: -10.0
      • max_value: 10.0
      • unit:
      • is_normalization: False
      • delta: 0.15000000000000002
      • free: True
    • beta:
      • value: -2.5
      • desc: Index after the break xb
      • min_value: -10.0
      • max_value: 10.0
      • unit:
      • is_normalization: False
      • delta: 0.25
      • free: True
    • piv:
      • value: 1.0
      • desc: Pivot energy
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: False

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

[6]:

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)
../_images/notebooks_Broken_powerlaw_8_0.png

F\(_{\nu}\)

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

[7]:

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)

../_images/notebooks_Broken_powerlaw_10_0.png

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

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

[8]:

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)
../_images/notebooks_Broken_powerlaw_12_0.png