DoubleSmoothlyBrokenPowerlaw
[3]:
# Parameters
func_name = "DoubleSmoothlyBrokenPowerlaw"
wide_energy_range = True
x_scale = "log"
y_scale = "log"
linear_range = False
Description
[5]:
func.display()
- description: A smoothly broken power law with two breaks as parameterized in Ravasio, M. E. et al. Astron Astrophys 613, A16 (2018).
- formula: $\begin{array}{l}\begin{aligned}f(x)=& A x_{\mathrm{b}}^{\alpha_{1}}\left[\left[\left(\frac{x}{x_{\mathrm{b}}}\right)^{-\alpha_{1} n_{1}}+\left(\frac{x}{x_{\mathrm{b}}}\right)^{-\alpha_{2} n_{1}}\right]^{\frac{n_{2}}{n_{1}}}\right.\\&\left.+\left(\frac{x}{x_{\mathrm{j}}}\right)^{-\beta n_{2}} \cdot\left[\left(\frac{x_{\mathrm{j}}}{x_{\mathrm{b}}}\right)^{-\alpha_{1} n_{1}}+\left(\frac{x_{\mathrm{j}}}{x_{\mathrm{b}}}\right)^{-\alpha_{2} n_{1}}\right]^{\frac{n_{2}}{n_{1}}}\right]^{-\frac{1}{n_{2}}}\end{aligned}\\\text { where }\\x_{\mathrm{j}}=x_{\mathrm{p}} \cdot\left(-\frac{\alpha_{2}+2}{\beta+2}\right)^{\frac{1}{\left.\beta-\alpha_{2}\right) n_{2}}}\end{array}$
- parameters:
- K:
- value: 0.0001
- desc: Differential flux at the pivot energy
- min_value: 1e-50
- max_value: None
- unit:
- is_normalization: True
- delta: 1e-05
- free: True
- alpha1:
- value: -0.66
- desc: photon index below xb
- min_value: None
- max_value: None
- unit:
- is_normalization: False
- delta: 0.066
- free: True
- xb:
- value: 100.0
- desc: break energy below xp
- min_value: 1e-10
- max_value: None
- unit:
- is_normalization: False
- delta: 10.0
- free: True
- n1:
- value: 2.0
- desc: curvature of the first break
- min_value: 0.0
- max_value: None
- unit:
- is_normalization: False
- delta: 0.2
- free: False
- alpha2:
- value: -1.5
- desc: photon index between xb and xp
- min_value: None
- max_value: None
- unit:
- is_normalization: False
- delta: 0.15000000000000002
- free: True
- xp:
- value: 300.0000000000001
- desc: nuFnu peak
- min_value: 1e-10
- max_value: None
- unit:
- is_normalization: False
- delta: 30.000000000000014
- free: True
- n2:
- value: 2.0
- desc: curvature of the break at xp
- min_value: 0.0
- max_value: None
- unit:
- is_normalization: False
- delta: 0.2
- free: False
- beta:
- value: -2.5
- desc: photon index above xp
- min_value: None
- max_value: 2.0
- 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
- K:
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)
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)
\(\nu\)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)
