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.. only:: html

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.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_c_profiles_plot_comparing_density_profiles.py:


=====================================
Comparing Common Density Profiles
=====================================

This example compares several widely used spherically symmetric density
profiles in astrophysics:

- :class:`~profiles.density.NFWDensityProfile`
- :class:`~profiles.density.HernquistDensityProfile`
- :class:`~profiles.density.EinastoDensityProfile`
- :class:`~profiles.density.TNFWDensityProfile`
- :class:`~profiles.density.SNFWDensityProfile`

We plot the radial dependence of density on log–log axes to highlight
differences in the central cusp/core and outer slope behavior. In doing so,
we see how users can easily instantiate and evaluate these profiles using
the `pisces` package. For more detailed documentation on profiles, see :ref:`profiles_overview`.

.. GENERATED FROM PYTHON SOURCE LINES 20-23

.. code-block:: Python


    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 24-30

Setup
-----
We'll need to import the relevant profile classes as well as standard
scientific Python packages. We'll use `unyt` for unit handling, `numpy`
for numerical operations, and `matplotlib` for plotting. We can import all
of the relevant profiles from the :mod:`~profiles.density` module.

.. GENERATED FROM PYTHON SOURCE LINES 30-41

.. code-block:: Python

    import numpy as np
    import unyt

    from pisces.profiles.density import (
        EinastoDensityProfile,
        HernquistDensityProfile,
        NFWDensityProfile,
        SNFWDensityProfile,
        TNFWDensityProfile,
    )








.. GENERATED FROM PYTHON SOURCE LINES 42-47

Building Profiles
-----------------
To create instances of a particular radial profile, we simply need
to specify the relevant parameters. Each profile class has a different
set of parameters, but they all share a common interface for evaluation.

.. GENERATED FROM PYTHON SOURCE LINES 47-63

.. code-block:: Python


    # Define a set of characteristic quantities that we'll use as
    # parameters for the different profiles.
    rho_0 = unyt.unyt_quantity(1.0, "Msun/kpc**3")  # Characteristic density
    r_s = unyt.unyt_quantity(10.0, "kpc")  # Scale radius
    r_t = unyt.unyt_quantity(100.0, "kpc")  # Tidal radius for TNFW
    M = unyt.unyt_quantity(1e4, "Msun")  # Total mass for SNFW

    profiles = {
        "NFW": NFWDensityProfile(rho_0=rho_0, r_s=r_s),
        "Hernquist": HernquistDensityProfile(rho_0=rho_0, r_s=r_s),
        "Einasto": EinastoDensityProfile(rho_0=rho_0, r_s=r_s, alpha=0.6),
        "TNFW": TNFWDensityProfile(rho_0=rho_0, r_s=r_s, r_t=r_t),
        "SNFW": SNFWDensityProfile(M=M, a=r_s),
    }








.. GENERATED FROM PYTHON SOURCE LINES 64-69

Plot Density Profiles
---------------------
We'll now evaluate and plot the density profiles over a range of radii.
We'll use logarithmic axes to clearly show differences in the inner
and outer slopes.

.. GENERATED FROM PYTHON SOURCE LINES 69-83

.. code-block:: Python

    r = unyt.unyt_array(np.logspace(0, 3, 500), "kpc")  # Radii from 1 kpc to 1000 kpc

    plt.figure(figsize=(8, 6))

    for name, profile in profiles.items():
        rho = profile(r).to("Msun/kpc**3")
        plt.loglog(r.to("kpc"), rho, label=name)

    plt.xlabel("Radius [kpc]")
    plt.ylabel(r"Density [$M_\odot \, {\rm kpc^{-3}}$]")
    plt.title("Comparison of Common Density Profiles")
    plt.legend()
    plt.grid(True, which="both", ls="--", alpha=0.5)
    plt.show()



.. image-sg:: /auto_examples/c_profiles/images/sphx_glr_plot_comparing_density_profiles_001.png
   :alt: Comparison of Common Density Profiles
   :srcset: /auto_examples/c_profiles/images/sphx_glr_plot_comparing_density_profiles_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.312 seconds)


.. _sphx_glr_download_auto_examples_c_profiles_plot_comparing_density_profiles.py:

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      :download:`Download Python source code: plot_comparing_density_profiles.py <plot_comparing_density_profiles.py>`

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