Units
===========

Geometrized units are often used in general relativity where
:math:`G=c=1`. For neutron stars, it is convenient also to set
:math:`M_{\odot}=1`. So, the overall units are :math:`G=c=M_{\odot}=1`.
This is the system of units used in QLIMR. That is equivalent to make
all quantities dimensionless with respect to one solar mass in units of
length (:math:`\ell_{\odot} \sim 1.5 \, \textrm{km}`). The following table shows the non-geometrized
dimensions (NGD), geometrized dimensions (GD), neutron star dimensions
(NSD) and the conversion factors between them for all the relevant
quantities (Q) used in the source code.

+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| Q                                      | NGD                                              | GD                      | NGD :math:`\rightarrow` GD     | GD :math:`\rightarrow` NGD     | NGD :math:`\rightarrow` NSD      | NSD :math:`\rightarrow` NGD     |
+========================================+==================================================+=========================+================================+================================+==================================+=================================+
| :math:`\varepsilon_{c}`                | :math:`\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}` | :math:`\mathsf{L}^{-2}` | :math:`G/c^{4}`                | :math:`c^{4}/G`                | :math:`G \ell^{2}_{\odot}/c^{4}` | :math:`c^{4}/G \ell^{2}_{\odot}`|
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`R_{\star}`                      | :math:`\mathsf{L}`                               | :math:`\mathsf{L}`      | 1                              | 1                              | 1/:math:`\ell_{\odot}`           | :math:`\ell_{\odot}`            |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`M_{\star}`                      | :math:`\mathsf{M}`                               | :math:`\mathsf{L}`      | :math:`G/c^{2}`                | :math:`c^{2}/G`                | :math:`G/\ell_{\odot}c^{2}`      | :math:`\ell_{\odot}c^{2}/G`     |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`I`                              | :math:`\mathsf{L}^{2}\mathsf{M}`                 | :math:`\mathsf{L}^{3}`  | :math:`G/c^{2}`                | :math:`c^{2}/G`                | :math:`G/\ell_{\odot}^{3}c^{2}`  | :math:`\ell_{\odot}^{3}c^{2}/G` |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\lambda^{\textsf{(tid)}}`       | :math:`\mathsf{L}^{2}\mathsf{T}^{2}\mathsf{M}`   | :math:`\mathsf{L}^{5}`  | :math:`G`                      | :math:`1/G`                    | :math:`G/\ell^{5}_{\odot}`       | :math:`\ell^{5}_{\odot}/G`      |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`Q`                              | :math:`\mathsf{L}^{2}\mathsf{M}`                 | :math:`\mathsf{L}^{3}`  | :math:`G/c^{2}`                | :math:`c^{2}/G`                | :math:`G/\ell^{3}_{\odot}c^{2}`  | :math:`\ell^{3}_{\odot}c^{2}/G` |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`e_{s}`                          | :math:`\mathsf{-}`                               | :math:`\mathsf{-}`      | :math:`\mathsf{-}`             | :math:`\mathsf{-}`             | :math:`\mathsf{-}`               | :math:`\mathsf{-}`              |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\delta R_{\textrm{eq}}`         | :math:`\mathsf{L}`                               | :math:`\mathsf{L}`      | 1                              | 1                              | 1/:math:`\ell_{\odot}`           | :math:`\ell_{\odot}`            |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\langle\delta R_{\star}\rangle` | :math:`\mathsf{L}`                               | :math:`\mathsf{L}`      | 1                              | 1                              | 1/:math:`\ell_{\odot}`           | :math:`\ell_{\odot}`            |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\delta M_{\star}`               | :math:`\mathsf{M}`                               | :math:`\mathsf{L}`      | :math:`G/c^{2}`                | :math:`c^{2}/G`                | :math:`G/\ell_{\odot}c^{2}`      | :math:`\ell_{\odot}c^{2}/G`     |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`h`                              | :math:`\mathsf{-}`                               |  :math:`\mathsf{-}`     |  :math:`\mathsf{-}`            | :math:`\mathsf{-}`             |  :math:`\mathsf{-}`              |  :math:`\mathsf{-}`             |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`R`                              | :math:`\mathsf{L}`                               | :math:`\mathsf{L}`      | 1                              | 1                              | 1/:math:`\ell_{\odot}`           | :math:`\ell_{\odot}`            |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\varepsilon`                    | :math:`\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}` | :math:`\mathsf{L}^{-2}` | :math:`G/c^{4}`                | :math:`c^{4}/G`                | :math:`G \ell_{\odot}^{2}/c^{4}` | :math:`c^{4}/G \ell_{\odot}^{2}`|
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`p`                              | :math:`\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}` | :math:`\mathsf{L}^{-2}` | :math:`G/c^{4}`                | :math:`c^{4}/G`                | :math:`G \ell_{\odot}^{2}/c^{4}` | :math:`c^{4}/G \ell_{\odot}^{2}`|
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\nu`                            | :math:`\mathsf{-}`                               |  :math:`\mathsf{-}`     |  :math:`\mathsf{-}`            | :math:`\mathsf{-}`             |  :math:`\mathsf{-}`              |  :math:`\mathsf{-}`             |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`Y`                              | :math:`\mathsf{-}`                               |  :math:`\mathsf{-}`     |  :math:`\mathsf{-}`            | :math:`\mathsf{-}`             |  :math:`\mathsf{-}`              |  :math:`\mathsf{-}`             |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\Omega`                         | :math:`\mathsf{T}^{-1}`                          | :math:`\mathsf{L}^{-1}` | :math:`1/c`                    | :math:`c`                      | :math:`\ell_{\odot}/c`           | :math:`c/\ell_{\odot}`          |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\varpi_{1}`                     | :math:`\mathsf{T}^{-1}`                          | :math:`\mathsf{L}^{-1}` | :math:`1/c`                    | :math:`c`                      | :math:`\ell_{\odot}/c`           | :math:`c/\ell_{\odot}`          |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`\xi_{2}`                        | :math:`\mathsf{L}`                               | :math:`\mathsf{L}`      | 1                              | 1                              | 1/:math:`\ell_{\odot}`           | :math:`\ell_{\odot}`            |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`h_{2}`                          | :math:`\mathsf{-}`                               |  :math:`\mathsf{-}`     |  :math:`\mathsf{-}`            | :math:`\mathsf{-}`             |  :math:`\mathsf{-}`              |  :math:`\mathsf{-}`             |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`K_{2}`                          | :math:`\mathsf{-}`                               |  :math:`\mathsf{-}`     |  :math:`\mathsf{-}`            | :math:`\mathsf{-}`             |  :math:`\mathsf{-}`              |  :math:`\mathsf{-}`             |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+
| :math:`m_{2}`                          | :math:`\mathsf{M}`                               | :math:`\mathsf{L}`      | :math:`G/c^{2}`                | :math:`c^{2}/G`                | :math:`G/\ell_{\odot}c^{2}`      | :math:`\ell_{\odot}c^{2}/G`     |
+----------------------------------------+--------------------------------------------------+-------------------------+--------------------------------+--------------------------------+----------------------------------+---------------------------------+

**Note:** The units for the input and output parameters are provided in the *Parameters* section.