Units
Geometrized units are often used in general relativity where \(G=c=1\). For neutron stars, it is convenient also to set \(M_{\odot}=1\). So, the overall units are \(G=c=M_{\odot}=1\). 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 (\(\ell_{\odot} \sim 1.5 \, \textrm{km}\)). 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 \(\rightarrow\) GD |
GD \(\rightarrow\) NGD |
NGD \(\rightarrow\) NSD |
NSD \(\rightarrow\) NGD |
|---|---|---|---|---|---|---|
\(\varepsilon_{c}\) |
\(\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}\) |
\(\mathsf{L}^{-2}\) |
\(G/c^{4}\) |
\(c^{4}/G\) |
\(G \ell^{2}_{\odot}/c^{4}\) |
\(c^{4}/G \ell^{2}_{\odot}\) |
\(R_{\star}\) |
\(\mathsf{L}\) |
\(\mathsf{L}\) |
1 |
1 |
1/\(\ell_{\odot}\) |
\(\ell_{\odot}\) |
\(M_{\star}\) |
\(\mathsf{M}\) |
\(\mathsf{L}\) |
\(G/c^{2}\) |
\(c^{2}/G\) |
\(G/\ell_{\odot}c^{2}\) |
\(\ell_{\odot}c^{2}/G\) |
\(I\) |
\(\mathsf{L}^{2}\mathsf{M}\) |
\(\mathsf{L}^{3}\) |
\(G/c^{2}\) |
\(c^{2}/G\) |
\(G/\ell_{\odot}^{3}c^{2}\) |
\(\ell_{\odot}^{3}c^{2}/G\) |
\(\lambda^{\textsf{(tid)}}\) |
\(\mathsf{L}^{2}\mathsf{T}^{2}\mathsf{M}\) |
\(\mathsf{L}^{5}\) |
\(G\) |
\(1/G\) |
\(G/\ell^{5}_{\odot}\) |
\(\ell^{5}_{\odot}/G\) |
\(Q\) |
\(\mathsf{L}^{2}\mathsf{M}\) |
\(\mathsf{L}^{3}\) |
\(G/c^{2}\) |
\(c^{2}/G\) |
\(G/\ell^{3}_{\odot}c^{2}\) |
\(\ell^{3}_{\odot}c^{2}/G\) |
\(e_{s}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\delta R_{\textrm{eq}}\) |
\(\mathsf{L}\) |
\(\mathsf{L}\) |
1 |
1 |
1/\(\ell_{\odot}\) |
\(\ell_{\odot}\) |
\(\langle\delta R_{\star}\rangle\) |
\(\mathsf{L}\) |
\(\mathsf{L}\) |
1 |
1 |
1/\(\ell_{\odot}\) |
\(\ell_{\odot}\) |
\(\delta M_{\star}\) |
\(\mathsf{M}\) |
\(\mathsf{L}\) |
\(G/c^{2}\) |
\(c^{2}/G\) |
\(G/\ell_{\odot}c^{2}\) |
\(\ell_{\odot}c^{2}/G\) |
\(h\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(R\) |
\(\mathsf{L}\) |
\(\mathsf{L}\) |
1 |
1 |
1/\(\ell_{\odot}\) |
\(\ell_{\odot}\) |
\(\varepsilon\) |
\(\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}\) |
\(\mathsf{L}^{-2}\) |
\(G/c^{4}\) |
\(c^{4}/G\) |
\(G \ell_{\odot}^{2}/c^{4}\) |
\(c^{4}/G \ell_{\odot}^{2}\) |
\(p\) |
\(\mathsf{L}^{-1}\mathsf{T}^{-2}\mathsf{M}\) |
\(\mathsf{L}^{-2}\) |
\(G/c^{4}\) |
\(c^{4}/G\) |
\(G \ell_{\odot}^{2}/c^{4}\) |
\(c^{4}/G \ell_{\odot}^{2}\) |
\(\nu\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(Y\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\Omega\) |
\(\mathsf{T}^{-1}\) |
\(\mathsf{L}^{-1}\) |
\(1/c\) |
\(c\) |
\(\ell_{\odot}/c\) |
\(c/\ell_{\odot}\) |
\(\varpi_{1}\) |
\(\mathsf{T}^{-1}\) |
\(\mathsf{L}^{-1}\) |
\(1/c\) |
\(c\) |
\(\ell_{\odot}/c\) |
\(c/\ell_{\odot}\) |
\(\xi_{2}\) |
\(\mathsf{L}\) |
\(\mathsf{L}\) |
1 |
1 |
1/\(\ell_{\odot}\) |
\(\ell_{\odot}\) |
\(h_{2}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(K_{2}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(\mathsf{-}\) |
\(m_{2}\) |
\(\mathsf{M}\) |
\(\mathsf{L}\) |
\(G/c^{2}\) |
\(c^{2}/G\) |
\(G/\ell_{\odot}c^{2}\) |
\(\ell_{\odot}c^{2}/G\) |
Note: The units for the input and output parameters are provided in the Parameters section.