New Black Hole Spin Values for Sagittarius A* Obtained with the Outflow Method

Six archival Chandra observations are matched with eight sets of radio data and studied in the context of the outflow method to measure and study the spin properties of $\mathrm{S}\mathrm{g}\mathrm{r}{\mathrm{A}}^{\ast }$. Three radio and X-ray data sets obtained simultaneously, or partially simultaneously, are identified as preferred for the purpose of measuring the spin properties of $\mathrm{S}\mathrm{g}\mathrm{r}{\mathrm{A}}^{\ast }$. Similar results are obtained with other data sets. Results obtained with the preferred data sets are combined and indicate a weighted mean value of the spin function of $\mathrm{F}=0.62\pm 0.10$ and dimensionless spin angular momentum of ${\mathrm{a}}_{\ast }=0.90\pm 0.06$. The spin function translates into measurements of the black hole rotational mass, ${\mathrm{M}}_{\mathrm{r}\mathrm{o}\mathrm{t}}$, irreducible mass, ${\mathrm{M}}_{\mathrm{i}\mathrm{r}\mathrm{r}}$, and spin mass-energy available for extraction, ${\mathrm{M}}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}$, relative to the total black hole dynamical mass, ${\mathrm{M}}_{\mathrm{d}\mathrm{y}\mathrm{n}}$. Weighted mean values of $({\mathrm{M}}_{\mathrm{r}\mathrm{o}\mathrm{t}}\mathrm{/}{\mathrm{M}}_{\mathrm{d}\mathrm{y}\mathrm{n}})=(0.53\pm 0.06)$, $({\mathrm{M}}_{\mathrm{i}\mathrm{r}\mathrm{r}}\mathrm{/}{\mathrm{M}}_{\mathrm{d}\mathrm{y}\mathrm{n}})=(0.85\pm 0.04)$, $({\mathrm{M}}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}\mathrm{/}{\mathrm{M}}_{\mathrm{d}\mathrm{y}\mathrm{n}})=(0.15\pm 0.04)$, ${\mathrm{M}}_{\mathrm{r}\mathrm{o}\mathrm{t}}=(2.2\pm 0.3)\times {10}^6{\mathrm{M}}_{\odot }$, ${\mathrm{M}}_{\mathrm{i}\mathrm{r}\mathrm{r}}=(3.5\pm 0.2)\times {10}^6{\mathrm{M}}_{\odot }$, and ${\mathrm{M}}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}=(6.2\pm 1.6)\times {10}^5{\mathrm{M}}_{\odot }$ are obtained; of course $({\mathrm{M}}_{\mathrm{r}\mathrm{o}\mathrm{t}}\mathrm{/}{\mathrm{M}}_{\mathrm{i}\mathrm{r}\mathrm{r}})=(0.62\pm 0.10)$ since $({\mathrm{M}}_{\mathrm{r}\mathrm{o}\mathrm{t}}\mathrm{/}{\mathrm{M}}_{\mathrm{i}\mathrm{r}\mathrm{r}})=\mathrm{F}$. Values obtained for $\mathrm{S}\mathrm{g}\mathrm{r}{\mathrm{A}}^{\ast }$ are compared with those obtained for M87 based on the published spin function which indicate that M87 carries substantially more rotational energy and spin mass-energy relative to the total (i.e., dynamical) black hole mass, the irreducible black hole mass, and in absolute terms.