New constraints on the central mass contents of Omega Centauri from combined stellar kinematics and pulsar timing
- Bañares-Hernández, Andrés et al
- arXiv:2408.00939CERN-TH-2024-131
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). The proper motion data are a combination of the HST and Gaia datasets reported in \cite{2017ApJ...842....6B} and \cite{2021MNRAS.505.5978V} respectively, while the LOS data are compiled from \cite{2006A&A...445..503R, 2010ApJ...719L..60N, 2018MNRAS.473.5591K} (see Sec.~\ref{sec:stardata}). All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). The proper motion data are a combination of the HST and Gaia datasets reported in \cite{2017ApJ...842....6B} and \cite{2021MNRAS.505.5978V} respectively, while the LOS data are compiled from \cite{2006A&A...445..503R, 2010ApJ...719L..60N, 2018MNRAS.473.5591K} (see Sec.~\ref{sec:stardata}). All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). The proper motion data are a combination of the HST and Gaia datasets reported in \cite{2017ApJ...842....6B} and \cite{2021MNRAS.505.5978V} respectively, while the LOS data are compiled from \cite{2006A&A...445..503R, 2010ApJ...719L..60N, 2018MNRAS.473.5591K} (see Sec.~\ref{sec:stardata}). All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). The proper motion data are a combination of the HST and Gaia datasets reported in \cite{2017ApJ...842....6B} and \cite{2021MNRAS.505.5978V} respectively, while the LOS data are compiled from \cite{2006A&A...445..503R, 2010ApJ...719L..60N, 2018MNRAS.473.5591K} (see Sec.~\ref{sec:stardata}). All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | Fits to stellar kinematic observables and the photometric light profile. The profiles are a function of projected radius at the assumed distance of $5.2$~kpc. The green lines and bands correspond to the maximum posterior values, and the 68\% and 95\% CL centered at the median (respectively). For comparison, the gray (gray-dashed) line indicates the velocity dispersion obtained when a fraction of the dark component in the maximum posterior result is concentrated in the form of a $40,000$ ($10,000$) $\MS$ IMBH. Such IMBH models are strongly disfavored in our analysis. The stellar stellar kinematics datasets are described in Sec.~\ref{sec:stardata}. All data, including the photometric profile, have been self-consistently binned with the center from \cite{anderson2010new}. \emph{Upper left:}~Tangential proper motion velocity dispersion. \emph{Upper right:} Radial proper motion velocity dispersion. \emph{Middle left:} LOS velocity dispersion. \emph{Middle right:} Surface brightness profile used to determine the photometric component of the distribution. The red line shows the best-fit profile that was used throughout the analysis (see Sec.~\ref{sec:overview_method} for details). For presentation purposes, this profile has been normalized to match the central luminosity density of \cite{1995AJ....109..218T} after correcting for extinction using the same approach as in \cite{2017MNRAS.468.4429Z} with the reddening reported in \cite{1996AJ....112.1487H} (2010 edition) catalog. \emph{Lower left:} Posterior distribution for the virial shape parameter 1 as a result of the fits, with the red data point indicating the value with 1$\sigma$ errors computed by \texttt{binulator} (see Sec.~\ref{sec:stardata}). \emph{Lower right:} The same as the lower left figure, but for the virial shape parameter 2. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | \emph{Upper left:} 3D enclosed mass profile including photometric, central remnants, black hole, and MSP mass components. The solid lines correspond to the maximum posterior with 68\% and 95\% CL regions. The black and gray dashed lines indicate the upper limit of the 95\% CL region for the black hole and MSP components, respectively. \emph{Upper right:} Symmetrized anisotropy profile including the maximum posterior and 68\% and 95\% CL regions. The posterior distributions for the anisotropy parameters are presented in Appendix~\ref{app:postani}. The profile is close to isotropic, with a mild radial (tangential) anisotropy in the inner (outer) regions. This translates to the $1\sigma$ CL band being well within $|\widetilde{\beta}| < 0.1,$ or $|\beta| \lesssim 0.15$ for the vast majority of the range covered. \emph{Lower left:} Posterior distributions for the masses of the various fitted components of our analysis, indicating the median and $68\%$ CL region at the top of each distribution. \emph{Lower right:} Posterior distributions for the morphological parameters of the fitted mass profiles with respective median and $68\%$ CL regions. |
 | Absolute values of MSP LOS accelerations. The black, solid line denotes the 95\%CL upper bounds as inferred from the mass profiles of the posterior distribution. This region marks the boundary between the excluded region (red) and the allowable one (blue), where it is possible to find a value of $l$ (i.e. a position within the cluster) compatible with the LOS acceleration at a given projected radius. The upwards (downwards) pointing triangles denote the observed MSP accelerations with positive (negative) values, as inferred from the MSP timing data. Errors are not included as they fall below the size of the data points. The vertical black lines denote the intrinsic spin-down components leading to the intrinsic LOS accelerations that trace the GC potential, based on the 68\% CL regions in the magnetic field strength posteriors. This interval accounts for 84\% of the posterior distribution as it includes the lower tail below the 16\% percentile value in addition to the 68\% CL interval contributions. The black, dotted line shows the corresponding bound for an illustrative model where $\sim 15$~\% of the central mass distribution is concentrated in the form of a $4\times10^4 \: \MS$ IMBH. As can be seen, this model is still consistent with the pulsar accelerations (triangles), but is in tension with the proper motion and line of sight velocity data. A lower mass IMBH is still allowed (see the central allowable region that reaches to higher accelerations). The gray, dashed line indicates the projected position of the innermost detected MSP in $\OC$ at $\sim 0.86$~pc from its center. |
 | Absolute values of MSP LOS accelerations. The black, solid line denotes the 95\%CL upper bounds as inferred from the mass profiles of the posterior distribution. This region marks the boundary between the excluded region (red) and the allowable one (blue), where it is possible to find a value of $l$ (i.e. a position within the cluster) compatible with the LOS acceleration at a given projected radius. The upwards (downwards) pointing triangles denote the observed MSP accelerations with positive (negative) values, as inferred from the MSP timing data. Errors are not included as they fall below the size of the data points. The vertical black lines denote the intrinsic spin-down components leading to the intrinsic LOS accelerations that trace the GC potential, based on the 68\% CL regions in the magnetic field strength posteriors. This interval accounts for 84\% of the posterior distribution as it includes the lower tail below the 16\% percentile value in addition to the 68\% CL interval contributions. The black, dotted line shows the corresponding bound for an illustrative model where $\sim 15$~\% of the central mass distribution is concentrated in the form of a $4\times10^4 \: \MS$ IMBH. As can be seen, this model is still consistent with the pulsar accelerations (triangles), but is in tension with the proper motion and line of sight velocity data. A lower mass IMBH is still allowed (see the central allowable region that reaches to higher accelerations). The gray, dashed line indicates the projected position of the innermost detected MSP in $\OC$ at $\sim 0.86$~pc from its center. |
 | Absolute values of MSP LOS accelerations. The black, solid line denotes the 95\%CL upper bounds as inferred from the mass profiles of the posterior distribution. This region marks the boundary between the excluded region (red) and the allowable one (blue), where it is possible to find a value of $l$ (i.e. a position within the cluster) compatible with the LOS acceleration at a given projected radius. The upwards (downwards) pointing triangles denote the observed MSP accelerations with positive (negative) values, as inferred from the MSP timing data. Errors are not included as they fall below the size of the data points. The vertical black lines denote the intrinsic spin-down components leading to the intrinsic LOS accelerations that trace the GC potential, based on the 68\% CL regions in the magnetic field strength posteriors. This interval accounts for 84\% of the posterior distribution as it includes the lower tail below the 16\% percentile value in addition to the 68\% CL interval contributions. The black, dotted line shows the corresponding bound for an illustrative model where $\sim 15$~\% of the central mass distribution is concentrated in the form of a $4\times10^4 \: \MS$ IMBH. As can be seen, this model is still consistent with the pulsar accelerations (triangles), but is in tension with the proper motion and line of sight velocity data. A lower mass IMBH is still allowed (see the central allowable region that reaches to higher accelerations). The gray, dashed line indicates the projected position of the innermost detected MSP in $\OC$ at $\sim 0.86$~pc from its center. |
 | Normalized cumulative distributions of MSPs (red), the more concentrated central mass emulating heavier stellar remnants (blue), stars (yellow) and X-ray emitting sources (black and gray) in $\OC$ as a function of projected radius. The inset shows a close-up view of the distribution normalized at a smaller radius, where all but one of the 18 MSPs are located. The MSP distribution is better constrained over these radii. The inset includes the 68\% and 95\% CL regions of the MSP profile fit (shaded bands). The red dashed line denotes the median of the inferred cumulative distribution from the MSP 3D density from Eq.~\eqref{eq:pul_3d}. The dashed-orange line indicates the predicted distribution derived from the stellar encounter rate that provides a remarkable match to the MSP distribution. We also show counts of X-ray sources observed in $\OC$ studied by \cite{2018MNRAS.479.2834H}, showing the total count of 233 objects (black) and a subset of $\sim 32$ of the objects that share luminosities and X-ray colors compatible with known MSPs from other GCs (gray), as presented in Figure 10 of \cite{2005ApJ...625..796H} (see also the discussion in \cite{2018MNRAS.479.2834H}). Over the radial range of the inset figure, this count is reduced to 105 and $\sim 17$ sources, respectively. |
 | Normalized cumulative distributions of MSPs (red), the more concentrated central mass emulating heavier stellar remnants (blue), stars (yellow) and X-ray emitting sources (black and gray) in $\OC$ as a function of projected radius. The inset shows a close-up view of the distribution normalized at a smaller radius, where all of the 18 MSPs are located. The inset includes the 68\% and 95\% CL regions of the MSP profile fit (shaded bands). The red dashed line denotes the median of the inferred cumulative distribution from the MSP 3D density from Eq.~\eqref{eq:pul_3d}. The dashed-orange line indicates the predicted distribution derived from the stellar encounter rate that provides a remarkable match to the MSP distribution. We also show counts of X-ray sources observed in $\OC$ studied by \cite{2018MNRAS.479.2834H}, showing the total count of 233 objects (black) and a subset of $\sim 32$ of the objects that share luminosities and X-ray colors compatible with known MSPs from other GCs (gray), as presented in Figure 10 of \cite{2005ApJ...625..796H} (see also the discussion in \cite{2018MNRAS.479.2834H}). Over the radial range of the inset figure, this count is reduced to 105 and $\sim 17$ sources, respectively. |
 | Normalized cumulative distributions of MSPs (red), the more concentrated central mass emulating heavier stellar remnants (blue), stars (yellow) and X-ray emitting sources (black and gray) in $\OC$ as a function of projected radius. The inset shows a close-up view of the distribution normalized at a smaller radius, where all of the 18 MSPs are located. The inset includes the 68\% and 95\% CL regions of the MSP profile fit (shaded bands). The red dashed line denotes the median of the inferred cumulative distribution from the MSP 3D density from Eq.~\eqref{eq:pul_3d}. The dashed-orange line indicates the predicted distribution derived from the stellar encounter rate that provides a remarkable match to the MSP distribution. We also show counts of X-ray sources observed in $\OC$ studied by \cite{2018MNRAS.479.2834H}, showing the total count of 233 objects (black) and a subset of $\sim 32$ of the objects that share luminosities and X-ray colors compatible with known MSPs from other GCs (gray), as presented in Figure 10 of \cite{2005ApJ...625..796H} (see also the discussion in \cite{2018MNRAS.479.2834H}). Over the radial range of the inset figure, this count is reduced to 105 and $\sim 17$ sources, respectively. |
 | MSP abundances as a function of stellar encounter rates. The red points are the observed cumulative number of MSPs as a function of the enclosed encounter rate at a projected radius $R$ (upper x-axis). The red line corresponds to a least-squares linear fit, showing a clear linear dependence. The black points denote the same quantities for the full list of 233 X-ray sources from \cite{2018MNRAS.479.2834H}, while the orange line corresponds to the stellar distribution, normalized to match these sources. These show a distinct, non-linear, dependence, with encounter rates that are not followed by the MSPs. The orange, dashed line is a linear extrapolation shown for comparison. Lastly, the gray dashed line indicates an upper estimate on the total number of MSPs as a function of total encounter rates of GCs, with $1\sigma$ error bands. This is based on the parametric fit performed by \cite{2022MNRAS.511.5964Z} using the phenomenological estimates of \cite{2011MNRAS.418..477B}, based on luminosity functions, and assuming the updated total stellar encounter rates of \cite{2013ApJ...766..136B}. Units for $\OC$'s total encounter have been normalized to match the 90.4 central value of \cite{2013ApJ...766..136B}. |
 | MSP abundances as a function of stellar encounter rates. The red points are the observed cumulative number of MSPs as a function of the enclosed encounter rate at a projected radius $R$ (upper x-axis). The red line corresponds to a least-squares linear fit, showing a clear linear dependence. The black points denote the same quantities for the full list of 233 X-ray sources from \cite{2018MNRAS.479.2834H}, while the orange line corresponds to the stellar distribution, normalized to match these sources. These show a distinct, non-linear, dependence, with encounter rates that are not followed by the MSPs. The orange, dashed line is a linear extrapolation shown for comparison. Lastly, the gray dashed line indicates an upper estimate on the total number of MSPs as a function of total encounter rates of GCs, with $1\sigma$ error bands. This is based on the parametric fit performed by \cite{2022MNRAS.511.5964Z} using the phenomenological estimates of \cite{2011MNRAS.418..477B}, based on luminosity functions, and assuming the updated total stellar encounter rates of \cite{2013ApJ...766..136B}. Units for $\OC$'s total encounter have been normalized to match the 90.4 central value of \cite{2013ApJ...766..136B}. |
 | Posterior distributions of the anisotropy parameters. The parameter space exhibits multiple degeneracies, but due to the correlations inherent to these, the resultant anisotropy profile is well constrained (cf.~Fig.~\ref{fig:masani}). Note that this is not inconsistent with our results and that these degeneracies are the result of our parametric modeling and not intrinsic to the anisotropy profile. |
 | Posterior distributions of the anisotropy parameters. The parameter space exhibits multiple degeneracies, but due to the correlations inherent to these, the resultant anisotropy profile is well constrained (cf.~Fig.~\ref{fig:masani}). Note that this is not inconsistent with our results and that these degeneracies are the result of our parametric modeling and not intrinsic to the anisotropy profile. |
 | Posterior distributions for the masses of the components considered during a fit performed without the inclusion of MSP LOS accelerations into the likelihood function. The median for the central mass from the full fit (cf. Fig.~\ref{fig:masani}) is $ \sim 21 \%$ greater than the one found during this fit, with the other components showing only moderate differences. |
 | Posterior distributions for the masses of the components considered during a fit performed without the inclusion of MSP LOS accelerations into the likelihood function. The median for the central mass from the full fit (cf. Fig.~\ref{fig:masani}) is $ \sim 20 \%$ greater than the one found during this fit, with the other components showing only moderate differences. |
 | Posterior distributions for the morphological parameters of the mass profiles without the inclusion of MSP LOS accelerations into the likelihood function. The median for the central mass length scale from the full fit (cf. Fig.~\ref{fig:masani}) is $\sim 18\%$ greater than the one found during this fit. The morphology of the MSP distribution is still constrained due to the projected radii included in the positional component of the likelihood function, favoring a somewhat different posterior distribution when accelerations are excluded. This, however, has a negligible effect on the remainder of the mass components in the absence of accelerations to constrain their kinematics. |
 | Posterior distributions for the morphological parameters of the mass profiles without the inclusion of MSP LOS accelerations into the likelihood function. The median for the central mass length scale from the full fit (cf. Fig.~\ref{fig:masani}) is $\sim 18\%$ greater than the one found during this fit. The morphology of the MSP distribution is still constrained due to the projected radii included in the positional component of the likelihood function, favoring a somewhat different posterior distribution when accelerations are excluded. This, however, has a negligible effect on the remainder of the mass components in the absence of accelerations to constrain their kinematics. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 16 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 4 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 18 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center. A small increase of $\sim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the MSP parameters agreeing at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 13 \%$ greater, indicating a somewhat more concentrated central mass distribution in this case. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 15 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 3 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 14 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center, although still with the $1 \sigma$ CL regions overlapping each other. A small increase of $\lesssim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the $1 \sigma$ CL regions barely overlapping each other. The MSP parameters agree at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 10 \%$ greater, indicating a somewhat more concentrated central mass distribution, but still showing $1 \sigma$ CL compatibility. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 16 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 4 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 18 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center. A small increase of $\sim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the MSP parameters agreeing at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 13 \%$ greater, indicating a somewhat more concentrated central mass distribution in this case. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 15 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 3 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 14 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center, although still with the $1 \sigma$ CL regions overlapping each other. A small increase of $\lesssim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the $1 \sigma$ CL regions barely overlapping each other. The MSP parameters agree at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 10 \%$ greater, indicating a somewhat more concentrated central mass distribution, but still showing $1 \sigma$ CL compatibility. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 16 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 4 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 18 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center. A small increase of $\sim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the MSP parameters agreeing at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 13 \%$ greater, indicating a somewhat more concentrated central mass distribution in this case. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 15 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 3 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 14 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center, although still with the $1 \sigma$ CL regions overlapping each other. A small increase of $\lesssim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the $1 \sigma$ CL regions barely overlapping each other. The MSP parameters agree at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 10 \%$ greater, indicating a somewhat more concentrated central mass distribution, but still showing $1 \sigma$ CL compatibility. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 16 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 4 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 18 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center. A small increase of $\sim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the MSP parameters agreeing at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 13 \%$ greater, indicating a somewhat more concentrated central mass distribution in this case. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | \emph{Upper-left:} Posterior distributions for the mass components considered in our kinematic models using the Noy10 center. The median of the central mass component for the And center, is $\sim 15 \%$ lower, consistent with a more extended central mass distribution for the Noy10 center. The stellar mass obtained is only marginally smaller ($\lesssim 3 \%$), with the other IMBH and MSP components remaining subdominant without significant statistically meaningful differences. \emph{Upper-right:} Same as the upper-left plot, but for the Noy08 center. In this case, the central mass for our main analysis with the And center is $\sim 14 \%$ higher than the result shown, consistent with a more concentrated distribution for the Noy08 center, although still with the $1 \sigma$ CL regions overlapping each other. A small increase of $\lesssim 2 \%$ is observed with respect to the stellar mass value, but these central values lie within their respective $1 \sigma$ CL regions. The IMBH and MSP mass components, once more, show approximate consistency with the previous results.$^\dagger$ \emph{Lower-left:} Posterior distributions of the morphological parameters for the mass models using the Noy10 center. The median of the scale radius using the And center is $\sim 11 \%$ lower, indicating a somewhat more extended central mass distribution for the Noy10 center, with the $1 \sigma$ CL regions barely overlapping each other. The MSP parameters agree at the $1 \sigma$ level. \emph{Lower-right:} Same as the middle-left plot, but for the Noy08 center. In this case, the median of the scale radius using the And center is $\sim 10 \%$ greater, indicating a somewhat more concentrated central mass distribution, but still showing $1 \sigma$ CL compatibility. As with the Noy10 center, the MSP parameters show $1 \sigma$ level consistency with the And center results. \\ $^\dagger$ Marginal differences in the morphology of the posterior distributions of the IMBH and MSP masses are not necessarily statistically meaningful, owing to the fact that, due to being inherently less constrained, these may require additional independent runs to fully establish such differences (which we did perform for the case of the And center). This, however, is not necessary for the purposes of the complementary analysis presented in this appendix. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Combined velocity dispersion profiles for the three components using the \cite{anderson2010new} center (And, \emph{left}) \cite{2010ApJ...719L..60N} (Noy10, \emph{middle}) and \cite{Noyola:2008kt} (Noy08, \emph{right}) kinematic centers. The maximum-posterior velocity dispersion profile (red) from our main analysis using the And center is shown for reference in all plots, yielding fits of comparable quality for all the cases considered. Due to the close-to-isotropic behavior of our inferred distribution at the 5.2 kpc distance employed, the three components of our maximum posterior fits are almost identical, with the large majority of the data points showing close overlap with each other. |
 | Posterior distributions for the mass model parameters using the generalized mass profile in Eq.~\eqref{eq:massmsp} for the extended dark component. |
 | Posterior distributions for the mass model parameters using a Gaussian profile (Eq.~\eqref{eq:deng}) for the extended dark component. |