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Median statistics estimate of the galactic rotational velocity

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Abstract

We compile a complete collection of 18 recent (from 2000 to 2017) measurements of \(\varTheta_{0}\), the rotational velocity of the Milky Way at \(R_{0}\) (the radial distance of the Sun from the Galactic center). These measurements use tracers that are believed to more accurately reflect the systematic rotation of the Milky Way. Unlike other recent compilations of \(\varTheta_{0}\), our collection includes only independent measurements. We find that these 18 measurements are distributed in a mildly non-Gaussian fashion and a median statistics estimate indicates \(\varTheta_{0} = 220 \pm 10\) km s−1 (2\(\sigma\) error) as the most reliable summary, at \(R_{0} = 8.0 \pm0.3\) kpc (2\(\sigma\) error).

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Notes

  1. This is consistent with the recent determination of \(R_{0} = 8.122 \pm0.031\) kpc (1\(\sigma\) error) from the orbit of star S2 at the Galactic center (Abuter et al. 2018).

  2. Often the same observational data has been analyzed a number of times to measure \(\varTheta_{0}\). In our compilation here we typically include only the most recent \(\varTheta _{0}\) determination from a data set. This is to ensure that our \(\varTheta_{0}\) compilation here is as independent as possible.

  3. It is very encouraging that our data compilation is only mildly non-Gaussian. This means that the error bars estimated by the observers are reasonable. If the error bars were not reasonable, we would have seen significant non-Gaussianity. Importantly, unaccounted for systematic errors are likely to be small. Of course, one possible explanation is that all the measurements we have included here could have a common systematic error.

  4. More properly one would use the rescaled angular velocities in the analysis and then convert the resulting angular velocity central value to a linear velocity central value. However, the uncertainty on \(R_{0}\) is small and so results from the two different approaches will only differ slightly.

  5. Perhaps the most famous example is the Hubble constant (Chen et al. 2003; Chen and Ratra 2011a). For other examples in astronomy, cosmology, and physics see Farooq et al. (2013, 2017), Crandall et al. (2015), Bailey (2017), Zhang (2017), and references therein. Significant effort is devoted to testing for intrinsic non-Gaussianity in physical systems (e.g. Park et al. 2001; Planck Collaboration et al. 2016), as opposed to measurement induced non-Gaussianity, since Gaussianity is usually assumed in parameter estimation (e.g. Samushia et al. 2007; Chen and Ratra 2011b; Ooba et al. 2018).

  6. An analogous equation for median statistics, for the case when the median is estimated from the data and so is correlated with the data, is not yet known.

  7. See C18 and Appendix 3 of O’Connor and Kleyner (2012) for more detailed discussion of the outputs of the KS tests and the critical values for below which \(D\) must fall.

  8. In fact, the data errors are quite consistent with Gaussianity, however the C1 weighted mean \(1\sigma\) error is \({\pm}2\) km \(\mathrm{s}^{-1}\). This is quite small and at this level there are a number of corrections that must be accounted for in the measurements of Table 1. We hence choose to use the median statistics over the weighted mean results.

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Acknowledgements

We thank A. Quillen and J. Vallée. This research was supported in part by DOE grant DE-SC0019038.

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Correspondence to Bharat Ratra.

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Camarillo, T., Dredger, P. & Ratra, B. Median statistics estimate of the galactic rotational velocity. Astrophys Space Sci 363, 268 (2018). https://doi.org/10.1007/s10509-018-3486-8

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