We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995Y2007) and radial velocity (RV; 2000Y2007) measurements from the W. M. Keck 10 m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R 0 ) of 8:0 AE 0:6 kpc, the enclosed mass (M bh ) of 4:1 AE 0:6 ; 10 6 M , and the black hole's RV, which is consistent with zero with 30 km s À1 uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e.g., has no massive companion to induce motion), we can further constrain the fit, obtaining R 0 ¼ 8:4 AE 0:4 kpc and M bh ¼ 4:5 AE 0:4 ; 10 6 M . More complex models constrain the extended dark mass distribution to be less than 3Y4 ; 10 5 M within 0.01 pc, $100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R 0 and the Galaxy's local rotation speed, which it is derived from combining R 0 with the apparent proper motion of Sgr A Ã , ( 0 ¼ 229 AE 18 km s À1 ), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M bh -relation.

We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995Y2007) and radial velocity (RV; 2000Y2007) measurements from the W. M. Keck 10 m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R 0) of 8:0 AE 0:6 kpc, the enclosed mass (M bh) of 4:1 AE 0:6 ; 10 6 M , and the black hole's RV, which is consistent with zero with 30 km s À1 uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e.g., has no massive companion to induce motion), we can further constrain the fit, obtaining R 0 ¼ 8:4 AE 0:4 kpc and M bh ¼ 4:5 AE 0:4 ; 10 6 M. More complex models constrain the extended dark mass distribution to be less than 3Y4 ; 10 5 M within 0.01 pc, $100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R 0 and the Galaxy's local rotation speed, which it is derived from combining R 0 with the apparent proper motion of Sgr A Ã , (0 ¼ 229 AE 18 km s À1), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M bh-relation.

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Background and ObjectivesBody mass index (BMI) and height are important indices of health. We tested the association between these outcomes and clinical characteristics in Friedreich ataxia (FRDA), a progressive neuromuscular disorder.MethodsParticipants (N = 961) were enrolled in a prospective natural history study (Friedreich Ataxia Clinical Outcome Measure Study). Age- and sex-specific BMI and height Z-scores were calculated using CDC 2000 references for participants younger than 18 years. For adults aged 18 years or older, height Z-scores were also calculated, and absolute BMI was reported. Univariate and multivariate linear regression analyses tested the associations between exposures, covariates, and BMI or height measured at the baseline visit. In children, the superimposition by translation and rotation analysis method was used to compare linear growth trajectories between FRDA and a healthy reference cohort, the Bone Mineral Density in Childhood Study (n = 1,535 used for analysis).ResultsMedian age at the baseline was 20 years (IQR, 13–33 years); 49% (n = 475) were women. A substantial proportion of children (17%) were underweight (BMI-Z < fifth percentile), and female sex was associated with lower BMI-Z (β = −0.34, p < 0.05). In adults, older age was associated with higher BMI (β = 0.09, p < 0.05). Regarding height, in children, older age (β −0.06, p < 0.05) and worse modified Friedreich Ataxia Rating Scale (mFARS) scores (β = −1.05 for fourth quartile vs first quartile, p < 0.01) were associated with shorter stature. In girls, the magnitude of the pubertal growth spurt was less, and in boys, the pubertal growth spurt occurred later (p < 0.001 for both) than in a healthy reference cohort. In adults, in unadjusted analyses, both earlier age of FRDA symptom onset (=0.09, p < 0.05) and longer guanine-adenine-adenine repeat length (shorter of the 2 GAA repeats, β = −0.12, p < 0.01) were associated with shorter stature. Both adults and children with higher mFARS scores and/or who were nonambulatory were less likely to have height and weight measurements recorded at clinical visits.DiscussionFRDA affects both weight gain and linear growth. These insights will inform assessments of affected individuals in both research and clinical settings.