Table 4
Differences between the data of the velocity structure of the BHB stars at the apocentre and spur feature of the trailing arm of the Sagittarius stream to which the data of the final (present-day) snapshots of the N-body simulations of the formation and evolution of the Sagittarius stream in the presence or absence of the LMC by Vasiliev et al. (2021) were scaled along heliocentric distance to match it.
| Label | Dist. | LOS vel. | LMC | f | χ2 |
|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | (6) |
| A | D11 | Heliocen. | No | ![]() |
![]() |
| B | B22 | Heliocen. | No | ![]() |
![]() |
| C | D11 | Corrected | No | ![]() |
![]() |
| D | B22 | Corrected | No | ![]() |
![]() |
| E | D11 | Heliocen. | Yes | ![]() |
![]() |
| F | B22 | Heliocen. | Yes | ![]() |
![]() |
| G | D11 | Corrected | Yes | ![]() |
![]() |
| H | B22 | Corrected | Yes | ![]() |
![]() |
Notes. The second column is the abbreviation for the equation that we used to calculate the absolute magnitude in Sloan gSDSS of the sample BHB stars, and as a result the distance modulus and heliocentric distance of the stars. D11 refers to Deason et al. (2011); B22 refers to Barbosa et al. (2022). Column (3) lists LOS velocity of each BHB star in the set that we study we consider for the rescaling: ‘Heliocen.’ refers to the heliocentric LOS velocity without a shift to correct for systematics as estimated from the velocity standard stars (see Fig. 3 or Fig. C.1 and left panel of Fig. 6); ‘Corrected’ refers to the corrected (heliocentric) LOS velocities (see right panel of Fig. 6). Column (4) indicates whether this is the data from the N-body simulation by Vasiliev et al. (2021) with (‘Yes’) or without (‘No’) perturbations by the LMC. Column (6) gives the approximate χ2 of the analysis as calculated from Equation (2) (more precisely the natural logarithm of the assumed Gaussian likelihood).
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