Outer field sample

A selection of data from the literature was used to refine the model and check the validity of our data. These extra velocity samples cover the region of our observations and out to several degrees beyond. Stars from outer regions in particular help constrain the model at larger radii, where our observations have not sampled. A sample of LMC stars in fields around globular clusters in the LMC from Grocholski et al. (2006) provided a sample of disk stars at larger radii, Figure 4.20d. The stars were identified as not belonging to the clusters but to the LMC disk in the background. A handful of stars identified as non- cluster with velocities less than 0 km s−1_{were assumed not to be LMC field stars}

but Galactic foreground objects.

The inner LMC field stars around the cluster NGC 2019 are within a few arcminutes of the rotation centre and have a mean heliocentric velocity of 254 km s−1_{. We expect the circular galaxy rotation to go to zero near the cen-}

tre, the velocity at this point should represent the systemic line of sight radial velocity of the galaxy. The LMC background stars around this cluster confirm the systemic velocity indicated by our sample.

We also included a set of red supergiant stars from Massey and Olsen (2003) which are within a few degrees of the galaxy centre, (Figure 4.20b). A large set of 377 RGB stars with velocities from Cole et al. (2005) are also sampled, (Figure 4.20a). These lie close to the rotation centre in the bar region. There is also a large set of velocities published for planetary nebulae in the bar region, Figure 4.20c, summarised by Reid and Parker (2006). We deal with this sample separately in the next section.

4.3. RESULTS

Figure 4.20: Locations of literature data

(a) Cole et al. (2005)

05:20 05:30 05:40 05:50 -70:00 -68:00 -69:00 05:10 05:00 04:50 -71:00 -67:00

(b) Massey and Olsen (2003)

05:20 05:30 05:40 05:50 -70:00 -68:00 -69:00 05:10 05:00 04:50 -71:00 -67:00

(c) Reid and Parker (2006)

05:20 05:30 05:40 05:50 -70:00 -68:00 -69:00 05:10 05:00 04:50 -71:00 -67:00 (d) Grocholski et al. (2006) 05:20 05:40 06:00 06:20 -68:00 05:00 04:40 -70:00 -72:00 -66:00

Table 4.2: Disk Models

Reference V0km s−1 R0kpc Vsyskm s−1 Prop.Mot.Vtranskm s−1

Luks and Rohlfs (1992)a _{70 1.4 274}

Kim et al. (1998)a _{63 2.4 279 286}

Alves and Nelson (2000) 72 4.0 286

van der Marel et al. (2002) 50 2.8 262 281

Olsen and Massey (2007) 74-107b _{2.1 263-266}b ₄₉₀

Piatek et al. (2008) 120 4.0 287 475

Olsen et al. (2011) 87 2.4 263 475

This study observed 57 1.0 254 475

This study observed & literature 85 1.9 257 475

This study final MCMC estimate 79 1.9 255 475

a_{HI gas studies;}b_{Various tracers, Carbon stars, red super-giant (RSG) stars} and HI gas.

We find that the additional data changess the model fit slightly. The high density of the 377 stars from Cole et al. (2005) adjacent the rotation centre dominate the statistics of the central 0.5 kpc and raise the systemic velocity from 254 km s−1_{to 257 km s}−1_{. The data in Figure 4.21 has unequal bin ranges}

to keep the number of stars in each radial category similar. We also explore the consequence of varying disk inclination angle in Figure 4.21. Using the model of Subramanian and Subramaniam (2010), which has a warped disk with less inclination at the centre, we see the basic rotation curve is preserved. The more face on central disk projects less disk velocity into the radial line of sight, so more disk velocity is required to account for the observed line of sight velocities. This increases the steepness of the central rotation curve slope. This demonstrates a simple rotation model is robust to variations in inclination angle.

0 1 2 3 4 5 6 0 20 40 60 80 Disk radius kpc Disk v elocity km s − 1

(a) The model fit to our sample plus lit- erature data (except PNe ), error bars show the standard error in the mean of the equal number bins.

0 1 2 3 4 5 6 0 20 40 60 80 100 Disk radius kpc Disk v elocity km s − 1

(b) Warped disk model of Subramanian and Subramaniam (2010) has a more face on central region and less rotation veloc- ity projected into line of sight. Higher ro- tation velocities are required to account for observations than in flat disk model (a) (dotted line).

Figure 4.21

The extra data updates the model parameters based on our sample alone. We originally fitted this model to our observations,V0=57 km s−1,R0= 1.0 kpc

andν= 2.5. The new model with extra data at larger radii where the rotation curve attains a steady maximum isV0= 85 km s−1, R0= 1.9 kpc and ν= 1.3.

The new model rises slightly less steeply to a higher maximum rotation velocity. This brings the maximum velocity closer to the HI velocity and agrees with the rotation model of Olsen et al. (2011).

4.3. RESULTS

Planetary Nebula

We also considered a set of PNe which were identified and measured spectro- scopically by Reid and Parker (2006). While the spectroscopic velocities are not of the central object, the higher excitation lines measured are thought to come from close to the central ionising object, within 10 km s−1_{rather than the}

outer regions which could be up to 50 km s−1 _{away. We find that this data set}

is systematically offset from our data in the same region by about 10 km s−1_.

The dispersion of the PNe velocities is 26 km s−1_{, which is exactly the same as}

our data plus the outer field sample dispersion which is also 26 km s−1_{. Our}

observations alone, which are in the inner bar region, have a standard deviation of 24 km s−1_.

The PNe velocities, with a median heliocentric velocity 267 km s−1, are sys- tematically higher than our data. The Zhao data with median 273 km s−1 is similarly higher. Both sets of observations were made on the2df spectrometer which may indicate a systematic difference with the AAOmega spectrometer. The2df spectrometer was located at the prime focus of the Anglo-Australian 4 metre and moved with the telescope. Mechanical stress on the spectrometer was a known problem at low elevations. We hypothesise that at the typical low ele- vations required when observing the LMC at declination−71◦ the2df spectra have been shifted systematically. This is not a problem for the extra-galactic redshifts which the instrument was designed to observe, but a systematic differ- ence has been noted by us in two data sets.

Apart from the offset, the PNe show an even more obvious disk rotation profile than our observations, Figure 4.22. Reid and Parker (2006) also find a rotation curve from their planetary nebula data in the centre that approximates a solid body linear profile. We transform the PNe velocity data, to the disk plane. A straight linear model of a rotation curve fit to the disk velocities gives a slope of 35 km s−1kpc−1with an intercept of−14 km s−1at the rotation centre, which represents the systematic offset of the order of 10 km s−1. It is once again the lack of data in the very inner regions which causes the PNe data to fail to show the steep inner rotation curve our data samples. The PNe sample has only 18 points inside 0.5 kpc which have a mean heliocentric velocity of 267 km s−1_{. Again the importance of sampling the central region of the LMC}

is demonstrated.