(1) Laboratoire d’Astrophysique de Marseille [F] – (2) Université de Montréal [Ca] - (3) Observatoire de Paris [F]

The Pattern Speeds of M100 (NGC 4321) from its HThe Pattern Speeds of M100 (NGC 4321) from its H2D Velocity Field Using the Tremaine-Weinberg Method.2D Velocity Field Using the Tremaine-Weinberg Method.

The Treimaine-Weinberg MethodThe Treimaine-Weinberg Method

ObservationObservations s

ResultsResults

AbstractAbstract

A direct and model independent method, not relying on any particular theory of density waves is due to Tremaine & Weinberg (1984, hereafter TW). The pattern speed P is determined from two observationally accessible quantities: the luminosity-weighted mean velocities and the luminosity-weighted mean densities throughout the disk of the galaxy. In the plane of the sky, <X> is the luminosity-weighted mean X-position integrated along a strip parallel to the X-axis

at Y coordinate and VLOS(X,Y) is the luminosity-weighted mean velocity along the X-axis at Y coordinate. Thus, P sin i =<VLOS>/<X>. The underlying assumption is therefore that the intensity is proportional to density. The TW method also requires a tracer population that satisfies the continuity equation (no significant creation or destruction of matter over an orbit).

O. Hernandez1,2, P. Amram1, C. Carignan2, L. Chemin2,3, O. Daigle2, H. Wozniak1

The Tremaine-Weinberg method was used to measure the bar, spiral and inner ring pattern speeds of the Virgo Cluster Galaxy M100 (NGC 4321) using its H velocity field, H monochromatic, 2MASS K-band and SPITZER 3.6 m images.

New observations of M100 were carried out at the Mont-Mégantic Observatory 1.6m telescope in February 2003 in the frame of a new large observational program of barred galaxies (Hernandez et al 2005). The Fabry-Perot instrument FaNTOmM equipped with an Image Photon Counting System (IPCS, Gach et al 2002) was used. Reduction of the data cubes were performed using a new Fabry-Perot package under the IDL environment. Adaptive spatial smoothing was done (Daigle et al, 2005). The Velocity Field and

the monochromatic image are presented Fig. 1 and Fig. 2.

The intensity-weighted line-of-sight (LOS) velocity VLOS,Y is plotted in

Fig. 6 & 7 , vs. the intensity-weighted position coordinate, XY.

The H velocity field Fig. 1 has been used to measure VLOS,Y. Both

H monochromatic image (Fig. 3), SPITZER 3.6 m Fig. 4 and

2MASS K-band image Fig. 5 have been used to measure XY. The degeneracy introduced during the calculation of XY (integration

along the X-axis) may be followed in using the bottom plots of Fig. 8 & 9 which give the position along the Y-axis of the gaussian used to fit the X-axis. For instance, the red dots in the bottom panels correspond to YX located at a distance ranging for 75” up to

100” from the major axis. Furthermore, on the upper plot of Fig. 6, it can be seen that the red dots correspond to the northern spiral arm of the galaxy and not to the bar. The (<X>,<Y>) plot produced

from the H image Fig. 2 clearly displays the inner ring of M100 (in green), the two edges of the bar (in blue and light green) and the spiral structure. At the opposite, neither the 2MASS K-band image

Fig. 5 nor the 3.6 m displays the spiral arms but the bar and the internal ring can be seen. In the internal region of the galaxy (between -10 and +10 arcsec) from the center, the slight change in the slope of the plot in the (<X>,<Y>) plot is more obvious in the (<X>,<V>) plot and corresponds to the internal ring. The bar is better seen in the H-band image than in the H image at the contrary of the spiral structure and of the inner ring.

Fig. 6 & 7: Mean line-of-sight velocity along versus the mean position. Fig. 8 & 9: Mean Y-position along versus the mean X-position.

Fig. 6 & 8 correspond to the H-band image + H velocity field

Fig. 7 & 9 correspond to the H image + H velocity field

Fig. 10: The rotation curve and, respectively, from the

top upper one to the bottom one, the (dash), (dash-dot),(continuous ),(dash-dot), (dash) curves.The expected position of the resonances for P =29 km s-1 kpc-1

leads to a Corotation radius at 90 arcsec.

Fig. 1: H Velocity Field

Fig. 7

Fig. 5: 2MASS

K-Band

Fig. 4

SPITZER 3.6 m

Fig. 2: monochromatic image

Fig. 8

Fig. 6

Fig. 9

Fig 3: Sketch of the galaxy showing the bar and a strip parallel to the major axis of the galaxy. The average luminosity-weighted mean X-position <X> is projected along the major and minor axis of the galaxy respectively.