Exercise explanation: Integral Field Spectrographs produce data cubes with 2 spatial dimensions, and one spectral one

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Exercise explanation: Integral Field Spectrographs produce data cubes with 2 spatial dimensions, and one spectral one. From these one can then determine the radial velocity at every position by looking at the position of absorption or emission lines. This produces maps with a large S/N ratio in the middle of the galaxy, and very low S/N in the outer parts. In order to get optimal information, often adaptive binning methods are used, such as Voronoi binning, resulting in irregularly spaced data with a high density of points in the middle and few points in the outer parts. The aim of this exercise is to determine rotation curves and from these data, and other characteristics of these velocity fields, with the aim of obtaining more information on the mass distribution. Dataset: The dataset to use is the set of maps describing the average radial velocity of the stars in a sample of nearby galaxies, obtained at the 3.5m Calar Alto Telescope in Spain. Details about the data are described in Falcon-Barroso et al. 2017, A&A 597, 48. Maps of many galaxies are shown. The data are available at https://califa.caha.es/?q=content/science-dataproducts and ftp://ftp.caha.es/CALIFA/dataproducts/Stellar_Kinematics_V1200 They are in the form of FITS-tables. You can read these with the programme topcat, available on the system. Exercise: *In Process* | | V 1. Model velocity fields. In Teuben (2002, https://ui.adsabs.harvard.edu/abs/2002ASPC..275..217T/abstract), it is explained how a velocity field of a galaxy can be modelled. A velocity field is generally given by the equation: V(r,θ)= Vsys+Vrot(r)cosθ sini Here Vrot(r) is the rotation curve of the galaxy, i is the inclination, and r and θ are polar coordinates centered on the galaxy. V sys is the systemic velocity of the galaxy. Start making a few model velocity fields, choosing realistic values for the parameters. *NEEDS TO BE DONE* | | V 2. Fit velocity fields. Select a large galaxy, so that you have enough data points to make good fits. Download the fits-file with the irregularly spaced velocities (as well as other parameters). Here x and y are cartesian coordinates centered on the galaxy center. Now on ellipses, with ellipticities (defined as 1 – b/a, (= cos i), where b and a are the minor and major axis) and major axis position angles θ0 given in the paper of Falcon-Barroso, the rotation velocity at a distance r from the galaxy center can be found by fitting the function V(r,θ−θ0) = Vsys+Vrot cos(θ−θ0) , giving the rotation velocity at a distance r. Since you have irregularly spaced data, you should think about how many ellipses you want to fit, and which data points should be used for each ellipse. This gives you the rotation curve, the rotation velocity as a function of distance from the galaxy center. *Will do it later* | | V 3. Sample. Fit rotation curves a sample of 10-20 galaxies; start with galaxies with many datapoints, then do some with only a few datapoints. Investigate the differences between the rotation curves of the galaxies, and estimate the errors in the results obtained, for example by removing datapoints and studying how the fit changes. When doing the fit, always pay attention to the residual maps, as a check. Plot the relation between galaxy luminosity (as given in Falcon-Barros et al. ) and maximum rotation velocity, corrected for inclination, i.e., the Tully-Fisher relation.