The exercise

  You are sitting in front of an X-window terminal. You can move from one of the three windows to the others moving the cursor with the mouse and clicking on the left button. UNIX commands can be issued from these windows (but do not lose time playing around!).

1. Move to the directory rband ( cd rband), where the CCD frames taken with the R band filter are stored. Open a MIDAS session typing inmidas. A black display window will appear.

2. Display the files of Table 1 with the command LOAD/IMAGE command (for example, LOAD 691016222) and identify on the screen the galaxies indicated on the finding charts (Fig. 4 and 5), checking the orientation of the CCD. Estimate with the help of the cursor (GET/CURSOR) the ellipticity of the objects. You can optimize the contrast changing the displayed lower and upper limits with the command cut name lower, upper. Display the image typing again LOAD/IMAGE name to see the result.

3. Derive the average surface brightness profiles and curves of growth (expressed in magnitudes) of (at least) 9 of the galaxies signed on the finding chart (and listed in Table 1) with the commands @@ dodel and @@ docog. Give priority to the galaxies marked with a in Table 1.

   After having typed @@ dodel, you will be asked to give a name of a frame, which will then appear on the screen. Try to identify possible morphological properties of the galaxy. Can you see a disk? Can you see spiral arms? Is there a bar?

   Following the instructions, measure first the value of the sky (in counts per pixel) with the cursor in several positions around the galaxy and type the average in. Is the sky background flat? For one frame, quantify the percentage variations of its value across the image and compare this value with the expected shot noise (see Eq. 2 with ). Then measure the position of the center of the galaxy, and finally, delete all of the (foreground) stars or unwanted objects around the galaxy with cursor. The frame will appear on the screen with black spots where deletions were made. Check that all of the unwanted objects have been deleted. If some are still present, delete them with the command @@ domoredel. Now you are ready to run @@ docog. The scale of the telescope+CCD detector system is 0.396 arcsec/pixel. Now you have created a file with extension .cog (for example, 691016222.cog).

4. Quit the MIDAS session typing bye and open a SUPERMONGO session typing sm. Give the command macro read praktikum.macro to read in the plotting programs. Plot the instrumental surface brightness profiles you have derived above as a function of the 1/4 power or of the of the distance from the center with the command plquat file or plexp file, where file is, for example, 691016222. You can obtain hardcopies of the plots by typing device postland, executing the plotting programs once more and giving again device x11.

   Classify the galaxy as elliptical, spiral or S0 with the help of these plots, of the morphological information you collected in the previous step, and by comparing the central surface brightnesses. Use the brightness of the sky in the R band (20.63 mag/arcsec) to get the calibration (see Eq. 13). Determine its flattening (if it is an elliptical) or its inclination angle, from the ellipticity you measured above. Get a first estimate of or h drawing a line on these plots (see Eq. 14 and 15).

5. Plot the measured curves of growth (in magnitudes) with the command plcog file to obtain a linear radial scale, or with pllgcog file to obtain a logarithmic radial scale. Get hardcopies of the logarithmic scale plots. Derive the total magnitudes , the half-luminosity radii and the average surface brightnesses of the galaxies, knowing the sky in the R band (see Eq. 13 and point (4) above). Use both methods described in Section 2.4.

   Compare the values of determined here with those obtained above. For one galaxy determine what would be the change in if your determination of the sky would have been wrong by % (you do not need to derive again the curve of growth).

6. Write the values of into Kpc. If D is the distance of the object in Mpc (240 for A2593, see Sect. 1), one has:

    

   where the numerical factor converts arcsec into radiants. Convert into absolute values using Eq. 6. Convert into solar luminosities, remembering that the R band solar luminosity is . You do not need to convert into erg/s: Eq. 8 gives the ``number of suns'' present in the galaxy.

7. Plot on a cartesian plane against and against . Draw the ``best-fit'' lines to these points and determine the coeffecients a and b of Eq. 22 and c and d for Eq. 23. Estimate the standard deviation (rms) around these relations. How this translate on the precision of the estimate of the distance of the cluster (see Eq. 24)? How can Eq. 23 be used to estimate distance ratios?

8. Move to the directory ~/bband, where the CCD frames taken with the B filter are stored. Derive the total blue magnitude for the objects marked with a in Table 1, repeating what described above. The sky in the B band is 22.17 mag/arcsec. Compute the total magnitude in the B band using the fact that the total magnitude of the sun in the B band is 5.48. Finally, compute the total colour . Discuss the results having in mind the classification of these objects.

9. Investigate the influence of sky subtraction errors on the surface brightness profiles, by producing profiles where the sky value has been modified by %. To do this, open a MIDAS session and give the MIDAS command write/descr file himmel/r/1/1 value. Running again @@ docog). Quit the MIDAS session and enter in SUPERMONGO. Plot the resulting profile with plquat file. Discuss the results in view of galaxy classification.

Answer the following questions when writing your report:

A1

Compute using Eq. 15 and 16.

A2

Compute numerically the half-luminosity radius of an exponential disk as a function of h, then derive and .

A3

Describe the results of the tests on the sky values of point (3).

A4

For each of the 9 galaxies you have analysed, write a short description of its morphology and of the properties of its calibrated luminosity profile and curve of growth. On this basis classify the galaxy. Discuss the colours derived for the 3 objects of Table 1 marked with a .

A5

Produce a table giving galaxy type, ellipticity or inclination angle (see point (4)), in arcsec and Kpc, , , , for the 9 galaxies analyzed, as determined from the analysis of the R frames. Quote the percentage error on that you get by comparing the different methods of points (4) and (5). Quote the variations of expected from point (5).

A6

Produce the plots of point (7) and write the equations of the best-fit lines. Quote the rms around the relations, explain how these relations could be used to estimate the distance of A2593 and what would be the precision.

If you have time and will, answer these questions too:

B1

Derive using Eq. 14 and 16 (the computation is somewhat tedious).

B2

Describe the results of point (9).