VRI Photometry of M 100: Two Ways to Measure Color Gradients of a Late Hubble Type Galaxy

Yurii Pidopryhora

2002 June 3



Abstract

An Sc-type galaxy M 100 (NGC 4321) was observed in V, R and I broad bands to the limiting surface brightness of about 23 mag/arcsec2 using the Great Ohio 0.25 m Telescope (GOT) with ST-8 CCD camera and applying subsequent image processing with IRAF software. The photometric measurements of the target were made by averaging azimuthally both inside circular apertures and on elliptical isophotes. The surface brightness profile of the galaxy in all three bands and V-R, V-I and R-I color indices as a function of aperture radius/semimajor axis were measured in each case. All three color indices, averaged inside circular apertures, clearly show linear dependence on the aperture logarithm in mid-galactic region, similar to what was recently noticed for a late Hubble type galaxies in UBV bands. Color gradient measurements were made both using the circular apertures and elliptical isophotes.

1. Introduction

   Like total magnitude, radius and color indices, color gradients are important integral photometric parameters of galaxies. They are becoming even more important with the development of CCD photometry, which permits differential evaluation of color along an extended source and thus gives an excellent opportunity to study the radial color distribution in the disk and bulge components. Color gradients are extensively used in recent statistical studies of spiral galaxies (Marquez & Moles 1996 and 1999, Marquez et al. 1999, Gadotti & dos Anjos 2001, Prugniel & Heraudeau 1998 and others) and there is a hope that study of color gradient value distribution in addition to other photometric parameters may help in determining how the photometric properties of galaxies are connected to their age, metallicity, morphological type and environment. Thus study of color gradients could provide clues to better understand the evolution of spiral galaxies (Bell & Bower 2000). Color gradient of a galaxy is defined as (Gadotti & dos Anjos 2001, Prugniel & Heraudeau 1998):
G = d(X-Y)/d(log A).

where X-Y represents the color index in magnitudes correspondent to an aperture A in units of 0'.1 = 6 arcsec. In most cases the "integral" color indices, averaged inside each circular aperture are used for gradient calculation. This has become a convention because this is the only way how color indices could be calculated in photoelectric aperture photometry and photoelectric data are still extensively used in many studies. However this definition could be extended also for "differential" color indices, e. g. measured on a set of isophotes. In this study we will use elliptical isophotes, measuring surface brightness difference X-Y for an isophote as a function of its semimajor axis A and calculating the gradient using the same formula. Recent studies (Gadotti & dos Anjos 2001) of hundreds of late Hubble type spiral galaxies show that B-V and U-B color indices are close to linear functions of the logarithm of aperture (see Fig. 1) in the disk of galaxy and thus the correspondent color gradients are constants. This discovery makes them an important single-number integral photometric parameter, very useful in statistical studies - similar to total magnitude, mass etc. However it is yet unknown if this feature is a characteristic only of blue and UV observational bands or is a universal color property of galaxies. This is why a color gradient study of late Hubble class spirals in other parts of the spectrum is important.
Figure 1. Examples of color gradients B-V (squares) and U-B (circles) for NGC 1425. The color indices in magnitudes are plotted against the decimal logarithm of the aperture in units of 0'.1. Figure is reproduced from Gadotti & dos Anjos 2001.

   M100 Sc-type spiral galaxy (Fig. 2) (RA 12 22 55 Dec +15 49 19.5) was chosen for the project not only because it's very well studied, bright (visual magnitude 9.3) and large (about 7 x 6 arcmin) and thus fairly suitable for a photometry with the equipment available. It's also seen face on and thus the internal reddening in it could be neglected (cf. Gadotti & dos Anjos 2001). Galactic reddening is irrelevant in this case, not affecting the gradient evaluation. Also for a face-on galaxy the use of simple circular apertures is easier justifiable and the maximum possible photometric area is available.
Figure 2. Approx. 8'x8' sky subtracted color composite image of M100 made by combining V, R and I images obtained in this study. 05/15/2002, 0.25 m GOT with ST-8 CCD, effective exposure (total from all images used) 50 min.

The field of imaging (Fig. 3) was chosen based on two reasons: a) so that a bright guiding star GSC0144502528 (RA 12 22 40.48, Dec +15 40 13.7) of 9.49 V magnitude was available to the south of M 100 to ensure stable autoguiding; b) so that a relatively clear region of the sky to the east could be used for the sky brightness estimation.
Figure 3. Approx. 18'x12' (the ST-8's field of view) sky subtracted color composite image of the field of observation (made the same way as Fig. 2). NGC 4322 galaxy could be seen below the M 100.

All three broadband filters available were used to get three different color index dependencies for analysis. 3 x 300 s exposures in V, 3 x 300 s in R and 4 x 300 s in I were chosen based on calculation by IRAF ccdtime calculator to get comparable signal to noise ratio in all three bands.

  

2. Observations

   M 100 and 6 standard stars (4 secondary Landolt standards, 2 of which were observed at two different altitudes) were observed using the 0.25 meter Great Ohio Telescope with ST-8 CCD camera (operating at -18 deg. C) on 2002 May 15 UT in V, R and I. Conditions were close to photometric at the beginning of the night when the primary target and two first standards were observed, but abruptly changed during the second half of the night so 4 other standards were observed through a cirrus of changing degree of thickness. 3 x 300 s in V, 3 x 300 s in R and 4 x 300 s in I exposures of M 100 were made as planned. Standards were taken with single 30 s exposures in each filter. At the beginning of the night 7 zero and 7 dark exposures (4 x 30 s, 3 x 300 s) were made. Observations were started too late to get the evening flat-fields, so all 15 flats were taken in the morning.

3. Reductions

   The basic reductions were done using IRAF ccdred package. The seven zero frames were combined and used to explicitly zero-correct the flat-fields and darks; the flats were then dark-corrected using the combined dark frame. Then four combined darks of 30 s exposure were used to dark-correct standard star frames and three combined darks of 300 s exposure were used to dark-correct the primary target frames. Flats were carefully examined but only the first one was found to be faulty because of a strange white spot. Other 14 showed no difference in quality although eight of them had very short exposures of 3 and 1 s. Finally all 14 good flats were combined in each filter and used to flat-field object frames. Then the cosmic rays were removed from all the primary target frames using the xzap task of IRAF. In order not to damage the data, very soft parameters (number of sky sigma for zapping threshold equal to 7 and zapping box size 8) with careful visual evaluation of results were used. Then the sky was subtracted from the galaxy images. The value of the sky to be subtracted was estimated by using imstat task over visually empty regions of about 15 000 - 30 000 pixels and taking the average of the mean values returned by the task. This procedure also revealed that the flat-fielding of the image was a success leaving no discernable residue bias. For different frames though the measured sky values proved to be rather different, especially in I (Fig. 4).
Figure 4. Sky levels as a function of time in different filters.

After subtracting the sky, primary target images in each filter were registered and co-added and the composite image in I was also multiplied by the factor of 0.75 to compensate for an additional frame. So finally for each band one composite image with effective exposure 900 s was obtained. These images were used for the photometric measurements. Standard star photometry was done by the tasks of IRAF digiphot package following instructions given in "A User's Guide to Stellar CCD Photometry with IRAF" (Massey & Davis 1992). Unfortunately the quality of standard star frames was found to be very low, approximately one third of images were smeared, others were distinctively elongated and in one case there was even a strange double image of a standard star. FWHM of star PSFs were measured to be in the range from 5.3 to 12.2 (pixels), but in most cases close to 8 or 9. That is why huge apertures and sky annuli of 40-60 pixels were used to measure the flux, much increasing the risk of hitting a PSF wing of another nearby star or spoiling the measurement because of bad pixels. Nevertheless instrumental magnitudes were successfully measured for all but two frames. When attempting to solve for the photometric transformation equations, reasonable errors were found only by fixing not only nonlinear, but also linear color terms to be zero constants and, in case of I, also by artificially removing two out of five data points. As we were using an average airmass value for each of three composite frames, the photometric transformation was simplified to just subtracting a constant: 6.58+/-0.61 in V, 6.25+/-0.45 in R and 6.29+/-0.33 in I.

4. Results

   Figures 5 through 7 present the original photometric images of M 100 in all three bands with corresponding contour flux plots.
Figure 5. Approx. 8' x 8' sky subtracted image of M 100 in V (GOT with ST-8, effective exposure 900 s) with a contour plot built by IRAF contour task. FWHM of the PSF was measured to be approximately 4.5 arcsec.


Figure 6. The same in R. FWHM PSF = 4.9 arcsec.


Figure 7. The same in I. FWHM PSF = 5.5 arcsec.

The images were analyzed in two ways: a) integrating the flux inside a set of circular apertures and b) covering the surface of the galaxy with elliptical isophotes and averaging the surface brightness on each isophote.

I. Circular aperture photometry

   The circular aperture photometry was done using phot task of IRAF, which has an advantage of negligible centering errors. We have applied a set of circular apertures centered on the photometric maximum of the galaxy. Then the flux F inside each aperture was evaluated, determining the instrumental magnitude m = m0 - log(F/F0), where m0 is a "zero" reference magnitude corresponding to a "zero" reference flux F0. Photometry of standards and of the primary target must be done with the same m0 and F0 for the transformation equations to be of use. In our case the values were left at IRAF defaults 25 and 1 count per second correspondingly (i. e. for 900 s exposure zero flux is 900 counts). Because we are working with sky subtracted images, sky fitting algorithm of phot was fixed at const=0 with the standard deviation measured by imstat task. The step of increasing aperture radius was chosen to be 5 arcsec with the maximum radius determined by the phot task based on the noise level. Finally, the instrumental magnitudes were corrected with the photometric constants to obtain real magnitudes. The results of these measurements are presented in Figures 8 through 10. They are compared to the published aperture photometric points (18", 24", 36" and 60" aperture measurements in I are from Boroson et. al. 1983, 261.9" aperture measurements in V, R and I are from de Vaucouleurs & Longo 1988). The curves were extrapolated with a power-law fit and asymptotes were drawn determining the total magnitude of M 100 in each band: V = 9.14+/-0.61 consistent with published (by de Vaucouleurs et al. 1991) 9.35+/-0.08; R = 8.43+/-0.45 consistent with the known aperture measurement (see Fig. 9). Comparison with known photometric points in I has shown that our photometric transformation constant needs to be corrected (see Fig. 10) by subtracting 0.75 with new photometric error 0.20, thus new transformation constant in I is 5.54+/-0.20. Finally total I magnitude is estimated to be 8.55+/-0.20.
Figure 8. Circular aperture photometry of M 100 in V compared to published data.


Figure 9. The same in R.


Figure 10. The same in I.

By subtracting counts in neighboring apertures we can get the flux in the ring between them. This in turn could be used to calculate the average surface brightness of that ring. The brightness profiles obtained this way are shown in figures 11 through 13.
Figure 11. Brightness profile of M 100 in V as a function of circular aperture radius.


Figure 12. The same in R.


Figure 13. The same in I.

Next the color indices were calculated, by subtracting the total magnitudes measured inside the same aperture in different filters, in agreement with "photoelectric" definition of the color index. Not to be confused with the local color calculated by subtracting surface brightness in different bands, let us call this one "integral" color index. These color index measurement vs. the aperture radius are presented in figures 14 through 16. Note that in this case error of magnitude measurement is determined not by the photometric transformation error but by the sum of statistical instrumental magnitude errors in each filter.
Figure 14. V-I "integral" color index of M 100 as a function of circular aperture radius. No remarkable regions can be seen.


Figure 15. The same for V-R.


Figure 16. The same for R-I.

Though showing the actual color change across the galaxy and already interesting in this way, the graphs above show no remarkable features. Let us now redraw them vs. the logarithm of the aperture (we measure aperture in units of 0'.1 to be consistent with other studies).
Figure 17. V-I "integral" color index of M 100 as a function of logarithm of circular aperture radius. Regions of constant color gradient are clearly visible.


Figure 18. The same for V-R.


Figure 19. The same for R-I.

Just by looking at the last three graphs it is easy to see the linear regions. We may now confirm their existence in VRI bands at least for one late Hubble type galaxy. The linear fits were done with correlation coefficients R2 equal to 0.9932, 0.9843 and 0.9898 correspondingly. The color gradients were found to be    GV-I=-0.1012+/-0.0027, GV-R= -0.0523+/-0.0025 and GR-I=-0.0620+/-0.0017.

II. Elliptic isophote photometry

   Compared to photoelectric observations using CCD provides a unique opportunity to do differential photometry. In our case we used IRAF ellipse task to build a set of elliptical isophotes over the galaxy and calculated the average flux on each isophote. Following Beckman et al. 1996 we have chosen the set of ellipses with fixed ellipticity 0.37. The position angle was first fitted by the ellipse task for the central region of the galaxy and then fixed to constant (-55 degrees) for actual photometric measurements. The orientation of the isophotes is shown in Fig. 20:
Figure 20. Elliptic isophote orientation (isophotes shown with step 10 arcsec. in semimajor axis length).

Differently from the picture though, for the photometric measurements we totally covered the galaxy (i. e. using step 1 pixel) starting from the center. For the center of galaxy we used the coordinates provided by phot during circular aperture photometry. Then all the calculations were basically the same as in the case of rings in between the circular apertures: average flux for each isophote was converted into the corresponding instrumental surface brightness, which was then corrected to get real surface brightness. The standard deviation of average flux was used to estimate the statistical error. The statistical error found is much larger in this case than in the case of circular apertures because of much smaller number of the data points used. The resulting brightness profiles are shown in figures 21 through 23. The foreground stars that were not removed produce undesirable profile variations (if we carefully look at the circular aperture profiles we can see the same "bumps" there).
Figure 21. Brightness profile of M 100 in V, calculated by averaging on elliptical isophotes.


Figure 22. The same in R.


Figure 23. The same in I.

However, the photometric data points obtained this way would not be independent of each other because neighboring isophotes use the same pixels for flux calculation. That is why in the next step we reduced the number of data points in half by averaging them in pairs. By using this trick we also reduced the statistical error. Then we calculated color indices for each "reduced" isophote by subtracting the correspondent values of surface brightness from each other. Note that the color index calculated in this way (i. e. on an isophote) is significantly different from the one calculated in the previous section. We are going to call this one "differential" color index to avoid confusion. Next three figures show "differential" color indices vs. the decimal logarithm of isophote's semimajor axis length.
Figure 24. V-I "differential" color index of M 100 calculated on elliptical isophotes in logarithmic scale. A deep feature at logA=1.42 corresponds to a contaminating foreground star.


Figure 25. The same for V-R.


Figure 26. The same for R-I.

No clear "linear" regions could be seen on these graphs. However we steel did linear fits for the linear-like zones in between 1 and 1.2 in logA. These regions are also remarkable because they have the smallest error and they roughly correspond to linear regions of circular apertures. The gradients obtained with correspondent correlation coefficients are shown in figures.

5. Discussion

   First of all, by comparing the brightness profiles obtained in this study to those published by Beckman et. al. 1996 (see Fig. 27) we conclude that both photometric measurements were sufficiently good to provide useful data above 23 mag/ arcsec2 or approximately for radii below 200 arcsec. (1.52 in our logarithmic scale).
Figure 27. Surface brightness profiles of M 100 from each of two photometric measurements of this study compared to those from Beckman et al. 1996. For convenience I values are subtracted 2 and R are subtracted 1.

This project has clearly shown that regions of constant "integral" color gradients exist in VRI bands. In all three bands these regions exist approximately in between 1 and 2 arcmin. (corresponding to 1 to 1.3 in our logarithmic scale). More extended linear region in R-I may be just a coincidence, a slight but definite curving could be seen for apertures less than 1' (Fig. 19). Gadotti & dos Anjos 2001 speculate that this linearity is a disk feature and by subtracting modeled bulge colors they managed to show linear behavior even for very small apertures. By looking into image we see that scale of 1' to 2' corresponds to inner disk region, probably just outside the bulge. So we may conclude that the linearity is really a property of inner disk. The fact that the linear regions are observed in late Hubble type galaxies (i. e. those having small bulges) also confirms that. Obviously the question of the nature of the linear color region requires detailed theoretical investigation and many more observations. Regarding a use of color gradients in statistical studies another question that requires additional development is what bands are better for such studies? Of three indices measured in this study only two are independent and just by looking at three colors together (Fig. 28 - "integral" part) it seems that V-I is the best in the current study because it has the largest of all three curvature of non-linear parts and thus the linear region could be observed and measured much more clearly.
Figure 28. "Integral" color index profiles of M 100 compared to the "differential" ones.

Another issue that is raised by figure 28 is a relation between "integral" and "differential" colors. Though their connection is obvious both from theoretical considerations and comparing observational data, the exact relationship, especially in current case of circular vs. elliptic symmetry needs special treatment. In particular, it is not clear if "almost linear" region of "differential" colors is directly related to linear region of "integral" colors. And if they are related, could a model be built translating the color gradient calculated in "differential" colors into the one for "integral" colors? This would have made the "linear" color gradient value really universal characteristic of a galaxy.

6. Acknowledgements

First of all, I want to thank class instructor Thomas Statler for taking a great responsibility of creating and teaching this class, exceptionally thorough preparation of course materials and maintenance of class website, and, of course, his very helpful attitude to me and other students of the class and lots of things he has done well beyond usual professor's duties. I am very grateful to my co-observers David and Laura Rafferty and Russel Ryan. Without their cooperation this project would not be fulfilled. I also thank the TAC committee for their helpful comments on my proposal and George Eborts for letting us use his premises for observations. Special and very warm thanks go to my wife Elena who endured my almost total absence in the real world during the time I was working on this project and who was helping me in all ways possible. And yet other special thanks go to my scientific advisor Daniel Phillips for his understanding and providing time needed to finish this project.

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