Exponential Profile Fitting on the Unusual SAB(s)bc galaxy M106 Alex K Chen Astronomy Department, University of Washington

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1 Exponential Profile Fitting on the Unusual SAB(s)bc galaxy M106 Alex K Chen Astronomy Department, University of Washington Abstract M106 is a late type spiral galaxy with an inclination of 64 degrees. In this paper, we will discuss how the surface brightness profile of the galaxy varies as a function of semimajor axis. We used an Arcsat telescope to take pictures of M106 through three different filters and then used IRAF to reduce the images. We then used the task ELLIPSE to take measurements of both the surface brightness profile and the length of the semimajor axis of the galaxy so that we could see how the surface brightness profile fell as a function of semimajor axis. We then used MATLAB to create an exponential function whose coefficients determined the galaxy s falloff with respect to time. Our results showed that our galaxy s brightness fell off with a Sersic parameter of 3.05, which is closer to the Sersic parameter for ellipticals than the Sersic parameter for spirals. Future studies should examine whether the inclination has an effect to the fitting, as well as on new functional forms that might better approximate the falloff of surface brightness in a more varied distribution of galaxies. Introduction M106 is a Seyfert spiral galaxy in the constellation Canes Venatici, at a distance of 7.3 Mpc from Earth. Other specifications are listed below. Right Ascension 12h, 18m, 57.5s Declination +47:18:14 Type SAB(s)bc Inclination 64 degrees Apparent magnitude (Visual) 9.1 Table 1: Basic Information about our object. Much of our data comes from [4]. We collected flux counts from the object in 3 different filters. As in the case with other spiral galaxies, we expect the intensity of the disk component to fall off as according to the exponential profile I( r) =I(0)exp[-R/R e ], and we expect the intensity of the bulge component to fall off as according to devaucouleur s profile I(r ) = I e exp(-7.67*((r/r e ) 1/4-1)), where R e is the effective radius and I e is the intensity at such radius. These profiles are merely special cases of the Sersic profile. I(r ) = I e exp(- 7.67*((R/R e ) 1/n -1)), which has a key parameter of n that distinguishes between elliptical galaxies and spiral galaxies. Here, the exponential profile would have a parameter of n=1, and the devaucoleur s profile would have a parameter of n=4. In this paper, we will first describe how we obtained our image and the conditions that affected the image that we retrieved. We will then go into how we obtained the Sersic parameter of our galaxy. Finally, we will discuss the potential flaws of our research, and the research gaps that may give us a more informed view of why we obtained the Sersic parameter we had. Description of Observations We remotely controlled an 2.5-meter Arcsat telescope in New Mexico on 9:23 PM (MST) on May 24 th, The weather conditions were very clear and the object was almost overhead, as the hour angle

2 was only +0h 10 min and the airmass was The CCD temperature was -30 degrees Celsius. We collected 3 60-second observations of the target one for each filter (G, U, and I). These correspond to the green, ultraviolet, and infrared SDSS filters. We also took 60 minute flat frames, 60 second dark frames, and 60 second frames of our object. Telescope Brand ARCSAT Aperture(cm) 250 Focal ratio f/5 Focal length(mm) 12,500 CCD Camera brand Alta U47 CCD Dimensions 13.3 x 13.3 mm Pixel Size(microns) 13 x 13 Plate Scale(arcsec/pixel) 2.1 Field of View(arcseconds) x Dark Current 0.2 e-/pixel/sec Read Noise 9 e- RMS Filter Types SDSS u, g, I filters Table 2: Description of our CCD and telescope. Much of our data is found in references [1] and [3]. Our signal to noise ratio could be found through the formula S/N = N*/Sqrt[N*+n pix *(N s +N D +N R 2 )] (Howell 73). Here, we use 1 pixel, and a representative value of N* was 1800 for regions around the center of the galaxy. A good value for N D is 0.2*60 = 12. N R = 9, and N S = 980. So plugging our values into the formula, we get a S/N of around for regions around the center of the galaxy. For the spiral arms, however, with values of N* around 1100, we get a S/N of Reduction We calibrated the data using the program IRAF. We averaged the 60-second darks by running imcombine on all of our dark frames. Then we used imarith to subtract the averaged dark from each flat. We used imcombine to average the dark-subtracted flats. We then used imarith to divide the darksubtracted flats by the mode of the dark subtracted flats to get the normalized flats. We subtracted the 60-second darks from the 3 science images and then divided each of the 3 science images by the new normalized flats. This produced our calibrated science images that we would then use for our analysis. Analysis The inclination of our galaxy was 64 degrees, which is an intermediate inclination that does not easily lend itself to an analysis as easy as edge-on galaxies or face-on galaxies. We then ran the task ellipse to get isophotes of our galaxy. This generated an output file that we could then use with IDL to plot a graph of surface brightness with respect to semimajor axis. We generated isophotes through all three filters, which are displayed below as red ellipses.

3 Figure 1: Our object in the G filter Figure 2: Our object in the U filter

4 Figure 3: Our object in the I filter We concluded that the green filter would be the best filter to use for our analysis, as it shows a clear image of the spiral arms and clearly differentiates the galaxy's spatial structures from each other. So we ran the task stsdas.analysis.isophote.ellipse in order to get the falloff with respect to semimajor axis of the ellipse (corresponding to a rough distance, although this distance is smaller on the semiminor axis than the semimajor axis). For the most part, we used default arguments, although we set the step size to 3, linear scaling to yes, x0 to 255, y0 to 210, and sma0 to 5. The ellipse task generates an output file that contains numerous columns. The columns relevant for our analysis were the semimajor axis length and the total magnitude enclosed by the ellipse. We used MATLAB to extract the columns. There were 60 ellipses, which was why we set the iteration counts to 60. The code was as follows: clear all; load gfilt.txt x = gfilt(:,1); flux = gfilt(:,21); tmag = gfilt(:,23); npix = gfilt(:,25); diffflux = diff(flux); diffarea = diff(npix); diffmag = -diff(tmag); for i=1:1:60 timestep(i) = i; fluxperpixel(i) = diffflux(i)/diffarea(i); magperpixel(i) = diffmag(i)/diffarea(i); mag(i) = 2.5*log10(fluxperpixel(i)/fluxperpixel(1)) + 9.5; end x = gfilt(:,1); x = x(1:i);

5 Magnitude figure(4), plot(x,mag) Since the total flux enclosed by the ellipse included the flux counts enclosed by all smaller ellipses, we had to subtract the flux counts of ellipse n-1 from ellipse n in order to get the additional flux added by the additional ellipse. So we subtracted the flux of ellipse n-1 from ellipse n. This could easily be done through MATLAB s diff(flux) command. We also subtracted the area of ellipse n-1 from the area of ellipse n (which we did through diff(npix)).we then had to convert fluxes into magnitudes, so we used the formula mag(i) = 2.5*log10(fluxperpixel(i)/fluxperpixel(1)), where the magnitude of the first ellipse would be set to 0, and where we would want the magnitude to be a decreasing curve. We also added a constant value of 9.5 to the magnitude of the first ellipse. The magnitude of M106 is 9.1, and although the magnitude of the first ellipse is probably not 9.5, we used 9.5 as an approximation that is more accurate than 0. We then graphed the enclosed magnitude with respect to semimajor axis and tried to see which parameters would best achieve a fit to the Sersic profile with the general form f(x) = a*exp(b*x^d)). While a generalized Sersic profile is of the form I e exp(-7.67*((r/r e ) 1/n -1)), we did not need to include the extra argument of -1 to our fitting, as it gets absorbed in the coefficient of a. We used the MATLAB toolbox Curve Fitting to achieve a fit to the exponential curve. We had to add a constant c to the fit, where constant c is the value that the exponential curve would fall off towards. Otherwise the outputted curve would have a positive value of b and a negative value of d, as the curve a*exp(b/x^d) falls off towards a constant nonzero value, unlike the curve a*exp(b*x^d) with negative b and positive d, which falls off towards Falloff of Magnitude with Semimajor Axis Semimajor Axis Figure 4: Curve fitting with a decreasing exponential function. X-axis is semimajor axis (in pixels), y- axis is magnitude. Our fit is in green, and our raw data in blue. General model: f(x) = a*exp(b*x^d)+11.1 Coefficients (with 95% confidence bounds): a = (-5.65, ) b = (-1.013, ) d = (0.2814, 0.375) Goodness of fit: SSE: R-square: 0.988

6 Adjusted R-square: RMSE: So here, our profile has an exponent of , corresponding to a Sersic parameter of 1/ = This parameter is larger than the Sersic parameter with an exponent of 1 (which would be expected for the disk of the galaxy) but smaller than the Sersic parameter of 4 for elliptical galaxies (which would be expected for elliptical galaxies and the bulges of spirals). Discussion Why does our model fail to predict an exponential falloff profile, which we would predict in a spiral galaxy? Our galaxy is a late-type spiral, which would imply a smaller Sersic parameter than most other spirals. The high inclination of our galaxy may explain why our galaxy s Sersic parameter did not match the parameter we expected. The inclination made the galaxy look somewhat more elliptical than it would look face-on. We also used the task ellipse, which is specifically designed for elliptical galaxies and not spiral galaxies. While people use the task ellipse on spiral galaxies as well as ellipticals, it may create some complications in the analysis, perhaps making the galaxy look more elliptical than it already is. Our semimajor axes and semimajor axes were significantly different from each other, but they should not be too different from each other in a face-on spiral galaxy. This may have caused some stars in a face-on isophote to switch isophotes when viewed from an inclination as high as M106 s. There is a usercreated SPIRAL package that is ported to the IRAF program, although it is not installed on the astronomy computers at the University of Washington. Perhaps there could be different falloff profiles for different filters. We do not believe that this complicates our situation, however. Our observing conditions were nearly optimal and our S/N ratio was decent, so we do not think these would be factors in our discrepancy. Summary Our analysis suggests that the Sersic profile makes our galaxy appear more elliptical than it really is, with a Sersic parameter of Of course, our analysis was very basic, and our results may be an artifact of the ellipse task as applied to spiral galaxies. In short, we believe that there is a lack of literature that explores how inclination affects the Sersic profiles of various galaxies. For our next steps, we suggest that we should measure the Sersic profile parameters for similar galaxies of various inclinations, just so that we can see how inclination affects the Sersic profile of a specific type of galaxy, such as the SAB(bc) galaxy that we observed. We should also carry out this analysis to different filters, especially the radio filter of M106, as M106 has arms in the radio wavelengths that cannot be seen in other wavelengths. Appendix

7 Figure 5: Quantum Efficiency of our CCD as a function of wavelength. We see that the quantum efficiency is near its maximum in the green filter (510 nm). [1] References [1] Apogee Instruments. Alta Series CCD Cameras. Retrieved 9 June [2] Howell, Steve B. Handbook of CCD Astronomy. Cambridge: Cambridge UP, [3] James E. Gunn et al 2006 The Astronomical Journal [4] "NASA/IPAC Extragalactic Database". Results for Messier Retrieved