Data analysis: CMD and SED

Transcription

1 Chapter 5 Data analysis: CMD and SED 5.1 Astrometric reduction Astrometry should be carried out to the objects first to derive celestial coordinates for each star. This is necessary to cross-identify between different bands and match the magnitudes for each star. Astrometry was carried out using the tasks ccmap and cctrans in Iraf. The two tasks computes the plate solution and convert (x,y) coordinates in the image into (RA,Dec) in J epoch. The procedure was as follows: 1. Input (x,y) and (RA,Dec) coordinates of several stars in each image to be used to derive coordinate transformation. A number of four to seven stars were used for this purpose. The (RA,Dec) coordinates for the stars were acquired from the ALADIN database (Bonnarel et al., 2000). 2. Calculate transformation solution (ccmap) and apply to the (x,y) coordinates of other stars (cctrans). 3. Match each star in photometric catalog of each image (tables with RA,Dec,Mag columns) using tjoin task in Iraf. The result of the astrometry reduction is presented in Figure 5.1. The result is accurate to less than 1 arcseconds. This enabled a unique identification of each cluster star among tens to hundreds others. 58

2 CHAPTER 5. DATA ANALYSIS: CMD AND SED 59 Figure 5.1: Coordinates for Ru 8 (left) and M13 (right) stars. 5.2 CMD fitting CMD of M13 and Ru 8 After matching photometric catalog for each band, it was found that for band #1, only very few (less than five) stars has been successfully detected and measured in both clusters. This is because this bluest band has a very low throughput (less than 5%), while most of the object are supposed to be red stars (red giants in the case of M13 and reddened stars in Ru 8 due to the location in the Galactic plane). Thus, we may say that the photometry is effectively only in 13 colors. In the final catalog, almost no stars have measurements in all fourteen bands. This is because of the effect on star brightness, color, and also position in the image. The brightest stars which should be detected immediately in every band may lose several bands because of the different field of view in each band. In total, there are 336 stars in the final M13 catalog while only 24 in Ru 8 catalog. Again, most stars do not have complete measurements in all 14 bands.

3 CHAPTER 5. DATA ANALYSIS: CMD AND SED 60 Figure 5.2: Sample CMD for M13 (left) and Ru 8 (right). In Figure 5.2 we can immediately see that the color-magnitude diagram (CMD) for M13 and Ru 8 are different. The star magnitudes in the CMDs were calibrated using zero-point shift. CMD for M13 shows a typical globular cluster CMD: a well-defined red giant branch and blue horizontal branch. The observation apparently did not went deep enough to cover the turnoff point and lower main sequence (limiting magnitude 16.5mag). In the other hand, the CMD for Ru 8 is so sparsely populated. The main sequence is very vague, although shows a hint of turn-off point at around (0.1,12). The brightest star in Ru 8 field is TYC (B = 10.73, V = 10.4; SIMBAD database). The DMC magnitude for this star in band #4 (5460 Å) is Since M13 was taken at different fields (north, east, south, west), Figure 5.3 is presented to investigate any sistematic trend related to any specific field. It seems that the CMD scatter for all four fields are consistent.

4 CHAPTER 5. DATA ANALYSIS: CMD AND SED 61 Figure 5.3: CMD for M13 from different fileds Constructing isochrones in DMC bands Before we determine the astrophysical parameters of the objects by employing isochrone fitting technique, it is necessary to have a set of isochrones defined in the DMC bands. However, since DMC is a unique instrument no isochrone defined in DMC system available yet. In the observation plane, isochrones are usually defined in well-known photometric systems e.g. Johnson-Morgan- Cousins UBVRI, Strömgren uvby. Therefore, some particular technique should be employed to generate isochrones in DMC bands. The comparison between DMC and UBVRI (Bessell, 1990) passband is shown in Figure 5.4. Since the DMC system does not cover the U band region, this band was omitted. The DMC analog for B is band #1, V #4, R #6, I #11.

5 CHAPTER 5. DATA ANALYSIS: CMD AND SED 62 Figure 5.4: Comparison between DMC and UBVRI system. The general strategy to transform UBVRI isochrones into DMC system was to compute synthetic magnitudes in both photometric system for a sample of stars with different spectral types, then calculate the transformation equation by using the synthetic magnitudes. In this work I used the STELIB (Le Borgne et al., 2003) empirical spectral library for this purpose. The spectra were radial velocity corrected and dereddened, thus hopefully will provide accurate color and magnitudes. The synthetic magnitudes were computed such as described in section Comparison between BVRI and DMC system is shown in Figure 5.5.

6 CHAPTER 5. DATA ANALYSIS: CMD AND SED 63 Figure 5.5: Synthesized photometry for BVRI (red) and DMC (green) system. Figure 5.6 shows the transformation from V to DMC#4 along with the residuals. Each data point represent one star. Overall, 58 stars were used to calculate the transformation; the sample of stars consists of main sequence (spectral type from B to G) as well as red giant stars. It could be seen that the relation was linear, with 45 gradient of the regression line. This means that the DMC#4 band could be easily reproduced from the V band.

7 CHAPTER 5. DATA ANALYSIS: CMD AND SED 64 Figure 5.6: Transformation from V to DMC#4. In Figure 5.7 the linear fit for BRI bands is presented. The RMS for B band is the highest among the other bands. This is expected because usually the B band region has low S/N ratio, and also the Balmer jump region is contained inside the B passband. In Figure 5.8 the color dependence of each transformation is presented. The color in the abscissa directly represent the spectral type. Isochrone construction was done using this set of transformations.

8 CHAPTER 5. DATA ANALYSIS: CMD AND SED 65 Figure 5.7: Transformation from BRI bands to each DMC analog.

9 CHAPTER 5. DATA ANALYSIS: CMD AND SED 66 Figure 5.8: Transformation from BVRI colors to each DMC analog.

10 CHAPTER 5. DATA ANALYSIS: CMD AND SED 67 In this work I used the isochrone set from the Pisa evolutionary library (Castellani et al., 2003) for low-metallicity cluster, and from the Padova 1 database (Bertelli et al., 1994) for higher metallicity. Figure 5.9 shows an example of isochrone from the Pisa database (15.0 Gyr age, z = ). Figure 5.9: Isochrone in V(B-V) (left) and DMC analog (right) Isochrone fitting M13 Since there are two methods to calibrate the star magnitudes i.e. zero-point shift and transformation equations, the cluster CMD could be used as a tool to evaluate the two methods. Figure 5.10 shows the CMD derived from zeropoint shift calibration method. The CMD is presented in band #4 #11 color (m 4 m 11 ) vs. band #4 magnitude (m 4 ) analogous with V (V I) CMD. Superposed with red color is the theoretical Pisa isochrone (15.0 Gyr,z = ), shifted with distance modulus (m 4 M 4 ) = and without reddening. It could be seen that the isochrone does not fit the data scatter very well. The distance modulus agree quite well with the references (14.48, see Table 2.1) but the color is not; either the isochrone too red or the data too blue. To match the isochrone color to the data we must shift it to the bluer color, which means negative reddening this physically does not make any sense. 1

11 CHAPTER 5. DATA ANALYSIS: CMD AND SED 68 Figure 5.10: CMD of M13, from zero-point shift. To compare with, in Figure 5.11 I present the CMD derived from color transformation (equations 4.3 and so on). In the figure also superposed the same isochrone as in Figure 5.10, but shifted with distance modulus This value of distance modulus differs significanly with previous results, and seems unlikely to be the correct value. However, the color seems to be right. Figure 5.11: CMD of M13, from transformation. Therefore, the best-fit isochrone combines both methods of zero-point

12 CHAPTER 5. DATA ANALYSIS: CMD AND SED 69 shift and color transformation (Figure 5.12). The colors were derived from the transformation, and the m 4 magnitude is from zero-point shift. The superposed isochrone yield distance modulus (m 4 M 4 ) = 14.80, color excess E(m 4 m 11 ) = 0.0, age T = 15.0 Gyr, metallicity z = Figure 5.12: Preliminary CMD fit of M13. However, this result should be more thoroughly checked. It was necessary to compare different isochrones to determine which isochrone fits the data scatter best. Four parameters should be tuned carefully: age and metallicity (depends on the selection of the isochrone), distance modulus and reddening (depends on the fit to the scatter). Although all this four parameters should be determined simultaneously, let us begin with comparing the isochrone ages first.

13 CHAPTER 5. DATA ANALYSIS: CMD AND SED 70 Figure 5.13: Selection of isochrones of different ages; z = In Figure 5.13 we can see that the position of the red giant branch is not too sensitive to age; age could be more easily determined from the main sequence turn-off point. Unfortunately the photometry did not went deep enough to reach the turn-off point, thus could produce a wild range of ages if it is determined from the giant branch fit only. The isochrone with age as the known youngest age for Milky Way globular cluster, 6.5 Gyr (Whiting 1, Carraro et al. 2007) is plotted for comparison. Although the giant branch is not sensitive to age parameter, the red end of the horizontal branch is. We can see in figure 5.13 that older isochrones tend to reach bluer region of the horizontal branch than the younger ones. This could be used as an estimate to the cluster age. Figure 5.14 shows the dependance of the isochrones to metallicity. It is also quite hard to determine which isochrone fits the data best because of the large scatter. A good combination of isochrone age and metallicity should be achieved to match the data scatter.

14 CHAPTER 5. DATA ANALYSIS: CMD AND SED 71 Figure 5.14: Selection of isochrones of different metallicity; T = 15 Gyr. After trial-and-error with several isochrones, the best fit parameters was derived and the fitting is presented in Figure The fit yielded T = 18.0 Gyr, z = , (m 4 M 4 ) = 14.9, E(m 4 m 11 ) = 0.0.

15 CHAPTER 5. DATA ANALYSIS: CMD AND SED 72 Figure 5.15: M13, final isochrone fit. Ru 8 For the open cluster Ru 8 the same procedure of isochrone fitting such as employed to M13 has been applied as well. However, due to different CMD characteristics between M13 and Ru 8, different problems are encountered. The CMD of Ru 8 is very sparse. If we try to plot the m 4 (m 4 m 11 ) CMD such as presented for M13, only four stars could be plotted (see Figure 5.16). Moreover, those four stars do not show a hint of main sequence. Therefore, I used m 4 (m 4 m 12 ) CMD as a V (V I) CMD analog rather than m 4 (m 4 m 11 ).

16 CHAPTER 5. DATA ANALYSIS: CMD AND SED 73 Figure 5.16: Ru 8 CMD, m 4 (m 4 m 11 ). The transformation from (V I) into (m 4 m 12 ) is presented in Figure This transformation later applied to the (V I) color of the isochrone.

17 CHAPTER 5. DATA ANALYSIS: CMD AND SED 74 Figure 5.17: Transformation from (V I) into (m 4 m 12 ). Best-fit CMD of Ru 8 in m 4 vs. (m 4 m 12 ) is presented in Figure Superposed on the data scatter are the Padova isochrones of log T = 8.55 (blue) and log T = 8.70 (red). Both isochrones have the same metallicity z = 0.004, distance modulus (m 4 M 4 ) = 11.54, and color excess E(m 4 m 12 ) = 1.05.

18 CHAPTER 5. DATA ANALYSIS: CMD AND SED 75 Figure 5.18: Final isochrone fit for Ru SED fitting The measurement of program stars magnitude done at several passbands across the optical region could be arranged into object s spectral energy distribution (SED). Figure 5.19 shows the SED of a sample of M13 stars. Different symbols in the diagram represents different type of stars. The star type classification noted on the diagram i.e. red giants, horizontal branch (HB) stars, and subgiants, are based on the star position in the CMD. In Figure 5.2 red giant stars are located in the upper right of the diagram, HB stars are located in the left (blue) region of the CMD, and subgiants are located below the red giant sequence.

19 CHAPTER 5. DATA ANALYSIS: CMD AND SED 76 Figure 5.19: SED of several M13 stars. In Figure 5.19 several reference SEDs are also plotted. Those reference SEDs were templates taken from Pickles (1998), scaled to match the absolute magnitudes defined by Drilling & Landolt (2000), and shifted with the amount of distance modulus derived from isochrone fitting. It could be seen that for example, red giant stars, the reference SED could fit the observed SED very well. The shapes of star SED are just as expected for their classification. Red giant stars definitely show a typical red star SED; the red part of the SED is brighter than the blue part. The other two types of stars also show a consistency between their classification and SED appearance, but with lower S/N compared to the red giants. To Ru 8 the same procedure also applied. The resulting SEDs are presented in Figure The SEDs are from the four brightest stars of the cluster, since only those four stars constraint the isochrone fit (see Figure 5.18).

20 CHAPTER 5. DATA ANALYSIS: CMD AND SED 77 Figure 5.20: SED of several Ru 8 stars. From the cluster CMD and by taking account the amount of reddening, the four stars should be aroud spectral class A, but we could see that the SEDs do not show a typical blue star SED. SEDs of the four stars seem to be best represented by a G star with luminosity class II III. This inconsistency of spectral type derived from CMD and SED indicates that the cluster Ru 8 may be not a genuine cluster after all. However, it is rather difficult to draw a strong conclusion based on only a handful stars in Ru 8 field. We need data of more stars in the cluster area to draw a more conclusive result.