Lab 4 Radial Velocity Determination of Membership in Open Clusters

Lab 4 Radial Velocity Determination of Membership in Open Clusters Sean Lockwood 1, Dipesh Bhattarai 2, Neil Lender 3 December 2, 2007 Abstract We used the Doppler velocity of 29 stars in the open clusters NGC 752, Kronberger 1, & NGC 7063 in order to confirm their status as such. We also determined that 4 of these target stars are likely to be non-members in the foreground or background of the clusters. enough emissions lines and comparing its wavelength offset to other stars. 2. Observations On 2007 October 21-23, we observed open clusters and a possible extrasolar planetary transit. We used the PRISM instrument on the Perkins 72 telescope in Flagstaff, AZ. The weather was reasonably clear on all nights, with the exception of a few clouds. The weather was not consistent enough for absolute photometry, but was acceptable for spectroscopy and differential photometry. Gusts of wind occurred on the second night, but remained within acceptable parameters. 1. Introduction Groups of stars that appear in close proximity to one-another on the sky may or may not be physically associated. One way to determine if they do indeed form an open cluster is to measure the radial velocity component of each member and study the distribution (Rutledge, 1997). If a cluster exists, this process can also be used to eliminate individual stars from the field that are non-members. If the distribution shows no correlation between the velocities, the apparent group of stars are not physically associated, and are known as an asterism. Doppler velocities can be measured by observing a region of the stellar spectrum with 1 email: lockwood@bu.edu 2 email: dipesh@bu.edu 3 email: nlender@bu.edu 2.1. Subframing Subframing is a process where unnecessary pixels are not read out of the CCD in order to save read time and disk space. We imaged our clusters in full frame in order to find targets for spectroscopic analysis, and then we proceeded with sets of images in appropriate subframes. We defined three types of subframes to aid in our data collection. Subframe 1 was a small thumbnail always used with the slit in and the grism out in order to check stellar centering before the spectrum was taken. They were also used in analysis in an attempt to determine velocity corrections due to centering errors. Subframe 2 was used with both the slit and grism to obtain a spectrum of the centered star (see fig. 3). This subframe was fairly large, so we were able to obtain spectra from the night sky for calibration purposes. Finally, subframe 4 was used without the slit or grism in order to

2 image our transit target and calibration stars. 2.2. Image Calibration Each night we took 9 bias images in each subframe. We subtracted the median of each row s overscan region to remove local variations in bias due to voltage fluctuations during readout. When subtracting the bias from other images, the images overscan regions were also subtracted in this way. In order to reduce read-noise and cosmic-ray interference in individual bias images, we stacked each set and median smoothed over all pixels. Sets of flat-field images were obtained for each night in all applicable filters and with the grism. Each flat-field image was overscan and bias corrected. Then, the flat-field images were median smoothed similarly to the bias image. In the case of the grism flat-field, we needed to remove the blackbody curve induced by the temperature of our dome lamp (see fig. 1). In order to do this, each row was divided by its median value. Non-uniformities in CCD sensitivity, as well as the remaining interference fringe pattern (see fig. 2) were successfully divided out of spectral images using these grism flats. Finally, all flats were normalized so that their median value is 1 in order to keep flux values in calibrated images near their original scale. In order to reduce an image, we apply: Image = Image o Bias (Flat Bias)/median(Flat Bias) Fig. 1. A bias-subtracted, median-stacked dome flat-field image with the grism in place. The overall shape is characteristic of the dome lamp s blackbody temperature. In order to remove this unwanted effect, this image needs to have each spectral row divided by its median value. Finally, the entire array needs to be renormalized. 2.3. Spectral Extraction One-dimensional spectra were then extracted from the two-dimensional spectral images, removing spatial information about the star s location in the slit. Data points located too far away from an image s target spectrum contribute unwanted noise to the signal from the sky and other stellar sources in the slit. So, we fit a polynomial to the slit s position over wavelength space (see fig. 3). For each spectral row, 31 points centered on this fit were summed together to find stellar flux versus pixel. However, a problem was noted with this method quantization errors occurred when the fit shifted between discrete pixels (see fig. 4). In order to fix this, each row was shifted via cubic interpolation the appropriate fractional number of pixels from the fit (with the cubic parameters set to op-

3 Fig. 2. A close-up view of a median-stacked dome flat-field image with the grism in place. Note the interference fringes and other nonuniformities that are divided out of spectrometry images. While the interference fringe pattern is never quite the same between images, flat-fielding tends to decrease its presence in our data. timize flux conservation). To get a sense of the flux distribution about the slit, see fig. 6. Along with the reduced one-dimensional flux (see fig. 7), we are also able to extract background sky lines from most exposures. This method of spectra extraction assumes that a horizontal row of our array always corresponds to a constant in wavelength space. While this approximation has proved to be fairly accurate, a more prudent approach would involve fitting background sky lines at different places along the spectral dimension in order to remove their curvature. If this is of concern, we recommend using IDL s poly 2d and polywarp routines to remove any such curvature before extracting spectra. Fig. 3. A bias-subtracted, flat-fielded spectral image in subframe 2 with an overlaid (red) fit used to extract the spectrum. 2.4. Baseline Removal As the goal of our reduction process is to prepare for cross-correlation between multiple images, it was useful to remove the broad blackbody shape from each spectrum so that it would not interfere with the comparison of stellar absorption lines. To do so, we fit a fourth-order polynomial to a median-smoothed version of each stellar spectrum and subtracted this baseline (see fig. 8). While not perfect, this process proved fast and effective for our purposes. Note that absorption lines will now appear as negative flux, as one would expect. 2.5. Wavelength Solution An approximate wavelength solution for all of our spectra was found by manually identifying the pixel location of known background sky emission lines (Hanuschik, 2003) and fitting a second-order polynomial. The process of identifying emission lines was aided by iterating solu-

4 Fig. 4. The central stellar spectrum with each spectral row shifted by a discrete amount, as determined by a fit to the stellar spectrum. Note the quantization errors that occur where the shading becomes discontinuous when the fit crosses pixel boundaries in the spatial dimension. tions with more and more lines. Thus, we were able to generate a rest wavelength solution as a function of pixel number: λ = 4877.9209 + 1.4803y 8.0880 10 5 y 2 We resampled the spectra via interpolation over a standard wavelength range and step in order to remove the nonlinear components that would decrease the effectiveness of crosscorrelation algorithms. Fig. 5. By shifting each row by a fractional number of pixels (via cubic interpolation), as determined by a fit to the stellar spectrum, we are able to avoid the quantization errors that occurred in fig. 4. 2.6. Velocity Conversion In order to convert wavelengths, λ, to velocities, v, we used the non-relativistic Doppler shift equation: λ λ = v c where we chose λ = 6809 Å, the central wavelength of our spectra. Note that the y-intercept of this wavelength solution is not entirely accurate. So for this paper, we adopt the definition that NGC 7063 A (as observed in 071022.020.fits) has zero Doppler shift. It happens that this star has one of the highest Doppler shifts of the observation run, leading to negative values for almost all other shifts.

5 Fig. 6. A three-dimensional view of the flux contained in the spectral line, shifted to a straight line via interpolation. Fig. 8. A fourth-order polynomial was fit to the stellar baseline and subtracted off in order to remove the blackbody temperature dependence from each stellar spectrum. Fig. 7. The stellar spectrum (above) and corresponding background sky emission spectrum (below), as summed up along the spatial dimension. Note the presence of sky emission lines superimposed on the stellar spectrum.

6 2.7. Cross-correlation Using IDL s c correlate function, we compared the relative shift of each spectrum to a reference spectrum, NGC 7063 A. This reference spectrum was selected based on its high maximum cross-correlation coefficient with most other spectra. We shifted the target spectrum relative to the reference spectrum by a few pixels in discrete steps. In order to find the fractionalpixel shift, we fit a quadratic to the top few points from this shift and found the peak (see fig. 9). of these, we find that errors in cross-correlation range from 0.06 pixels to 0.5 pixels (in one case), corresponding to velocity errors of 3900 m/s to 32,000 m/s. A reasonable error could be 0.15 pixels, corresponding to 9,800 m/s. While individual shift errors undoubtedly depend on a number of independent factors, each set of observations that can be used to find these errors consisted of only two or three data points, leading to a great amount of uncertainty in the estimate of this error. 2.8. Velocity Corrections with Thumbnail Images One problem with high-precision spectroscopy that we anticipated was the occurrence of random shifts in wavelength due to misalignment of the target star with the slit. While this error might not be very big, it is important to note that the shifts we are looking for are very small on the order of pixels. Fig. 9. The degree to which two arrays correlate with one another is found as a function of shift between them. This best shift is then quadratically interpolated to a fractional pixel. The red curve is the quadratic fit to the top 5 points, and the red line marks the peak of this fit. While the wavelength solution of any particular spectrum had errors on the order of Angstroms, the differential error between the position of any two spectra usually turned out to be small. In a few cases, we took multiple observations of the same object without moving the telescope. By comparing the pixel shifts of each Fig. 10. A sample thumbnail image. The centering of the central star relative to the slit turned out to range over only a few pixels. It was our hope to develop a method to char-

7 acterize this spectroscopic shift due to star misalignment by imaging each target without the grism before taking the longer spectroscopic exposure. These exposures were small subframes, nicknamed thumbnail exposures (see fig. 10). Since we did not move the telescope between these two types of exposures, pointing errors caused by moving the telescope were not present. We parameterized the shift ( thumbnail parameter ) by first determining the center of the target star with a Gaussian fit. We then fit a line to the slit s position across the array, ignoring points contaminated with starlight. Then, we removed any vertical component of the slit by interpolating each row of the array by the proper amount. Next, we summed the regions 1.5-3*FWHM from the center and fit a Gaussian in order to determine the star s centering relative to the horizontal slit. This process yielded values that correspond to the number of pixels that the star is shifted above or below the slit. We observed a calibration source, M67 MMJ 6480, at various slit positions by moving the telescope various amounts and taking sets of thumbnails and spectroscopy exposures (see fig. 11). By cross correlating the reduced spectra from these observations, we were able to determine how many (fractional) pixels the spectrum had shifted and plot this against the thumbnail parameter. Unfortunately, the scatter in this calibration curve is too great for the purpose of correcting the rest of our data. To correct this problem in the future, we recommend taking more calibration images of these types over a larger range of slit misalignments. Fig. 11. An attempt to calibrate misalignment when centering the slit on a target star. Due to the large amount of uncertainty in our linear fit, we chose to ignore this calibration in our spectral reduction pipeline. It should be noted that the calibration range is smaller than the range of thumbnail parameters over which we had hoped to apply this correction, which would have led to questionable extrapolation in many cases. 3. Results Table 1 shows the mean and standard deviation for our three target clusters. Furthermore, figures 12, 13, & 14 display these distributions as histograms. By noting the Gaussian-shaped groupings of velocities, it appears that all three target clusters are indeed clusters. It is usually visually apparent that a few stars fall outside the expected Gaussian distribution of velocities, meaning that they could possibly be nonmembers of the cluster in the foreground or background. See table 2 for information on individual stars within these clusters.

8 Fig. 12. Based on this histogram, we conclude that the star on the right is the interloper. However, this result may be incorrect due to incomplete coverage of the cluster, leading to what appears to be a gap in velocities. Fig. 14. Note that the bump on the left is actually two stars due to the size of the bins. Fig. 13. It appears that Kronberger-1 is indeed an open cluster. The star on the right (labeled g ) appears to be a promising candidate as an interloper.

9 Unfortunately, the quality of these results must be questioned because we do not have enough redundant measurements to accurately determine the errors due to cross-correlation and slit misalignment. We must be careful, as adapting our reduction pipeline to minimize errors a priori in the few redundant measurements we do have will not necessarily reduce overall error. There are just not enough of these points to accurately describe the statistics. It appears that our initial goal of optimizing exposure times for Doppler velocity determination cannot be achieved because all of our images exceed the criteria needed to determine this value to reasonable accuracy. We recommend that future work on this question focus on observing fewer targets, but with parameters such as exposure time and slit alignment position studied in further depth. To circumvent part of this problem, we could add random noise to our spectra to simulate the effects of a lower signal-to-noise ratio on our results. Cluster v σ v NGC 752-99,200 13,877 Kronberger 1-1,617 9,434 NGC 7063-26,413 30,981 Table 1: Cluster statistics. Cluster Star v v /σ v NGC 752 a 0.06 b 1.16 c 0.07 d 0.29 e 0.27 f 1.25 g* 1.71 Kronberger-1 a 0.69 b 0.83 c 0.07 d 0.27 e 0.40 f 0.19 g* 2.33 h 0.38 NGC 7063 a 0.86 b 0.68 c 0.28 d 0.68 e 0.15 f 0.60 g 0.90 h 0.34 i 0.09 j 0.22 k 0.47 l 0.39 n* 2.03 o* 2.32 Table 2: Distance from mean in standard units. Probable interloping star denoted by *.

10 4. References Rutledge, et al. Galactic Globular Cluster Metallicity Scale From the Ca II Triplet, PASP 109, 883R (1997). Hanuschik R.W. A flux-calibrated, high-resolution atlas of optical sky emission from UVES. <Astron. Astrophys. 407, 1157 (2003)> 5. Acknowledgments We would like to thank Prof. K. Janes of Boston University for organizing, participating in, and providing guidance for our observation run.