Photometry of Messier 34 J. Kielkopf November 12, 2012 1 Messier 34 The open cluster Messier 34 (M34) is in the solar neighborhood, lying roughly in the plane of the Milky Way galaxy in the direction of the constellation Perseus. With an angular size about that of the full Moon, and with many bright stars, it is ideal for study with small telescopes. Since the stars in an open cluster are usually all formed at nearly the same time (at least on a galactic time scale), and the stars originate from the same material, we assume when we observe a cluster such as this that we are seeing a snapshot of an aging population of stars. Their apparent differences now are the result of being formed with different masses, and that very property determines not only what a star is like when it begins its life, but also how it ages. Thus open clusters like this one are a laboratory for exploring the evolution of a stars all with the same initial composition. Distance The cluster M34 is marginally too far from us to find an accurate distance by parallax with current technology. However, the Tycho-2 catalog compiled from Hipparcos satellite data yields a distance of 499 pc (Kharchenko et al. 2005). Another way to establish astronomical distance is to compare the apparent and absolute magnitudes of stars of known spectral type. The distance modulus m M measures how much fainter stars appear than they would be if seen at 10 pc, the reference distance for absolute magnitude M. This type of measurement is most accurately done by considering an ensemble of many stars and taking into account the aging of the stars in the group too. For example, recently, Sarajedini et al. (2004) found a distance modulus (m M) V = 8.98 ± 0.06 after adopting a reddening of E(B V ) = 0.10 giving a distance d of 625 pc from m M = 5 log d 5 (1) In earlier similar work, Ianna et al. (1993) found (m M) V = 8.28, for d of 453 pc. At 3.261 light years per parsec, the cluster M34 is at least 1500 light years from us. 1
Figure 1: The open cluster Messier 34 recorded with the University of Louisville s CDK20 north telescope at Moore Observatory. This is a color composite of 100 second exposures taken in the Sloan i, r and g filters, shown here in red, green, and blue. 2
Apparent magnitudes Stars in the cluster will have a range of absolute magnitudes the brightest ones are those born with the most mass, unless they have already aged off the main sequence of the Hertzsprung-Russell (HR) diagram. An HR diagram based on the Hipparcos catalog is shown here. The brightest blue stars on the main sequence of the HR diagram are at absolute magnitude -3, but some supergiants are brighter at -5. Red giants are around magnitude -1, and stars like the Sun are about magnitude 5. There is a knee where the HR digram turns downward at about magnitude 8, and the low mass red dwarf stars may be as faint as magnitude 15. The brightest white dwarfs on the blue side of the HR diagram at around magnitude 10. You can find the corresponding apparent magnitude for these stars by adding the distance modulus to the absolute magnitude. For example, stars that would be absolute magnitude -1 would have an apparent magnitude of 1 + 8 or +7. Cluster size and age The cluster M34 appears to cover about θ = 30 arcminutes on the sky. If its distance d is known, then its radius in space is approximately r = d tan(θ/2) (2) In this case, with d = 1500 light years, the physical distance across the cluster (2r) is 13 light years: the image shown above covers 13 light years side-to-side at the distance of the cluster. Since most open clusters appear symmetrical, we usually make the assumption they are spherical with a depth along the line of sight about the same as their extent across the sky. The cluster remains compact because its member stars have not had enough time to disperse under the dynamical effects of differential gravitation (e.g. tidal) influences of other stars in the Milky Way. For example, since we know from stellar evolution that M34 is approximately 250 million years old, stars that we see in the cluster cannot be move farther than 13 light years in 250 million years, or 5 10 8 light years/year. Since a light year is 9.46 10 15 meters and a year is 3.16 10 7 seconds, the space velocity of a star that is in the cluster must be less than about 15 m/s. This is a very small velocity on the astronomical scale (Earth s orbital velocity is about 30 km/s.) The small value means than on the time scale of an astronomer s lifetime, all the stars in the cluster must share the same apparent motion through space. We can observer spatial motion in two ways: Transverse to the line of sight by proper motion. Along the line of sight by radial velocity. It follows, that to establish membership in the cluster we can require that its stars share the same radial velocity and proper motion. 3
Figure 2: Hertzsprung-Russell diagram. A plot of luminosity (absolute magnitude) against the color of the stars ranging from the high-temperature blue-white stars on the left side of the diagram to the low temperature red stars on the right side. Created by Richard Powell from 22000 stars in the Hipparcos catalog. (Creative Commons License). 4
Table 1: Selected bright stars in M34. Bright Stars in M34 Star Number ID RA Dec V B-V 70 HD16605 02 40 58.94 +42 52 16.579 9.53 0.03 82 HD16627 02 41 11.00 +42 40 41.414 9.37-0.03 108 HD16655 02 41 31.92 +42 35 39.1420 8.51 0.05 141 HD16679 02 41 48.49 +42 46 14.169 8.88 0.00 156 HD16693 02 41 56.72 +42 47 23.19 8.61 0.00 160 HD16705 02 41 58.43 +42 47 30.37 8.61 0.01 174 HD16719 02 42 05.78 +42 42 26.6937 8.61-0.01 194 HD16728 02 42 13.13 +42 41 57.1777 8.51 0.00 240 HD16782 02 42 45.75 +42 49 13.075 8.54 0.01 299 HD16857 02 43 32.42 +42 37 17.474 8.79-0.02 Cluster membership Ianna et al (1993) studied cluster membership and they found that for 354 stars in their program, most showed proper motions less than 0.005 arcseconds/year, as expected. Stars that show much larger proper motion would most likely be in the foreground, but this technique cannot exclude background stars that probably would show much less proper motion. Since the cluster is moving through the galaxy, on the average it has an intrinsic proper motion. These tests are done to insure that the stars share a common behavior. Based on this, the brightest stars that are almost surely in M34 are shown in Table 1. This table is based on data in Ianna et al (1993), with recent coordinates from SIMBAD. Stars 156 and 160 are the bright pair at the center of the cluster. 2 CCD data on cluster We have new images of the cluster taken with the Sloan filter set using the CDK20 north telescope at Moore Observatory. Because the brightest stars in the cluster will saturate the CCD image in typical exposure times of 100 seconds, we recorded exposures with times of 1, 10, and 100 seconds to span the full range of measurable stars. At the longest exposures the images of the fainter stars are comparable to the signal from the urban night sky at the observatory. At the shortest exposures, the bright stars are not saturated and can be compared accurately to one another. All of the images have been dark subtracted to remove the intrinsic dark pattern and offset of the detector, and flat-fielded to divide by a response to the uniformly illuminated sky. As a result, the signal in each pixel is simply the sum of 5
the sky and the star. Subtract a sky background from the measurement, and you have the signal in that pixel from only the star. The images available include: m34_g_100s_00006_dfw.fits m34_g_10s_00007_dfw.fits m34_g_1s_00008_dfw.fits m34_r_100s_00009_dfw.fits m34_r_10s_00010_dfw.fits m34_r_1s_00011_dfw.fits m34_i_100s_00012_dfw.fits m34_i_10s_00013_dfw.fits m34_i_1s_00014_dfw.fits All of them were recorded sequentially on 2012-11-05 at 02:48 to 02:56 UT. Similar images in z included on our server but needed for this experiment. The coding letters d, f, and w in the file names indicate dark subtraction, flat fielding, and the addition of a world coordinate system (WCS)header. When the header information is present, ds9, aladin, and AstroImageJ will show you the celestial coordinates of the pixel at the cursor. This is very helpful identifying stars in the images. 3 filters The filters indicated are g, r, and i. These approximately cover the bands g blue-green (400-530 nm) r yellow-red (530-700 nm) i near infrared (700-825 nm) z infrared (825-1100 nm) The Sloan filter set has replaced the Johnson-Cousins set for most current new photometry, which leaves us with the problem of converting archival data for comparison to new data. The issues involved in this are discussed on the Sloan Digital Sky Survey (SDSS) website http://www.sdss.org/dr7/algorithms/sdssubvritransform.html The transformation is made by linearly combining data in in one filter set to estimate the data in another filter set, assuming a model spectrum (in this case for stars). For example the following are good to residuals of better than 0.04 magnitude: 6
g-r = 1.09*(B-V) - 0.23 r-i = 0.98*(R-I) - 0.22 B-V = 0.62*(g-r) + 0.15 V-R = 0.38*(r-i) + 0.27 g = V + 0.60*(B-V) - 0.12 = 0.6*B + 0.4*V - 0.12 r = V - 0.42*(B-V) + 0.11 = 1.42*V - 0.42*B + 0.11 B = g + 0.33*(g-r) + 0.20 = 1.33*g - 0.33*r + 0.20 V = g - 0.58*(g-r) - 0.01 = 0.42*g + 0.58*r - 0.01 Thus if you know V and B-V you can calculate the magnitudes in the g and r bands of the Sloan system. Likewise, if you know g and r, you can calculate B and V. To calculate R you also need i. 1. For the stars in the table, find r and g-r. These are the values we will be measuring on the images. 4 Photometry calibration Begin with the 1-second r and g exposures. For now, we ll do these by hand using ds9. You can also automate the process with AstroImageJ, and do hundreds of stars at once. For each star in the table, and for each of the r and g 1-second exposures, find the star in the image, note the peak value at the brightest spot in the stellar image, and also note the background somewhere near the star by not influenced by it. You may simply be able to use the same background for all stars. For each star, subtract the background from the signal. 2. Provide a spreadsheet with these measurements. Let s assume the g-band data for a star have a signal s. The magnitude m g corresponding to that signal s g is m g = m g0 2.5 log 10 s g (3) where m g0 is an unknown scaling constant for the g-band. Each of the stars you have measured in the g-band image will yield values for this constant. For the r-band we have similarly m r = m r0 2.5 log 10 s r (4) The unknown constant is simply the sum of the known magnitude of the star, and the value of 2.5 log 10 s for the star in that band. Average all the values for each band, and you ll have a calibration of the image for photometry. 3. What are the values you found for m r0 and m g0 in 1-second exposures? The signals in 100-second exposures should be 100 larger than those in 1-second exposures, but of course the magnitudes are the same. Consequently for 100-second exposures the calibrations you would use for m r0 and m g0 are increased by 2.5 log 10 100 = 5. For example, suppose you measure a signal of 200 in a 1-second exposure with m 0 = 20.0. The calculated magnitude m would be 20 2.5 log 10 200 = 14.24. In a 100 second exposure 7
the same star should give a signal of 100 200 = 20000. To give the same magnitude we need m 0 = 25.0 such that 25 2.5 log 10 20000 = 14.24. In practice we may not rely on exposure time scaling if high precision in needed because of non-linearity in the detector response and a so-called shutter effect in which the shutter is open longer in some parts of a frame (usually the center) than in others (usually the edges). 4. What are the values you found for m r0 and m g0 for 100 second exposures? 5 Color-magnitude or HR diagram of M34 The brightest stars in the table isolate a small portion of the HR diagram. To have a more comprehensive view of it, you would need to measure fainter stars. For example, if the brightest stars you measure are actually absolute magnitude -3, then to reach the brightest of the faint white dwarf stars at absolute magnitude 10, you would have to explore 13 magnitudes fainter than the brightest stars in the cluster. You may just reach this limit in 100 second exposures, but probably not! Work on white dwarf stars in open clusters usually requires the largest telescopes we have, especially for spectroscopy. However, you have enough range to reach down along the main sequence and to explore the red stars in the cluster. As you look at fainter and fainter stars, the probability they will not be cluster members increases because we can see through the cluster and detect distant bright stars. At a given color, it is most likely that the brightest stars you see are those in the cluster, with the exception of the occasional foreground star. For this part unless you have extraordinary patience you ll need AstroImageJ (AIJ). Download a copy from our website and install it on your own computer. If you cannot do this, then you are welcome to use one of the computers in the astronomy lab or conference room. Download and save the 1-second images in the g and r bands. If you have time, you may also look at the 100 second images. Start AIJ, and click the Data Processor button DP. It may help to also open the pdf of the manual and work through some of the examples there first. What follows is a step-by-step guide to get useful photometric information from the two images returned to you as a spreadsheet. 1. Create a separate directory on your computer with only copies of the g and r 1-second images, nothing more. 2. Start AIJ 3. Use the File menu, and go to Import, Image Sequence, then select the directory (not the file) 4. You should see a display of the two images as one stack. The bar under the image display selects which image is shown. The scaling at the bottom controls how this appears to you. It does not affect the data itself. 8
5. Select Analyze and Multi-Aperture 6. On the new panel you should see Maximum number of apertures 2 First slice 1 Last slice 2 Radius of object aperture 30 Inner radius of background annulus 50 Outer radius of background annulus 70 Uncheck Use previous apertures Uncheck Use single step mode Check Reposition aperture... Check Remove stars from background... Uncheck Assume background is plane, Update plot Uncheck Compute relative flux in all apertures Uncheck Compute relative flux error and Compute relative flux signal-tonoise Check Total comparison star counts Check Vary photometer aperture radii... and enter a factor of 1.4 if it is not there already Check Allow left/right double click... 7. When you have this form set, click OK. 8. Use the image display, move the cursor over star, and left click to select it. You may zoom in (press + key or use the scroll wheel, if enabled). Pan by pressing the center mouse and dragging, or by the hand icon on the main ImageJ panel. 9. Continue selecting stars with the left click. Pick the first 50 or more brightest stars. 10. You may remove an errant click with another one on the same star. 11. When you have these chosen, right click to process the images. 12. A measurement table appears in a new window. It should have Source-Sky entries for all your targets. Save this table using the File menu on the Measurements window. 13. There may be additional options using the DP (Data Processor) button on the main AIJ window, but for now this is all we will do here. 9
14. You may also measure individual stars yourself in this mode by moving the cursor around and noting the RA and Dec coordinates, and the data in Value, Peak, and Int Cnts (Integrated Counts). You can use these data for calibration too if you note which star number corresponds to which standard star in the table. 15. On the image display select File and Close Window. 16. Select File and Quit on the main AIJ panel to be done with this part for now. The Measurements file that results is a conventional space-delimited spreadsheet. Each column is a star. Row 1 is the first image of the stack and row 2 is the second image. Following our directions above will make row 1 the g image and row 2 the r image. The entries in the spreadsheet are the sky-subtracted signals for the stars you selected. You may have to use some tricks to get this sheet into a form you can use in your favorite spreadsheet software. It is in plain text, so you can always edit it and cut and paste, but the simplest solution is to find a way to load it in one pass. For example, with Libre Office or Open Office I first open the file in any text editor and copy the two data rows to the computer s buffer (e.g. File and Copy). Then open Libre Office as a new spreadsheet and use File with Paste Special. You ll get two rows in the new sheet. The first two columns may have numbers 1 and 2 for the two images, and blank space. You may delete those. Finally simply copy the first two rows into the buffer for the spreadsheet, right click on a cell in the first column underneath these rows, Paste Special again, and select Transpose. This will make two columns instead of two rows. The first column is the g image and the second one is the r image. From this point forward you are on your own with whatever tools you usually can bring to process and plot these data. Use the transformation coefficients you found above and convert each column into a magnitude with m = m 0 2.5 log 10 s using the appropriate m 0 for each filter. Evaluate a data set which is the difference in the magnitudes m g m r. 5. Plot a graph of m r on the vertical (y) axis, m g m r, on the horizontal axis. Note that in the HR diagram it is conventional to put bright stars at the top, red stars at the right. 6 Analyzing the HR diagram Inspect the plot you produced and compare it to the HR diagram for the Hipparcos catalog shown above. You should be able to get them to match if you adjust m M, the distance modulus. Remember, however, that you re plotting r and g r, so there s some scaling difference from the transformation of photometric coordinates too. 6. What is the distance modulus you measure for M34, and what would be its distance in parsecs (pc) and light years (ly)? 7. What are the faintest stars you see that are clearly in the cluster? How can you tell what is in the cluster and what is in the foreground or background? 10
Extra If you have time and have worked out the process successfully so far, try the 100 second exposures following exactly the same process. Pick 200 or more stars, but avoid the really bright ones that show signals over 40,000 counts at the peak. These are saturated and will distort your results. Apply the calibration for the 100 second images, and plot a new HR diagram for the faint stars. 8. Extra Credit. What happens when you extend this to very faint stars? How faint and how red can you explore? Can you detect the white dwarf stars, and if not, what exposure time would it take to do it? References 1. Kharchenko, N. V., Piskunov, A.E., Roeser, S., Schilbach, E., and Scholz, R.-D., Astron. Astrophys. 438 1163-1173 (2005). 2. Sarajedini, A., Brandt, K., Grocholoski, A. J., and Tiede, G. P., A. J. 127 991-999 (2004). 3. Ianna, P. A., and Schlemmer, D. M., A. J. 105 209-219,317 (2004). 11