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 mag- nitude -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 × 1015 meters and a year is 3:16 × 107 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.