Aperture Photometry: Obtaining and analyzing a H-R Diagram of M38 Arturo Ruiz Martin January, 17th 2011
1
Abstract The objective of the paper is to perform a study of one or several open clusters with the help of color-magnitude diagrams. The importance of clusters in this kind of study lies in the fact that all the stars in the cluster have been formed by the contraction of one cloud made of dust and gas. Therefore, it is reasonable to consider that they have the same age and also that they are approximately at the same distance from our Sun. This allows us to directly compare their brightness and determine some important parameters of the cluster, such as its age or distance. This type of diagrams (known as Hertzprung-Russell Diagrams), which relate the magnitude or intrinsic brightness of the stars and their color, have been used to model the evolution not only of a particular cluster, but the stars in general, because of the fact that an examination of the diagram shows that the stars tend to come together in some regions of it. This study was performed on the open cluster M38 and our observations were made with the telescope at the observatory of Centre de Natura Caixa Catalunya in Lleida and at the Montsec Astronomical Observatory with the great collaboration of Enrique Herrero and Francesc Vilardell. With this diagram we determined the age of the M38 cluster in approximately 500 million years.
1 – Introduction 1.1 – Fundamental basics of photometry Since the beginning of the time, the man has not had enough with the study of what he has on his planet, the Earth. He has always been curious about what is outside of it, all that environs us: the space. One of the first men who started to make observations was Hipparchus, considered by some the greatest astronomer of antiquity. It is known that he classified the stars visible to the naked eye into six magnitudes. The brightest stars were thought to be in the first magnitude (m= +1), while the faintest stars were classified in the sixth magnitude (m= +6). Due to the fact that the response to the light by the eye is logarithmic, this scale was also logarithmic. In 1856, Norman Robert Porson realized that, in Hipparchus scale, the stars in the first magnitude were approximately 100 times brighter than the stars classified in the sixth magnitude. Then, he proposed to adopt a magnitude scale system in which each magnitude is ≈ 2.512 times less bright than the magnitude above it (fifth root of 100). This is also known as Pogson´s Ratio. Nowadays, Vega (Alfa Lyrae) is the star where the scale of magnitudes is fixed to. According to this, the magnitude of a star (a) with respect to Vega can be defined as: (1)
2 Where Fa is the light flux received from the star a FVEGA is the light flux received from Vega
The brightness of a star is heavily dependent on its distance to the earth, so it would be better to compare the intrinsic brightness of the stars to have a scale where the distance would not influence the value of the magnitude. That is the reason why there is a so called the absolute magnitude (M).1 It can be calculated by the following equation: (2)
Where m is the apparent magnitude of the star d is the distance to the star in parsecs
2
See: (Strobel, 2007) (Stellar Magnitudes)
1.2 – Color / Temperature of the stars To determine the color of a determined star, we use a parameter called color index (B-V), which is defined as the difference of two magnitudes of the same star, measured in different color filters (Visual and Blue). So the relation between these two magnitudes will be: (3) (
)
(
)
Where FB is the flux measured with the B filter FV is the flux measured with the V filter
The hottest stars radiate in the short wavelength region, so if we measure the apparent bright of a star using a B filter, this bright would be higher than if we use a V filter, which has its transmission peak in the green part of the spectrum. That is why the apparent magnitude of the blue filter would be less (brighter) than the magnitude of the visual filter.
1
As an example, the Sun is obviously the star with the highest apparent magnitude (-26.74) because it is the closest star to the Earth, however, in the absolute magnitude scale, compared with other stars of the universe, the Sun is not one of the brightest stars (M = 4.83). 2 The parsec is the distance that an object has to be to accomplish that its parallax is 1 arc second. A parsec is equal to 3.26 light-years.
3 Stars are classified in different spectral types depending on the wavelength of their emission peak, i.e. their color. The temperature of a star is directly related with this radiation, as it can be considered as a black body. [For further information consult Black Body Radiation (La radiación del cuerpo negro) and Planck´s Law (Wikipedia - Plank´s Law, 2011)]
Since 1943 there is a scale of spectral types, named each one with a letter: O: Stars very hot and luminous, very blue. B: Extremely luminous and blue stars, which tend to cluster together. A: The most common naked eye stars, white-bluish white color. F: White stars, commonly called yellow-white dwarfs. G: Sun type. K: These stars are slightly cooler than our Sun. Most of them have an orange color. M: The most common class (76% of stars in the solar neighborhood). They have a red color, and most of them are dwarfs. With this information we can deduce that A-type stars (white) will have a color-index value close to 0; the hottest stars (O and B-type) will have negative color index and, the higher the index is, the colder is the star and more advanced is its spectral type (F, G, K . . .). See: (Kaler, 1989) (Morgan & Keenan, 1973)
1.3 – The HR Diagram Ejnar Hertzprung and Henry Noris Rusell were two astronomers who, in 1910, developed the diagram which today allows us to explain stellar types and evolution. Separately, they also performed and published several works. As an example, Rusell co-wrote an influential textbook in 1927: Astronomy: A Revision of Young´s Manual of Astronomy which became the standard astronomy book for two decades. In a Hertzsprung-Rusell Diagram, each star measured is represented by a dot. The position of each dot on the diagram tells, about each star, its luminosity and its temperature or color index. The vertical axis of the diagram represents the magnitude or luminosity of the stars. The horizontal axis represents the star’s surface temperature (not the star’s core temperature – we cannot see into the core of a star, only its surface) usually this is labeled using the Kelvin temperature scale. But in most graphs and diagrams, zero (or the smaller numbers) exists to the left on the diagram. This is not the case here. On our diagram, the higher (hotter) temperatures will be on the left, and the lower (cooler) temperatures will be on the right.
4 Some HR diagrams include the color index of stars as it can be measured through photometric filters or its spectral type, which is usually obtained from low-resolution spectroscopy.
Figure 1 – Example of an H-R Diagram from http://www.daviddarling.info/encyclopedia/H/HRdiag.html
The HR Diagram also gives us a good overview of properties of the star sample that we are representing. A star in the upper left corner of the diagram would be hot and bright. A star in the upper right corner of the diagram would be cool and bright. The Sun would be approximately in the middle of the diagram, and it is the star which we use for comparison. A star in the lower left corner of the diagram would be hot and dim. A star in the lower right corner of the diagram would be cold and dim. A further examination of a HR Diagram shows that the stars tend to be in some regions of it. The most part of the stars are present in a region called Main Sequence (diagonal going from the lower right of the diagram, cool and dim stars, to the upper left, hottest and brightest stars in the diagram). The lowest-left is the place where White Dwarfs are found, and the sub giants, giants and super giants are located in the upper right sections (red, cold and bright stars). This diagram is an important tool because it can help us to determine the evolution of the stars and to present it graphically. See: (Sekiguchi & Fukugita, 2000) (Smith, 1995)
1.4 – Role of clusters in the making of a HR Diagram Clusters are groups of hundreds to thousands of stars bound to each other by mutual gravitational attraction that were formed by the collapse of the same cloud, so all the stars can be considered approximately the same age and chemical composition. The only difference between the stars of a cluster is a matter of mass. The fact that one star in a cluster is brighter than other, is due to the initial mass of each one, being the most massive stars brighter.
5 If we take the equation (2), which relates the apparent and absolute magnitude depending on the distance, and apply it to a cluster, knowing that the distance is fairly the same for each stars, we can determine that the difference between apparent and absolute magnitude is the same for all the stars (M – m = K). This fact allows us to compare the magnitudes of these stars easily and understand that the shape of the HR Diagram will be the same either we use the apparent magnitude or the absolute magnitude.
2 – Observations and data reduction 2.1 – Equipment The observations for the present paper were carried out in October of 2010 in the observatory located on the Centre de Natura de Catalunya Caixa in Planes de Son, Lleida (for NGC 7789) and in November of 2010 in the fully robotic Montsec Astronomical Observatory (for M38). The equipment at the Planes de Son Astronomical Observatory consists on a 40 cm Schmidt Cassegrain3 telescope (Meade LX200 GPS 16”), a 1024 x 1024 pixel CCD camera (SBIG STL 1001-e) which gives a resolution of 1.2 arcseconds/pixel [for further information see (Maier & Heil, 2008)] and a set of Bessel filters (BVR). A second run of observations was carried out at the Montsec Astronomical Observatory (OAdM), and they were executed in robotic mode. The observatory is equipped with the large and most advanced telescope in Catalonia: an 80 cm telescope (Optical Mechanics, Inc. RC08) with a hyperbolic mirror giving a focal relation of F/3. The mechanic part of the telescope consists in an equatorial mount4 controlled by high precision motors which allow a maximum speed of 10 ° /sec. The system is capable to work in an automatic way, remotely or totally robotic. To do the measurements a 2024*2024 pixel CCD sensor Finger Lakes ProLine with a set of Johnson-Cousins filters (B and V) was used. [See (Montsec Astronomical Observatory)]
2.2 – Observations For the first run of observations, which were carried out at Planes de Son, the first step was to turn on the system and to cool down the CCD sensor to -20ºC in order to minimize the noise produced by the electronic components of the CCD (thermic noise). Due to the fact that the observatory was still in commissioning phase, before the observable clusters had not acquired the adequate high in the sky to be observed, the telescope was pointed to several reference stars in order to check and adjust the pointing of the telescope system.
3
The Schmidt - Cassegrain reflector system is a combination of a primary concave mirror and a secondary convex mirror used in optical telescopes. This system allows developing telescopes with a great focal distance in less space. 4 An equatorial mount is a mount that follows the rotation of the celestial sphere. The advantage of this mount lies in its ability to allow the telescope to stay fixed on any object in the sky that has a diurnal motion by driving the axis at a constant speed.
6 The correction images taken were:
Bias frame: It´s an image with zero exposure time, where it can be observed the readout noise (electrons created by the CCD sensor read-out and the internal electronics, not by the incidence of photons), Dark frame: It contains the effects produced by the thermal noise. It has to be made with the same exposure time than the image of the astronomical object that will be taken, because the thermal noise is proportional to the exposure time. As the CCD response is linear (also regarding noise generation) another option is to rescale the averaged dark frame to the exposure time of each of your object images, previously correcting from bias frame. Flat field: This correction consists in taking an image of an object with a flat illumination (in our case was a white screen illuminated with a lamp, situated in the dome) to see (and subtract to the final image later on) defects on the sensibility of the pixels of the CCD, dust on the detector, etcetera.
A sample of observable open clusters for different nights was selected using the software The Sky 6 (Bisque Software) and the internet tool Staralt [(URL 1) http://catserver.ing.iac.es/staralt/ )]. We pointed to that clusters and several images with different exposure time were taken. Due to bad meteorological conditions on the night at Planes the Son, we could only take images of the open cluster NGC 7789. These data were subsequently reduced and measured, but not finally analyzed due to uncorrectable effects of reddening probably caused by the cirrus and high level of humidity during the data acquisition. The observations in the Montsec Astronomical Observatory were done the same way as in Planes de Son, with the same filters and calibration images, but in an automatic way. The whole observation was previously programmed and scheduled to observe the open cluster M38. This automation includes all the necessary operations to do the observations correctly such as turning on, acquisition of calibration and object images and stop and shut down (also in case of meteorological alerts).
2.3 – Data reduction and photometry All the images obtained were processed with the software Maxim DL 5. First, all the calibration images (darks, bias and flat frames) were subtracted to the images in order to correct the noise and defects of the objects images. There were 5 images for each filter so all the images of each filter had to be combined in one final image (figure 2), from which the photometry was measured to make the color-magnitude diagram. The parameters of the images were the following:
Object NGC 7789 M38
Images / Filter 5 5
Filters used R, V, B R, V, B
Exp. Time 20”/50” 20”
Table 1 – Images´ parameters from the two objects analyzed
Aper. Radius 6 6
Annulus Thickness 5 5
7 With the final images obtained, we selected a sample of a hundred stars distributed in the entire cluster to do the final diagram. With Maxim DL 5 and its tool Information, we obtained the magnitude of that stars in each one of the filters required to do the diagram (in our case the V and B filters). The value of this magnitude is calculated by subtracting to the flux that is measured in the central ring – aperture – the flux measured in the external ring, which is also known as background. It is very important that the size of these two rings remains constant for all the measurement in a single image. If not, the final look of the diagram could be erroneous and highly distanced to its actual appearance. Also it has to be considered the fact that, if we want to obtain a complete HR diagram, the range of magnitudes of the analyzed stars has to be as wide as the image permits, trying to measure from the brightest stars (always below saturation) to the faintest which are above a certain single-to-noise ratio.
Figure 2 – Adaptation of the final stacked image of M38 in the B filter
The value of the magnitude obtained is highly dependent on some parameters of the image (such as exposition time, brightness, etc.) so it had to be converted to a value not dependent of the telescope and CCD used. This conversion was done comparing our magnitudes with another ones from astronomical catalogues [we used Simbad database (URL 2) http://simbad.u-strasbg.fr/simbad/] for a section of 6 o 7 stars in the field in order to obtain a constant that would be later added to our instrumental magnitudes.
8
3 – Data analysis 3.1 – Making the HR Diagram All the calculations performed were realized in a sheet using Excel 2010 (Microsoft). First, we converted all the instrumental magnitudes5 into apparent magnitudes. From Simbad database, we took a small sample of stars that we had already measured in our image and we compared the magnitude from Simbad with ours. Then, we did an average of all that differences and obtained a constant that we added to our instrumental magnitudes to finally obtain the apparent magnitude that could be plotted in the diagram. To obtain the color – magnitude index of the stars we also had to consider the reddening. This is a consequence of the absorption and scattering of radiation emitted by the astronomical objects by matter (dust and gas) between the object and the observer. This phenomenon was corrected by subtracting a constant to the B-V index that we found in the WEBDA database: (URL 3) http://www.univie.ac.at/webda/cgi-bin/ocl_page.cgi?cluster=m38
3.1.1 – Isochrone fit To obtain some conclusion from our diagram, we used isochrones. The isochrones or evolutionary tracks are the representation in color-magnitude diagrams of the output from models of star evolution. They are plots on the H-R diagram at constant time across all masses. For this work, a sample of isochrones was generated from (Siess L., 2000) models. These can be calculated and downloaded with a web tool6 that creates a group of different stars with their color index (mB-V) and mV that later can be plotted in the diagram and compared to the real shape of the graph. It depends mainly on three factors: the age, distance and metallicity of the star cluster. The older a star cluster is, the more advanced the star development; i.e. heavy, blue stars have already transformed into giants (or supergiants). This has an effect on the profile of the turnoff-point. We took this into account by choosing from model-isochrones for different ages (100-500 million years) for best fit. The color index B- V is also influenced by composition of the stars. In our case, we considered solar metallicity for the generated isochrones. We generated some isochrones that we later plotted in our diagram, allowing us to compare their shapes and determine the age of that cluster. The data of the isochrones is given in absolute magnitude (which is not dependent on the distance to the cluster), so it had to be converted to apparent magnitude adding the distance-modulus obtained from URL 1, which has the value of 10.91 magnitudes.
5
The instrumental magnitude is simply the result of 2.5 times the logarithm of the number of counts that the CCD sensor generates from the amount of incised photons. 6 (URL 4) http://astropc0.ulb.ac.be/~siess/server/iso.html]
9
4 – Results and discussion
B-V -0.500 9
0.000
0.500
1.000
1.500
10
11
HR Isoc 2.2e8
V
12
13
Isoc 1e8 Isoc 5e8
14
15
16
Figure 3 – M 38 HR Diagram
Figure 3 shows the color – magnitude diagram obtained. This diagram allows us to conclude that, according to our observations and data reduction, the age of that cluster is approximately 500 million years because its isochrone is the one that best fits with the shape of our graphic. However, this result is only qualitative, and a further analysis considering a larger sample of stars an improved reddening correction should be performed in order to accurately determine the distance to the cluster. The stars that are far from the main sequence of the diagram are probably field stars that were also measured in the same field of M38. The result of our research may seem far from other results for this cluster such as the obtained from the URL 1, which set the age of the cluster in 220 Myr. In 1999, A. Subramaiam et al. (Annapurni Subramaniam, 1999) performed a study of several clusters including M38 (also known as NGC 1912) which determined through Color-Magnitudes diagrams and isochrones fits the age of this cluster in 250 Myr. With this study they also estimated the distance to M38 in 1820 ± 265 Pc.
10
5 – Acknowledgements I would like to thank in first place to Obra Social Catalunya Caixa to offer, not only to me but to lots of young and talented people a chance to expand their capacities and initiate them in the world of science. I would also like to thank my tutor Enrique Herrero for his invaluable contribution and help even when it was difficult to, and to Francesc Vilardell for programming and supervising the data acquisition at the Montsec Astronomical Observatory. Finally, I wish to thank personally all my partners from Joves I Ciencia for helping me giving their support when it was possible.
6 – Appendix mB
mV
B
V
B-V
2.291
1.686
13.350
12.788
0.313
1.224
0.543
12.283
11.645
0.389
3.935
3.092
14.994
14.194
0.551
2.546
1.427
13.605
12.529
0.827
0.457
-0.075
11.516
11.027
0.240
-0.101
-0.763
10.958
10.339
0.370
-0.202
-1.385
10.857
9.717
0.891
4.169
2.273
15.228
13.375
1.604
0.783
0.357
11.842
11.459
0.134
0.243
-0.117
11.302
10.985
0.068
4.101
3.316
15.160
14.418
0.493
0.117
-0.302
11.176
10.800
0.127
4.390
3.609
15.449
14.711
0.489
1.381
0.888
12.440
11.990
0.201
0.622
0.191
11.681
11.293
0.139
3.583
2.271
14.642
13.373
1.020
3.277
2.574
14.336
13.676
0.411
2.557
1.857
13.616
12.959
0.408
4.280
3.407
15.339
14.509
0.581
2.624
2.010
13.683
13.112
0.322
1.630
1.110
12.689
12.212
0.228
0.875
0.400
11.934
11.502
0.183
3.362
2.456
14.421
13.558
0.614
0.932
0.451
11.991
11.553
0.189
3.534
2.513
14.593
13.615
0.729
-0.310
-0.791
10.749
10.311
0.189
1.619
1.082
12.678
12.184
0.245
1.551
0.981
12.610
12.083
0.278
2.795
2.157
13.854
13.259
0.346
0.155
-0.286
11.214
10.816
0.149
3.165
2.471
14.224
13.573
0.402
11 3.681
2.907
14.740
14.009
0.482
2.899
2.255
13.958
13.357
0.352
2.994
2.235
14.053
13.337
0.467
1.677
1.198
12.736
12.300
0.187
1.753
1.210
12.812
12.312
0.251
4.891
3.971
15.950
15.073
0.628
0.880
0.417
11.939
11.519
0.171
4.400
3.498
15.459
14.600
0.610
3.980
3.404
15.039
14.506
0.284
4.525
3.417
15.584
14.519
0.816
-0.099
-1.293
10.960
9.809
0.902
2.979
2.332
14.038
13.434
0.355
1.641
1.150
12.700
12.252
0.199
1.565
0.355
12.624
11.457
0.918
2.977
2.333
14.036
13.435
0.352
1.520
1.014
12.579
12.116
0.214
2.235
1.563
13.294
12.665
0.380
2.913
2.208
13.972
13.310
0.413
1.802
1.292
12.861
12.394
0.218
2.698
2.055
13.757
13.157
0.351
-0.046
-0.538
11.013
10.564
0.200
0.616
0.157
11.675
11.259
0.167
2.713
2.028
13.772
13.130
0.393
2.215
1.335
13.274
12.437
0.588
-0.372
-0.865
10.687
10.237
0.201
2.029
1.486
13.088
12.588
0.251
2.281
1.696
13.340
12.798
0.293
0.850
0.328
11.909
11.430
0.230
2.281
1.696
13.340
12.798
0.293
2.717
1.531
13.776
12.633
0.894
2.701
1.985
13.760
13.087
0.424
2.609
1.950
13.668
13.052
0.367
-0.480
-0.983
10.579
10.119
0.211
1.471
0.884
12.530
11.986
0.295
1.620
1.016
12.679
12.118
0.312
-0.166
-0.596
10.893
10.506
0.138
0.479
-0.054
11.538
11.048
0.241
3.271
2.274
14.330
13.376
0.705
1.425
0.907
12.484
12.009
0.226
2.240
1.489
13.299
12.591
0.459
-0.056
-0.529
11.003
10.573
0.181
-0.507
-0.969
10.552
10.133
0.170
0.637
0.149
11.696
11.251
0.196
3.189
2.368
14.248
13.470
0.529
1.115
0.641
12.174
11.743
0.182
12 2.160
1.581
13.219
12.683
0.287
1.608
1.027
12.667
12.129
0.289
3.209
2.507
14.268
13.609
0.410
1.247
0.854
12.306
11.956
0.101
3.058
2.365
14.117
13.467
0.401
4.051
3.254
15.110
14.356
0.505
1.207
0.694
12.266
11.796
0.221
1.225
0.734
12.284
11.836
0.199
1.353
0.843
12.412
11.945
0.218
1.493
0.955
12.552
12.057
0.246
1.395
0.870
12.454
11.972
0.233
-0.342
-0.797
10.717
10.305
0.163
1.813
1.243
12.872
12.345
0.278
1.354
0.779
12.413
11.881
0.283
1.148
0.625
12.207
11.727
0.231
1.633
1.043
12.692
12.145
0.298
-0.034
-0.839
11.025
10.263
0.513
2.586
1.936
13.645
13.038
0.358
1.628
0.967
12.687
12.069
0.369
Table 2 - Data of the 95 stars from M38 analyzed in the present paper. The first and second columns are the instrumental B and V magnitudes. The second column is the apparent magnitude of the star in the B filter. The third column is the V magnitude and the last is the color index of the star.
6 - References Wikipedia - Plank´s Law. (2011, January). Retrieved January 2011, from http://en.wikipedia.org/wiki/Planck's_law Annapurni Subramaniam, R. S. (1999). Multicolor CCD Photometry and Stellar Evolutionary Analysis of NGC 1907, NGC 1912, NGC 283, NGC 2384 and NGC 6709 Using Synthetic CMD. The Astronomical Journal. Kaler, J. B. (1989). Stars and their Spectra: An Introduction to the Spectral Sequence. Cambridge University Press. La radiación del cuerpo negro. (n.d.). Retrieved 2011, from http://www.sc.ehu.es/sbweb/fisica/cuantica/negro/radiacion/radiacion.htm Maier, M., & Heil, K. (2008). CCD Photometry. Montsec Astronomical Observatory. (n.d.). Retrieved from http://www.oadm.cat/eng/infgeneral_oam.php?section=tech&subsec=instr Morgan, W., & Keenan, P. (1973). Spectral Classification. Anual Review of Astronomy and Astrophysics, vol 11, p.29.
13 Sekiguchi, M., & Fukugita, M. (2000). A Study of the B-V Color-Temperature Relation. The Astronomical Journal. Siess L., D. E. (2000). Astronomy and Astrophisycs, 358, 593. Smith, R. C. (1995). Observational Astrophysics. Cambridge University Press. Stellar Magnitudes. (n.d.). Retrieved October 23, 2010, from http://csep10.phys.utk.edu/astr162/lect/stars/magnitudes.html Strobel, N. (2007, June 2). Magnitude System. Retrieved October 23, 2010, from http://www.astronomynotes.com/starprop/s4.htm
