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Astronomy 123: Assignment 2
Our Place in the Milky Way
Due: in class on Revised: 31 Jan 2012

Globular Clusters and the Center of the Milky Way Galaxy

Globular clusters are spheroidal groups of stars typically 100 light years across and containing thousands of stars. Globular Clusters are ancient, at least 11 billion years old forming when the Galaxy was still young. They are scattered in our halo and require hundreds of millions of years to orbit the galactic center. In this exercise we use the fact that the Globular Clusters are distributed about the center of the Mikly Way to find the direction to the center of the Galaxy.

Three globular clusters. On the left is NGC 2419, it is a large but very distant globular cluster lying far beyond the edge of the galaxy. M13 in the middle is much closer, it is one of the brightest globular clusters in the sky. On the right is Pal 11, a small globular cluster in Aquila.

Below is a list of most of the globular clusters and their properties that populate the halo of the Milky Way galaxy. The data used in this execise are the coordinates of the globular clusters given in Columns 3 & 4, the Equatorial Coordinates, RA (Right Ascension) and Dec (Declination).

    1          2         3       4       5     6      7       8       9      10
 Catalog |   Other   |  Equatorial   |  Galactic  | Visual|Angular|Distance|Con
 Number  |   Name    |  Coordinates  | Coordinates|  Mag. | Diam. | (kly)  |
_________|___________|__RA______Dec__|___l°____b°_|_______|__(')__|________|___
NGC 104   47 Tuc      00 24.1  -72 05  305.9 -44.9   3.95    50'      15    Tuc
NGC 288               00 52.8  -26 35  152.3 -89.4   8.09    13'      29    Scl
NGC 362               01 03.2  -70 51  301.5 -46.3   6.40    14'      28    Tuc
NGC 1261              03 12.3  -55 13  270.5 -52.1   8.29     7'      53    Hor
Pal 1                 03 33.4  +79 35  130.1 +19.0  13.18     1'      36    Cep
AM 1      E 1         03 55.0  -49 37  258.4 -48.5  15.72     1'     398    Hor
Eridanus  UGCA 91     04 24.7  -21 11  218.1 -41.3  14.70     1'     294    Eri
Pal 2                 04 46.1  +31 23  170.5  -9.1  13.04     2'      90    Aur
NGC 1851              05 14.1  -40 03  244.5 -35.0   7.14    12'      39    Col
NGC 1904  M79         05 24.2  -24 31  227.2 -29.4   7.73    10'      42    Lep
NGC 2298              06 49.0  -36 00  245.6 -16.0   9.29     5'      35    Pup
NGC 2419              07 38.1  +38 53  180.4 +25.2  10.39     5'     275    Lyn
Pyxis                 09 08.0  -37 13  261.3  +7.0  12.90     3'     129    Pyx
NGC 2808              09 12.0  -64 52  282.2 -11.3   6.20    14'      31    Car
E 3       ESO 37-01   09 21.0  -77 17  292.3 -19.0  11.35     5'      14    Cha
Pal 3                 10 05.5  +00 04  240.1 +41.9  14.26     2'     302    Sex
NGC 3201              10 17.6  -46 25  277.2  +8.6   6.75    20'      16    Vel
Willman 1 SDSS1049+51 10 49.4  +51 03  158.6 +56.8  15?       7'     147    UMa
Pal 4                 11 29.3  +28 58  202.3 +71.8  14.20     2'     356    UMa
NGC 4147              12 10.1  +18 33  252.9 +77.2  10.32     4'      63    Com
NGC 4372              12 25.8  -72 40  301.0  -9.9   7.24     5'      19    Mus
Rup 106               12 38.7  -51 09  300.9 +11.7  10.90     5'      69    Cen
NGC 4590  M68         12 39.5  -26 45  299.6 +36.1   7.84    11'      33    Hya
NGC 4833              12 59.6  -70 52  303.6  -8.0   6.91    14'      21    Mus
NGC 5024  M53         13 12.9  +18 10  333.0 +79.8   7.61    13'      58    Com
NGC 5053              13 16.5  +17 42  335.7 +78.9   9.47    10'      53    Com
NGC 5139  Omega Cen   13 26.8  -47 29  309.1 +15.0   3.68    55'      17    Cen
NGC 5272  M3          13 42.2  +28 23   42.2 +78.7   6.19    18'      34    CVn
NGC 5286              13 46.4  -51 22  311.6 +10.6   7.34    11'      36    Cen
AM 4                  13 56.4  -27 10  320.3 +33.5  15.90     1'      98    Hya
NGC 5466              14 05.5  +28 32   42.2 +73.6   9.04     9'      52    Boo
NGC 5634              14 29.6  -05 59  342.2 +49.3   9.47     6'      82    Vir
NGC 5694              14 39.6  -26 32  331.1 +30.4  10.17     4'     113    Hya
IC 4499               15 00.3  -82 13  307.4 -20.5   9.76     8'      62    Aps
NGC 5824              15 04.0  -33 04  332.6 +22.1   9.09     7'     104    Lup
Pal 5                 15 16,1  -00 07    0.9 +45.9  11.75     5'      76    Ser
NGC 5897              15 17.5  -21 01  343.0 +30.3   8.53    11'      40    Lib
NGC 5904  M5          15 18.6  +02 05    3.9 +46.8   5.65    23'      24    Ser
NGC 5927              15 28.0  -50 40  326.6  +4.9   8.01     6'      25    Lup
NGC 5946              15 35.5  -50 40  327.6  +4.2   9.61     3'      35    Nor
BH 176    ESO 224-08  15 39.1  -50 03  328.4  +4.3  14.00     4'      51    Nor
NGC 5986              15 46.1  -37 47  337.0 +13.3   7.52    10'      34    Lup
Lynga 7   ESO 178-11  16 11.1  -55 19  328.8  -2.8            3'      23    Nor
Pal 14    AvdB        16 11.1  +14 57   28.8 +42.2  14.74     2'     241    Ser
NGC 6093  M80         16 17.0  -22 59  352.7 +19.5   7.33    10'      33    Sco
NGC 6121  M4          16 23.6  -26 32  351.0 +16.0   5.63    36'       7    Sco
NGC 6101              16 25.8  -72 12  317.8 -15.8   9.16     5'      50    Aps
NGC 6144              16 27.2  -26 01  351.9 +15.7   9.01     7'      28    Sco
NGC 6139              16 27.7  -38 51  342.4  +6.9   8.99     8'      33    Sco
Terzan 3              16 28.7  -35 21  345.1  +9.2  12.00     4'      24    Sco
NGC 6171  M107        16 32.5  -13 03    3.4 +23.0   7.93    13'      21    Oph
1636-283  ESO 452-11  16 39.4  -28 24  351.9 +12.1  12.00     3'      25    Sco
NGC 6205  M13         16 41.7  +36 28   59.0 +40.9   5.78    20'      25    Her
NGC 6229              16 47.0  +47 32   73.6 +40.3   9.39     5'      99    Her
NGC 6218  M12         16 47.2  -01 57   15.7 +26.3   6.70    16'      16    Oph
NGC 6235              16 53.4  -22 11  358.9 +13.5   9.97     5'      37    Oph
NGC 6254  M10         16 57.1  -04 06   15.1 +23.1   6.60    20'      14    Oph
NGC 6256              16 59.5  -37 07  347.8  +3.3  11.29     4'      27    Sco
Pal 15                17 00.0  +00 33   18.9 +24.3  14.00     3'     145    Oph
NGC 6266  M62         17 01.2  -30 07  353.6  +7.3   6.45    15'      23    Oph
NGC 6273  M19         17 02.6  -26 16  356.9  +9.4   6.77    17'      28    Oph
NGC 6284              17 04.5  -24 46  358.4  +9.9   8.83     6'      50    Oph
NGC 6287              17 05.2  -22 42    0.1 +11.0   9.35     5'      30    Oph
NGC 6293              17 10.2  -26 35  357.6  +7.8   8.22     8'      29    Oph
NGC 6304              17 14.5  -29 28  355.8  +5.4   8.22     8'      20    Oph
NGC 6316              17 16.6  -28 08  357.2  +5.8   8.43     5'      36    Oph
NGC 6341  M92         17 17.1  +43 08   68.3 +34.9   6.44    14'      27    Her
NGC 6325              17 18.0  -23 46    1.0  +8.0  10.33     4'      26    Oph
NGC 6333  M9          17 19.2  -18 31    5.5 +10.7   7.72    12'      26    Oph
NGC 6342              17 21.2  -19 35    4.9  +9.7   9.66     4'      28    Oph
NGC 6356              17 23.6  -17 49    6.7 +10.2   8.25    10'      50    Oph
NGC 6355              17 24.0  -26 21  359.6  +5.4   9.14     4'      31    Oph
NGC 6352              17 25.5  -48 25  341.4  -7.2   7.96     9'      19    Ara
IC 1257               17 27.1  -07 06   16.5 +15.2  13.10     5'      82    Oph
Terzan 2  HP 3        17 27.6  -30 48  356.3  +2.3  14.29     2'      28    Sco
NGC 6366              17 27.7  -05 05   18.4 +16.0   9.20    13'      12    Oph
Terzan 4  HP 4        17 30.6  -31 36  356.0  +1.3  16.00     2'      30    Sco
HP 1      ESO 455-11  17 31.1  -29 59  357.4  +2.1  11.59     3'      46    Oph
NGC 6362              17 31.9  -67 03  325.6 -17.6   7.73    15'      25    Ara
Liller 1              17 33.4  -33 23  354.8  -0.2  16.77     1'      31    Sco
NGC 6380  Ton 1       17 34.5  -39 04  350.2  -3.4  11.31     4'      35    Sco
Terzan 1  HP 2        17 35.8  -30 29  357.6  +1.0  15.90     2'      18    Sco
Ton 2     ESO 333-16  17 36.2  -38 33  350.8  -3.4  12.24     3'      26    Sco
NGC 6388              17 36.3  -44 44  345.6  -6.7   6.72    10'      33    Sco
NGC 6402  M14         17 37.6  -03 15   21.3 +14.8   7.59    11'      30    Oph
NGC 6401              17 38.6  -23 55    3.5  +4.0   9.45     5'      34    Oph
NGC 6397              17 40.7  -53 40  338.2 -12.0   5.73    31'       8    Ara
Pal 6                 17 43.7  -26 13    2.1  +1.8  11.55     2'      19    Sgr
NGC 6426              17 44.9  +03 10   28.1 +16.2  11.01     4'      68    Oph
Djorg 1               17 47.5  -33 04  356.7  -2.5  13.60     2'      39    Sco
Terzan 5  Terzan 11   17 48.1  -24 47    3.8  +1.7  13.85     2'      34    Sgr
NGC 6440              17 48.9  -20 22    7.7  +3.8   9.20     4'      27    Sgr
NGC 6441              17 50.2  -37 03  353.5  -5.0   7.15    10'      38    Sco
Terzan 6  HP 5        17 50.8  -31 17  358.6  -2.2  13.85     1'      31    Sco
NGC 6453              17 50.9  -34 36  355.7  -3.9  10.08     8'      31    Sco
UKS 1                 17 54.5  -24 09    5.1  +0.8  17.29     2'      27    Sgr
NGC 6496              17 59.0  -44 16  348.0 -10.0   8.54     6'      38    Sco
Terzan 9              18 01.6  -26 50    3.6  -2.0  16.00     2'      21    Sgr
Djorg 2   ESO 456-38  18 01.8  -27 50    2.8  -2.5   9.90     2'      22    Sgr
NGC 6517              18 01.8  -08 58   19.2  +6.8  10.23     4'      35    Oph
Terzan10              18 03.0  -26 04    4.4  -1.9  14.90     1'      19    Sgr
NGC 6522              18 03.6  -30 02    1.0  -3.9   8.27     9'      25    Sgr
NGC 6535              18 03.8  +00 18   27.2 +10.4  10.47     3'      22    Oph
NGC 6528              18 04.8  -30 03    1.1  -4.2   9.60     5'      26    Sgr
NGC 6539              18 04.8  -07 35   20.8  +6.8   9.33     8'      27    Oph
NGC 6540  Djorg 3     18 06.1  -27 46    3.3  -3.3   9.30     2'      12    Sgr
NGC 6544              18 07.3  -25 00    5.8  -2.2   7.77     9'       9    Sgr
NGC 6541              18 08.0  -43 30  349.5 -11.1   6.30    15'      23    CrA
2MS-GC01  2MASS-GC01  18 08.4  -19 50   10.5  +0.1                    12    Sgr
ESO-SC06  ESO 280-06  18 09.1  -46 25  346.9 -12.6            1'      71    Tel
NGC 6553              18 09.3  -25 55    5.3  -3.0   8.06     9'      20    Sgr
2MS-GC02  2MASS-GC02  18 09.6  -20 47    9.8  -0.6                    13    Sgr
NGC 6558              18 10.3  -31 46    0.2  -6.0   9.26     4'      24    Sgr
IC 1276   Pal 7       18 10.7  -07 12   21.8  +5.7  10.34     8'      18    Ser
Terzan12              18 12.3  -22 45    8.4  -2.1  15.63     1'      16    Sgr
NGC 6569              18 13.6  -31 50    0.5  -6.7   8.55     6'      35    Sgr
NGC 6584              18 18.6  -52 13  342.1 -16.4   8.27     7'      44    Tel
NGC 6624              18 23.7  -30 22    2.8  -7.9   7.87     9'      26    Sgr
NGC 6626  M28         18 24.5  -24 52    7.8  -5.6   6.79    14'      18    Sgr
NGC 6638              18 30.9  -25 30    7.9  -7.2   9.02     7'      31    Sgr
NGC 6637  M69         18 31.4  -32 21    1.7 -10.3   7.64     7'      30    Sgr
NGC 6642              18 31.9  -23 29    9.8  -6.4   9.13     6'      27    Sgr
NGC 6652              18 35.8  -32 59    1.5 -11.4   8.62     6'      33    Sgr
NGC 6656  M22         18 36.4  -23 54    9.9  -7.6   5.10    32'      10    Sgr
Pal 8                 18 41.5  -19 50   14.1  -6.8  11.02     2'      42    Sgr
NGC 6681  M70         18 43.2  -32 18    2.9 -12.5   7.87     8'      29    Sgr
NGC 6712              18 53.1  -08 42   25.4  -4.3   8.10    10'      23    Sct
NGC 6715  M54         18 55.1  -30 29    5.6 -14.1   7.60    12'      87    Sgr
NGC 6717  Pal 9       18 55.1  -22 42   12.9 -10.9   9.28     5'      23    Sgr
NGC 6723              18 59.6  -36 38    0.1 -17.3   7.01    13'      28    Sgr
NGC 6749              19 05.3  +01 54   36.2  -2.2  12.44     4'      26    Aql
NGC 6752              19 10.9  -59 59  336.5 -25.6   5.40    29'      13    Pav
NGC 6760              19 11.2  +01 02   36.1  -3.9   8.88    10'      24    Aql
NGC 6779  M56         19 16.6  +30 11   62.7  +8.3   8.27     9'      33    Lyr
Terzan 7              19 17.7  -34 39    3.4 -20.1  12.00     3'      76    Sgr
Pal 10                19 18.0  +18 34   52.4  +2.7  13.22     3'      19    Sge
Arp 2                 19 28.7  -30 21    8.6 -20.8  12.30     4'      93    Sgr
NGC 6809  M55         19 40.0  -30 58    8.8 -23.3   6.32    19'      17    Sgr
Terzan 8              19 41.8  -34 00    5.8 -24.6  12.40     5'      85    Sgr
Pal 11                19 45.2  -08 00   31.8 -15.6   9.80     3'      42    Aql
NGC 6838  M71         19 53.8  +18 47   56.7  -4.6   8.19     7'      13    Sge
NGC 6864  M75         20 06.1  -21 55   20.3 -25.8   8.52     7'      68    Sgr
NGC 6934              20 34.2  +07 24   52.1 -18.9   8.83     7'      51    Del
NGC 6981  M72         20 53.5  -12 32   35.2 -32.7   9.27     7'      55    Aqr
NGC 7006              21 01.5  +16 11   63.8 -19.4  10.56     4'     135    Del
NGC 7078  M15         21 30.0  +12 10   65.0 -27.3   6.20    18'      34    Peg
NGC 7089  M2          21 33.5  +00 49   53.4 -35.8   6.47    16'      38    Aqr
NGC 7099  M30         21 40.4  -23 11   27.2 -46.8   7.19    12'      26    Cap
Pal 12                21 46.6  -21 15   30.5 -47.7  11.99     2'      62    Cap
Pal 13                23 06.7  +12 46   87.1 -42.7  13.47     1'      84    Peg
NGC 7492              23 08.4  -15 37   53.4 -63.5  11.29     4'      84    Aqr

Column 1: Usual catalog number of the globular cluster.
Column 2: Other name (usually a Messier number).
Column 3: Right Ascension in hours and minutes for epoch 2000.
Column 4: Declination in degrees and minutes for epoch 2000.
Column 5: Galactic longitude of the globular cluster.
Column 6: Galactic latitude of the globular cluster.
Column 7: The visual magnitude.
Column 8: Approximate angular diameter of the globular cluster in arcminutes.
          (This is a rough estimate of the cluster's visual isophotal diameter.)
Column 9: Distance to the globular cluster in thousands of light years.
          The error on these distances is typically about ±10%.
Column 10: Constellation the globular cluster is in.

References:
Harris W, (2003), Catalog of parameters for Milky Way globular clusters.
Willman B, Blanton M, West A, Dalcanton J, Hogg D, Schneider D, Wherry N,
      Yanny B, Brinkmann J, (2005), A New Milky Way Companion: Unusual Globular
      Cluster or Extreme Dwarf Satellite?. Astron J, 129, 2692.

Celestial Sphere

Equatorial Coordinates

To define locations on the sky, the Greeks constructed the Celestial Sphere wherein they imagined that the Earth was surrounded by a large cystalline sphere on which the stars were attached. To mimic the daily rising and setting of the stars, it was imagined that the Celestial Sphere spun on its axis (defined by the rotation axis of the Earth). Coordinates of stars on the Celestial Sphere were defined similarly to the manner in which positions are defined on the Earth. The equator of the Celestial Sphere (the projection of the Earth's equator) was defined as 0o Declination (the equiivalent of latitude) and the location of the Vernal Equinox defined 0 hours Right Ascension (the equivalent of longitude, where longitude on Earth begins at Greenwich, England). The above figure shows a flattened version of the Celestial Sphere on which are marked some famous constellations and the ecliptic the path of the Sun through the stars.

In this exercise, you will approximately locate the center of the Milky Way galaxy by plotting and tabulating the locations of the Globular Clusters in our Galaxy.

1. The above plot shows the Celestial Sphere within 50o north and south of the Celestial Equator. Place a dot at the locations on the plot and then tabulate the number of globular clusters in the given right ascension and declination bins in the following Table.

Numbers of Globular Clusters in Different Galactic Locations

 

12 h to 14 h

14 h to 16 h

16 h to 18 h

18 h to 20 h

20 h to 22 h

22 h to 24 h

0 h to 2 h

2 h to 4 h

4 h to 6 h

6 h to 8 h

8 h to 10 h

10 h to 12h

75o to 90o

 

 

 

 

 

 

 

 

 

 

 

 

60o to 75o

 

 

 

 

 

 

 

 

 

 

 

 

45o to 60o

 

 

 

 

 

 

 

 

 

 

 

 

30o to 45o

 

 

 

 

 

 

 

 

 

 

 

 

15o to 30o

 

 

 

 

 

 

 

 

 

 

 

 

0o to 15o

 

 

 

 

 

 

 

 

 

 

 

 

-15o to 0o

 

 

 

 

 

 

 

 

 

 

 

 

-30o to -15o

 

 

 

 

 

 

 

 

 

 

 

 

-45o to -30o

 

 

 

 

 

 

 

 

 

 

 

 

-60o to -45o

 

 

 

 

 

 

 

 

 

 

 

 

-75o to -60o

 

 

 

 

 

 

 

 

 

 

 

 

-90o to -75o

 

 

 

 

 

 

 

 

 

 

 

 

2. Circle the region on your plot in which globular clusters appear to cluster.

3. Roughly, based on your Table, what are the rough coordinates for the Galactic center and, based on your plot, in which constellation is the direction to the center of the Milky Way galaxy located?

4. The coordinates for the galactic center are Right Ascension, R.A. = 17h 45m 40.04s, and Declination, Dec = -29o0.5'. You will estimate the distance to the center of the Milky Way by assuming that the globular clusters are clustered about the center of the Milky Way (as shown in the top panel). Consider the globular clusters in the direction of the center of the Milky Way. Find the average distance to the Globular clusters in the directions between R.A. = 16h 45m and 18h 45m and Dec = -24o to -34o. What is the distance to the center of the Milky Way (based on your estimate). This average distance is roughly the distance to the center of the Milky Way galaxy.

[You can arrive at a more accurate estimate if you find the average of D x cosine(galactic latitute) x cosine(galactic longitude) rather than using the simple average D. Here, D is the distance to the globular cluster.]