Download HR Diagram of a Star Cluster

Name ____________________________________ Date _____________
Astronomy Exercise #9: The H-R Diagram of a Star Cluster
by M.L. West after Joseph Holzinger and Michael Seeds
Objective : to become familiar with the measurement and calibration of photographic brightness
of stars. To experience making and interpreting a Hertzsprung- Russell diagram from
measurements.
Equipment: Plastic overlay with wedge scale, ruler, computer with HRDataTable.xls, plastic
overlay with isochrons, a colored pencil
1. Background
A cluster of stars which is localized in space is usually localized in time also.
Surprisingly, the brightness (magnitude) of the stars in two different color bands can be
interpreted to tell the cluster's age and distance from Earth. This is done by plotting a magnitude
vs. color diagram (as Hertzsprung and Russell did) of the values for the cluster members, and
then comparing this to computer models of how stars change as they age.
Blue (B) magnitudes are measured through a filter centered on the wavelength 4400 Å
(440 nm), while visual (V) magnitudes are determined through a yellow filter centered at 5430 Å
(543 nm). The difference between these magnitudes is called B-V, the color index.
Define:
Apparent magnitude:
Absolute (true) magnitude:
Isochron:
Age of the solar system = ________________________ years.
2. Measuring visual magnitudes
One way to measure the brightness of a star is by the size of its image on a photograph.
We will use a wedge scale with arbitrary units. Trace the wedge in Figure 1 onto tracing paper or
use a plastic photocopy as an overlay.
Use the wedge to measure the diameters of the numbered stars in Figure 2 (a portion of
the star cluster NGC 6819). Estimate values to the nearest tenth of a wedge unit. Record these
image diameters in the HR Data Table. If a star is invisible on your photocopy of the photograph
then list its diameter as zero.
These diameter values can be converted into standard apparent magnitude values if we
can calibrate the photograph. Eight of the numbered stars have had their apparent brightness (V
magnitude) measured individually by a photometer attached to a telescope. You can make a
calibration curve by plotting their accepted apparent V magnitudes vs. their image diameters as
measured by your wedge. Draw the best straight line through the eight points. Open the Excel
spreadsheet and type in your names and date, then save the spreadsheet as
HRDataTable_yourinitials.xls, or some such. (This will leave a clean template for another
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student later.) Then type in your data. Ask Excel to fit a trendline and record its equation and its
R squared value:
Your equation
y = accepted apparent V mag =
Your R squared value
Use this calibration line to find the apparent V magnitudes of the rest of the stars in the table.
3. Plotting a Hertzsprung-Russell diagram
A true Hertzsprung-Russell diagram is an XY plot of absolute magnitude vs. temperature
(or equivalently, color or spectral class). We will assume that every one of the stars on this
photograph is a member of the cluster NGC 6819 and so we will assume that they all lie at about
the same distance from us. Then we can use their apparent magnitude (V) in place of the
(preferred) absolute magnitude as the Y-axis. The X-axis will be color index = B-V which is
related to the (preferred) temperature. The hottest stars in this sample have B-V = 0, while the
coolest stars have B-V= 1.4. This quantity is a difference between the apparent magnitudes of the
stars through a blue filter or a visual filter. Astronomers arrange the axes with V magnitudes in
reverse order, that is, low numbers high on the Y-axis. In order to compare our data to theoretical
models we need to match the scale on the plastic overlay, so plot your points on the graph
provided in Figure 4.
Plot the 49 points of apparent V magnitude vs. B-V color index. Sketch in the best Main
Sequence straight line. This is a diagonal line through most of the points from (low V, low B-V)
to (high V, high B-V). Ignore distant outliers, please.
4. Finding the Distance to Cluster NGC 6819
Your Main Sequence line can be used to find the relationship of your apparent
magnitudes to absolute magnitudes. This is done by comparing your line to the Main Sequence
line of another cluster nearer to the solar system which has had its distance measured directly,
and so we know the relationship of apparent magnitude to absolute magnitude for that cluster.
The Hyades cluster in Taurus has been well measured. Its visual absolute magnitude values (Mv)
corresponding to values of B-V are given below. Fill in the values of V from your cluster’s Main
Sequence line at the same B-V values. The difference between your values and the Hyades values
is called the distance modulus.
Distance Modulus Data
B-V
Mv for Hyades
0.0
1.5
0.2
2.5
0.4
3.6
0.6
4.8
0.8
5.9
Your V for NGC
6819
Difference = V-Mv
= distance modulus
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Average distance modulus = ___________________
We can calculate the distance to cluster NGC 6819 by
distance (parsecs) = 10 * 10^((average distance modulus)/5) = __________________ pc.
distance (light years) = distance (parsecs) * 3.26 = ____________________________ ly
5. Age of the Cluster
We will assume that all the stars in NGC 6819 formed at the same time. The more
massive stars are at the hot end of the Main Sequence. They consume their nuclear fuel quickly
and are the first to evolve into red giants. As a cluster ages, the Main Sequence gets shorter at the
hot end and more stars become red giants. Computer models can be made to show this
progression of star types from a range of initial masses.
Trace the isochrons of Figure 3 onto tracing paper or use a plastic photocopy overlay.
These are lines of constant age from models. Slide the tracing up and down (but not right or left)
on your HR diagram to find the best match to the data of NGC 6819. Be careful to keep the B-V
values the same. Interpolate the date of the closest isochron.
Age of NGC 6819 = _______________________ years.
Age of the solar system = ___________________ years.
So, this cluster’s stars are (older, younger) than our sun.
In a different color, plot a point for the Sun (Mv = 4.79, B-V = .62) on your cluster HR diagram
and label it. Note that you have to add your average distance modulus to the Sun’s 4.79 in order
to plot the point on your graph. It should lie on the Main Sequence line.
6. Discussion Questions
1. Why is the image of a brighter star larger than that of a fainter star? Aren't the stars so far away
that they are all just points?
2. Is it all right to assume that all the stars in the photo are in the cluster? How could we tell if
this were a poor assumption?
3. Is it all right to assume that all the stars are the same distance from us?
(Hint: What is the diameter of a cluster? What percent is this of the distance to this cluster?)
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References:
Burkhead, Martin S., "Photometric Observation of the Star Cluster NGC 6819", 1971,
Astronomical Journal, Vol. 76, p 251-259
Holzinger, Joseph R., and Michael A. Seeds, "Laboratory Exercises in Astronomy", New York,
Macmillan Publishing, 1976, p 201-210
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HR Data Table for star cluster NGC 6819
Star
Image diameter,
wedge units
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
V magnitude
17.06
15.97
15.03
13.97
13.29
12.87
17.90
16.69
B-V, color index
0.58
0.77
0.59
1.21
0.98
0.62
0.66
1.16
1.37
0.58
1.12
0.73
1.25
0.46
0.73
0.49
0.47
0.54
0.70
0.55
0.11
0.70
0.50
0.67
0.90
0.77
1.10
0.87
1.01
0.64
0.74
0.62
0.46
0.69
0.62
0.55
1.09
0.98
1.05
0.65
1.02
0.59
6
43
44
45
46
47
48
49
Calibration Curve Data
Star
5
6
10
11
13
21
27
31
0.50
0.67
1.05
0.82
0.48
0.59
0.49
Image diameter
V magnitude
17.06
15.97
15.03
13.97
13.29
12.87
17.90
16.69
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