Astronomy 101
Hertzsprung-Russell Diagram & the Evolution of Stars
Stars
How countlessly
they congregate
O'er our tumultuous snow,
Which flows in shapes as tall as trees
When wintry winds do blow!--
As if with keeness for our fate,
Our faltering few steps on
To white rest, and a place of rest
Invisible at dawn,--
And yet with neither love nor hate,
Those stars like some snow-white
Minerva's snow-white marble eyes
Without the gift of sight.
-- Robert Frost
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Introduction
During
the late 19th and earth 20th centuries, astronomers obtained spectra and
parallax distances for many stars, a powerful tool was discovered for
classifying and understanding stars. Around 1911-13, Ejnar
Hertzsprung and Henry Norris Russell independently found that stars could be
divided into groups. You are charged
with attempting to reproduce their efforts and find the groups that lie buried
in the data.
We
will construct portions of the H-R diagram using a software spreadsheet and
graphics package, Microsoft Excel . This and similar
programs are used in millions of jobs in modern society. It is thus very
important for undergraduate students to get experience using spreadsheets and
to understand their capabilities.
Excel
Data Entry
Launch
Microsoft Excel. To enter an item in a cell, simply click
at the cell and type. Use arrows to move between cells. In Row 1, type in the
column headings: Temperature in A1 and L/Lo (luminosity in units of solar
luminosity) in B1. Input temperatures
and luminosities for the two datasets: the 15 stars closest to Earth; and the
15 brightest stars. You can type in the star name in a separate column if you
wish, but we will not be using names in the plot. If you put the two datasets
into different columns (e.g. cols A-B for Nearest Stars and D-E for Brightest
Stars), then you can plot them with different symbols. The data are obtained
from < 1992 Lang, R. Kenneth Stars, and Planets Data: Astrophysical>.
Nearest stars
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Name |
Temperature
(K) |
Luminosity
(Lo) |
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Sun |
5860 |
1.0 |
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Proxima Cen |
3240 |
0.00006 |
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alpha Cen A |
5860 |
1.6 |
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alpha Cen B |
5250 |
0.45 |
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Barnard's
star |
3240 |
0.00045 |
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Wolf 359 |
2640 |
0.00002 |
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BD +36 2147 |
3580 |
0.0055 |
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L 726-8A |
3050 |
0.00006 |
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UV Ceti |
3050 |
0.00004 |
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Sirius A |
9230 |
23.5 |
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Sirius B |
9000 |
0.003 |
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Ross 128 |
3100 |
0.0004 |
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Ross 154 |
3240 |
0.00048 |
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Ross 248 |
3050 |
0.00011 |
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epsilon Eri |
4900 |
0.30 |
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61 Cyg A |
4000 |
0.08 |
Brightest stars
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Name |
Temperature
(K) |
Luminosity
(Lo) |
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Sun |
5860 |
1.0 |
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Sirius A |
9230 |
23.5 |
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7700 |
1400. |
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alpha Cen A |
5860 |
1.6 |
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Arcturus |
4420 |
110. |
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Vega |
9520 |
50. |
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Capella |
5200 |
150. |
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Rigel |
11200 |
42000. |
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Procyon |
6440 |
7.2 |
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Betelgeuse |
3450 |
12600. |
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Achernar |
15400 |
200. |
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beta Cen |
24000 |
3500. |
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Altair |
7850 |
10. |
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alpha Cru |
25400 |
3200. |
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Aldebaran |
15400 |
95. |
Print your
spreadsheet by
highlighting the data (hold the mouse button down as you drag across the data),
enter the File menu, click Print Area, Print Preview
and Print.
Activity
1: Plotting the H-R diagram
To
plot a diagram, open the Chart Wizard (bar-chart icon, 17th from the left at
the top). Specify the cell ranges to be plotted; e.g. C2:c15,D2:D15.
Select the XY scatter plot, Format 1 or 3, and the plot should appear. Double
click on the chart to make changes. You might add an informative title, change
axes. Astronomers historically plot the H-R diagram with temperature decreasing
to the right. To do this, click on the labeled X axis, enter the axis Scale
page, and reverse the order of the X axis. You will notice that the graph looks
range due to the great range in luminosities.
To make it more understandable, it is best to view it at a logarithmic
scale. You can change the y-axis to a
logarithmic scale by clicking on the axis and selecting the logarithmic
option. Finally, combine both sets of
data onto one graph. You should have
three graphs. Be certain that each has a
useful title and labeled axes.
Print your H-R
diagrams for the Nearest and Brightest stars, and then
a third graph with the combined data. This is done by double-clicking on the chart, entering the
File menu, Print Preview and (if you like it) Print.
1. Upon review of your printed charts, do you
see any obvious groupings of stars?
Identify the main sequence stars, red giants and white dwarfs. Label a
horizontal axis with the spectral type classifications used by astronomers: O (52000-33000
K), B (30000-11000), A (9500-7600), F (7200-6200), G (6000-5600), K
(5200-4100), M (3900- 2600).
2. Study the graphs and describe any trends you
see relating temperature and luminosity for stars in general. A major trend should appear. Label this the “main sequence.”
3. Suggest which three stars on the diagram seem
most unusual. Describe the
characteristics of these stars.
4. Study the diagram and explain how you would
deduce what kinds of stars are probably the most common.
5. Where does our sun lie on the diagram? What other stars are similar to our sun and
what characteristics do they share?
6. What stars would be the most visible? Which would be least visible? Why? What factors
determine how visible a star is in the sky?
7. If a star were seen in the sky and measured
to have a temperature or 7000 K, predict the luminosity it should have, explain
how you arrived at this, and include any assumptions you make in this
prediction
8. Reflect on this activity. What have you learned with respect to the
scientific study of stars? What elements
were physically measured, and what elements were logically inferred
from your analysis?
Activity
2: Stellar populations and radii
On
a separate sheet discuss the differences between the Nearest
and Brightest stars in the H-R diagram. Can you deduce which kinds of stars are
most common in the galaxy and which kinds are rare? Are the bright stars we see
at night that make up the constellations mainly the
common or rare types?
Stellar
surfaces are approximately `blackbody' emitters which obey the Stefan-Boltzmann
Law: Luminosity ~ Area x Temperature4. The shapes of stars are spheres with Area ~
Radius2. We can combine these formula to
deduce the size (radii) of stars in different portions of the H-R diagram:
Radius ~ Luminosity½ x Temperature. Using
the Sun's radius as a unit, estimate the radius of a selected red giant star
(upper right in the H-R diagram) and a white dwarf (lower left).
Activity
3: Stellar evolution
Use
a new part of the spreadsheet to input data showing the stages of evolution for
the Sun. The table below gives the calculated solar properties during the T Tauri (pre-main sequence), main sequence, and red giant
phases. The current age of the Sun is 4.6 billion years. Print
out an H-R diagram showing the Sun's evolution . Use a format that
connects the dots. What is the Sun's radius at its most luminous point as a red
giant? Comment on the fate of the planets when the Sun becomes a red giant (1
A.U. is roughly 200 solar radii).
Evolution of the Sun
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Age (yr) |
Temperature
(K) |
Luminosity
(Lo) |
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10^6 |
4800 |
3. |
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10^7 |
4800 |
0.3 |
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10^8 |
5800 |
0.8 |
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4.6 10^9 |
5800 |
1.0 |
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10 10^9 |
5800 |
1.8 |
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10.02 10^9 |
4800 |
3.0 |
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11 10^9 |
3400 |
350. |
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