Instructions-AgeGlobularClusters-Fall2023v01
pdf
keyboard_arrow_up
School
Georgia Southern University *
*We aren’t endorsed by this school
Course
1000
Subject
Astronomy
Date
Jan 9, 2024
Type
Pages
9
Uploaded by ElderIbex1351
1 |
P a g e
ASTR 10000
Mini Project Age of Stellar Clusters
Instructions
Updated: 10/30/2023
To get credit, the poster you will submit must be saved in pdf format and uploaded to the dropbox
available in folio.
Scientific objective
In this project, you will apply what you have learned about the brightness and colors of stars, the H-R
diagram, and stellar evolution, to analyze real data from stars in
clusters,
and to determine the ages of
the clusters and, in turn, come up with your own estimate for the minimum age of the Universe.
Background
Astronomers have discovered that some of the oldest stars are often found in globular clusters.
Globular clusters
are tightly bound groups of stars. In fact, as you can see by looking at the M80 globular
cluster in
Figure 1
, there are so many stars in one place that at the center of the cluster it can be hard to
distinguish one star from another! The stars within a globular cluster are all approximately the same age
because they all formed at approximately the same time from a common gas cloud.
As you’ve already learned in this course, a Hertzsprung
-Russell diagram sorts stars by their luminosity on
the vertical axis, and their surface temperature on the horizontal axis (
Figure 2
). All stars start off with
the same evolutionary path: they form from a stellar gas cloud, spend hundreds of millions or even
billions of years as
main-sequence
stars, fusing hydrogen into helium and giving off light. Later, as they
die, they leave the main sequence and turn into either red giant or red supergiant. Their death course
from a red giant or supergiant can end in several different forms, including either white dwarf, neutron
star, or black hole. In this project, you will mainly be interested in the length of time a star spends as a
main-sequence star.
Figure 1.
Globular cluster M80 contains hundreds of thousands
of stars held together by mutual gravitational attraction.
Credits: The Hubble Heritage Team (
AURA/STScl/NASA
)
2 |
P a g e
Figure 2.
Hertzsprung-Russell diagram, showing the
location of the Main sequence stars, and other
stellar classes: giant stars, supergiant stars and
white dwarfs. Credit: Astronomy.starrynight.com
Main-sequence stars are characterized by their mass, temperature, luminosity (brightness), color, and
other parameters. Temperature is used to class stars into seven spectral types, as shown in
Table 1
.
Type O stars at the top of Table 1, are bluer, hotter, and more massive; they are located at the top-left
end of the main sequence. Type M stars are redder, colder, and less massive; they are located at the
bottom-right end of the main sequence.
When the star has exhausted the hydrogen available for atomic fusion in its core, the star "turns off" the
main sequence and moves onto being a red giant or supergiant. In general, the more massive the star
(higher to the left on the main sequence), the faster it burns the fuel available in its core, and the
shorter its main sequence lifetime will be. An O class star will turn off the main sequence after a few 40
million years, whereas a less massive G-class star stays on the main sequence for about 9 billion years.
Thus, stars located at the upper left tip of the main sequence leave first and are followed by stars
progressively more to the lower right.
You can watch the evolution of a star’s cluster in the following video:
https://www.youtube.com/watch?v=wbvgjzW3Xz0
.
Table 1.
Spectral type of stars, and some of their characteristics.
Spectral
Type
Apparent Color
Temperature
Mass
(Sun =1)
Lifetime on Main
Sequence (years)
O5
Blue
40,000 K
40
1 million
B0
Light blue
28,000 K
16
10 million
A0
White
10,000 K
3.3
500 million
F0
Light yellow
7,500 K
1.7
2.7 billion
G0
Yellow
6,000 K
1.1
9 billion
K0
Orange
5,000 K
0.8
14 billion
M0
Red
3,500 K
0.4
200 billion
3 |
P a g e
To estimate the age of a globular cluster, you can plot its Hertzsprung-Russell diagram and determine
the spectral type (or equivalently, the temperature) of stars currently leaving the main sequence.
Figure
3
shows the H-R diagram of a globular cluster; each dot corresponds to one member star. The point
where stars leave the main sequence is called the
turnoff point
and is marked with a red circle. Since
stars of a cluster are formed at approximately the same time, the age of the cluster corresponds to the
lifetime of stars located at the turnoff point. Stars to the upper right of the turnoff point are already
transitioning to red giants or supergiants.
The spectral type (and temperature) of the stars is equivalent to the value of the
g-r
color index
, which
is the difference between its brightness measured through green and red color filters. The g-r color
index has the advantage that it can be directly measured with astronomical instruments. Hot blue stars
will have a smaller or more negative color index, while cooler red stars will have a larger color index
value. Thus, the age of a cluster is a function of the g-r color index value of its turnoff point, as shown in
Figure 4
. For example, if the turnoff point is located at a g-r value of 0.2, the age of the cluster is about
6.5 or 7.0 billion years.
In this mini-project, you will create H-R diagrams for two globular clusters, determine their turnoff point,
and use that information to estimate the age of each cluster.
Figure 3.
Hertzsprung- Russell diagram of globular cluster 47
Tucanae. Each point in the plot represents the luminosity
and Temperature of a star in the cluster.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
4 |
P a g e
Procedure
To get you started,
Table 2
contains the catalog names and celestial coordinates (right ascension
‘
ra
’
and
declination
‘
dec
’)
of the clusters to be analyzed. You will analyze only two of those clusters, assigned by
the initial of your last name.
To complete the mini project you have to,
1.
Identify the clusters that have been assigned to you.
2.
Obtain a picture of the clusters from an astronomical database.
3.
Download the data files of your assigned clusters, available in the folio module of this project.
4.
Use the data files to create your own H-R diagrams
5.
Identify the turnoff point of each cluster and use them to estimate their age.
Table 2.
Star clusters designated to each student according to the last name initial. The position of the
clusters is given in columns 3 and 4.
Student
’s
Last Name
Initial
Star Cluster Name
ra (HH:MM:SS)
dec (DD:MM:SS)
A to F
NGC 5024
13:12:55.2
+18:10:05.4
NGC 7089
21:33:27.0
-00:49:23.7
G to L
NGC 5272
13:42:11.6
+28:22:38.2
NGC 5053
13:16:27.1
+17:42:00.9
M to U
NGC 5904
15:18:33.2
+02:04:51.7
NGC 5466
14:05:27.3
+28:32:04.0
V to Z
NGC 7078
21:29:58.3
+12:10:01.2
NGC 6205
16:41:41.2
+36:27:35.5
Figure 4.
Age-Color diagram. The plot shows
the age of the cluster as a function of the g-r
color index of the turn-off point.
5 |
P a g e
The detailed procedure to complete steps 1 to 4 is described in the following pages.
1. Identify the clusters you will work with.
Identify which are your assigned star clusters from Table 2. For example, if your last name starts with ‘J’,
you will work with data of clusters NGC 5272 and NGC 5466.
Take note of the right ascension (ra) and declination (dec) celestial coordinates of your clusters.
2. Obtain a Picture of the Cluster
Astronomers use a variety of online catalogs and resources to access repositories of data and images of
the celestial objects. The
Sloan Digital Sky Survey (SDSS)
is a collection of images, spectra and
photometry data of over 1 billon objects in the sky. You will use the
SDSS
image-finding tool
to obtain
images of the clusters you were assigned.
i.
Go to:
http://skyserver.sdss.org/dr7/EN/tools/chart/navi.asp
ii.
As shown in
Figure 5
, input the right ascension and declination coordinates in the area circled in
blue
. You don’t need to convert the positions to decimal form, just copy the numbers with the
format shown in Table 2, the app will convert those into decimal form. Click the "Get Image"
button. Checkmark the boxes "Grid" and "Label," circled in green. You may also need to zoom in
or out to get a better view of your cluster; the zoom tool is marked within the red circle.
Figure 5
.
Screenshot of the SDSS
image-finding tool.
iii.
Use the “Snipping tool” or the “print screen” button of your keyboard to Save
a screenshot of
the cluster, with the image zoomed to include most of the cluster while still showing stars
individually. Repeat steps ii and iii, now for the second cluster. If you need help using the
snipping tool, watch this video:
https://www.youtube.com/watch?v=O_55eg00H-w
3. Download Cluster Data
Download the data files of your clusters. The files are available in the folio module of this project and
contain the positions and brightness in green and red colors of thousands of individual stars of the
clusters. You should be able to open the files with excel.
6 |
P a g e
4. Create an H-R Diagram
Important Note:
The instructions given here assume you are using Microsoft Excel version 2010 or later.
It is possible to use other spreadsheet programs such as
google sheets
or
Numbers
in mac, but you will
have to adjust your actions accordingly. You can find numerous YouTube video tutorials for each of the
required steps.
i.
Open one of the data files you downloaded from folio, in Microsoft Excel. Each row has
information about a single star in the cluster. Each column contains a different piece of
information about the star:
ra: right ascension celestial position in degrees
dec: declination celestial position in degrees
g: green filter magnitude
r: red filter magnitude
Scroll down to the bottom of the file and take note of the last row number with data.
ii.
Calculate the color index g-r.
The horizontal axis of the Hertzsprung-Russell diagram contains
the surface temperature of the star. Since the color of a star is an indication of its temperature,
we will use this parameter instead of temperature. Color is measured by a color index, which is
the difference of the star’s apparent magnitude measured in two different colors. We will use
the brightness magnitudes measured with green (g) and red (r) filters. On the first empty
column to the right of the spreadsheet you will calculate the
color
index “g
-
r”
of each star. You
don’t have to do it manually,
with the following procedure, Excel will do it automatically for you:
a.
Place your mouse on cell E2 of the spreadsheet, left-click and type:
=C2-D2
Do not omit the ‘=’ sign or you will not get the expected results.
This will calculate the
difference of cell C2 and D2, that is, color index
g-r
.
b.
To repeat this calculation automatically for the rest of the rows, right click on cell E2,
and select “copy”
in the context menu of excel. Next, left-click on cell E3, and scroll
down to the last row with data, use the scroll bar on the right side of the window to
scroll faster. On the last row with data, column E, left-click on the mouse while holding
“Shift”
key on your keyboard, this will select all the cells of column E. While all those
cells are selected, click ‘Paste’
in the ‘Home’ menu
. Column E will be automatically filled
will all the ‘g
-
r’ values for each star in the cluster
!
c.
If you need additional help, try the instructions in the following video:
https://www.youtube.com/watch?v=Dq4khIULb6Q
.
iii.
Luminosity g.
The luminosity of the star is estimated by its magnitude in the
green “g”
filter. In
Our H-R diagram, luminosity is the vertical axis, and we want to have more luminous stars
higher in the diagram. However, astronomers define luminosity in a way that less luminous
objects have larger “g” values, thus, less luminous stars would be higher
in the HR diagram. To
correct this “upside down” luminosity scale, you will have to invert the sign of the luminosities
in the data table, by multiplying all
“g” values
in column 3 by -1.0 . To do that, follow the next
two steps:
a.
Place your mouse on cell F2 of the spreadsheet, left-click and type:
= - C2
Don’t forget the negative “
-
“
sign, so that less luminous stars get more negative values.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
7 |
P a g e
b.
Repeat this calculation for the rest of the rows, as we did in step “ii.b”above. Right click
on cell F2, and select “copy” on the
context menu of excel. Next, left-click on cell F3, and
scroll down to the last row with data, use the scroll bar on the right edge of the window
to scroll faster. On the last row with data, column F, left-click on the mouse while
holding “Shift”
key on your keyboard, this will select all the cells of column F. While all
those cells are selected, click ‘Paste’. Column F will be automatically filled will all the ‘
-
g’
values for each star.
iv.
Now you can construct the H-R diagram with the plotting feature of Microsoft Excel. Highlight
columns E and F of the spreadsheet to select the data to be plotted. On the top menu bar, click
"Insert", then
“Charts”,
and "Scatter" to create a scatter-point plot. Select "Scatter with only
markers" to create a plot with only points (no lines connecting the points). This will create a
graph with luminosity (g) on the vertical axis, and color index (g-r) on the horizontal axis.
v.
Now
let’s do
some adjustments to the vertical and horizontal scales of the graph.
vi.
X-axis:
Double-click on the numeric labels on the x-axis to bring up the "Format axes" box.
Under "Axis Options," change the "Minimum" and "Maximum" values to get a useful zoom on
the data points. Repeat to adjust the
Y-axis
limits. Make sure the limits of the graph are such
that the region with higher concentration of stars extends across the extension of the graph,
and areas with low density of data points
are cropped, it doesn’t matter if you leave so
me data
points out of the plot. Usually limits of about -0.5 to 2.0 along the x-axis and about -25 and -15
along the vertical axis give reasonable results, but each cluster may require somewhat different
values.
vii.
Adjust the size of the markers. The markers are the symbols that represent each data point on
the plot. If you double click on one of the data points a menu opens that will allow you to make
the markers smaller and modify their color. This may be helpful to show the data in a form that
makes the identification of the turnoff point easier.
viii.
Change the axis name and the plot title by clicking on them. The y-axis should be labeled "Star
luminosity (g)" and the x-axis should be labeled "Star color (g-r)". Your graph should look similar
to the one shown in
Figure 6
.
ix.
Resize the graph to make the plot approximately squared, avoid having graphs that look
disproportionate, too wide or too tall. To do that, left-click on an empty area of the plot and
drag one of the small circles that appear at the edge of the chart area.
8 |
P a g e
Figure 6.
Example of a HR diagram with the
main sequence and turnoff point marked
for reference. The green dashed line shows
the g-r value that corresponds to the
turnoff point, approximately 0.8.
5. Match Your Turnoff Point to a Star Classification and estimate the age of the cluster
i.
Identify the turnoff point.
The turnoff point can be identified as the region where the main
sequence ends or decreases significantly in the density of points, further to the top left of the
diagram. If you have difficulty to identify the turnoff point, use
Figure 3
and
Figure 6
as example
references. As you can see from those figures, the main sequence may look a little bit different
in each cluster.
ii.
Add a mark to the location of the turnoff point. Use the “Insert” menu, then “Illustrations” and
“Shapes”. The line that delineates the main sequence is optional.
iii.
On the horizontal axis, determine the value of the (g-r) color index that corresponds to the
location of the turnoff point.
Figure 6
shows how to determine that value with the help of the
green vertical dashed line.
iv.
Use the graph shown in
Figure 4
of
the ‘Background’ section
to determine the age of the cluster
that corresponds to the (g
—
r) color index of the turnoff point.
v.
Repeat all steps for the second cluster
and compare the ages of the two clusters.
Communicate Your Results
Create an award-winning
poster
showing your results and, submit it in pdf format to the
project’s
folio
dropbox. PowerPoint is a good tool to create posters, but feel free to use your favorite software. The
poster must contain, as a minimum the following elements:
1.
Your name and Eagle ID.
2.
The H-R diagram of each cluster.
3.
The images of the clusters.
4.
A table or infographic design that provides: cluster names, value of the (g-r) color index at the
turnoff point and approximate age of each cluster.
5.
A summary discussing at least the following points:
a.
How many stars were included in your sample data of each cluster?
Turnoff
point
9 |
P a g e
b.
What is the minimum and maximum age of each cluster?
c.
Which cluster is older?
d.
Given that the universe must be older than objects in it, what is the minimum age of the
universe based on your cluster samples?
e.
How does this age compare to other estimations astronomers have made of the
universe's age? (Find the estimated age of the universe in our textbook or from reliable
internet resources, and write the reference of your source).
6.
Be creative! Design a poster that looks nice, organize the information in a way that is easy to
read. Use color, shapes, be original. A couple sample posters are available in the folio module of
the mini project.
7.
Save your poster in pdf file and upload. In
folio
, g
o to “Assessments >> Assignments >> Project
3.
Age of Stellar Clusters
”
.
Don’t hesitate to contact me if you have
questions:
Dr. Jorge Villa-Vargas
jvillavargas@georgiasouthern.edu
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help