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Stellar Evolution

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Abstract

The lifespan of stars can range from several million years to over a trillion years old. Such large

swaths of time make it impossible to directly observe the lifecycle of a star in its entirety. One way to

overcome this obstacle is to find and observe open star clusters - areas of star formation in which stars

formed at roughly the same time and are roughly the same distance away from Earth. Analyzing and

comparing different star clusters will reveal the life of a star after it reaches its zero age on the main

sequence, and how it will behave according to its mass. Charting the stars of a cluster on a Hertzsprung-

Russell Diagram gives us the clues we need to determine the distance of a cluster as well as its age. We can

then compare the H-R diagrams of different clusters, and solve the riddle of how stars evolve.

Background

At the beginning of the 20th Century, two astronomers independently discovered a way to chart

stars according to luminosity and spectral type. Danish astronomer Ejnar Hertzsprung began using this chart

in 1911, with American astronomer Henry Norris Russell following in 1913 (Illingworth & Clark). The

Hertzsprung-Russell Diagram is still used to this day, and has been the single most important instrument in

determining stellar evolution (Weintraub, 2011).

To chart an H-R diagram, one must know what is measured on the axes. For the vertical axis, the

absolute magnitude is measured. The more luminous a star is, the higher it will appear on the chart. For the

horizontal axis, the color index is measured. To get the value for the color index, two measurements of a

star’s apparent magnitude are gathered and then subtracted from another. Most often, the apparent

magnitude is gathered through a telescope using a blue light filter, which is then subtracted by an apparent

magnitude gathered using a visual light filter (Illingworth & Clark). Due to this method, the color index is

often referred to as B-V, and can be a negative number for hotter stars or a positive number for cooler stars.

Because one can determine a color index through B-V regardless of distance and its ease of gathering data,

it is usually preferred over surface temperature or spectral type (Illingworth & Clark). On an H-R diagram,

the hottest stars will appear on the left, and stars will become cooler moving towards the right.

Although the color index of a star is used to more accurately chart a star on an H-R diagram, it does

not tell us what spectral class of star it is. The spectral class of stars are divided into seven different groups;

O, B, A, F, G, K, M, ordered here from hottest to coolest. Each group is further divided into ten different

groupings, numbered 0 through 9, with 0 being the hottest, and 9 being the coolest (Chaisson & Steve,

2017). A B2 star would have a higher surface temperature than a B6 star, for example. The final part of the

spectral class of a star is noted by a Roman numeral, which tells us a star’s luminosity. Roman numeral ‘V’

stars are the most common, as this signifies a main sequence star. As we count down in Roman numerals,

the luminosity becomes brighter, meaning that the star is larger than a main sequence star. ‘III’ stars are

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giants, whereas ‘Ib’ stars are supergiants. Altogether, the spectral class of a star is shown by combining all

three symbols. Our Sun, for example, would be G2V. By knowing the spectral class of a star, we can

determine where it is in its stellar evolution as well as how it’ll behave on an H-R diagram.

After charting stars on an H-R diagram, either a few dozen or hundreds of thousands, one will see

a pattern that has remained constant throughout its hundred years of use; a band will appear, starting in the

upper left, and slanting down diagonally to the bottom right. This band is known as the main sequence, and

represents the region of stellar evolution that a star will spend most of its life on. In the upper right of the

diagram is the red supergiants, signifying stars reaching the end of their lives, and in the bottom left are the

white dwarves, which are stars that have already died, leaving behind a white-hot core that will slowly cool

and fade away over the course of billions of years (Weintraub, 2011).

After studying his diagram, Henry Norris Russell reached the conclusion that it is a star’s mass that

determines its temperature and luminosity (Weintraub, 2011). The more massive a star is, the hotter it burns

and the brighter it shines. The lifetime of a star is also entirely tied to how massive it is. More massive stars

will burn brighter and hotter, but it will also die much faster than cooler and fainter stars. The largest and

brightest O-type stars will only live for a few million years before dying. Many of the small M-type red

dwarves will live for more than a trillion years (Chaisson & Steve, 2017).

This correlation between how massive a star is and long it will live is an important factor of

determining the age of a star cluster. Because more massive stars have shorter lives, these stars will arrive

at the main sequence first as well as leave the main sequence first. After the hydrogen in the core is burned

up, stars will leave the main sequence, and journey to the giant branch of an H-R diagram (Schaaf, 2008).

The star will spend a short time there and will eventually die, leaving behind a white dwarf, neutron star,

or black hole.

The section of the H-R diagram where stars are leaving the main sequence is known as the turn off

point, and is a key tool in determining the age of a cluster (Illingworth & Clark). If only stars at the top of

the main sequence are leaving the main sequence, then it is safe to assume that it is a young cluster being

observed, because these stars have short lifespans. The further down the turn off point is in the main

sequence of a cluster, the older that cluster is.

Astronomers have discovered that the lifetime of a star is proportional to the mass of a star divided

by its luminosity (Chaisson & Steve, 2017). This can be expressed using the equation

𝑠𝑡𝑒𝑙𝑙𝑎𝑟 𝑙𝑖𝑓𝑒𝑡𝑖𝑚𝑒 ∝ 𝑠𝑡𝑒𝑙𝑙𝑎𝑟 𝑚𝑎𝑠𝑠

𝑠𝑡𝑒𝑙𝑙𝑎𝑟 𝑙𝑢𝑚𝑖𝑛𝑜𝑠𝑖𝑡𝑦

The units of measurement in this equation are expressed in solar masses. To use an example, the star Sirius

is about 2.1 times more massive than the sun, and is 22 times more luminous. 2.1/22 = 0.095. This means

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that Sirius has an expected lifetime only 9.5% of that of the Sun. The Sun is expected to live 10 billion

years, so Sirius is only expected to live for about 1 billion years.

To get an idea of how a star evolves off the main sequence, let’s follow the path a star with Sun-

like mass will take. Remember that the more massive a star is, the faster these processes will occur. The

same is true in the other direction, smaller stars will have a longer process. The beginning of the end of a

star’s life occurs when its core is depleted of usable hydrogen to fuse. Without the energy produced by

nuclear fusion to exert pressure on the crushing gravity of a star, the now pure helium core begins to shrink.

As it shrinks, the core heats up, prompting the hydrogen in the surrounding shell to fuse, and at faster rates

as the core continues to shrink and heat up. This hydrogen burning shell will cause the envelope of the star

to expand. This new surface area will increase the star’s luminosity, but it will also cool the surface

temperature (Schaaf, 2008). This process of core contraction and envelope expansion is marked on an H-R

diagram by moving upwards as the luminosity increase, and to the right as the surface temperature becomes

cooler. This process will continue until the core becomes hot enough to fuse helium into carbon, and will

last roughly 100 million years (Chaisson & Steve, 2017).

When the onset of helium fusion occurs, it happens explosively and quickly in a reaction known as

the helium flash (Illingworth & Clark). The star loses the equilibrium between the forces of gravity and

pressure from the core, and its core expands. The outer envelope in turn stops expanding, and even contracts

a little bit, dimming the giant star. About 100,000 years after the helium flash, the star reaches a comfortable

equilibrium and rests upon a notable feature of the H-R diagram, the horizontal branch, where stars burning

helium in their cores reside. They will stay here for a few tens of millions of years before resuming their

journey – 50 million years is a good estimate for a sun-like star (Chaisson & Steve, 2017).

Once the helium in the core is fused into carbon the process repeats itself, like after the hydrogen

in the core was used up. The core begins to contract, increasing its temperature. This in turn heats

surrounding helium in the envelope to temperatures that allow fusion, creating a helium fusion shell around

the core. This shell then heats the envelope beyond, beginning the process of hydrogen fusion in an even

larger shell surrounding the helium fusion shell (Weintraub, 2011). As the temperature in the core and

fusion shells continues to rise, the envelope of the star once again expands, and the star rises towards the

right in the H-R diagram, this time along a path known as the asymptotic giant branch (Illingworth & Clark).

As the carbon core contracts, its heat forces the hydrogen and helium-burning shells to fuse at increasingly

faster rates. The carbon core of a sun-like star will never heat up enough to enter the next stage of fusion,

however. The star is near the end of its life.

The sun-like star will stay on the asymptotic branch for less than a million years. Eventually it will

lose its equilibrium between gravity and outwards pressure generated by temperature. The star will begin

to pulsate as its envelope contracts when it loses to much heat, and then expand as it contracts too far and

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heats up much too quickly to reestablish equilibrium (Weintraub, 2011). In turn, the expansion of the

envelope will happen too quickly for gravity to reach equilibrium, and the outer layers of the star will shed.

The core of the star will burn up its last remaining fuel, and the expanding envelope of the star will be seen

as a planetary nebula. The core, all that remains of the star, will once again change the star’s position on

the H-R diagram. The core is white-hot, so the star will move left on the diagram; the core is also tiny, a

little larger than Earth, diminishing its luminosity greatly, so the star moves downward, into the area known

as the white dwarf region (Chaisson & Steve, 2017). The now dead star will slowly cool over the course of

billions of years, slowly inching downwards and the right of an H-R diagram, until it becomes a black dwarf.

If we add up the timeframes for each stage of stellar evolution after a star leaves the main sequence

to become a white dwarf, we see that after a sun-like star has stopped burning hydrogen in its core it will

continue to live for about another 151 million years. Dividing this timeframe by that of its main sequence

life of 10 billion years, we see that the total amount of time a star like the sun spends off of the main

sequence is 1.5% of its total lifespan.

How have scientists been able to determine this process? The answer lies in the creation and

analysis of H-R diagrams, “a graph that has proven to be as fruitful as any that scientists have ever

constructed” (Schaaf, 2008). To understand how the evolution of stars was determined, my class made an

H-R diagram using the stars of the Hyades and a simulation of gathering data on stars created by Project

CLEA.

Procedure

The process the class used to create an H-R diagram and analyze it consisted of four separate

sections, or labs. The first lab focused on observing stars with a telescope to obtain relevant light data. The

second lab took the light data to display the stars on an H-R diagram and to compare the class diagram to

those of other star clusters. The third lab had us re-observe our stars with a spectrometer to gather relevant

data about the spectra of our stars. The final lab had the class determine the stellar spectra classification of

our stars using the data gathered in the third section to see where our stars were on the class’ overall H-R

diagram.

To begin, each student was handed a list of 15 random stars located in the Hyades Cluster. Students

would take their stars and find them using the Project CLEA VIREO simulation. VIREO stands for Virtual

Educational Observatory (Gettysburg College, n.d.). Much like a real observatory, students had to open the

dome, turn on a tracking device to match the rotation of the Earth, and even had to ask permission to use

larger and more powerful telescopes for the fainter stars.

To gather light data on the stars in the first section of the H-R diagram process, students would first

look through a telescope with either a blue light filter or a visual light filter at a star on their list. After

gathering light data through the telescope for an amount of time that would negate any effect background

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noise might have on the data, the student would record the apparent magnitude of the star through that filter.

The process would then be repeated for the same star, only using the other filter. After the apparent

magnitudes through both filters were recorded, students now had the measurements needed to construct an

H-R diagram.

It should be noted that while H-R diagrams typically have absolute magnitude measure on its

vertical axis, the apparent magnitude was measured in the class’ process instead. This is because the

apparent and absolute magnitude values share a relationship that allow us to determine the distance to the

star cluster, which was another objective of the process, but will not be covered in this report.

The second section of the process had students combine their data with that of the instructor’s to

create an H-R diagram of the Hyades star cluster. To do this, students determined the color index of their

stars by subtracting the value they received through the blue filter (B) by the value of the visual filter (V),

or B-V. The V value of the star, or the apparent magnitude of the visual light, was then used to determine

the luminosity for the vertical axis. Altogether, 372 stars were plotted. Students then were asked to fit a

Zero Age Main Sequence plot line into the H-R diagram. The ZAMS line can then be used to help fit the

isochrone plot line, which determines the age of the cluster. The isochrone lines were provided by the

simulation, and students can change the age of an isochrone line to best fit the star cluster. The goal of

fitting an isochrone to an H-R diagram is to match the turn-off point of the isochrone to the turn off point

of the diagram. After students matched an isochrone to the Hyades cluster, they were able to determine the

age of the cluster. Students then matched isochrones to a number of different clusters, to show differences

in ages, and how the metallicity can slightly effect the shape of a cluster’s diagram. Also apparent by

arranging the different clusters in order from youngest to oldest, students saw the process of stellar evolution,

with the larger stars in the top left of an H-R diagram turning off in younger clusters, or completely missing

with turn off point further down the main sequence instead, indicating a greater age for the cluster.

The third section of the process is similar to the first section, only instead of gathering light data

through different filters of a telescope, students pointed a spectrometer at the stars on their list, to gather

the star’s spectra. Also similar was the requirement to ask for permission to use a stronger telescope for the

fainter stars. I myself was denied four times access to the largest telescope, measuring at 4 meters, and

equated to an eight minute wait. Astronomers must wait for much longer when they are denied, or might

not even get a chance at all.

After light was gathered in the spectrometer for a sufficient amount of time to negate any

background noise, students recorded the spectra to be used in the last lab. Also recorded was the apparent

magnitude of the stars, to begin the process of determining the distance to each individual star in a student’s

list.

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The last section of my class’ process of creating and analyzing an H-R diagram consisted of taking

the spectra data gathered in the third section and analyzing it to determine the spectral class of the fifteen

stars on each student’s list. To do this, the known spectra of a variety of stars of different spectral classes

was provided by the Project CLEA simulation to compare the collected spectra against. When the standard

spectra was compared with the collected spectra, a third window would show the differences in absorption

lines. The goal of the students was to get as straight a line as possible in the third window. When a straight

line - or as close as could be achieved - was observed, it signified that the spectra collected by the student

shared the standard spectra provided by the simulation. The student could then determine the spectral class

of their star, and where it was in its stellar evolution.

Students also obtained the absolute magnitude of the stars spectral classes, and could compare it to

the apparent magnitude gathered in the third section. The distance to each star was then calculated and

recorded. This concluded the students’ process of observing, measuring, and analyzing the Hyades cluster

through an H-R diagram.

Analysis

Through the data gathered I determined that the Hyades cluster is roughly 794 million years old.

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This cluster is still much too young for most of its main sequence stars to have reached their turn

off point, but all O- and B-type stars have left the main sequence by this point. A strong indicator of this is

the population of the white dwarf region, showing that stars have already died at this age. The green line in

the image represents the Zero Age Main Sequence line for the Hyades, and the pink line is the isochrone,

which I used to match the turn off point of the Hyades to the age supplied by the simulation: 794 million

years. Please note that while the ZAMS does not change for a cluster, its isochrone does. For comparison,

here is the H-R diagram of the oldest cluster observe by the students, a globular cluster called M 67.

I measured M 67 to 3.5 billion years old using this isochrone line. We can clearly see where stars are leaving

the main sequence, the horizontal giant branch, and the white dwarf region. There are no O or B type stars

in the diagram, and even the A type stars should be gone by this point, as my previous example with A type

star Sirius demonstrated it only has a lifetime of about 1 billion years. The stars we see in the red giant

sections of the diagram are likely F type stars, as 3.5 billion years is much too soon for the longer living G

type stars to be turning off.

Because the Hyades is 794 million years old, its turn off point lays in the hottest areas of the A-

type stars. Let’s look at the data that I collected for my fifteen stars, and see if I have any stars that falls

into this region of spectral class. I will note here that I am missing the spectra data for my final star, N1500-

00908, due to an error of the simulation. For whatever reason, the VIREO program was unable to gather

light from this star using a spectrometer, even after restarting the program. I assume it is an extremely faint

star, though, likely sharing a class with the few stars above it, an M2V star. Its distance is unknown to me.

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These stars are listed in order of apparent brightness, meaning if you were to look at these stars

through a telescope the first star, N1500-01175, would appear to be the brightest star. However, this star is

not the hottest star on my list. N1500-00096 is an A5V star, making it the hottest and brightest main

sequence I observed. Why is it not at the top of my list, then? Distance. This A5V star is 181.1 parsecs

away from Earth, making it the furthest star I observed. I determined the distance to the Hyades cluster to

be 41.1 parsecs away from earth, with an allowance of 5 parsecs closer and farther away from Earth to

Star Name RA Dec B V B–V Sp. Type MV V–MV Distance (pc)

N1500-01175 04 30 08.6 +15 38 15 5.901 5.581 0.320 F0 V 2.3 3.28 45.3

N0730-00750 04 19 57.6 +14 02 06 5.869 5.590 0.279 F1 V 2.8 5.59 36.1

N1500-00323 04 42 37.0 +18 44 21 7.715 7.039 0.676 G8 V 5.6 1.44 19.4

N1500-00306 04 25 27.9 +18 53 03 7.774 7.097 0.677 G8 V 5.6 1.50 20.0

N1500-00461 04 21 42.6 +19 28 06 8.770 8.369 0.401 F5 V 3.4 4.97 98.6

N1500-00096 04 36 27.7 +18 39 56 8.667 8.400 0.267 A5 V 2.1 6.29 181.1

N1500-00879 04 43 15.6 +17 04 09 10.881 9.842 1.039 K0 V 5.9 3.96 61.9

N1500-00414 04 07 43.1 +16 31 08 10.965 9.926 1.039 K0 V 5.9 4.04 64.3

N1500-00136 04 26 47.5 +21 14 06 12.619 11.238 1.381 K5 V 8.0 3.24 44.5

N0730-1183 04 41 29.6 +13 13 16 12.707 11.248 1.459 M1 V 9.7 1.54 20.3

N1500-00212 04 27 16.5 +17 14 31 14.523 13.062 1.461 M1 V 9.7 3.35 46.8

N1500-01084 04 25 13.4 +17 16 06 14.734 13.193 1.541 M1 V 9.7 3.52 50.6

N1500-00747 04 11 18.6 +15 58 36 16.692 15.084 1.608 M1 V 9.7 5.39 119.7

N1500-00044 04 15 15.6 +15 01 50 16.705 15.651 1.054 M2 V 10.6 5.05 102.3

N1500-00908 04 14 06.0 +15 51 00 18.586 16.697 1.889 CLEA

ERROR - - -

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include it in the cluster, giving the Hyades star cluster a generous range of 10 parsecs for stars to be included.

This puts my range for the Hyades cluster between 36.1 and 46.1 parsecs. N15-00096 is more than four

times as distant. This star is in no way a member of the Hyades cluster, and therefore does not fit well with

the H-R diagram constructed by my class. If it was a member of the cluster, it would still lie on the main

sequence, as its turn off point is likely somewhere between 1 to 2 billion years.

By utilizing my established range of 10 parsecs for the Hyades cluster, only three stars belong to

the cluster itself; N1500-01175, an F0V star at 45.3 parsecs; N0730-00750, an F1V star at 36.1 parsecs;

and lastly N1500-00136, a K5V star at 44.5 parsecs. All other stars I observed fall outside the 10 parsec

range, making it extremely unlikely that they are part of the cluster. After all, clusters are called as such

because there are a great many stars in a small volume of space. All three of these stars (and actually, every

star I observed) are main sequence stars, and still have a long time to go before they turn off of the main

sequence.

Here is an example of how I determined the spectral class of each star. As seen below, I have the

standard spectra for F0V stars, as well as the absorption lines for N1500-01175. That bottom red line

shows the difference between the two spectra. My goal was to get the red line to center on the middle black

line, meaning I wanted the smallest possible difference between the standard spectra and my star’s spectra.

F0V was a better fit than the A5V or the F5V standard spectra the simulation provided. The standard spectra

didn’t always match completely, however. As you can see in this next example, I am again using the F0V

standard spectra, however, the red line is slightly raised above the black middle line in a few places,

indicating to me that N0730-00750 is slightly cooler than a standard F0V star. For this reason, I classified

it as an F1V spectral class star.

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Unfortunately, none of my stars showed any signs of being off the main sequence. For that reason,

I have no spectra data to analyze for giant or supergiant stars. Because of the relatively young age of the

Hyades cluster, not very many stars have evolved yet, only the rare O and B type stars. As we saw in the

H-R diagram, there were only a few giant and supergiant stars out of the 372 stars observed.

The next oldest cluster after the Hyades that we studied was NGC 752, the H-R diagram seen here,

measured at 1.585 billion years old. As seen, quite a few stars have begun to turn off the main sequence.

Because of the age of the cluster, these stars are likely the cool A-type stars, and perhaps the hottest F-type

stars. The age difference between the Hyades and NGC 752 is a little under 1 billion years, but we can

observe a large change in the turn off point. The turn off point changes rapidly the younger the cluster is,

but it slows down as longer living stars remain. Recall the H-R diagram for M 67, measured to be 3.5 billion

years old. This is 2 billion years older than NGC 752, yet the turn off points between the two clusters has

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not changed as drastically as between the Hyades and NGC 752. This is because it is the hotter F-type stars

in M 67 that are turning off, the point that NGC 752 is about to reach, despite being 2 billion years younger.

This shows that the stellar evolution for O, B, and A type stars happens rather quickly, and slows down

immensely once the turn off point reaches F-type stars.

Summary/Conclusions

H-R diagrams have been essential in determining the process of stellar evolution. Analyzing the

diagram made by the class for the Hyades, as well as the other diagrams available, has shown how mass is

the single determining factor of how a star will live and behave. Extremely massive stars leave the main

sequence first, revealing that they burn through their fuel at a faster rate because of their higher temperature.

As time passes, the turn off point of a main sequence will descend the main sequence. However, it will

move at a slower rate as it reaches longer living stars. We see this by comparing older open clusters with

ancient globular clusters, such as the NGC 752 and M 67 comparison I made earlier.

Also apparent is the massive number of stars that reside on the main sequence. As I mentioned

earlier in this report, the sun will spend only 1.5% of its life off the main sequence, after it has finished

fusing hydrogen into helium. All of the stars I personally observed were main sequence stars, staying true

to this idea that main sequence stars far outnumber the subgiant, giant, and supergiant classes of stars. To

a main sequence star, these classes will disappear relatively quickly.

A detail that disappointed me was how many stars I studied appeared to not belong to the Hyades

cluster itself, and rather just happen to lie in the cluster’s direction. Only three stars I observed fell within

the range I had established for the cluster. This has made me wonder if I had performed my observations

correctly, or if this is a common occurrence for astronomers studying clusters. I like to think it is the latter,

as astronomers are unable to determine the distance to a star until after close observations. A closer look at

the Hyades H-R diagram the class made convinces me that I wasn’t the only with stars outside of the Hyades

as well. If all the stars observed by students were in the Hyades, the main sequence would not appear so

spread out, and would hug the green zero age main sequence line. This does not occur on the class’ diagram

because of the lesser and greater redshifts of the closer and further stars. A diagram like the class’ would

tell a professional astronomer that there are a number of stars observed that don’t actually reside in the

cluster.

The most common spectral class of stars that I observed were M-type stars, numbering 5 (6 if we

include N1500-00908), strengthening the observation that low mass stars are the most populous in the

universe. This is probably due to the extremely long lives of such stars, often more than a trillion years, as

well as the low amount of gas needed for such stars. Hundreds or thousands of M-type stars can be made

from the same amount of gas that makes an O-type star.

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To conclude this paper, the observations provided by the class’ H-R diagram, as well as the other

diagrams, shows convincing evidence regarding the evolution of stars as I outlined in the background

section of this paper. Always worth repeating, the mass of the star determines its fate. On these diagrams,

we always find the more massive stars either turning off, or already gone, having turned into either a white

dwarf, neutron star, or black hole. When a star does turn off, it behaves predictably; rising in luminosity

and cooling in temperature as its core contracts to raise the temperature to start the next stage of nuclear

fusion; resting comfortably on the horizontal branch as it find a new equilibrium with a new nuclear process;

rising and cooling again as the core contracts until it can no longer fuse atoms; finally shedding (or

exploding) the outer envelope and leaving behind a white hot core that will slowly cool over billions of

years. Astronomers have charted stars at every stage of this process during the hundred years the H-R

diagram has been in use, and it is the diagram itself that revealed the process of stellar evolution.

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References

Chaisson, E., & Steve, M. (2017). Astronomy: A Beginner's Guide to the Universe (8th ed.).

Pearson Education, Inc.

Gettysburg College. (n.d.). Project CLEA. Retrieved from Project CLEA:

http://www3.gettysburg.edu/~marschal/clea/cleahome.html

Illingworth, V., & Clark, J. O. (n.d.). The Facts on File Dictionary of Astronomy Fourth Edition.

Checkmark Books.

Schaaf, F. (2008). The Brightest Stars. Hoboken, New Jersey: John Wiley & Sons, Inc.

Weintraub, D. A. (2011). How Old Is the Universe? Princeton: Princeton University Press.