THE DAILY ASTRONOMER
Thursday, March 30, 2023
Your H-R Diagram Guide

Named for its two inventors, American astronomer Henry Norris Russell
(1877-1957) and Danish astronomer Enjar Hertzsprung (1873-1967), this
diagram plots stars according to their spectral types and luminosities.
Astronomers have used this diagram to ascertain so many stellar properties.
We offer the first glimpse of this powerful tool below:

The lower horizontal axis lists the spectra types* OBAFGKM. On this scale,
O is the hottest and M is the coolest. We can see the associated
temperature range at the upper horizontal axis. Along the left vertical
axis is the absolute magnitude. Absolute magnitude equals the star's
magnitude at a distance of 10 parsecs. Absolute magnitude is the measure of
a star's intrinsic brightness. At the right hand axis we see the luminosity
in terms of the Sun. A star with a luminosity value of 1 is as luminous as
the Sun. A star less luminous would appear lower on the graph and one more
luminous would appear higher.

The luminosity equation equates a star's energy output with its size and
temperature. The larger and hotter the star, the more luminous it will be.
When we plot the stars according to luminosity and spectral type
(temperature), we should expect to see a direct correlation. Indeed, we do
observe this correlation for the majority of stars, those that appear along
a band called the main sequence.

Even though each star within the main sequence is considered a "dwarf"
star, their sizes and masses vary considerably. As we will discover next
week, a star's luminosity is related to its mass. (In fact, mass determines
a star's entire life cycle.) Main sequence stars are those within a band
that begins at the lower right and continues to the upper left. At the
lower right one finds red dwarf stars, such as Ross 248. These are the low
mass, low temperature, low luminosity stars. They are also the most common,
representing approximately 76 percent of all main sequence stars. Red
dwarfs are those stars that just became hot enough to ignite and sustain
the core thermonuclear fusion reactions that power stars. As one proceeds
toward the left of the main sequence, it ascends up the diagram as we
should expect. When we reach the G-section we find the Sun, classified as a
G2 V star. (The V is a luminosity class distinction meaning dwarf.)
Continuing on to the left, we climb higher until reaching the pinnacle of
the main sequence at the ultra hot, blue-white stars that are about 100
times more massive and a million times more luminous than the Sun.

The image below shows us the relative sizes and predominant colors of the
various main sequence stars.

At the left the M type red dwarfs; at the right the 0 type blue "dwarfs."

Main Sequence Stars:

   - Every star begins its life cycle on the main sequence. As a star
   evolves, it will move away from the main sequence to other regions within
   the H-R diagram.
   - Every main sequence star is fusing hydrogen into helium
   - The more massive and hotter the main sequence star the more luminous
   it will be.
   - The Sun serves as a demarcation within the main sequence. The stars
   that are more luminous are part of the upper main sequence; those less
   luminous comprise the lower main sequence
   - The more massive and therefore luminous main sequence stars have a
   shorter life cycle than those that are less massive and luminous. The life
   spans of the high mass/high luminosity stars range between 8 - 12 million
   years while the red dwarf lifetimes can exceed one trillion years.
   - Every main sequence star is a "dwarf."
   - The majority of main sequence stars are M type dwarfs (76%). As we
   move left along the spectral classes, the proportions decrease. K stars
   (12.1%), G (7.6%), F (3%), A (0.6%), B (0.12%), O (0.00003%) '

The H R Diagram will enable us to follow any star's evolutionary cycle.

Ever since the H-R Diagram was developed around 1910, it has proven to be
astronomy's most powerful tool for discerning stellar properties. Named for
its two developers, Henry Norris Russell and Enjar Hertzsprung, this
diagram relates stars' spectral types (or effective temperatures) to their
absolute magnitudes (or luminosities.)

The image below shows the basic H-R Diagram again. Along the lower row are
the spectral types. Along the upper row, are listed the effective
temperatures corresponding to the spectral types. Along the left is listed
the absolute magnitude and to the right the corresponding luminosities.

Now that we've established the main sequence, we will start using the
diagram to learn how to discern the properties of stars. We'll begin with
two examples: Betelgeuse, Orion's eastern shoulder star and Sirius B, the
companion star to Sirius, the brightest star in Canis Major.

BETELGEUSE:

Absolute magnitude: -5.85

Spectral type: M2

First, the absolute magnitude places Betelgeuse high along the H-R Diagram,
while the spectral type places it well to the right. We see that Betelgeuse
occupies a position toward the upper right of our diagram. What inferences
can we now make about Betelgeuse based on the information provided?

   - Betelgeuse is highly luminous. [It is more than 90,000 times more
   luminous than the Sun. This luminosity changes because Betelgeuse is a
   variable star. More on that topic later.]
   - Betelgeuse is quite "cool." [As an M2 star, its effective temperature
   is approximately 3,600 K.]
   - Since Betelgeuse is both cool, but highly luminous, we can also
   conclude it is quite large. Remember that a star's luminosity is
   proportional to the square of its surface area and to the fourth power of
   its effective temperature. [Betelgeuse's radius is approximately 900 times
   that of the Sun's.]
   - As it is not on the main sequence, it is no longer fusing hydrogen
   into helium. We know that Betelgeuse is toward the end of its life
   cycle, but we cannot know precisely what fusion reactions are occurring in
   its core. All we know is that its core hydrogen fusion days are over.
   - Betelgeuse is a supergiant star

SIRIUS B

Absolute magnitude: +11.18

Spectral type: A2

We can set Sirius B low on the H-R Diagram due to its high absolute
magnitude. However, with a spectral type of A2, Sirius B would also be
placed along the right. What can we conclude about Sirius B based on this
information and its lower right position on the HR Diagram?

   - Sirius B's luminosity is very low! [It is about 5% as luminous as the
   Sun.]
   - Sirius B is quite hot. [With a spectral type of A2, Sirius B's
   effective temperature equals 25,000 K.]
   - Since Sirius B is both cool, but not very luminous, it must be quite
   small. [Its radius is 0.8% that of the Sun.] In fact, Sirius B is not an
   active star at all. It is, instead, a stellar remnant known as a "white
   dwarf." It is no longer generating energy in its core through
   thermonuclear fusion reactions. We will be discussing white dwarf stars in
   greater detail later this week.

In these two examples, we were able to infer more information about these
two stars merely by knowing their absolute magnitudes and spectral types.
Before proceeding, we will introduce another stellar category: luminosity
class.

   - O-Ia+ Hypergiants. Extremely rare form of high luminosity star.
   Example Cygnus OB2-12: luminosity 2 million times that of the Sun.
   - Ia Luminous supergiants. Also quite rare. Luminosity more than a
   hundred thousand times that of the Sun. Example: Eta Carinae.
   - Iab Intermediate luminous supergiants. Luminosity: tens of thousands
   of times greater than the Sun. Example: Betelgeuse
   - Ib Less luminous Supergiants Stars that are just luminous enough to be
   classified as supergiants. Luminosities more than 10,000 times that of the
   Sun.
   - II Bright giants Still highly luminous, but not considered supergiants
   due to their spectra. Luminosity thousands of times greater than the Sun's.
   Example: Omicron Scorpii
   - III Normal giants Generally stars between 10 and a couple thousand
   times that of the Sun. Example: Arcturus
   - IV Subgiants Stars that are more luminous than main sequence stars but
   not as luminous as giant stars. Example: Bellatrix
   - V Dwarfs Main sequence stars. The luminosity is directly related to
   mass. Example: The Sun
   - VI Subdwarfs Stars that are still fusing hydrogen into helium in their
   cores but are less luminous than main sequence stars. These stars are
   believed to be "metal poor," which decreases their outer layer opacity
   resulting in reduced radiation pressure. Example: Kapteyn's Star
   - VII White dwarfs. Stellar remnants. All thermonuclear fusion reactions
   have ceased. Example: Sirius B

Below we can see the different luminosity class locations within the H-R
Diagram:

[Note: The L and T spectral types refer to "brown dwarfs," those gaseous
bodies that did not become sufficiently massive to produce temperatures
necessary for thermonuclear fusion reactions to occur. We will discuss
brown dwarfs in greater detail later.]

Now that we've included these sections, the H-R Diagram will also enable us
to determine a star's luminosity class.

Let's now classify some of the night sky's best known stars: Aldebaran,
Altair, Antares and Deneb.

[Note: The Sun's absolute magnitude is 4.86. Any star with a lower absolute
magnitude will be intrinsically brighter than the Sun. Any star with a
higher absolute magnitude will be intrinsically fainter.]

Aldebaran (Taurus the Bull)
Absolute magnitude: -0.641

Spectral type: K5

Cooler than the Sun, but much more luminous.

When we place Aldebaran in its proper HR position, we see that it is a
giant star.

Luminosity class III

Altair (Aquila the Eagle)

Absolute magnitude: 2.22

Spectral type: A7

Hotter than the Sun

We can fit Altair directly into the main sequence.

Luminosity class V

Antares (Scorpius the Scorpion)

Absolute magnitude: -5.28

Spectral type: M1

Cooler than the Sun but significantly more luminous

Antares is located in the upper right hand region, the realm of the
supergiants. Luminosity class: Iab

Deneb (Cygnus the Swan)

Absolute magnitude: -8.38

Spectral type: A2

Much hotter and much more luminous than the Sun. We place Deneb high along
the H-R Diagram, but much farther left than Betelgeuse and Antares. Still a
supergiant.

Luminosity class: Ia

One can see those stars and many others on this H-R Diagram sample provided
below.

We can now place any star on the H-R Diagram with just two pieces of
information. That placement alone yields more information pertaining to the
star's luminosity class.

These classes range from the hypergiants (O-Ia+) to white dwarfs (VII).
Now, we'll add more details to the HR Diagram so as to learn other stellar
properties. The first of the new details involves stellar radii.

Before we proceed, let's quickly review two important geometric terms:
spherical radius and spherical volume.

A radius is the straight line distance from a sphere's center to any point
along the sphere's surface. Most stars can be considered spherical to a
fair degree of accuracy.

One can calculate a sphere's volume if the radius is known. For instance,
the volume of a sphere with a ten foot radius is 4/3(pi)(1000) = 4,188
cubic feet. Even though the radius is small, the volume is quite large.
Numbers become impressively big when you cube them. It is for this reason
that stars which have radii only a few times greater than the Sun's will
actually be much larger in terms of volume. For instance, a star with a
radius ten times greater than the Sun's will be 1000 times larger by volume.

RADIUS:

We next present the H-R Diagram that includes stellar radii demarcations:

Merely by placing a star on the diagram one can readily determine its
radius and therefore also its volume. Let's look at two examples: the stars
Arcturus and Deneb.

Arcturus:

Spectral type: K0

Absolute magnitude: -0.30

With an absolute magnitude of -0.30, Arcturus' luminosity is 170 times
greater than the Sun's. Arcturus is then placed on the upper right of the
diagram. It is above the line marking 10 solar radii. Its actual radius is
25 times that of the Sun and is nearly 16,000 times larger in terms of
volume.

From yesterday: Its luminosity class is III, making it a normal giant.

Deneb:

Spectral type: A2

Absolute magnitude: -8.38

Deneb is brilliant! With a magnitude of -8.38, it is approximately 200,000
times more luminous than the Sun! Its spectral type and luminosity place it
high toward the left of the H-R Diagram. Its radius is 203 times greater
than the Sun's, making it 8.3 million times larger in terms of volume.
Deneb's luminosity class is Ia (luminous supergiant.)

MASS

The placement alone will yield direct information about any star's size.
However, just placing a star on the H-R diagram will not enable an
astronomer to ascertain a star's mass, unless that star is on the main
sequence. We now introduce the Mass-Luminosity relation. This relation
states that a star's mass determines its luminosity. The more massive the
star, the more luminous it will be. This relation applies to main sequence
stars. The relationship between a star's mass and luminosity depends on the
star's mass. If a star is up to 43% as massive as the Sun, its luminosity
equals its mass raised to the power of 2.3. If the star's mass is between
0.43 solar masses and 2 solar masses, the luminosity is equal to its mass
raised to the fourth power. [Note: 2 solar masses means twice as massive as
the Sun.] If a star is between 2 solar masses and 55 solar masses, its
luminosity is equal to its mass raised to the power 3.5. Finally, if a star
is more than 55 times as massive as the Sun, its luminosity equals 32,000
times its mass. These different relations are summarized below:

The H-R Diagram below shows the masses along the main sequence. It does not
show masses for the stars off the main sequence as those will vary
significantly.

We observe that even the most massive main sequence stars can be more than
60 times as massive as the Sun,while the least massive red dwarfs will be
less than 10% as massive. Let's look at two examples: Altair and Procyon

Altair:

Spectral type: A7

Absolute magnitude: 2.22

Altair is a main sequence star (luminosity class V) that is 1.79 times as
massive as the Sun and about 10 times more massive.

Procyon:

Spectral type: B1

Absolute magnitude: -3.55

Procyon is a main sequence star 11.5 times more massive and approximately
20,000 times more luminous than the Sun.

STELLAR LIFETIMES:

This brings us to stellar lifetimes or, more specifically, the amount of
time a star will remain along the main sequence. The H-R Diagram above also
contains this information. The more massive the star, the shorter the
lifetime. This relation seems counter-intuitive because a star generates
energy by fusing lighter elements into heavier ones. The more massive stars
do contain greater reserves of this material. However, the more massive
stars also exhaust their fuel reserves far more quickly. Also, the least
massive stars contain only convective interiors and so more of their
hydrogen reserves are available for the core fusion reactions.

A star's lifetime can be approximated with the following formula:

A star's lifetime the sun's mass divided by the star's mass raised to the
power 2.5 and then multiplied by 10 billion. Whereas a star as massive as
Spica will remain on the main sequence for slightly more than 10 million
years, a red dwarf such as Wolf 359 will be on the main sequence for more
than one trillion years.

By placing a main sequence star on the H-R Diagram, we can know its mass
and its main sequence lifetime.

EVOLUTION OF LOW-MASS STARS

We'll provide the H-R Diagram "Sun track" so we can follow our parent
star's progression from present day to its death. [We have already covered
the time period of the Sun's birth to its presently active stage.]

The Sun is currently stable. The internal energy pressure pushing outward
is balanced by the gravitational contraction. We refer to this precise
balance as "hydrostatic equilibrium." However, the solar interior shall
prove to be quite dynamic over long time periods. Every second, 647 million
tons of hydrogen is converted into helium. As more hydrogen is fused," more
helium collects and the core shrinks. The shrinking core allows the Sun's
outer layers to migrate closer to the core. Consequently, the outer layer
material draws closer to the core and the resultant gravitational
contraction intensifies. The pressures and temperatures increase, causing
an increase in the core fusion reactions. This accelerated fusion will
increase the Sun's luminosity by one percent every 100 million years. While
the Sun remains on the main sequence, it will slowly migrate upward and
slightly toward the left as a result of this increased temperature and
luminosity.

In 1.1 billion years, the Sun will be 10% brighter than it is today. Earth
and the other planets will become significantly hotter as a consequence.
This increased heat will render Earth uninhabitable around this time. Long
before the Sun exhausts its hydrogen reserves, Earth will have become
furiously hot and devoid of life.

In approximately five billion years, the Sun will have grown more than 58%
more luminous than it is today. Also, it will have depleted its core
hydrogen, leaving an ultra hot helium "ash." Without any energy pressure,
the core will shrink rapidly and its temperature will increase. Meanwhile
an outer hydrogen burning layer will form around the core. Within this
layer hydrogen will continue to fuse into helium. The Sun's outer layers
will expand and cool. The Sun will then become a red giant. Although its
effective temperature will be lower than it is presently, its luminosity
will increase due to its expanded size. On the H-R Diagram the Sun moves
upward and to the right: cooler and much more luminous. The Red Giant Sun
will consume Mercury, Venus and perhaps even Earth. Even if Earth remains
outside the Sun, its oceans will have boiled away and its land masses will
be nothing more than molten soup.

Life becomes quite interesting for the Sun after it enters this Red Giant
phase. As the helium core contracts and also receives heat energy from the
hydrogen burning shell, the Sun will experience a helium flash! Literally
within minutes, slightly less than ten percent of the core will be
converted into carbon. The helium burning phase will then begin. The Sun
will shrink back to a size equal to 10 times its present volume and 50
times its current luminosity. Over the following 100 million years the Sun
will convert helium into carbon in its core. Once the Sun exhausts its
helium reserve, the core will be a mixture of carbon and oxygen. The Sun is
not massive enough to produce the pressures and temperatures required to
ignite carbon fusion reactions. A helium burning shell will form around it.
A helium layer will then separate this shell from the hydrogen burning
shell on the outside. The Sun will expand again, this time encompassing
Earth and growing even more luminous than it had been during its previous
red giant expansion. At this time the Sun will be passing through the
Asymptotic Giant Branch phase. Remarkably, the Sun will become 5,000 times
more luminous than it is now!

Over the course of the next 20 million years, the Sun will become unstable
and will expel much of its material every 100,000 years through a series of
violet pulses. After the conclusion of this phase, the Sun will be half as
massive as it is today. The outer solar layers will then disperse, at first
slowly and then rapidly to form a planetary nebula. The exposed core, more
than 30,000 K at its surface will then slowly cool over trillions of years.
This stellar remnant is known as a white dwarf. A white dwarf will not
collapse in on itself because of electron degeneracy. The electrons within
the dwarf will repel each other, preventing any further contraction.

The Ring Nebula in Lyra is a well known example of a planetary nebula. We
have no idea how the planetary nebula that will form around the Sun will
appear. We do know that the nebula will likely disperse into invisibility
within 10,000 years after its formation.

The Sun that is blazing hot outside our windows right now is destined to
become a bloated red giant that will cover most of our sky. (Nobody will be
around to observe this expansion.) Eventually, the Sun will become an ultra
hot white dwarf: a stellar remnant that will slowly cool over trillions of
years. So, our Sun will certainly remain in the cosmos for quite a long
time. However, it won't always be the same as it is now.

EVOLUTION OF HIGH MASS STARS

The core of every active star is a thermonuclear fusion furnace. Within the
core lighter elements are fused to form heavier elements. This process
generates radiant energy that migrates out of the core through the star's
outer layers and then into space. Whenever you see sunlight, you're
observing energy that originated in the solar core about 300,000 years
before. Although stars seem immortal relative to our brief mortal lives,
they all have finite life spans as their fuel reserves are also finite.
They only have so much fuel to fuse before they perish. Of course, even the
most short lived stars will persist for a few million years. Counter
intuitively, the more massive the star the shorter its lifespan.

The more massive stars expend their fuel reserves far more quickly than the
low mass stars.

The following list shows a sample of main sequence lifetimes (the amount of
time a star of a given mass remains on the main sequence before evolving
away from it.)

[Note: a solar mass equals the mass of the Sun. For instance, a 3 solar
mass star is three times as massive as the Sun.]

   - 60 solar masses 3 million years
   - 30 solar masses 11 million years
   - 10 solar masses 32 million years
   - 3 solar masses 370 million years
   - 1 solar masses 10 billion years
   - 0.1 solar masses 1-2 trillion years

We’ve already learned the Sun's fate after it exhausts its hydrogen
reserves. It will expand to become a red giant and its core will start
fusing helium to produce carbon. As the Sun is not massive enough to
produce the core pressures and temperatures necessary to ignite carbon
fusion, it will expel its outer layers to form a planetary nebula. The core
will then form a white dwarf, a stellar remnant that will slowly cool to
become a black dwarf.

Not all stars follow the same life cycle, however. Stars that are at least
eight times as massive as the Sun undergo more complex changes before they
end their lives. First of all, more massive stars are able to produce the
core temperatures necessary to fuse carbon and other heavier elements.
[Next week we will be devoting an entire class to these element-creating
fusion reactions, a process known as stellar nucleosynthesis. Today we're
focusing solely on the stellar evolutionary track.]

The most massive stars will experience multiple phases of fusion reactions.
Hydrogen into helium; helium into carbon; carbon into oxygen or nitrogen or
another product. Various other fusion reactions will then occur in multiple
stages until the star's core collects iron heated to three billion degrees!
Iron is the end point of these reactions because iron fusion is
endothermic. The energy invested into this reaction is greater than the
energy the reactions impart back into the star. All lighter element
reactions produce more energy than is required to produce them. (The
hydrogen to helium reaction is the most energy efficient.) Consequently,
when a star collects iron in its core, the balance between the star's
gravitational contraction and outward energy pressure is violently
disrupted. The outer layers collapse down onto the star's inner region so
quickly that the gravitational potential energy is converted into kinetic
energy resulting in an explosion called a Type II supernova.

A type II supernova explodes from the inside out. The supernova energy
produces all the elements heavier than iron. It also disperses this heavy
element material throughout its local region, chemically enriching the
interstellar medium within its vicinity.

What happens next depends on two factors: the star's mass and metallicity.

Metallicity refers to the star's "metal content." The astronomical
definition of "metal" is profoundly different from the chemical definition.
Astronomically, a metal is any element heavier than helium. During the
earliest epochs of star formation, the Universe consisted primarily of
hydrogen and helium with scant traces of slightly heavier elements. The
first stars would have formed only out of clouds consisting of hydrogen and
helium. They and other stars that also form from hydrogen and helium are
considered metal free. The metal content of any star depends on its
'population.' Astronomers recognize three distinct stellar population types:

   - POPULATION I: "metal rich" stars. They are comparatively young, They
   formed out of interactions between heavy-element laden supernova debris and
   gas/dust clouds. They tend to revolve around the spiral arms of the Milky
   Way Galaxy. The Sun is a perfect example of a Population I star.
   - POPULATION II: "metal poor" stars. These stars formed much earlier
   when the nebulae were not as chemically enriched as they were when the
   later Population I stars formed. Population II stars are typically located
   around the galactic nucleus and in globular clusters in particular.
   Globular clusters are large, old, globe-shaped star clusters located in the
   galactic halo.
   - POPULATION III: the very first stars. This population is hypothetical,
   meaning none have yet been observed. They would have been highly massive
   and therefore lived briefly. These stars consisted of hardly any metals,
   except for any metals ejected by Population III star supernovae.

-Stars that are up to nine times more massive than the Sun will end their
lives as white dwarf stars.

More massive stars will form one of two objects: neutron stars or black
holes. [We'll be discussing these objects in greater detail in a later
class.]

-Stars between 9 - 25 times more massive than the Sun will end their lives
as neutron stars. Neutron stars are the densest objects in the known
Universe. When the stellar remnant is more than 1.4 times as massive as the
Sun, the gravitational compression overpowers the electron degeneracy that
sustains the shapes of white dwarf stars. The object is then compressed
down to a much smaller volume. If the progenitor star is between 9 - 25
times as massive as the Sun, neutron degeneracy will halt further collapse
to produce a neutron star. While a white dwarf is about the size of a
planet, a neutron star's size is that of a city. Even the largest cities
are minuscule compared to the size of Earth.

-

Stars 25-40 times more massive than the Sun can either become a neutron
star or a black hole "by fallback," depending on their metallicity. Stars
toward the lower end of this mass range will become black holes by fallback
unless they have comparatively mid to high metallicities. Stars at the mid
to upper range will only become neutron stars if they have high
metallicities. A black hole is a region where the gravitational attraction
is powerful that nothing can escape from it, not even light. [We will be
devoting an entire class soon just to black holes.] A black hole by
fallback occurs when the material within a star starts to push outward
after the supernova explosion, only to collapse back onto the core to form
the black hole.

-Stars more than 40 times more massive than the Sun will either become a
black hole directly (immediate without any fall back), a black hole by fall
back or a neutron star depending on the star's metallicity. Refer to the
chart below. For instance, a metal free star of 60 solar masses will become
a black hole directly, whereas a 60 solar mass star with a high metallicity
will form a neutron star. Note: Some stars are now believed to be able to
form black holes without an associated Type II supernova.

[The blank space between 140-260 solar masses refers to a region of pair
instability, a topic we haven't even mentioned yet and so won't discuss, at
least for now.]

I hope this answer proves helpful.

*Spectral types

The arrangement O B A F G K M is also a temperature sequence, with O stars
being the hottest and M the coolest. Remember the mnemonic "Oh, be a fine
girl kiss me!" Or, if you're worried about offending someone, you can
replace "girl" with "gorilla," or "goldfish" or "gerontologist," if you
happen to be fond of scientists who study aging.)

The associated temperatures are as follows:

   - O 28,000 - 50,000 K*
   - B 9,900 - 28,000 K
   - A 7400 - 9900 K
   - F 6000 - 7400 K
   - G 4900 - 6000 K
   - K 3500 - 4900 K