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:

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?

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?

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.

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.]

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:

-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.

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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: