Charting Cosmic Elegance: The HR Diagram’s Story of Stars
ABSTRACT
This article explores the Hertzsprung-Russell (H-R) diagram, a fundamental tool in astrophysics for understanding stellar classification, the life cycle of stars, and predicting their future. The H-R diagram serves as a visual representation of stellar properties, analogous to a librarian's chart categorizing books by color and size, specifically luminosity and temperature. This process honors the Morgan-Keenan (M-K) system of classification, which categorizes stars based on spectral and luminosity classes, helping them find their position on the H-R diagram. We delve into the distinct groups formed on the H-R diagram, including main sequence stars, white dwarfs, giants, and supergiants. Furthermore, we examine the differences in luminosity among stars using the Stefan-Boltzmann relation. The article concludes by discussing the significance of the H-R diagram in predicting stellar evolution and understanding the universe’s history.
INTRODUCTION
Look at the figure 1, Why do you think these stars differ in colour ? Which of them do you think is hotter, the red ones or the blue ones? Why do you think they differ in their luminosity? And how are these stars classified ? As we explore these questions, we can uncover the secrets of stars, their life stages, and their relationship with the universe through tools like the Hertzsprung-Russell (H-R) diagram. Imagine a huge library filled with books of different colors and sizes. The librarian's chart distinguishes the books based on these properties. Similarly, the H-R diagram acts like a librarian’s chart, organizing stars by their “color” (temperature) and “thickness” (brightness), helping us understand where each star is in its life journey.
The “absorption and emission spectra” from the stars are like unique book covers, revealing the story inside by showing the elements present and their conditions. By studying these “covers,” astronomers unlock vital clues about a star’s temperature and brightness, illuminating the mysteries of their life cycles and evolution.
The fundamental tool in astronomy that allows the scientist to analyze light from celestial objects through study of interaction between matter and electromagnetic radiation is called Spectroscopy. Absorption spectrum occurs when light from hot sources like stars passes through cooler atoms, where the atoms in gas absorb specific wavelengths of light leading to creation of dark bands called absorption lines. While the emission spectrum occurs when gas molecules get excited by heat or any other source and emit light of specific wavelengths, these appear as bright light across the dark bands.
Both absorption and emission spectrum plays a crucial role in identifying the chemical structure and actual conditions on a star. This also helps to predict the temperature and luminosity of a star and thereby helps astronomers to place stars on the H-R diagram.
For example the Sun is placed on the main sequence star cluster of H-R diagram (refer to fig:4) as its surface temperature corresponds to 5,800K and luminosity 1 solar unit. The H-R diagram basically places the stars into distinct groups based on their luminosity and temperature and helps astronomers to predict the future of a star. This diagram is like a "star map" that arranges stars based on their luminosity (brightness) and surface temperature, unveiling essential patterns that help us understand stellar evolution. This article deep dives into the explanation of Morgan - Kenan System, application of MK System in H-R diagram, explanation of different types of stars based on H-R diagram and finally application of H-R diagram.
1.1 What are Stars ? & How are they classified ?
Before getting into the H-R diagram it's important to know about stars. What are Stars ? The building blocks of galaxies composed of gas, producing light and heat are called Stars. Stars are usually made of a major amount of hydrogen, some helium and very little other elements. They produce massive amounts of energy through nuclear fusion. The process in which heavy atomic nuclei split into two smaller nuclei, releasing large amounts of energy along with neutrons is called Nuclear fission. Though there are a variety of ways to classify stars based on their distance from earth, color etc., the most popular and widely accepted method is classification based on the surface temperature and luminosity of stars, famously known as the Morgan-Kenan (MK) System of stellar classification. The MK System helps stars to find their position on the Hurtzsprung and Rusell diagram, which highlights the relationship of Star’s surface temperature and luminosity.
1.2 Importance of Star & their Evolution in Astronomy.
Stars are the lightsource and lifesource for the entire Universe as they create and distribute life essential elements through nuclear fission that occurs in their core. Besides stars also play a key role in galaxy formation and shaping their chemical evolution. They also provide suitable conditions for planet evolution which is an important phenomenon in astronomy. Also, studying about stars and their evolution can give footprints regarding the origin of the Universe by revealing the life cycles of matter and energy. While stellar nucleosynthesis connects to the Big Bang’s initial formation, the Universe's early conditions can be understood through thorough observations of ancient stars and galaxies.The elements essential for planet formation and life are often released during the formation and death of stars. Also, studying star evolution offers valuable insights regarding star lifecycle from their formation to end stages. All these events offer clues about cosmic history and the universe's development highlighting the importance of studying stars and their evolution.
1.3 Hertzsprung and Russell Model - Experiment’s Background
Plotting data into a graph helps visualize the relationship between two physical quantities, making patterns and trends easier to identify. One of such most useful and powerful tools in Astrophysics is the Hurtzsprung and Russell Model (H-R diagram). The story dates back to 1911, when Danish astronomer, Ejnar Hertzsprung plotted the absolute magnitude of stars against their effective temperature. Further the american astronomer Henry Norris Rusell in 1913, independently plotted the spectral lines across absolute magnitude. The findings of both the plottings indicated a close relationship between the luminosity and temperature of stars and clustered stars into distinct groups which can be clearly seen in the H-R diagram (refer fig:5).
Before proceeding further it's important to understand the difference between temperature and luminosity. Temperature refers to the surface temperature of a star, that determines the color and type of radiation emitted. With this reference stars like the sun can be approximated as black bodies meaning they emit electromagnetic radiation across a spectrum that depends solely on their temperature. The spectrum of this radiation is described by Planck’s Law, which shows how the intensity of radiation varies with wavelength for a given temperature. Although the full mathematical form of Planck’s Law is complex and beyond the scope of this article, it provides the foundation for understanding stellar radiation. The peak wavelength (??max) at which a star emits most of its energy is inversely proportional to its temperature, as given by Wien’s Displacement Law:
??max = b / T
Where b is wien’s constant (2.897 x 10^-3 m. K). This gives an explanation to an intriguing question: why cooler stars appear red (longer wavelength) and hotter stars appear blue (shorter wavelength).
Luminosity is the total amount of energy a star radiates per unit time in all directions. It is dependent on both surface temperature and the size of the star. Luminosity holds a close relation with black body radiation through the Stefan-Boltzman law. The Stefan-Boltzmann law relates a star's size to its temperature and luminosity; it applies not just to stars but to any object emitting a thermal spectrum (this includes the glowing metal burners on electric stoves and filaments in light bulbs). The mathematical form of the law states that the luminosity L is proportional to the star's surface area and the fourth power of its surface temperature:
L = 4 π R2 σ Τ 4
If the star's temperature is measured in kelvin and radius in meters then the value of a numerical constant ‘σ’ is 5.67 x 10-8 and the luminosity will come out in Watts. (Unsurprisingly, σ is called the Stefan-Boltzmann constant.) The relationship between temperature and luminosity of a star helps it to find its position on the H-R diagram. This relationship is governed by the Stefan-Boltzman Law.
RESEARCH METHODOLOGY
As previously stated the M-K System allows the stars to find their position on the H-R diagram so lets initially understand the Morgan-Kenan (M-K) System for star classification.
2.1 Morgan-Kenan(M-K) System of star classification
The M-K system classifies the stars according to spectral class (based on temperature & color) and luminosity class (based on brightness & size).
As shown in fig 3, in classification based on Spectral class, stars are classified into seven spectral types designated as O, B, A, F, G, K, M ordered by temperature from hottest to coldest respectively.
For M-K classification based on luminosity class, it categorizes stars from I-VII denoted by roman numerals. From fig. 4, it is understood that category
General relation between temperature (from hot, blue stars on the left to cool, red stars on the right) and luminosity class, with hotter stars at the top and cooler stars at the bottom, is highlighted through the diagram.
2.2 Hertzsprung and Russell(H-R) Diagram
The H-R diagram is one of the most influential tools of astronomy and astrophysics, providing visual insights of the relationship between stellar luminosity and the surface temperature of stars, allowing astronomers to classify them according to these properties. Let's understand more about the H-R diagram.
As it can be seen from Figure 5, the H-R diagram plots stellar luminosity on the vertical axis (increasing upwards), with hotter stars being more luminous. Surface temperature is plotted on the horizontal axis, typically in Kelvin, but in reverse order, with the hottest stars on the left and coolest stars on the right. This gives rise to the major regions on the diagram viz Main Sequence Stars (where our sun lies), Giants and Supergiant stars, and white dwarfs. These stages will be discussed in detail further in this article. This helps astronomers understand the star types and thereby predict the future of the stars.
Vertical Axis: Stellar luminosity: This is measured in units relative to the Sun’s brightness (solar luminosity). A star with luminosity of 1 has the same brightness as our Sun, while those above this level are brighter and below this level are dimmer. Star’s output is reflected through luminosity, which depends largely on its mass and its current life stage. For example, massive stars have higher luminosities; main-sequence stars burn hydrogen rapidly and shine super bright, while older stars shine brightly because they have expanded into giants or supergiants
Horizontal Axis- Surface temperature: Measured in Kelvin. This arrangement leads to the placing of the hottest stars on the left and cooler stars on the right. This helps to determine the color of the star. Blue and white stars are the hottest, with temperatures above 30,000K, while red stars are the coolest, often below 3,500K. The spectral type classification (M-K system, 2.1) follows this temperature gradient. For example, O-type stars (blue and very hot) occupy the far left side, while M-type stars (cool and red) occupy the far right side.
The H-R diagram can be viewed as both a theoretical and spectroscopic tool. The spectroscopic H-R diagram enhances the existing model by adding the detailed spectral data that reflects the characteristics of the star's atmosphere, allowing the astronomers to get information about a star's age, metallicity, and eventually the fate of the star. [1] Also, this adaptation allows more accurate placing of stars on the H-R diagram and understanding more about the distinct clusters. [2]
TYPES OF STARS
Star, any massive self-luminous celestial body of gas that shines by radiation derived from its internal energy sources. They start out as gas and dust clouds as shown in fig 5. These clouds create a dense core known as a star. As we can see in the diagram, after forming a star there are two ways one is a star like our sun and other one is stars which are larger than the sun. Then most of the stars follow a phase called the main sequence phase in which stars go through a process called nuclear fusion in which they release enormous amounts of energy, this energy supplies power to the star to generate heat and light for millions or even billions of years. Over time, as stars consume their fuel, they move into new stages of their life.
In the H-R diagram, stars are classified into groups that shows these stages: the main sequence, where stars like the Sun reside; the giants and supergiants, which stand for more developed stages of star life, and white dwarfs, which are tiny, highly dense and the leftover of the star. Now let’s explore these types one by one.
3.1 Main Sequence Stars
In the core of the main sequence stars, hydrogen reacts with itself and combines to get converted into helium, this reaction of converting hydrogen into helium releases vast amounts of energy. The star's mass affects both the rate of fuel supply and the fusion. Mass also affects the longevity, size, and brilliance of a main sequence star. Main sequence phase appears to be stable among others, because in this phase energy being radiated is stabilized by the star's gravity leading the star to become stable.
On the H-R diagram, main sequence stars are positioned along a diagonal band (refer Fig. 3) that stretches from the upper left corner to the lower right corner. The hottest stars, located in the upper left, are blue and have surface temperatures exceeding 30,000 K, while the cooler stars in the lower right are red and typically have temperatures below 3,500 K. Main sequence stars vary in size, color, and luminosity, showing diversity in their mass and energy they radiate per unit time. A massive O-type star may last only a few million years, while a smaller M-type star can shine for billions of years. This balance of mass, temperature, and lifespan is fundamental to the lifecycle of stars and has significant implications for the evolution of galaxies and the formation of planetary systems.
The star's 90% life remains as the main sequence period, and it is significantly longer than in other stages of a star's life. For instance, while our Sun took about 20 million years to form, it will spend approximately 10 billion years (1 × 101? years) as a main sequence star before evolving into a red giant. The main sequence lifespan of a star is determined primarily by its mass. Although it looks massive the size of the star will have more fuel to consume and will have greater lifespan, this is not actually the case. In fact, more massive stars have a stronger gravitational force acting inward, which leads to higher core temperatures. These elevated temperatures accelerate nuclear fusion reactions, causing massive stars to consume their hydrogen fuel much more rapidly than their lower-mass counterparts.
3.2 Giants
Imagine a star, much like our Sun, nearing the end of its life. As it comes to the end of its hydrogen fuel, it gets transformed into an enormous giant. The core contracts because of the intense gravity while its outer layer expands, engulfing nearby planets. This process is very important in the star's life as it begins to fuse helium into heavier elements like carbon and oxygen, shining even brighter. Refer Fig 6 to understand the difference between the sun and the red giant.
On the H-R diagram, giants are located above the main sequence (refer Fig. 3), showing their higher luminosity and different surface temperatures. These stars are divided into two subcategories, as red giants and yellow giants, based on their temperature and brightness. For example, red giants are cooler stars compared to yellow giants with surface temperatures between 2,500 K and 5,000 K, while yellow giants range from 5,000 K to 6,000 K. The growth of giants not only changes their physical looks but also plays a key role in enriching the interstellar medium with heavy elements, especially when they shed their outer layers or go through explosive events like supernovae.
Giant stars live shorter lives than main sequence stars. After they burn through their hydrogen fuel, giants can last for a few million to several hundred million years, lifespan depends on their initial mass. High-mass giants only last a few million years, and where lower-mass giants last longer, nearly the billions of years typical for low-mass stars.
3.3 Supergiants
Supergiant stars have greater luminosity and enormous size. In practice, distinctions among giants, supergiants, and other stellar classes are determined by specific lines in their spectra. Supergiants are some hundreds of million times greater than our Sun’s diameter and emit nearly 1,000,000 times its luminosity. Supergiants stars have lower density as compared to the main sequence and don't live for long, usually only a few million years.
In the H-R diagram, supergiant stars placed on upper right due to their strong luminosity, it is 10,000 to 1,000,000 times greater than of the Sun, and their large diameters, are up to 1,500 times the Sun's size. These stars can have surface temperatures ranging from 3,000 K for red supergiants, like Betelgeuse, to 50,000 K for blue supergiants, such as Rigel. Their brightness, places them far above most of the stars on the diagram. Despite their size and luminosity, supergiants have short lifespans of just a few million years, as they quickly burn their fuel. Positioned away from the main sequence, supergiants represent the final stage for massive stars before they explode as supernovae or collapse into neutron stars or black holes.
3.4 White Dwarfs
White dwarfs are known as the stellar remnants ("stellar remnants" refers to the remaining cores of stars after they have exhausted their nuclear fuel) left behind by the stars having low to intermediate mass, which have exhausted their nuclear fuel. When a star has a size less than or equal to 1.4 times the size of our Sun and it reaches to its end of its life, it blows out its outer layers to create a glowing shell of gas known as a planetary nebula, whereas its core contracts to form a white dwarf. This remnant core no longer undergoes nuclear fusion; instead, it glows faintly due to remaining heat and energy from its earlier active phase.
In the H-R diagram, white dwarfs occupy the lower left region; the lower left region is characterized by high temperatures but very low luminosity. This is due to white dwarfs being highly dense, having compact size and their temperature exceeding 10,000 K initially, as they are compact in size they have limited surface area to emit light causing their luminosity. White dwarfs are incredibly dense. For example a white dwarf has a mass comparable to the Sun but is compressed into a volume similar to that of Earth (approximately 1% of the Sun's radius). This extreme density leads to gravitational instability but this instability is stabilized by electron degeneracy pressure, making white dwarfs stable.
Cooling process of the white dwarfs is very slow, as they release their remaining heat into space very slowly, as there is no source to generate. After millions or billions of years later the temperature of white dwarf goes below 10,000 Kelvin, becoming a ‘cool white dwarf’. If they keep cooling eventually it will become dark, called a ‘black dwarf’. However our universe is not old enough for any black dwarf to exist since.
KEY INSIGHTS FROM THE H-R DIAGRAM
4.1 Glow Vs Size
The HR diagram not only helps to predict the future of the stars but also helps to understand the fact that stars differ in luminosity. This relation between luminosity and temperature could be explained with the help of the Stefan-Boltzman law, in which we have derived the relation that luminosity L is proportional to a star's surface area A and the fourth power of its surface temperature T. Stars differ in luminosity due to variations in their radius and temperature (T). Massive stars with high temperatures and large radii are extremely luminous, while smaller, cooler stars emit less light. Giants and supergiants have larger radii but low surface temperature but emit more light; on the other hand, white dwarfs have low luminosity due to their compact size. Stars on the main sequence have luminosity according to their mass, higher mass stars burn fuel faster and shine brighter. Like the Sun which lies on the main sequence, has a stable phase of its life, its position reflects its moderate mass, temperature and luminosity. This relationship explains how the HR diagram reflects both physical size and temperature in determining stellar luminosity.
4.2 Application to stars
A star's luminosity is determined by its surface area (4 π R2) and the energy emitted per square meter of its surface (σ T?). If we adjust the temperature or radius of a star, its luminosity changes accordingly. For instance, doubling the temperature causes the energy output to increase by 2? or 16 times, and if doubling the radius increases the output by only 4 times. This shows that temperature has a much greater impact on luminosity than radius. As the Stefan-Boltzmann Law applies to any star, astronomers use this law to determine the radius of a star just by rearranging the equation a little bit, but its luminosity and surface temperature should be known.
Hotter stars emit more light per unit area across all wavelengths and shine with a blue shade. Blue light carries more energy than red light, which is why a star appears brighter and its color changes as it heats up. This is similar to how an iron rod glows red when warm, then shifts to yellow and eventually white-hot as the temperature rises.
4.3 Mass of star And its life span.
A mass of star plays an important role in its lifespan. More massive star (nearly 5 times or greater than the sun) will consume fuel more rapidly due to higher temperature and pressure in its core leading to a shorter lifespan of only a few million years. Compared to this, stars having mass between one to five times that of the sun will last for another few billion years as they are burning their fuel at a moderate speed. Low mass stars (stars mass is less than the sun's mass) burn very slowly so that they can live for tens or hundreds of millions of years. This means that there is a relation between a star's mass and its life.
Conclusion
We can now easily deduce a star's key characteristics simply by observing its color, temperature, and brightness. For instance, the color of a star gives us clues about its temperature—blue stars are much hotter than red ones, emitting light at shorter wavelengths. The brightness or luminosity of a star tells of its size and energy output because the larger the star, the more luminous it is even though its temperature may differ. The diagram allows me to identify the stage of life: for example, a red giant reveals that it nears the end of life, while a blue supergiant shows it is early and energetic. By knowing where a star is on the diagram, we can classify it according to its current state and predict its future, effectively giving us a "time machine" into the evolution of the stars. In short, with the H-R diagram, we can make educated guesses about what temperature, size, and eventual death a star will undergo, just by its color and position, which helps unravel the mysteries of stellar life cycles and their relation to the greater universe.
REFERENCES
[1] Langer, N., & Kudritzki, R. P. (2014). The spectroscopic Hertzsprung-Russell diagram. Astronomy & Astrophysics, 564, A52.:- HR diagram
[2] DeVorkin, D. H. (1978). Steps toward the Hertzsprung-Russell diagram. Physics today, 31(3), 32-39. :- HR diagram
[3] Stefan-Boltzmann Law - Tech Astronomy
[4] https://www.britannica.com/science/Hertzsprung-Russell-diagram : Article on HR diagram by ‘Britannica’
[5] https://astronomy.swin.edu.au/cosmos/h/hertzsprung-russell+diagram : Article on HR diagram by ‘COSMOS- the SAO Encyclopedia of Astronomy’
[6] https://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_hrintro.html : Article on HR diagram by Australia Telescope National Facility
[7] https://chandra.cfa.harvard.edu/edu/formal/variable_stars/bg_info.html : Article on HR diagram by NASA
[8] Types of stars: https://www.britannica.com/science/Hertzsprung-Russell-diagram
[9]https://www.mpia.de/en/psf#:~:text=Star%20formation%20is%20a%20key,for%20the%20formation%20of%20planets. : Article on HR diagram by Max Planck Institute for Astronomy
[10] M-K diagram images - Secrets of Universe - https://www.secretsofuniverse.in/wp-content/uploads/2020/03/Spectral-types-of-stars.jpg [Fig 1] ; https://www.secretsofuniverse.in/wp-content/uploads/2020/03/Yerkes-spectral-classification.png [Fig 2]
[11] H-R diagram - Western Washington University-https://astro101.wwu.edu/101/hrdiagram_01.jpg [Fig 3]
[12] https://astronomy.swin.edu.au/cosmos/m/Morgan-Keenan+Luminosity+Class - Article on MK diagram by ‘COSMOS- the SAO Encyclopedia of Astronomy’
[13] Introduction image - https://static.scientificamerican.com/sciam/cache/file/13325585-D9F6-48B8-BF2D1AC187CEAE60_source.jpg?w=1200