The stary night is a nice view for everyone I guess quite often we like to lie on the ground and gaze at the sky full of stars. In the whole Milky Way, we have about 100K of stars, whereas only 7K can be visible by the naked eye under the pristine night sky, completely free of light pollution. I am heading to describe to you 50 of the brightest stars, which can be easily spotted even in intensively illuminated urban areas. However, this description cannot be progressed without the basic knowledge about the brightness of the stars and what elements rule them. I hope to expand this topic in the future because the subject of stars will be back here at least several times and some piece of knowledge compacted in the separate articles is essential. For now, my goal is to run you through the most basic information about the stars.
I. A FEW WORDS ABOUT THE HERTZSPRUNG-RUSSEL DIAGRAM
The Hertzsprung-Russel Diagram (known also as H-R Diagram) is a scatter plot of stars, which displays the relationship between the star’s absolute magnitudes or luminosities and their classification based mostly on the surface temperatures. The H-R Diagram comprises regions with different types of stars with respect to their types and evolutionary stages. Most of the stars occupy the middle region of the diagram along the main-sequence line. The main-sequence line is a continuous and distinctive band of stars which variation is based on their color (temperature) versus brightness. All these stars represent their “adult” period of the lifecycle, where the hydrogen is fused in their cores. The lower region of the main sequence is more crowded than the upper region. At the lower end, the stars are red in color (due to their low temperature) and small in size. They’re called therefore as the red dwarfs. The red dwarf is the most common type of star in the Milky Way, at least in the vicinity of the Sun.
At the bottom end of the H-R diagram, we can see the brown dwarfs. Brown dwarfs are substellar objects, that are not massive enough to sustain nuclear fusion. Their mass straddle somewhere between the most massive giant planets and red stars. It can correspond to between 13-80 masses of Jupiter on average.
The bottom left part of the H-R diagram is represented by white dwarfs – the stellar core remnants, which no longer undergo fusion reaction. They are very hot when form, but because they have no source of energy they gradually cool and radiate their energy away. In general, the white dwarfs are about 10 magnitudes fainter than the main sequence stars of the same spectral class and so must have a very small surface area and radius (Bhatia, 2001).
Between the white dwarfs and the main sequence, we can find subdwarfs. Subdwarfs are classified as stars with a magnitude 1.5 – 2 lower than stars from the main sequence at the same spectral type. We can distinguish cool subdwarfs, hot subdwarfs, and heavy metal subdwarfs.
Moving on the other side of the main sequence we can list the giant stars. The smallest in this region are subgiants, which represent the same type of star from the main sequence which is simply older. The subgiants can be treated as the former main-sequence stars. It means, that they have the same mass as their main-sequence counterparts, but their chemical composition includes more helium than hydrogen. Going up we have giant stars, which are substantially larger and brighter than stars in the main sequence. The typical giant stars are 10-100x larger than Sun and 10-1000x more luminous than Sun (Moore, 2002).
Between ordinary giants and supergiants, we have the bright (blue) giants. This type of star is at the finish of burning its hydrogen yet before it has started burning helium. The blue color and high temperature are the effects of the intensive burn of the remaining hydrogen. This process will last shortly until the star starts to burn helium and become the red giant.
Red giants represent the late stage of stellar evolution, where star burns helium. The atmosphere of the red giant is inflated and tenuous with a quite low surface temperature, giving the star a reddish appearance. The essence of the red giant has been explained later in this article.
Supergiants are brighter by giants by about 5 magnitudes and have about 100 solar radii (Bathia, 2001). Their mass exceeds between 8-12x solar mass. The supergiants mark the advanced evolutionary stage of the star, which starts to burn helium into carbon and oxygen. That heats the interior of the star and causes its exteriors to swell, which is typical before the star dies. The star at this stage can become the red supergiant or blue supergiant if other elements in its core are fused. The blue color of supergiant is an effect of a significant size drop from hundreds of solar radii to around 25 of solar radii. The biggest and very rare type of star is hypergiant. The hypergiants are the most massive stars in the universe and the most massive stars ever measured. They are significantly brighter than supergiants. They can be divided into blue, yellow, and red hypergiants. They live only a few million years.
The last interesting element, which can be noticed in the H-R diagram is the empty region, which is called the Hertzsprung gap. The primary feature of this region is the absence of stars, which is driven by rapid star evolution. This region covers the early evolutionary period when the hydrogen is being burnt in a shell around the core of helium before the onset of helium burning. The stars during their evolution move rapidly through the Hertzsprung gap compared to their whole lifetime. This stage can last as little as a few thousand years.
Thanks to the H-R diagram scientists can roughly determine the distance of a given star cluster or galaxy from Earth. This can be done by comparison of the apparent magnitude of the stars in the cluster to absolute magnitudes of stars with known distances. The H-R diagram is one of the most useful tools for the study of stars and their physical properties (Bhatia, 2001).
II. WHAT DETERMINES THE BRIGHTNESS OF THE STAR?
Watching the sky, we often ask ourselves – why some stars are brighter than others? By the naked eye, we can see up to 7000 stars in areas free of light pollution. In the next article, I would like to mention about just only 50 stars, the brightest ones? If you are a little green at astronomy, you might think that the brightest stars are also the biggest or the closest. Partially you will be right, but we should take into account also other factors. The crucial factors determining the brightness of the star are:
- Spectral characteristic (temperature of the photosphere) – which is based on the Star’s electromagnetic radiation. The light from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum likewise visible in the rainbow. Each element indicates a particular chemical element or molecule with the line strength indicating the abundance of that element. They vary predominantly due to the temperature of the photosphere. Most stars are classified under the Morgan – Keenan (MK) system with the letters following the photosphere temperature from hot to cool: O, B, A, F, G, K, M. To be funny – it’s a good mnemonic for this sequence: “Oh Be A Fine Girl [or Guy], Kiss Me.” Each letter class is subdivided using numeric digits from 0 to 9, where 0 means hot and 9 means cool. Furthermore, additional letters have been used for describing novas, dwarfs, or carbon stars. It’s also another – Yerkes classification based on temperature and luminosity, which classifies the stars under roman numbers, but the Morgan – Keenan (MK) classification remains commonly in use.
By knowing the color of the star we can estimate its surface temperature. The surface temperature determines the star brightness, which explains the Stefan-Boltzmann law. It says, that hotter stars emit more radiation per unit surface than cooler stars. If the reddish and bluish stars have the same luminosity, then the reddish star must be larger than a bluish star because the reddish star must have more surface area than the bluish star to produce the same luminosity, the Stefan-Boltzmann law says so. The law considers the effective temperature, which corresponds to the temperature of a black body with the same luminosity per surface area. The dependence of the star colors from the temperature explains also Wien’s displacement law, which states, that for higher temperatures the wavelength of thermal radiation is shorter. The star colors are the output of three electromagnetic wavelengths, whereas each of them represents the major chemical component building the star. The combination of these three wavelengths is referred to as the Plank’scurve.
- Mass – there is a strong relationship between the star’s mass and its luminosity, which can be described by the following formula: L = (M)3+β, where the L is the luminosity of a star in the main sequence and M the star’s mass given in the solar units. It means that if the star’s mass is doubled by 2, the luminosity increases by a factor of 2 3.5 = 11 times. This relationship comes arises out of determining the size, radius, and temperature of the star and it’s called the mass-luminosity relation. In a practical sense, it’s the correlation between the mass of a star and the rate at which it emits (and therefore produces) the energy (Duric, 2004). The star masses vary across the main HR sequence. The lowest mass main sequence stars have about 0.07 of the solar mass, and the most massive stars commonly encountered have about 60 solar masses (Kutner, 2003).
- Evolutionary stage – is somewhat an output of the major star properties like mass, size, temperature, or spectral type. All these factors combined together place stars in their evolutionary sequence. The same as spectral characteristic and mass, the evolutionary stage is an element of stars classification in the Hertzsprung-Russel diagram (Pic. 3).
The brightness of the star at its certain evolutionary stage is shaped by its mass and composition. Since the star reaches the main-sequence stage, the lifecycle is based on the fusion of hydrogen to helium, which accumulates in the star’s core eventually. As the percentage of helium, which is thought to be like “ash” from nuclear “burning” of hydrogen. As the helium accumulates in the center of the star, the temperature and density in the inner regions slightly increase. By increment of the temperature, the level of fusion goes up, thereby the rate at which energy is being generated also rises, which leads to gradual boosting of luminosity by that. As long as the star’s evolutionary stage remains in the main-sequence band these changes are minor. Everything changes when there is no more hydrogen for fusion reactions. Helium requires a much higher temperature for fusion, which is impossible. In turn, gravity takes over and the core begins to contract. The energy of inward-falling material is converted to the heat, which is generated this way flows outward to cooler regions, which now expand. The star grows until enormous proportions, whereas the temperature of its outer layers drops simultaneously shifting the star’s overall color towards red. This is the moment, at which the star is more luminous and cooler. The red giant stage indicates also the higher brightness of the star in its lifecycle.
- Chemical composition – as it has been told just previously, the chemical composition changes throughout the star’s lifecycle. In turn, it impacts its brightness slightly as per the evolutionary stage. Looking at it from a different point of view, the chemical composition is the element, which helps to distinguish the types of stars. It refers mostly to the proportion of heavy elements against hydrogen and helium. Since the average atmosphere of the star consists mostly of hydrogen (87%) and helium (10%), the remaining 3% are heavy elements, which include carbon, sodium, silicon, iron, calcium, lithium, or magnesium. The star’s brightness is shaped mostly by the first two chemical elements, although when the star becomes older, the other chemical elements remain more visible through the emission of a particular wavelength. The relation between the chemical composition and temperature and therefore brightness is based on atom movement. As temperature increases the electrons are kicked up to higher levels by collision with other atoms. Large atoms have more kinetic energy, so their electrons are excited first, followed by lower mass atoms. At high temperatures, the collision is strong enough to atom ionization. In practice, the low-temperature stars will feature the abundance of heavy atoms like calcium or magnesium on the contrary of high-temperature stars, where lighter atoms (like hydrogen) prevail.
- Size – can be gained by star radius measurement. Assuming, that two stars with the same surface temperature have a different radius, the star with a bigger radius will be brighter. The difference in the luminosity is proportional to the square of the size. The calculation here is really straightforward, and looks as below:
L – luminosity, R – radius
L = R2
L = 52 = 5 x 5 = 25
So according to the formula above, the star with a 5x bigger radius will be 25x brighter.
- Distance – there is a simple relation between the brightness of the star and the distance to it. The brightness decreases proportionally to the square of the distance as one moves away from the star. It’s explained by the inverse square law.
- Behaviour – it refers to any kind of variable star, which brightness, as seen from Earth, fluctuates. These brightness fluctuations might be driven by periodical swelling and shrinking of the star or by a simple change in the amount of light reaching Earth. The first case – intrinsic variable stars, refers to pulsating variable stars, cepheids, or long period variable stars. The last ones are characterized by fairly regular light fluctuations and require many months or several years to complete the cycle. They can change even a hundredfold in brightness.
The second group of variable stars – extrinsic variable stars is featured by changing the amount of light reaching Earth. As it has been told earlier, it can be caused by the following:
-> rotation of the star – it applies to the stars with sizeable sunspots, which may show the significant variation of brightness as they rotate,
-> eclipsing binaries – if we face the binary system of stars, then for the terrestrial observer, watching them from a certain angle, one star may eclipse another one resulting reduction in brightness.
-> planetary transits – can also cause variations in brightness, although they are much smaller and can be detected by extremely accurate observations.
- Lifespan – is strongly related to the star mass. Generally, the more massive a star is, the faster its fuel supply depletes, which translates into a shorter lifecycle. The reason behind it is, that as the star is heavier, the greater gravitational force makes it contract. Therefore the bigger internal pressure is needed to stop that contraction. It results in a hotter core by the increment of the nuclear reaction. The high rate of nuclear reaction decreases the lifespan of a star. As the star burns its fuel out much faster, it’s more luminous. By knowing the luminosity of a star we can determine how rapidly the star is using up its fuel supply. Thereby the lifetime of the star is proportional to the mass of fuel available divided by the luminosity. It’s associated with the mass-luminosity relationship explained above.
From a practical point of view, more massive stars feature shorter lifecycle but are brighter.
III. HOW THE BRIGHTNESS OF THE STAR CAN BE MEASURED?
The basic unit, which measures the brightness of the star (or other celestial body) is a magnitude. The magnitude is the logarithmic-based scale, which appears to work in reverse. The dimmer object appears the higher the numerical value is given to its magnitude. This is because the initial scale system was designed like this. In the Hipparchus times, the brightness of the celestial objects was estimated by the eye and then split into 6 categories, where the 1st magnitude was meaning the brightest object and the 6th magnitude the faintest one. As humans developed proper instruments to make the brightness measurements more detailed, the astronomers decided to expand this scale. In turn, the magnitude scale remained intact to this day. Its basis is still the same as it was in ancient times – the brighter the object, the lower the number assigned as a magnitude.
There are two types of magnitude, which can define the star brightness. This is the apparent magnitude and absolute magnitude. Firstly we will discuss the apparent magnitude, on which the very first star’s brightness classification was based. Apparent magnitude defines the brightness of an object as it appears in the night sky. As of 1850, the magnitude scale is defined much more precisely than just eyeball judgment. The scale was expanded down to 30th magnitude (Inglis, 2007) for the least bright celestial objects, which are about 2,5 billion times dimmer than the faintest objects visible by the naked eye (Schaaf, 2008). The scale was also expanded up to the Sun, which is blindingly bright and 1.6 trillion times brighter than the faintest star we can see by unaided eye (Schaaf, 2008) It was also noticed, that the brightest stars at 1st magnitude were around 100x brighter than 6th magnitude stars, and conversely, the 6th magnitude star is 100x dimer than 1st magnitude star. It led to the split of this scale logarithmically, where five magnitude steps corresponded precisely to a factor of 100 in brightness (Tassoul, 2004). In practice, the gap between each magnitude is equal to the fifth root of 100, which corresponds closely to 2.5118864 exactly (Schaaf, 2008). This is the Pogson ratio.
The final formula for the apparent magnitude is: where:
m – magnitude (mref – reference magnitude)
I – brightness (Iref – reference brightness)
By using this formula we can attend to practical measurements of brightness instead of simple classification.
1m: brightness factor of 2.512 2m: brightness factor of 2.512 x 2.512 = 6.31 3m: brightness factor of 2.512 x 2.512 x 2.512 = 15.84 4m: brightness factor of 2.512 x 2.512 x 2.512 x 2.512 = 39.81 5m: brightness factor of 2.512 x 2.512 x 2.512 x 2.512 x 2.512 = 100 10m = 100 x 100 = brightness factor of 10,000 times 15m = 100 x 100 x 100 = brightness factor of 1,000,000 times 20m = 100 x 100 x 100 x 100 = brightness factor of 100,000,000 times
The apparent magnitude can be measured by three common methods:
-> photoelectric photometer – the most efficient method, because the instrument measures the intensity of light it receives. Moreover, it should be calibrated to the brightness of the Vega star, which apparent magnitude is close to 0. The measurement can be based on differential photometry, where the brightness of at least 2 stars is measured and absolute photometry, which is based on the instrument calibration, as mentioned above.
-> long-exposure photography – this kind of photography is nonlinear itself, although in digital cameras we can know the brightness number of each pixel. This number will be proportional to the number of photons falling onto that pixel during the exposure.
-> human eye – the least efficient method, which is based only on the visual comparison between the stars of known brightness and stars of unknown brightness. Some experienced astronomers can make a comparison such as this with 10% accuracy.
Another way of defining the brightness of the stars is absolute magnitude. The basic difference between these two types of magnitude is the distance, from which the star is seen. Since the apparent magnitude defines the star’s brightness as seen from Earth, the absolute magnitude measures its brightness from a certain distance. This distance is roughly 10 parsecs, which corresponds to about 32.6 light-years.
Moreover, the value of absolute magnitude is assumed to be free of extinction of the starlight caused by cosmic dust and interstellar matter. The absolute magnitude can be expressed by the following formula:
m – apparent magnitude
M – absolute magnitude
d – distance to the star measured in parsecs (pc)
The value of absolute magnitude allows scientists to compare the intrinsic brightness of stars.
If we know both the apparent magnitude and absolute magnitude of the given star, we can easily calculate the distance to this star.
The basic limitation of the absolute magnitude is the determination of the light wavelength for measurements and sensitivity of the instrument used for these measurements, which is different for various wavelengths of the light due to the type of light detector. That’s why we should mention the bolometric magnitude, which measures the total radiation of the star emitted across all wavelengths of the electromagnetic spectrum. The basic difference between monochromatic and bolometric magnitude states the spectrum of light measurement. Monochromatic magnitude measures a very narrow segment of the spectrum, which is the visual band of the spectrum. In turn, the bolometric magnitude measurements include a star’s entire radiation, including also the bands unobservable due to instrumental passbands and extinction by Earth’s atmosphere and interstellar dust. In the star brightness measurements, we can use the bolometric correction, which must be made to the absolute magnitude of an object in order to convert an object’s visible magnitude to its bolometric magnitude.
IV. RELATION BETWEEN BRIGHTNESS AND LUMINOSITY
Luminosity is the rate at which the star radiates energy into space. Otherworldly is the total power output of the star and another celestial object. The relationship between a star’s brightness and luminosity can be explained by the inverse square law. It can be expressed by the following formula:
b – apparent brightness of the star,
d – the distance to the star,
L – the luminosity of the star,
Luminosity doesn’t depend on the distance to the star. It states roughly how “bright” the star is, and it’s expressed in Watt units. Luminosity can be measured by the amount of flux radiation hitting the Earth and the distance to the star. The flux is energy per unit area, which can be measured i.e. by detector attached to the telescope. Thereby we can get the distance to the star.
The image above shows the relation between a star’s luminosity and its brightness. Brightness decreases proportionally to the square of the distance as we move away from the star. The rate of energy which reaches the observer on Earth is the apparent brightness. Apart from the magnitude scale presented above, the apparent brightness can be expressed in watts/m2. For example, the apparent brightness of the Sun is 1370W/m2. It means, that if we could have the solar panel held perpendicularly to solar rays, we would receive 1370 Watts of electricity. It’s only the pure theoretical assumption because solar rays go through Earth’s atmosphere ad solar panels are not perfectly efficient. For the comparison, the brightest star – Sirius has its apparent brightness of 10-7 W/m2. It means, that if you would like to light u a 10 watt bulb with the energy of Sirius you would need a 10km length of solar panel.
The consideration about Sirius as well as other brightest stars have been left for another text immediatelly following this one.
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- The brightness of the stars
- The astronomical magnitude scale
- Stellar brightness
- Apparent and absolute magnitude
- Star magnitude calculator
- Star brightness calculator based on the apparent magnitude
- Libraries of the stellar spectra
- The evolutionary cycle of stars
- The life and death of the stars
- The life of a star
- How do we determine the life cycles of stars and tag some as “young” and some as “old?”
- Wien’s displacement law
- Astro.rug.nl: Basic properties of stars
- Plank Radiation Formula
- Luminosity – how far the things are
- Classifying stars
- Pulsating stars
- Long period variable star
- Stellar brightness
- Stellar lifetimes
- Skyandtelescope.org: How do stars die and how long do stars live?
- Astronomynotes.com: Stellar evolution
- Are they planets or what?
- The difference between red giants and blue giants
- What are red giants?
- What are Hypergiant Stars Like?
- Astroquizzical.com: What’s the Hertzsprung gap?
- Earthsky.org: What-is-stellar-magnitude
- Dictionary.com: Pogson ratio
- Magnitudes – measuring the brightness of the stars
- Brightness of the stars
- The stellar magnitude system
- How bright is a star?
- Mass & luminosity_relation
- Planck’s law
- How bright the starlight is?
- The role of contrast in ability of human vision
- Light around us and how to measure it?