# Distance and absolute brightness

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This is an exercise from a text, I'm learning from and I can't understand it so I'm asking just to develop my knowledge:

The explosion of V603 Aql (Nova Aquilae) took place in June 1918. The nova reached maximum brightness -1.1 mag. The nova's spectrum was observed to shift absorption lines corresponding to a radial speed of 1700 km/s. In 1926, a weak envelope was observed around the nova with an angle of 16".

Determine the distance and absolute brightness at maximum for V603 Aql.

## How does the brightness of a star change with distance?

Read full answer here. Also know, what is the relationship between the brightness of a star and its distance?

How bright a star looks from the perspective of Earth is its apparent brightness. The apparent brightness of a source of electromagnetic energy decreases with increasing distance from that source in proportion to the square of the distance&mdasha relationship known as the inverse square law.

Also Know, what affects the brightness of a star? Luminosity Is Caused By As the size of a star increases, luminosity increases. If you think about it, a larger star has more surface area. That increased surface area allows more light and energy to be given off. Temperature also affects a star's luminosity.

Also asked, how do you measure the brightness of a star?

If they know the star's brightness and the distance to the star, they can calculate the star's luminosity: [luminosity = brightness x 12.57 x (distance) 2 ]. Luminosity is also related to a star's size. The larger a star is, the more energy it puts out and the more luminous it is.

Why is it difficult to judge the distance of a star by measuring only its brightness?

There is no direct method currently available to measure the distance to stars farther than 400 light years from Earth, so astronomers instead use brightness measurements. It turns out that a star's color spectrum is a good indication of its actual brightness.

• The Light Year - Distances to the Stars
• The Naming of Stars
• Apparent and Absolute Magnitude - Measures of Stellar Brightness
• Using Binoculars to Look at the Stars
• The Constellations
• Ursa Major and Ursa Minor
• The Pole Star (Polaris)
• Cassiopeia
• The Orion Constellation
• Stellar Brightness - Orion and Canis Major
• Stellar Variety - Sirius, Rigel and Betelgeuse
• Stars to Blow the Mind
• The Summer Triangle
• Albireo and Algol
• The Southern Cross and Centaurus
• Alpha Centauri
• Our Star - Our Sun
• A Total Eclipse of the Sun
• Conclusions

One of the great fascinations of astronomy is the mind-boggling scale of everything. The statistics - more than in any other area of human interest - are quite literally astronomical. Some of these statistics are included on this page and the next, but of course there is one unit of measure not applied to terrestrial facts and figures, which is synonymous with astronomy, and that is the light year. I wrote about the light year on Page 1 of this series, but I think it will be useful at this stage just to again put the scale of stellar distances into perspective in relation to the light year.

What is a light year? Well, a light year is NOT a measure of time. It is a measure of distance. It is simply the distance that light can travel in one year. The speed of light is incredibly fast - faster than anything else we know of - indeed, possibly the fastest that anything can travel. It is 300,000 kilometres per second (186,000 miles per second).

Now for some statistics, which illustrate just how distant the stars are from the Earth.

• The distance from the Earth to the Moon is approximately 1.5 light seconds. It takes light just 1.5 seconds to travel to the Moon.
• The distance from the Earth to the Sun is more than 8 light minutes. The Sun is about 400 times further away than the Moon.
• The average distance from the Earth to the planet Neptune, the most distant of the planets, is 4.2 light hours. (Pluto is no longer considered a planet).
• The distance from the Earth (or Sun) to the very nearest star is more than 4 light years.

In other words, the very nearest star is about 280,000 times further away from us than our Sun is. And if you would like a more graphic illustration, let us suppose we reduce the Earth to the size of a pea. On this scale, the Moon would be about 18 cm (7 inches) away. The Sun would be about 72 metres (80 yards) away. And the nearest star? Well that would be on the other side of the world, 20,000 kilometres (12,500 miles) distant. And most stars are much further away still.The stars are at truly immense distances.

## What is the difference between a star's apparent brightness and its absolute brightness?

The apparent brightness is how much energy is coming from the star per square meter per second, as measured on Earth. The units are watts per square meter (W/m 2 ). Astronomers usually use another measure, magnitude . (Our book calls it apparent magnitude .)

Likewise, what does absolute brightness mean? absolute brightness: The apparent brightness a star would have if it were placed at a standard distance of 10 parsecs from Eart. Page 1. A. absolute brightness: The apparent brightness a star would have if it were placed at a standard distance of 10 parsecs from Earth.

Herein, which star has the greatest absolute brightness?

The Brightest Stars, as Seen from the Earth

Common Name Scientific Name Apparent Magnitude
Sun -26.72
Sirius Alpha CMa -1.46
Canopus Alpha Car -0.72
Rigil Kentaurus Alpha Cen -0.27

How do you measure the apparent brightness of a star?

What you actually measure with a telescope (or with your eyes) is not luminosity, but a different quantity, called apparent brightness. The apparent brightness of a star is the rate at which energy (in the form of light) reaches your telescope, divided by the area of your telescope's mirror or lens.

## Distance and absolute brightness - Astronomy

We normally characterize the apparent brightness of a star by its apparent magnitude, mv. The brightest stars in the sky have magnitudes of roughly 0, while the dimmest stars you can see with the unaided eye from a clear, dark location have magnitudes of about 6. Note that brighter stars have smaller magnitudes. Most Cepheids in M100 have apparent magnitudes around 25, which is 40 million times dimmer than the dimmest stars you can see with the unaided eye!

How can we express the intrinsic brightness of a star in terms of magnitudes? One means is to imagine moving the star to a predetermined distance. The absolute magnitude of a star, Mv, is defined to be the apparent brightness of a star when the star is at a distance of 10 pc (32.6 light years). The difference between the apparent magnitude and absolute magnitude provides (almost) enough information to calculate the distance to the star. If you are interested, you can read more about apparent and absolute magnitudes.

In order to find the distance to M100, you need to find the absolute magnitudes for each of the Cepheids. Henrietta Leavitt of the Harvard College Observatory discovered the relationship between the period of Cepheids and their average apparent magnitude mv. She had studied Cepheids in the Large and Small Magellanic Clouds, but did not know the distance to the Cepheids, and therefore could not establish absolute magnitudes or luminosities for the Cepheids. Harlow Shapley determined the calibration needed to turn Leavitt's period - apparent magnitude diagram (P-mv relation) into a period-luminosity relation (P-L relation) for Cepheids. Since the luminosity of a star is related to its absolute visual magnitude (Mv), we can express the P-L relationship as a P-Mv relationship. The P-Mv relationship for M100 is shown graphically below:

The relationship is described by the equation (from Ferrarese et al., 1996)

where P is in days. If logarithms are a faint memory, you may wish to peruse a refresher on logs.

For each Cepheid you discovered, use the above equation to determine the absolute magnitude of the Cepheid from its period.

For example, in the demonstration of the Cepheid hunt, you found Cepheid C46. Part I, Section B of your lab sheet for this Cepheid looks like this: From column 4, the period of the Cepheid is 25.3 days. Using the equation above, the average absolute magnitude of C46 is

Enter the absolute magnitude in column 5 of Part I, Section B of your lab sheet. The entry for C46 now looks like:

Find the absolute magnitudes for all your Cepheids, and enter the result in column 5 of Part I, Section B of your lab sheet.

## Distance and absolute brightness - Astronomy

In the 1540's Nicolaus Copernicus removed the Earth from the center of the universe. He put the Sun at the center. Copernicus' view held up against the observational evidence for hundreds of years. In the 1910's the Sun was removed from the center of the universe and relegated to a typical patch in the galactic disk far from the center of the Galaxy. Harlow Shapley (lived 1885--1972) made this discovery by determining the distances to very old star clusters. He used the inverse square law of light brightness on a particular type of variable star in those old star clusters.

Some stars are very useful for finding distances to clusters and to other galaxies because they have a known luminosity that is large, so they can be seen from great distances away. Bright objects of a known luminosity are called standard candles (though, in our modern day we should perhaps call them "standard bulbs"). Standard candle objects are used to measure large distances. The particular standard candle stars Shapley used are in the last stages of their life and pulsate by changing size. They are trying to re-establish hydrostatic equilibrium but the thermal pressure is out of sync with the gravitational compression. The expanding star overshoots the equilibrium point. Then gravity catches up and contracts the star. But gravity contracts the star beyond the equilibrium point. The thermal pressure increases too much and the cycle continues.

#### Cepheids

Astronomers had to wait a few years for Harlow Shapley to calibrate Leavitt's relation using Cepheids in our galaxy for which the distances could be determined. In the calibration process Shapley put actual values to the luminosity part of the period-luminosity relation. With a calibrated period-luminosity relation astronomers could use Cepheid variables as standard candles to determine the distances to distant clusters and even other galaxies.

are from young "high-metallicity" stars (made of gas with significant amounts of processed materials from previous generations of stars) and are about 4 times more luminous than Type II Cepheids. Below is the light curve (the plot of brightness vs. time) of a classical Cepheid from the Hipparcos database of variable stars.

are from older "low-metallicity" stars (made of less polluted, more primordial gas) and are about 4 times less luminous than Type I. Below is the light curve of a W Virginis Cepheid from the Hipparcos database of variable stars. Note the differences in the shape of the light curve. The two types of Cepheids are distinguished from each other by the shape of the light curve profile. In order to compare the shapes without having to worry about the pulsation periods, the time axis is divided by the total pulation period to get the "phase": one pulsation period = one "phase".

Because the luminosity of Cepheids can be easily found from the pulsation period, they are very useful in finding distances to the star clusters or galaxies in which they reside. By comparing a Cepheid's apparent brightness with its luminosity, you can determine the star's distance from the inverse square law of light brightness. The inverse square law of light brightness says the distance to the Cepheid = (calibration distance) × Sqrt[(calibration brightness)/(apparent brightness)]. Recall that brightnesses are specified in the magnitude system, so the calibration brightness (absolute magnitude) is the brightness you would measure if the Cepheid was at the calibration distance of 10 parsecs (33 light years). In some cases the calibration distance may be the already-known distance to another Cepheid with the same period you are interested in. As described below, Cepheid variable stars are a crucial link in setting the scale of the universe.

Early measurements of the distances to galaxies did not take into account the two types of Cepheids and astronomers underestimated the distances to the galaxies. Edwin Hubble measured the distance to the Andromeda Galaxy in 1923 using the period-luminosity relation for Type II Cepheids. He found it was about 900,000 light years away. However, the Cepheids he observed were Type I (classical) Cepheids that are about four times more luminous. Later, when the distinction was made between the two types, the distance to the Andromeda Galaxy was increased by about two times to about 2.3 million light years. Recent studies using various types of objects and techniques have given a larger distance of between 2.5 to 3 million light years to the Andromeda Galaxy (a measurement using eclipsing binaries gives a distance of 2.52 million light years another measurement using red giants gives a distance of 2.56 million light years another measurement using Cepheids gives 2.9 million light years and measurements using RR-Lyrae give 2.87 to 3.00 million light years).

#### RR Lyrae

RR Lyrae are found in old star clusters called globular clusters and in the stellar halo part of our galaxy. All of the RR Lyrae stars in a cluster have the same average apparent magnitude. In different clusters, the average apparent magnitude was different. This is because all RR Lyrae have about the same average absolute magnitude (=+0.6, or 49 solar luminosities). If the cluster is more distant from us, the RR Lyrae in it will have greater apparent magnitudes (remember fainter objects have greater magnitudes!).

RR Lyrae stars can be used as standard candles to measure distances out to about 760,000 parsecs (about 2.5 million light years). The more luminous Cepheid variables can be used to measure distances out to 40 million parsecs (about 130 million light years). These distances are many thousands of times greater than the distances to the nearest stars found with the trigonometric parallax method. The method of standard candles (inverse square law) provides a crucial link between the geometric methods of trigonometric parallax and the method of the Hubble-Lemaître Law for very far away galaxies. (The Hubble-Lemaître Law is explained further later.) In fact, this link between the parallax and the Hubble-Lemaître Law was so crucial that the diameter of the Hubble Space Telescope's mirror was primarily determined by how large a mirror (its resolving power and light gathering power) would be needed to pick out Cepheids in the other galaxies and the Cepheid distance measurement of 18 galaxies was one of the three Key Projects for the Hubble Space Telescope during its first decade of operation (see also). All of the pretty pictures of other objects during that time were just an extra bonus.

## Brightness and Magnitude in Astronomy

Magnitude is an astronomical term that is used to describe precisely how bright a stellar object is. It can be done with both objective scientific measurements and a more qualitative classification of how bright the object is in the sky. Magnitude is measured on an inverse scale where lower numbers equal a brighter object. The traditional magnitude scale used in astronomy runs from 1 to 6.

The two major scales of magnitude are visual magnitude and absolute magnitude. Absolute magnitude is a scientific scale of how much light an object would shed if the observer was precisely 10 parsecs away from it. This distance equals about 33 light years, or 200 trillion miles, and the exact absolute brightness value of a heavenly body is determined by complex calculations of the elemental composition of the object, the amount of light it sheds measured in lumens and other scientific considerations. Absolute magnitude is rarely used outside of the scientific context.

Apparent magnitude, also known as visual magnitude, is a more intuitive form of classification. It measures how bright the object is by the time that its light reaches the earth. This value can be measured precisely through the use of light meters and telescopes, or it can be approximated simply by looking at the stellar objects with binoculars or the naked eye.

In fact, the magnitude scale of stellar brightness was invented thousands of years before telescopes or binoculars. The scale of apparent magnitude that we use today was laid down by the ancient Greek astronomers Hipparchus and Ptolemy, who classified the objects in the sky according to six categories of brightness. They chose about twenty of the stars that looked brightest to them and assigned them to the category of the first magnitude. The next brightest set of stellar objects was assigned to the second magnitude, all the way to the ones which could only barely be seen, which were all grouped in the sixth magnitude.

When telescopes, prisms and other optical devices were invented, they brought with them two important discoveries related to magnitude. The first was that there were a whole lot more stars below the sixth category than anyone had ever expected. The telescope revealed uncountable numbers of tiny lights that were far too dim to be seen with the unassisted eye. What is more, the telescope made it possible to measure the brightness coming from a particular star with ever-increasing specificity. Since the first magnitude was such a well-defined category and the sixth magnitude was used to apply to a vast number of objects at the very edge of human decision, the arbitrary decision was made to set the brightness of the sixth magnitude at 100 times less than the 1st magnitude. This transformed the magnitude scale into a logarithmic scale, which means that the quantities measured increased exponentially as the measurements increased arithmetically.

This historical tradition of astronomy explains why the stellar magnitude chart appears almost upside-down. Since the scale has been extended to cover things far outside the original scope, and since the measured brightness falls as the magnitude climbs, the chart can sometime seem to operate in a counter-intuitive manner. However, so long as one remembers that a bright star has a magnitude of about one, it is easy to reason the rest through.

The magnitude chart was expanded in the other direction as well. It became possible to measure exactly how much brighter planets such as Venus were than the heavenly bodies around them. In other words, they recorded precisely how much light there was coming from Venus when it was at its fullest brightness. It was found to be about a hundred times brighter than the objects that made up the traditional first magnitude, so the scale was simply extended into the negative numbers to accommodate. Venus has a visual magnitude of about -4. The Moon, by far the brightest of the planets we can see in the sky, has a magnitude of about -12 when it is at its fullest. The sun puts out about 400,000 times as much light as the full moon. This means that its visual magnitude is about -26.

As can be seen, this scale represents an excellent way to deal with the widely divergent lights seen in the sky. Although local atmospheric conditions are always paramount, on a clear night it should be possible to see stellar bodies all the way up to magnitude 6. A typical pair of field binoculars should be sufficient to see objects as dim as magnitude 9.5, which is more than a hundred times darker than the eyes can see alone. A telescope will naturally improve this ability to detect dimmer objects to an almost unimaginable degree. The wider the diameter of the telescope, the more light it will capture and the higher magnitude objects that can be seen. The only limits to this are found in the diameter of lens that can be procured and the atmospheric conditions prevailing at the viewing location. The Hubble Space Telescope has been able to resolve objects as dim as 31.5 magnitude in its nearly perfect viewing conditions outside the Earth’s atmosphere.

## 6) Summary

• Geometric parallaxes have been measured out to distances which are already challenging the less-than-10,000-year "young universe hypothesis". In the next few years, with the launch of GAIA, the results will go out to more than 30,000 light years.
• Geometric measurements to objects which are thousands, millions and even billions of light years away are available, using sensible physical models for the observed objects.
• Other methods rely on a well-established model for just what stars are and how they change during their life times. At least, the billions of stars in our galaxy, if they are stars at all (rather than just mysterious points of light), have to be many tens of thousands of light years away.
• The methods for determining distances to very distant objects rely on well-studied "standard candles".
• All the findings so far have been consistent with predictions of the theory of stellar development and the Big Bang theory.

Finally, one has to realize that although the methods used to determine distances seem to rely heavily on each other (as I mentioned in the introduction, one uses a kind of "ladder" of different methods), there exists instead a whole web of self-correcting and interlocking methods which all come to the same conclusions. The assumptions which go into the methods are justified by the fact that we get consistent results if we use these assumptions.

## Contents

### Astronomical Unit Edit

The astronomical unit is the mean (average) distance of the Earth from the Sun. This we know quite accurately. Kepler's Laws tell the ratios of the distances of planets, and radar tells the absolute distance to inner planets and artificial satellites in orbit around them.

### Parallax Edit

Parallax is the use of trigonometry to discover the distances of objects near to the solar system.

As the Earth orbits around the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in a right triangle, with 2 AU making the short leg of the triangle and the distance to the star being the long leg. The amount of shift is quite small, measuring 1 arcsecond for an object at a distance of 1 parsec (3.26 light-years)

This method works for distances up to a few hundred parsecs.

Objects of known brightness are called standard candles. Most physical distance indicators are standard candles. These are objects which belong to a class that has a known brightness. By comparing the known luminosity of the latter to its observed brightness, the distance to the object can be computed using the inverse-square law.

In astronomy, the brightness of an object is given in terms of its absolute magnitude. This quantity is derived from the logarithm of its luminosity as seen from a distance of 10 parsecs. The apparent magnitude is the magnitude as seen by the observer. It can be used to determine the distance D to the object in kiloparsecs (kiloparsec = 1,000 parsecs) as follows:

where m the apparent magnitude and M the absolute magnitude. For this to be accurate, both magnitudes must be in the same frequency band and there can be no relative motion in the radial direction.

Some means of accounting for interstellar extinction, which also makes objects appear fainter and more red, is also needed. The difference between absolute and apparent magnitudes is called the distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.

### Problems Edit

Two problems exist for any class of standard candle. The principal one is calibration, finding out exactly what the absolute magnitude of the candle is.

The second lies in recognizing members of the class. The standard candle calibration does not work unless the object belongs to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious.

A significant issue with standard candles is the question of how standard they are. For example, all observations seem to indicate that Type Ia supernovae that are of known distance have the same brightness, but it's possible that distant Type Ia supernovae have different properties than nearby Type Ia supernovae. [1]

With few exceptions, distances based on direct measurements are available only up to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance.

Physical distance indicators, used on progressively larger distance scales, include:

— In the last decade, measurement of eclipsing binaries offers a way to gauge the distance to galaxies. Accuracy at the 5% level up to a distance of around 3 million parsecs. [2] — are periodic variable stars, commonly found in globular clusters, and often used as standard candles to measure galactic distances. These red giants are used for measuring distances within the galaxy and in nearby globular clusters.
• In galactic astronomy, X-ray bursts (thermonuclear flashes on the surface of a neutron star) are used as standard candles. Observations of X-ray burst sometimes show X-ray spectra indicating radius expansion. Therefore, the X-ray flux at the peak of the burst should correspond to Eddington luminosity, [3] which can be calculated once the mass of the neutron star is known (1.5 solar masses is a commonly used assumption). and novae
• Cepheids are a class of very luminous variable stars. The strong direct relationship between a Cepheid variable's luminosity and pulsation period, secures for Cepheids their status as important standard candles for establishing the Galactic and extragalactic distance scales. [4]
• Novae have some promise for use as standard candles. For instance, the distribution of their absolute magnitude is bimodal, with a main peak at magnitude −8.8, and a lesser one at −7.5. Novae also have roughly the same absolute magnitude 15 days after their peak (−5.5). This method is about as accurate as the Cepheid variable stars method. [5]
. Because the white dwarf stars which become supernovae have a uniform mass, Type Ia supernovae produce consistent peak luminosity. The stability of this value allows these explosions to be used as standard candles to measure the distance to their host galaxies, because the visual magnitude of the supernovae depends primarily on the distance. [6] and Hubble's Law By using Hubble's law, which relates redshift to distance, one can estimate the distance of any particular galaxy.
• ### Main sequence fitting Edit

In a Hertzsprung-Russell diagram the absolute magnitude for a group of stars is plotted against the spectral classification of the stars. Evolutionary patterns are found that relate to the mass, age and composition of the star. In particular, during their hydrogen burning period, stars lie along a curve in the diagram called the main sequence.

By measuring the properties from a star's spectrum, the position of a main sequence star on the H-R diagram can be found. From this the star's absolute magnitude is estimated. A comparison of this value with the apparent magnitude allows the approximate distance to be determined, after correcting for interstellar extinction of the luminosity because of gas and dust.

In a gravitationally-bound star cluster such as the Hyades, the stars formed at approximately the same age and lie at the same distance. This allows relatively accurate main sequence fitting, providing both age and distance determination.

This is not a complete list of methods, but it does show the ways astronomers go about estimating the distance of astronomical objects.

## Star brightness versus star luminosity

The ancient astronomers believed the stars were attached to a gigantic crystal sphere surrounding Earth. In that scenario, all stars were located at the same distance from Earth, and so, to the ancients, the brightness or dimness of stars depended only on the stars themselves.

In our cosmology, the stars we see with the eye alone on a dark night are located at very different distances from us, from several light-years to over 1,000 light-years. Telescopes show the light of stars millions or billions of light-years away.

Today, when we talk about a star’s brightness, we might mean one of two things: its intrinsic brightness or its apparent brightness. When astronomers speak of the luminosity of a star, they’re speaking of a star’s intrinsic brightness, how bright it really is. A star’s apparent magnitude – its brightness as it appears from Earth – is something different and depends on how far away we are from that star.

Astronomers often list the luminosity of stars in terms of solar luminosity. The sun has a radius of about 696,000 kilometers, and a surface temperature of about 5800 Kelvin, or 5800 degrees above absolute zero. Freezing point of water = 273 Kelvin = O o Celsius

For instance, nearly every star that you see with the unaided eye is larger and more luminous than our sun. The vast majority of stars that we see at night with the eye alone are millions – even hundreds of millions – of times farther away than the sun. Regardless, these distant suns can be seen from Earth because they are hundreds or thousands of times more luminous than our local star.

That’s not to say that our sun is a lightweight among stars. In fact, the sun is thought to be more luminous than 85% of the stars in our Milky Way galaxy. Yet most of these less luminous stars are too small and faint to see without an optical aid.

A star’s luminosity depends on two things:

2. Surface temperature

Let’s presume a star has the same surface temperature as the sun, but sports a larger radius. In that scenario, the star with the larger radius claims the greater luminosity. In the example below, we’ll say the star’s radius is 4 solar (4 times the sun’s radius) but has the same surface temperature as our sun.

We can calculate the star’s luminosity – relative to the sun’s – with the following equation, whereby L = luminosity and R = radius:

L = R 2
L = 4 2 = 4 x 4 = 16 times the sun’s luminosity

Although the star VY Canis Majoris in the constellation Canis Major has a much cooler surface temperature than our sun, this star’s sheer size makes it a super-luminous star. Its radius is thought to be around 1400 times than of our sun, and its luminosity 270,000 greater than our sun.

Surface temperature

Also, if a star has the same radius as the sun but a higher surface temperature, the hotter star exceeds the sun in luminosity. The sun’s surface temperature is somewhere around 5800 Kelvin (9980 o Fahrenheit). That’s 5800 degrees above absolute zero, the coldest temperature possible anywhere in the universe. Let’s presume a star is the same size as the sun but that its surface temperature is twice as great in degrees Kelvin (5800 x 2 = 11600 Kelvin).

We use the equation below to solve for the star’s luminosity, relative to the sun’s, where L = luminosity and T = surface temperature, and the surface temperature equals 2 solar.

L = T 4
L = 2 4 = 2 x 2 x 2 x 2 = 16 times the sun’s luminosity

Luminosity of Star = R 2 x T 4

The HR Diagram categorizes stars by surface temperature and luminosity. Hot blue stars, over 30,000 Kelvin, at left and cool red stars, less than 3,000 Kelvin, at right. The most luminous stars – over 1,000,000 solar – are at top, and the least luminous stars – 1/10,000 solar – at bottom.

The luminosity of any star is the product of the radius squared times the surface temperature raised to the fourth power. Given a star whose radius is 3 solar and a surface temperature that’s 2 solar, we can figure that star’s luminosity with the equation below, whereby L = luminosity, R = radius and T = surface temperature:

L = R 2 x T 4
L = (3 x 3) x (2 x 2 x 2 x 2)
L = 9 x 16 = 144 times the sun’s luminosity

Color and surface temperature

Have you ever noticed that stars shine in an array of different colors in a dark country sky? If not, try looking at stars with binoculars sometime. Color is a telltale sign of surface temperature. The hottest stars radiate blue or blue-white, whereas the coolest stars exhibit distinctly ruddy hues. Our yellow-colored sun indicates a moderate surface temperature in between the two extremes. Spica serves as prime example of a hot blue-white star, Altair: moderately-hot white star, Capella: middle-of-the-road yellow star, Arcturus: lukewarm orange star and Betelgeuse: cool red supergiant.

Bottom line: Some extremely large and hot stars blaze away with the luminosity of a million suns! But other stars look bright only because they’re near Earth. Astronomers call the true, intrinsic brightness of a star its luminosity.