What are apparent and absolute magnitudes and how are they related to apparent brightness and luminosity?

Additional reading from www.astronomynotes.com

• Distances -- Inverse square law

Perhaps the easiest measurement to make of a star is its apparent brightness. I am purposely being careful about my choice of words. When I say apparent brightness, I mean how bright the star appears to a detector here on Earth. The luminosity of a star, on the other hand, is the amount of light it emits from its surface. The difference between luminosity and apparent brightness depends on distance. Another way to look at these quantities is that the luminosity is an intrinsic property of the star, which means that everyone who has some means of measuring the luminosity of a star should find the same value. However, apparent brightness is not an intrinsic property of the star; it depends on your location. So, everyone will measure a different apparent brightness for the same star if they are all different distances away from that star.

For an analogy with which you are familiar, consider again the headlights of a car. When the car is far away, even if its high beams are on, the lights will not appear too bright. However, when the car passes you within 10 feet, its lights may appear blindingly bright. To think of this another way, given two light sources with the same luminosity, the closer light source will appear brighter. However, not all light bulbs are the same luminosity. If you put an automobile headlight 10 feet away and a flashlight 10 feet away, the flashlight will appear fainter because its luminosity is smaller.

Stars have a wide range of apparent brightness measured here on Earth. The variation in their brightness is caused by both variations in their luminosity and variations in their distance. An intrinsically faint, nearby star can appear to be just as bright to us on Earth as an intrinsically luminous, distant star. There is a mathematical relationship that relates these three quantities–apparent brightness, luminosity, and distance for all light sources, including stars.

Why do light sources appear fainter as a function of distance? The reason is that as light travels towards you, it is spreading out and covering a larger area. This idea is illustrated in this figure:

Fig. 4.5: The Inverse Square Law

Again, think of the luminosity—the energy emitted per second by the star—as an intrinsic property of the star. As that energy gets emitted, you can picture it passing through spherical shells centered on the star. In the above image, the entire spherical shell isn't illustrated, just a small section. Each shell should receive the same total amount of energy per second from the star, but since each successive sphere is larger, the light hitting an individual section of a more distant sphere will be diluted compared to the amount of light hitting an individual section of a nearby sphere. The amount of dilution is related to the surface area of the spheres, which is given by:

A = 4 π  d 2 This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. .

How bright will the same light source appear to observers fixed to a spherical shell with a radius twice as large as the first shell? Since the radius of the first sphere is d, and the radius of the second sphere would be 2 x d This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , then the surface area of the larger sphere is larger by a factor of   4 = ( 2 2 ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.. If you triple the radius, the surface area of the larger sphere increases by a factor of   9 = ( 3 2 ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.. Since the same total amount of light is illuminating each spherical shell, the light has to spread out to cover 4 times as much area for a shell twice as large in radius. The light has to spread out to cover 9 times as much area for a shell three times as large in radius. So, a light source will appear four times fainter if you are twice as far away from it as someone else, and it will appear nine times fainter if you are three times as far away from it as someone else.

Thus, the equation for the apparent brightness of a light source is given by the luminosity divided by the surface area of a sphere with radius equal to your distance from the light source, or

F = L / 4 π  d 2 This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , where d is your distance from the light source.

The apparent brightness is often referred to more generally as the flux, and is abbreviated F (as I did above). In practical terms, flux is given in units of energy per unit time per unit area (e.g., Joules / second / square meter). Since luminosity is defined as the amount of energy emitted by the object, it is given in units of energy per unit time [e.g., Joules / second ( 1 Joule / second = 1 Watt ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. ]. The distance between the observer and the light source is d, and should be in distance units, such as meters. You are probably familiar with the luminosity of light bulbs given in Watts (e.g., a 100 W bulb), and so you could, for example, refer to the Sun as having a luminosity of 3.9 x  10 26  W This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. . Given that value for the luminosity of the Sun and adopting the distance from the Sun to the Earth of 1 AU = 1.5 x  10 11  m This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , you can calculate the Flux received on Earth by the Sun, which is:

F = 3.9 x  10 26  W / 4 π  ( 1.5 x  10 11  m ) 2  = 1,379 W per square meter This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

This value is usually referred to as the solar constant. However, as you might guess, since the Earth/Sun distance varies and the Sun's luminosity varies during the solar cycle, there is a few percent dispersion around the mean value of the solar "constant" over time.

Contents

• Magnitude is the a measure of how bright an object is that we can see.
• Apparent and Visual Magnitude are terms for the same thing, that is how bright an object is that we see.
• The Apparent Magnitude of the Sun is -23
• The smaller the number, the brighter the object and vice versa.
• The human eye is able to see objects up to 6.5 without using visual aids.

In short, Magnitude is the measure of how bright an object in space is. The brightest object in space is measured at -26.74 and it comes as no surprise that that object is the Sun. The dimmest objects that we can see unaided, that is without using a pair of binoculars or a telescope has a magnitude of 6.5. To see something at that magnitude without assistance, you would need to go somewhere that is very dark, somewhere away from street lights.

The star magnitude system was first devised by the ancient Greek astronomer Hipparchus. His original system had star brightness starting from 1(Brightest) to 6 (Dimmest). The scale stayed. Stars and objects that are brighter than the stars he recorded at the time have therefore negative numbers. The scale has been revised over time hence why some stars such as Sirius has a negative number. Caltech

Apparent Magnitude is the magnitude of an object as it appears in the sky on Earth. Apparent Magnitude is also referred to as Visual Magnitude. The magnitude of a star excluding the Sun has no bearing on how big the star is or how near the star is.

The star UY Scuti has apparent magnitude of 11.2 which means it is not something that can be seen from Earth with the naked eye. UY Scuti is bigger than Sirius which has an apparent magnitude of -1.44 and is the brightest star in the night sky. Sirius is visible in the night sky whereas UY Scuti isn't.

Below is a small selection of what objects are possible at a selected amount of magnitudes. For a complete list, you should visit Wiki. The values in brackets are the values that Astronomy Notes give for examples and are more precise excluding Vega.

Anything that is dimmer than 32 magnitude is something we are not able to see at the moment even with the most powerful telescope. When the James Webb Space Telescope eventually goes into orbit, we could well see something of a lower magnitude, whether it be a galaxy that is further than the current record holder GN+z11 is open to debate. GN+z11 is not something that can be seen unaided.

Absolute Magnitude is a calculated value of how bright the star would be at a distance of 10 parsecs (32.6 Light Years). Using this value, you can get an idea of just how bright the object really is and compare like for like. The value is calculated by the following formula.

Mv = mv -5 (log d -1)

Lets take Regulus as an example, the distance (d) of Regulus as measured in parsecs is 41.13 using the 2007 figures. mv is the apparent visual magnitude which in 2007, it was 1.36 which means our absolute magnitude is -0.57.

The formula can make the star on some occasions seem dimmer than it is seen from Earth. Take Promixa Centauri, the reason for the star to seem dimmer is because from Earth, the star is less than 10 parsecs from Earth, it is only 1.3 parsecs from Earth so the absolute magnitude is how it is seen further away than from the Earth.

The below is a selection of stars, their apparent magnitude, the absolute and how far away they are in Light Years. The reason for choosing V762 Cassiopeiae is because it is the furthest star you can see with the naked eye in good conditions.

App. Magnitude vs Abs. Magnitude

Essentially, apparent magnitude is the magnitude of the object that we see from Earth. Absolute magnitude is the magnitude of an object that we see if we are 32.6 light years away from it.

Lets take two stars with the same apparent magnitude (6.5) but are at different distances, Star A (9 Monocerotis) and Star B (TY Fornacis). They have the same brightness in the sky but they are different distances to the Earth (937.25 LY and 328.13) respectively. Taking a short-cut, we can see that 9 Monocerotis has a lower absolute magnitude and is therefore the brighter of the two when both seen at the same distance.

The Absolute Magnitude is a means of comparing like for like. When you take into account the distance they are, you can then work out the real solar magnitude and which is the brighter. When you apply the calculation, you find that 9 Monocerotis has a brighter absolute magnitude and therefore is the real brighter of the two stars. The lower the value of the Absolute Magnitude, the brighter the object is.

Luminosity is the amount of energy that a star pumps out every second. The lower the absolute magnitude of a star is, the more luminous the star is. Take for instance Sirius, the absolute magnitude of the star is 1.45 and its Luminosity is 25.82. Compare it to Tarazed which has an absolute magnitude of -3.03 and a Luminosity of 2948.48.

What is the Brightest / Luminous Star?

Brightest (Apparent Magnitude

The brightest star is the Sun but you probably want that excluded from the answer. The brightest star in the night sky using the apparent magnitude system is Sirius with an apparent magnitude of -1.44. The Sun for comparison is as mentioned above -27.

Luminous (Absolute Magnitude)

The brightest in terms of absolute magnitude is R136a1 star in the nearby Large Magellanic Cloud. The cloud can be located in the constellation of Dorado. The star is a large Wolf-Rayet Star which are stars that have used up or nearly used all their hydrogen and are blowing out huge amount of gases.

Asteroid Absolute and Apparent Magnitude

Magnitudes don't just apply to stars, they can apply to other objects such as planets. When talking about Asteroids, the Apparent Magnitude is how we see it on Earth. The Absolute Magnitude is how bright the object is from 1 Astronomical Unit (A.U.), that is the distance from the Sun to Earth. Absolute Magnitude of asteroids are denoted with a H. Ref: N.A.S.A.

Last Modified : 5th September 2022

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