How Does Luminosity Help Us Understand Stars and Energy?
What is Luminosity?
We have an almost intuitive understanding of the relationship between light and temperature like if we look at the stove when it is turned on, then there would be no difference whether it is turned on or off especially when the temperature is not specifically high. As the temperature increases, we would see that a red glow of the flame blows about the stove and when the temperature continues to increase, the flame turns to a bright yellowish-white color, as you can see in the two images below.
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Now, if we look at other sources, like iron being heated turns blue, stars emit light, the electric bulbs emit energy in the form of small packets called photons.
Since the light has energy, therefore, the stove and the candle emit light energy.
So the light energy emitted by it per second is called its luminosity, denoted by symbol L.
The unit used for measuring the luminosity is Joules per second or J/s.
What Does Luminosity Mean?
Luminosity is described as an inherent property of objects that emit light such as a star, flame of a burning candle, iron rod on getting heated, electric bulbs. They all give off light energy in all directions every second.
So, this is the same as saying that the more the object emits light, the more it gives off the power in watts, the more will be its luminosity.
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What is the Definition of Luminosity?
We define luminosity as the total amount of energy given off by an object every second.
The graph below shows that the wavelength of the yellow light is at the peak.
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Let’s take a real-life example:
If an electric bulb gives off 100 watts of power, it means it gives off 100 Joules of energy every second.
We can see that the luminosity of the sun is 3.85 x 1026Watts which is a very high luminosity.
As you compare between the Sun and the bulb, the sun is four trillion times trillion more powerful light is being radiated by the Sun every second.
What is the Meaning of Luminosity?
Let’s talk about an astronomical body like a star (an imperfect blackbody); they are spherical objects, primarily made up of very hot elements .i.e., hydrogen and helium that emits light continuously.
We can’t measure the temperature of a star, all we can do is just observe the light with maximum wavelength and use the Wein’s displacement law which states that the temperature can be found at the point where the radiation curve peaks, i.e. 入peak = x 10\[^{m}\] nm (nano microns).
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As you can see, this graph shows the spectrum of a star and through this, we can determine the wavelength where the emission peaks are given by, 入peak.
By Wein’s formula:
入peak = (0.29 cm K)/T
Here, T = 5500 K
Putting the value in the above equation, we get:
入peak = 5.27 x 10\[^{-5}\] m
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Then, compare to the spectra of computer models of stellar spectra of different temperatures (as you can see in Fig.2), and develop an exact color-temperature relation.
Luminosity Theory
In this theory, we will discuss the relationship of luminosity to temperature and the surface area of an object.
Let’s talk about the factors here:
Luminosity: The total amount of energy emitted per second in Watts.
Apparent brightness: It determines how bright a star appears to be; the power per meter squared as measured at a distance from the star.
Its unit is Watt/meter\[^{2}\].
Luminosity is denoted by L.
So, LSUN = 3.85 x 10\[^{26}\] J/s or watts.
In the CGS system, it is 3.8 x 10\[^{33}\] erg/s.
So, the surface area of a star can be calculated as A = 4πR²
Where R is the radius of a star.
If we consider a star to be a completely black body, the radiation emitted per second can be calculated by using the Stefan- Boltzmann law.
Stefan-Boltzmann states that the total energy emitted by a body is directly proportional to the fourth power of temperature.
Here s= Stefan’s constant whose value = 5.7 x 10\[^{-8}\] Wm\[^{-2}\] K\[^{-4}\],
A = Surface area of a star, and
T = Absolute temperature of a star.
Let’s consider radius of a star like the Sun = 6.96340 x 10\[^{8}\]
Surface area of star = 4πR² = 4 x 3.14 x(6.96340 x 10\[^{8}\])\[^{2}\]
TSUN = 6000 K
On calculating, we get
A = 6.09 x 10\[^{18}\] m\[^{2}\]
Now using the equation(1):
E = (5.7 x 10\[^{-8}\]) * (6.09 x 10\[^{18}\]) * (6000)\[^{4}\]
Therefore, we get the energy radiated by the sun = 4.4998 x 10\[^{26}\] J.
FAQs on Luminosity in Physics: Meaning, Formula & Applications
1. What is luminosity in Physics?
In physics and astronomy, luminosity is the total amount of electromagnetic energy—primarily light—emitted per unit of time by a celestial object like a star or galaxy. It is an intrinsic property of the object, meaning it measures the object's absolute or inherent brightness, independent of the observer's distance. The standard unit for luminosity is Watts (W).
2. What is the fundamental difference between luminosity and apparent brightness?
The key difference lies in what they measure. Luminosity is an intrinsic, fixed measure of the total energy an object radiates per second. In contrast, apparent brightness is an observer-dependent measure of how bright an object appears from a specific distance. Apparent brightness decreases as the distance from the object increases, following the inverse-square law. For example, a very luminous star far away can appear dimmer than a less luminous star that is much closer to us.
3. What is the formula for luminosity and what are its units?
Luminosity (L) can be calculated using the Stefan-Boltzmann law, which relates it to a star's size and temperature: L = 4πR²σT⁴. Here, 'R' is the star's radius, 'T' is its surface temperature in Kelvin, and 'σ' is the Stefan-Boltzmann constant. The SI unit for luminosity is Watts (W). In astronomy, it is often expressed in terms of the Sun's luminosity, known as solar luminosity (L☉), where 1 L☉ ≈ 3.828 × 10²⁶ W.
4. How is a star's luminosity related to its temperature and size?
A star's luminosity is directly dependent on both its temperature and its size (radius), as defined by the Stefan-Boltzmann law (L = 4πR²σT⁴). The relationship is as follows:
Temperature: Luminosity is proportional to the fourth power of the surface temperature (T⁴). This means a small increase in temperature results in a massive increase in luminosity. A star twice as hot as another of the same size is 16 times more luminous.
Size (Radius): Luminosity is proportional to the square of the radius (R²). If two stars have the same temperature, the one with twice the radius will have four times the luminosity because it has a larger surface area to radiate energy from.
5. What are some key applications of measuring luminosity in astronomy?
Measuring luminosity is crucial for understanding celestial objects. Its primary applications include:
Classifying Stars: Luminosity, along with temperature, is used to plot stars on the Hertzsprung-Russell (H-R) diagram, which helps classify them into types like main-sequence stars, giants, and dwarfs.
Determining Stellar Properties: By knowing a star's luminosity, astronomers can infer its mass, age, and evolutionary stage.
Calculating Cosmic Distances: Certain objects with known luminosities, called standard candles (like Cepheid variables), are used to calculate distances to faraway galaxies.
Studying Galaxy Evolution: The total luminosity of a galaxy helps estimate its star formation rate and overall mass.
6. If two stars have the same surface temperature, can they have different luminosities? Explain how.
Yes, two stars with the same surface temperature can have vastly different luminosities. This is because luminosity also depends on the star's surface area (which is determined by its radius). According to the formula L = 4πR²σT⁴, if the temperature (T) is constant, luminosity (L) is directly proportional to the square of the radius (R²). For instance, a red giant star and a red dwarf star can have similar cool surface temperatures, but the red giant's enormous radius gives it a much larger surface area, making it thousands of times more luminous than the small red dwarf.
7. Why is luminosity considered an intrinsic property of a star, unlike its apparent brightness?
Luminosity is considered an intrinsic property because it is determined by the star's fundamental physical characteristics: its mass, radius, and temperature. These factors dictate the total amount of energy the star produces and radiates per second, a value that does not change based on who is observing it or from where. In contrast, apparent brightness is observer-dependent. It measures how much of that total energy reaches a specific observer and is affected by the distance to the star. The farther away the observer, the dimmer the star appears, even though its actual energy output (luminosity) remains constant.
