Concepts

Brightness

The ratio between the radiation emitted by celestial bodies and the brightness we perceive depends on the distance of the celestial body, and therefore we distinguish between absolute brightness and apparent brightness.

The symbol for apparent brightness is m, and its unit is magnitude. The symbol for absolute brightness is M, which is also measured in magnitudes.

We differentiate between several types of "brightness," so let's review them first:

Brightness: primarily a physical quantity perceived by the eye. Denoted by m or M.
Magnitude: the unit of measurement for brightness, but in astronomy, we also use it as a synonym for brightness. When we say a 4.7m star, we mean a "star of 4.7 magnitude." Its symbol is the superscript $^m$ or $^M$ . We distinguish between magnitude and brightness. The limiting brightness of human vision is 6 magnitudes.
Intensity: often referred to as flux, which is the strength of electromagnetic radiation emitted by a star. Denoted by I.
Luminosity (radiant power): the total amount of radiative energy emitted by a star per unit time. Denoted by L.

Apparent Brightness

Brightness of Celestial Bodies

Sun: $-26.8^m$ .
Moon: averages $-12.74^m$ during the full moon phase.
Jupiter's moons discovered by Galileo: between $5^m$ and $6^m$ .
Mercury: ranges from $-1.4^m$ to $-2.2^m$ up to superior conjunction.
Venus: the brightest celestial body after the Sun and Moon. Its brightness varies between $-4.5^m$ and $-3.9^m$ .
Mars: Varies on average between $-2.9^m$ and $+1.8^m$ .
Jupiter: $-2.6^m$ and $-1.7^m$ .
Saturn: $-0.4^m$ and $+0.1^m$ .
Uranus: $5.7^m$ and $5.9^m$ .
Neptune: $7.8^m$ and $8.0^m$ .

Bolometric Brightness

When we measure all the radiation coming from a celestial body, we refer to its bolometric brightness, denoted by $m_\text{bol}$ . Bolometric brightness is measured with a bolometer, which detects temperature changes resulting from electromagnetic radiation.

Absolute Brightness

Absolute brightness (M) is the brightness of a celestial body observed from a specified distance, measured in magnitudes.

In the case of stars and galaxies, it shows how bright they would appear from a distance of 10 parsecs---for planets and other solar system bodies, it shows how bright they would appear if they were at a distance of 1 astronomical unit (AU) from both the Earth and the Sun.

The absolute brightness of stars ranges between $-10^M$ and $+17^M$ , while galaxies have much lower absolute magnitudes because they are brighter; for example, the absolute brightness of the M87 elliptical galaxy is $-22^M$ .

We can calculate the absolute brightness as follows:

M = m + 5 - 5 \lg r

where M is the absolute brightness, m is the apparent brightness, and r is the distance of the star in parsecs.

If we need to consider interstellar absorption:

M = m + 5 - 5 \lg r - Ar

where A is the value of interstellar absorption. In the plane of the Milky Way, $A = 1^{m/kpc}$ . The value of A is highly direction-dependent.

Stellar Evolution

Stars are formed in interstellar molecular clouds, such as those found in the Orion Nebula or the Eagle Nebula. The average lifespan of these clouds is about 40 million years.

<figure id="fig:Orion Nebula" alt="Orion Nebula" title="Orion Nebula" data-align="center"> <img src="../assets/orion.jpg" /> <figcaption>Orion Nebula</figcaption> </figure>

Observations show that there are dense cores within the clouds. The formation of these cores is the first phase of star formation, which we do not fully understand. The second phase occurs when the core begins to contract under its own gravity. At the beginning of the contraction, the material of the core is still so sparse that the gravitational energy released is freely radiated away, so the temperature of the core does not rise. The process initially leads to the formation of a denser core (protostar), onto which less dense material falls.

Initially, the cloud has some angular momentum, that is, rotation. As the cloud contracts, its radius decreases significantly, which, due to the conservation of angular momentum, leads to an increase in rotational speed. This results in the flattening of the contracting cloud and the formation of the stellar core and the surrounding disk of material, known as the accretion disk. At this point, the material of the star is so dense that radiation cannot escape unhindered, so the released gravitational energy heats the protostar, making it visible.

<figure id="fig:Formation of Accretion Disk" alt="Formation of Accretion Disk" title="Formation of Accretion Disk" data-align="center"> <img src="../assets/megmaradas-shu.jpg" /> <figcaption>Formation of Accretion Disk</figcaption> </figure>

When the temperature in the interior of the protostar reaches 10--15 million Kelvin (10 million Celsius), the probability of hydrogen transforming into helium increases, and fusion reactions begin in the interior of the star. At this point, the contraction stops because the pressure within the star balances the inward gravitational force. In this phase, the star reaches the main sequence. Part of the circumstellar accretion disk falls onto the star, while from the other part, dust and gas particles coalesce to form planetesimals, which then form planets. By the time the star reaches the main sequence, most of the accretion disk has disappeared. This is how our Solar System was formed.

Stars mostly form in groups because, during the contraction of the cloud, individual fragments separate and continue to evolve independently.

<figure id="fig:Pleiades" alt="Pleiades" title="Pleiades" data-align="center"> <img src="../assets/fiastyuk.jpg" /> <figcaption>Pleiades Open Cluster</figcaption> </figure>

In the Pleiades open cluster, the stars have not yet dispersed into space.

Spectral Classes

I discuss this topic in more detail on the Astronomical Spectral Analysis page.

Spectral analysis refers to the electromagnetic radiation of an object broken down into its components. The field of science that deals with spectral analysis is called spectroscopy, and this chapter will also cover it.

Knowing the composition of stars' atmospheres has been made possible by astronomical spectral analysis, which we can perform by examining the intensity, strength, and brightness of various wavelength ranges, as well as the position and width of the so-called Fraunhofer lines.

The continuous spectral distribution of light intensity depends on the temperature and the material composition of the celestial body in question. Furthermore, through spectral analysis, we can determine one of the most important properties of stars, the surface temperature. Additionally, by analyzing the Doppler shift of these spectral lines, we can obtain even more information about the celestial body in question, such as the line-of-sight (radial) velocity---and if we are talking about a binary or multiple system---we can also infer the masses of the system's members and other physical properties.