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Stars plotted by luminosity and surface temperature fit into patterns in a Hertzsprung–Russell diagram. A rough diagonal subset of this plot is called the main sequence. Is this in any sense a temporal sequence? There's a clue in the stellar physics section of the wikipedia article that the answer is no, but that it once was thought so:

Contemplation of the diagram led astronomers to speculate that it might demonstrate stellar evolution, the main suggestion being that stars collapsed from red giants to dwarf stars, then moving down along the line of the main sequence in the course of their lifetimes.

So does the word "sequence" in this case now mean just a particular ordering, and not a progression over time that any one star makes? Is the main sequence just some kind of plateau in stellar evolution where stars spend a significant duration?

enter image description here

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Is this in any sense a temporal sequence?

Not really. At least not in the sense of a star sliding along the main sequence. That doesn't happen. Instead, a star remains more or less parked at one spot on the main sequence during it's lifetime as a main sequence star.

A protostar is more luminous and cooler than the zero age main sequence star it will become. Once a star "ignites" (starts fusing hydrogen (not deuterium)) is when a star enters the main sequence. This is where the star spends the majority of its life. In the case of small stars, stars whose mass is less than about 40% of the Sun's mass, this is where the star will spend the entirety of its life as a star. Small stars get dimmer and dimmer as they age.

Larger stars don't thoroughly mix from the innermost core to the outermost regions. These larger stars build up an ash of helium as they age. This hydrogen fusion eventually comes to an end when all of the hydrogen in the core has been fused into helium. That's when the star departs the main sequence. Unlike small stars, larger stars get brighter (more luminous) as they age.

Larger stars (stars larger than 40% solar masses) might double or triple in luminosity as they age. That's a third to a half order of magnitude increase, and that's tiny compared to the eleven or twelve orders of magnitude difference in luminosity shown on an HR diagram between the smallest red dwarf and the largest blue giant. What this means is that once a non-tiny star enters the main sequence, it more or less stays at that spot on the main sequence until it leaves the main sequence.

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No, the Main Sequence is more like a starting line. Most stars spend a long time on one point of it (10 billion years for the sun) while they fuse hydrogen into helium. Then they wander off it.

In this diagram the black line is the Main Sequence. The colored lines show temporal sequences. This progress through time of an individual star is called its evolutionary track.

enter image description here

The numbers along the black line are solar masses (1=the sun). This diagram evolved through a sequence of images by Wikimedia users Rursus, G.A.S, and Jesusmaiz.

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    $\begingroup$ Sometimes a picture is worth a thousand words. $\endgroup$ – John Duffield Jan 6 '18 at 17:26
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The main sequence is mostly a plateau that a star reaches after it is fully formed but before it begins to run low on hydrogen to fuel normal fusion reactions. And yes, the sequence is mostly an ordering - by mass, not age. I say mostly because age does have some effect (see the section from the Wikipedia article on the main sequence regarding temperature-luminosity variation). The result is that older stars a slightly hotter and brighter than younger stars.

For most stars, much of the light it emits is black-body radiation. The amount of energy that a star produces is complicated (as explained on the page for the mass-luminosity relation) but the bottom line is that for stars with a larger mass, the energy output increases significantly relative to its surface area and thus is hotter. The page on black-body radiation has a nice explanation including a temperature graphic showing how the surface temperature of smaller stars red and as mass increases, orange, yellow, green, and blue.

The higher fusion rate (relative to size) explains why larger stars run out of hydrogen faster than smaller stars.

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Short Answer

The answer is no. The main sequence is a sequence in mass (and not a sequence in time).

The most massive stars are located at the the top left (since they are the brightest and hottest/bluest). The lowest mass stars are are located at the bottom left ( since they dimmer and cooler/redder).

Following the main sequence from the top left to the bottom right is thus a sequence from high to low mass.

A little bit more background

The astronomers Hertzsprung and Russel were among the first to note that the brightness and colors of stars are not just random, but that the large majority of stars show a narrow relation between brightness and color. The brightest stars are typically bluer (= hotter) and the dimmer stars are typically redder (= cooler).

When plotting the properties of stars in a diagram that shows the brightness on the vertical axis and the color (or temperature) on the horizontal axis, it turns out that the large majority of stars lie in a fairly narrow strip in this diagram. We call this stip the main sequence, simply because most stars lie on it. ( There are exceptions, for example red giants and white dwarfs do not lie on this sequence, but these are more rare). We now call this diagram the Hertzsprung-Russel diagram.

Most stars lie on this sequence because they spend about 90% of their life time there, without changing much. The sun is also one of the many stars on the main sequence. All stars on the main sequence are powered by nuclear fusion of hydrogen in their hot centers. This is such an efficient source of fuel for a star, that it lasts for 90% of its life.

Computer models helped astronomers to understand how stars move through the Hertzsprung-Russel diagram when they get older. When stars run out of hydrogen fuel in their centers they start changing and they leave the main sequence. This is when they can grow to become red giants. These changes relatively fast. This is why we do not see many stars away from the main sequence. The tracks of how stars move through the diagram as they grow older are called evolutionary tracks. These evolutionary tracks can be thought of as a sequences of time.

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