A Hertzsprung Russell diagram or HR diagram is a tool common in astrophysics, used for the purpose of analyzing properties of populations of stars. It's a simple two-axis plot with luminosity increasing as you go up on the vertical axis and temperature increasing as you move leftward on the horizontal axis. The temperature axis is flipped. By observing a large number of stars and plotting each one as a point on one of these diagrams, we can begin to notice several patterns. Perhaps the most striking of which is what we call the main sequence. The main sequence of stars represented on the HR diagram is a roughly diagonal swath of points, stretching from the low luminosity, low-temperature region in the diagram to the high luminosity, high-temperature region in the diagram. These are the stars which originated from the formation scenario we described in the previous section. Fusion rates have stabilized in their cores and they're living out their adulthood in a state of hydrostatic equilibrium. The main sequence phase of a star's life, when considered relative to formation and to retirement, meaning prior to the death of a star, is the longest. As a note, we consider the death of a star to be any end state such as the formation of a white dwarf, neutron star or a black hole. We'll see more about these in the coming sections. During the main sequence phase, a stable source of fuel is present in the form of hydrogen, which the star consumes converting it through fusion processes into helium. Elderly stars which have left the main sequence source that energy not only from hydrogen but from other elements as well. For main sequence stars, there's a strong relationship between mass and luminosity. The more mass of the star, the brighter it is. The intense gravity of a massive star means its core will be denser and as a result, hotter. This is important because fusion rates, meaning the rate at which energy is produced, is highly dependent on core temperature. So, the more mass of a star, the more energy per unit time it produces and as this energy leaves the core and eventually reaches the surface, we observe a greater luminosity, meaning a brighter star. You'll notice in taking this course that we often refer to stars by their color. So when we say color, what do we mean? Well, as we learned in module one, electromagnetic radiation or light is a spectrum, visible light being just one portion of it. What we call blue is just an even smaller portion of the spectrum. Instead of simply calling it blue, we could define it in numbers because as we know, light is characterized by its wavelength. Blue light has a wavelength of about 450 nanometers. So when we refer to a blue star, what we are saying is that much of its radiation is coming from this portion of the spectrum. When we say a star is bluer than another star, what we mean is that the bulk of the bluer star's radiation is coming from even shorter wavelength light. The same can be said of red and redder stars. As a redder star will have the bulk of its radiation in longer wavelength light. Just like the filament of a light bulb, a star's light is produced by incandescence or formally, blackbody radiation. Blackbody radiation is temperature dependent. The hotter a blackbody radiator is, the brighter it is. As the temperature of a blackbody emitter increases or decreases, it also changes color. This is why colder stars appear dim and red, and hotter stars are brighter and bluer. The hottest stars in the sky, blue hyper-giants are upwards of 40,000 degrees centigrade and can shine about five million times brighter than our own sun. We say that hotter stars are blue and the colder stars are red but the reality with blackbody radiation is that every star produces at least a little bit of every color of the spectrum. When we say a star is blue, we're saying that the majority of its radiation is being produced in this portion of the spectrum. This majority exists because each blackbody emitter has a spectrum that is peaked. Meaning there's a wavelength at which the star produces more light than at any other wavelength. These peak wavelength are directly related to the surface temperature of a star. The relationship is described by Wien's law which takes the form of this equation. The peak wavelength Lambda peak is equal to 0.0029 meters Kelvin divided by the temperature T of the blackbody emitter. As we mentioned earlier, more massive stars are brighter because they're more luminous as a result of having higher fusion rates. Despite having more material to burn, more massive stars live shorter lives. The more massive a main sequence star is, the quicker it exhaust the fuel in its core. Hot blue star might live on the main sequence for 10 million years whereas the dim red star could live as long or longer than a trillion years, that's 100,000 times longer. This is why we like to personify stars. We'd like to think of blue stars as rock stars that live fast and die young. Red stars live long and much more uneventful lives. At midday, there's one star visible to our eyes, the sun. At this point, you might be wondering where the sun lies on an HR diagram. Meaning how does it compare to other stars? Well, the sun happens to be pretty average. It's not terribly hot or particularly cold. The sun's spectrum peaks at a wavelength of about 500 nanometers, which is greenish. It appears whitish or yellowish to our eyes because it is emitting a lot of light across the entire visible spectrum. In terms of mass, the sun lies fairly close to the lower end of what's possible for a main sequence star. At the high end, massive blue stars can be a couple of 100 times as massive as our sun. At the low end, a red main sequence star can be as massive as a 10th of our sun. The most massive star that is currently known lives at the edge of our galaxy. Scientists have given it the name R136A1, but we call it Rob. Rob has been measured at a whopping 256 solar masses. However, Rob has lost a great deal of material through fusion and winds and it's thought that 20 percent of its mass has been ejected already. This would mean that at birth Rob was about 320 solar masses. In terms of luminosity, the sun is fairly average. Blue stars can be several million times as luminous as our sun and red stars can be much dimmer such that their luminosity is only a ten-thousandth that of our sun. One of the difficulties associated with constructing an HR diagram of a population of stars is figuring out how bright the stars actually are versus how bright they look to us in the night sky. Luminosity is a measure of how bright a star actually is. Apparent brightness is how bright a star will look to us. Apparent brightness is affected by distance because the further away a star is, the dimmer it will appear to be and we're not interested strictly in appearances. We want to be able to infer characteristics of the stars themselves. What we need to do then is measure a star's brightness knowing already how far it is from us, that way we can correct for its appearance meaning its distance and compare it fairly to other stars. Astronomers have spent hundreds of years constructing catalogs of objects with known properties, distances, and luminosities so that when we discover new objects, we can know much more about them. Being able to measure apparent brightness and distance accurately is very important. It means that we can construct an accurate HR diagram and that's crucial because an HR diagram is a tool which allows us to learn even more, specifically, characteristics about an entire population of stars. For instance, we can use an HR diagram to learn about the age of a population of stars. We can do this by determining the main sequence turnoff point. As a star exhaust the hydrogen fuel supply in its core, its time on the main sequence ends. This is because the surface of the star cools as its core runs out of fuel and so it moves rightward on the HR diagram away from that diagonal swath of stars. Imagine we have a population of stars with a large variety of masses, all born at roughly the same time. Hot blue stars, if you remember, live fast and die young. In other words, the stars in the high temperature, high luminosity region of the diagram will exhaust the fuel in their course first, they will move off the main sequence and continue with the later stages of their lives. Next to move off the main sequence will be stars which are slightly less massive than those first stars because, as you remember, the lower the mass of the star, the longer its main sequence lifetime. Over time, the main sequence will be slowly eaten away as less and less massive stars begin to move away. The points along the main sequence where stars are departing is called the main sequence turnoff point. We can measure the properties of the stars at this point and because we know how long every type of main sequence star typically lives, we can learn the age of the entire population of stars.
