Introduction 

Created in the early 1900s by Danish astronomer Ejnar Hertzsprung and American astronomer Henry Norris Russell, the Hertzsprung-Russell diagram is of critical use in studying the properties of stars and their evolution, from the first moments that a star begins to form until its ultimate end as a white dwarf or in a supernova explosion.   The diagram also reveals key connections between fundamental properties of stars, such as luminosity, temperature, and mass.   This article will focus on these fundamental properties and how they are measured.  Understanding these properties and the connections between them is critical for astronomy students at all levels, from general education college-level classes to advanced graduate level courses, and for professional and amateur astronomers as well.    Here at 24HourAnswers.com we have astronomers and astrophysicists who not only work with the stellar properties in their professional lives but also frequently teach this information to students in their classes.    We are here to help make the properties of stars second-nature to you – don’t go it alone, let us help you!

Properties of Stars

At its purest form, the Hertzsprung – Russell diagram is an illustration of the relationship between two important properties of a star: the star’s temperature at the surface (i.e. the photosphere) and the total amount of energy it is emitting per second (its luminosity).   Digging a little deeper, for main sequence stars the mass of the star is also revealed through the diagram.   Before we start looking at these specific relationships, which will be the subject of another article, it is worth a brief discussion into how these properties are measured in the first place.   This discussion will take us through journeys into measuring distance, calculating spectral types, and examining binary star systems.  

Luminosity.  The luminosity of a star is defined as the amount of energy it is putting out each second.   This is analogous to the idea of a 100 Watt light bulb versus a 60 Watt light bulb.   The 100 Watt light bulb is putting out more energy and therefore has a higher luminosity than the 60 Watt light bulb.   Measuring luminosity, however, for stars is much more difficult than it might appear at first glance.   Consider this question:  Does our Sun have a high luminosity compared to other stars?   At first, your answer might be, “Yes it does have a high luminosity.  After all, just look at how bright the Sun is.  It is so much brighter than any other star.”   However, why is the Sun so bright in the sky?  It could be because it has a very high luminosity or it could be because it just happens to be very close to us compared to the nearest other stars.   It is in fact 260,000 times closer to us than just the closest star to the Sun, Proxima Centauri.   To be able to calculate a star’s luminosity with great accuracy we must know the distance to the star.   On a side note, the answer is actually that our Sun has average luminosity but, looks as bright as it does because of its proximity to us.

Distance.  Since distance is critical to measuring luminosity for a star, how do we go about calculating the distance to a star?   The most accurate way to measure distance to a star is called stellar parallax.   Stellar parallax relies on the idea that if you look at the location of a nearby star now compared with background stars and then measure its location compared with background stars when the Earth has moved part way around the Sun, it will appear that the nearby star has moved compared with the background.   A star that is closer to us will appear to move or shift more compared with the background stars than a star that is farther away from us.   To see why this is, you can actually recreate the ideas behind stellar parallax by using your eyes.    Try this experiment:   Close one eye and hold your finger out arm’s length in front of you.   Now line your finger up with some object in the distance.   Finally, without moving your head or finger, switch which eye is open.   It should look like you finger moved or jumped compared with the background object.   Now, repeat the experiment but this time bend your elbow so that your finger is closer to your head.   When you change which eye is open this time, you should notice that your finger seems to move more.   In other words, the shift or parallax is larger when your finger is close to you compared with when your finger is farther away.   This is exactly how stellar parallax works as well.  

If you tried this experiment but this time used a star as your nearby object, you would not be able to notice any shift or parallax.   The distance between your eyes is simply too small for any shift to be noticeable.   The larger that you can get between the two measurements, the farther away you can measure distance.  As a result, when measuring stellar parallax, we want to time the observations so that the distance between the two measurements is as great as possible.   For stellar parallax that means waiting 6 months between the two observations.   Why 6 months?   Imagine we make one measurement now.   If we wait 6 months, what has happened to the Earth?  It has moved in its orbit to the exact opposite side of the Sun.   This gives a distance between the two observations of 2 AU (1 Astronomical Unit or AU = Distance from the Earth to the Sun), the largest possible value for the Earth.

There is a limit, however, to how far an object can be and still have its distance measured using stellar parallax.   The stellar parallax gets smaller as you look at stars that are more distant; if a star is too far away the stellar parallax will simply be too small to measure with any accuracy.   What limits this accuracy?   From Earth the primary limit is turbulence in our atmosphere, which limits the angular resolution we are able to achieve with any telescope from the surface of the Earth.   This is why from Earth we can only reliably calculate distances to objects within about 325 light years of Earth.  

However, if you conduct these experiments using a satellite in space, the atmospheric turbulence suddenly does not become an obstacle.    Instead, the observer is limited by the diffraction limit, which is the theoretical angular resolution that can be achieved by a telescope without any interference from atmospheric effects.   The diffraction limit is determined by the size of the mirror or lens of a telescope – the larger its diameter, the better the diffraction limit.   

There have been two space missions that had as a major focus the measuring of distances to nearby stars using stellar parallax.   The Hipparcos Mission from 1989 until 1993 was an 11” diameter telescope in space that was able to measure distances to stars up to 600 light years from Earth.   In total it determined distances to approximately 50,000 stars.    More recently the Gaia mission, headed by the European Space Agency and containing a significantly larger aperture, was launched with a goal of measuring distances to over one billion stars located at distances out as far as 30,000 light years from Earth.  Distances to stars located beyond the distance limits for the Gaia mission can be estimated in other ways, which will be discussed in another article, but all of these ways rely on stellar parallax data for calibration and are not as accurate as stellar parallax observations.

Connecting It Together

Bringing together measurements of distance to nearby stars and actual observations of how bright a star appears in the sky allows scientists to calculate the luminosity, or total energy emitted per second, of a star.    Since the luminosity is easily calculated by the equation:  Luminosity = 4 pi (distance)2 x brightness, let’s examine why this equation works.   Brightness is the amount of energy crossing a square meter in space each second, while luminosity is the total amount of energy emitted per second in total.   First imagine a ball surrounding a star.   The surface area of this ball can be calculated by surface area = 4 pi diameter2, where in this case the diameter is another way of saying the distance from the star.  As the distance increases, the surface area increases even more quickly.   Imagine here on Earth we are on that ball surrounding a star and measuring the amount of energy coming through every square meter from that star.   Once we know the amount through each square meter (i.e. the brightness of the star) and we know how many square meters the light from the star is distributed over at our distance (i.e. the surface area), then simply multiplying the brightness of a star by the surface area will give us the total amount of energy coming from the star each second (i.e. its luminosity), one key part of the data that appears on the H-R diagram.

Surface Temperature

The other critical property of a star is the star’s surface (or photospheric) temperature.   Here we are not referring to the temperature deep in the star’s core, but rather the temperature of the star at its visible “surface” – the part of a star where light can finally freely shine out into space.    There are two key ways that the surface temperature of a star can be estimated.   We’ll first discuss the simpler, but not as accurate, method of blackbody radiation and then pivot to the more precise spectral type approach.

Blackbody Radiation.  The details of blackbody radiation could easily occupy a whole article in itself, so let’s focus on the most important concepts.   A blackbody is an object whose spectrum, and by implication, also its color, is determined strictly by its temperature.   Typical blackbodies are solid objects, like a piece of charcoal, an iron rod, or even a person or entire planet, or dense balls of gas, such as, most importantly for this paper, stars.   You may have seen someone heat up an iron rod with a blow torch.   As the iron starts to get hot it will first seem to glow red and then slowly change to an orange, yellow, and then ultimately blueish-white glow.   Even after the blowtorch is removed from the iron rod, you will still notice the iron rod glowing, but this time as the rod cools it will go from being blueish-white to yellow and then ultimately orange and red until there reaches a point when it does not appear to be glowing.  

These different colors correspond to different temperatures in the iron rod.   Redder colors (which have longer wavelengths and less energy than blue colors) appear at cooler temperatures and then as the object gets hotter it goes through all the colors of the rainbow until at its hottest it will glow a blueish color.   Note that when we are talking about objects glowing different colors, we require temperatures in the many thousands of degrees range.  Most objects that have normal temperatures (like a person walking around at 98.6oF) would “glow” in much longer wavelengths such as infrared or even microwaves, undetectable to the human eye.   This is NOT the reason why someone’s shirt might be red or might be blue.   Their shirt is not thousands of degrees, so it is not about blackbody radiation.   Instead, it has everything to do with the various wavelengths of light that the pigments in the dyes of their shirt will absorb and which they will reflect.   

Moving back to stars and true blackbodies, however, we see how color can be a way to estimate the temperature of a star.   Stars that are glowing with a reddish color (Betelgeuse and Antares being two classic examples) are cooler in temperature at the surface than stars like our Sun which have a more yellow/green color and stars like Sirius or Rigel which have more of a blueish appearance.   For example, Antares, a red star, has a surface temperature of 3,660 K (6,130oF), compared with our yellow Sun’s temperature of 5570 K (9,940oF) and Rigel, a blueish star, which has a temperature of 12,100 K (21,320oF).  Although people talk about someone or something being “red hot”, that’s not nearly as hot as the thing could be—imagine if it was “blue hot”.  

The color of a star is one way to estimate the star’s surface temperature.   However, it is far from perfect.  There are a number of things that can affect the color of a star and make it look artificially redder (and therefore cooler) than it actually is.   These include most notably any gas or dust in between the star and us here on Earth or any dense gravitational sources (neutron stars, black holes, galaxy clusters, etc.) that the light from that star might pass near in its journey to Earth.   Therefore, astronomers prefer a different way to talk about the temperature of a star at the surface: its spectral type.

Spectral Type.   Every star can also be ordered and grouped with similar stars based on the spectral lines present in its spectrum.  There are two types of spectral lines:  emission and absorption.   Both types are produced by electrons in an atom or molecule moving from one energy state to another.    If the electron “falls” to a lower energy level, then it has lost energy and this energy is emitted as light.   Since the energy levels are fixed, then this restricts the energy that is emitted as light to only be at certain wavelengths of light (remember that the energy of an electromagnetic wave depends only on the wavelength of that wave).   Therefore, when looking at the energy coming from an object emitting emission lines, the emission lines will only be at certain wavelengths, each one matching up to the energy lost as an electron falls from one specific energy level to another specific energy level.   An everyday life example of emission lines is a “neon light”.  

Gas inside the neon light tube contains typically one specific element or molecule.   Emission lines come from the gas inside that light tube, and the tube will appear to glow a specific color, matching up to the color of the most prominent emission line.   That is why a neon sign looks red—the main emission line for neon is also red.   So what is different about absorption lines?   A lot is different, but the fundamental principles are the same.  

This time imagine shining a bunch of light or energy on a collection of gas.   Electrons in the atoms or molecules inside a collection of gas grab energy from that light source and use that energy to move to a higher energy level.   The only energies that are taken are ones that match up directly to the difference between two energy levels.   In other words, imagine that an atom had energy levels of 1, 2, and 5.   Then, the atom could grab light with an energy of 1, 3, and 4 since each of these would allow the electron to move to a higher energy level (1 -> 2, 2 -> 5, and 1 -> 5, respectively).   However, light with an energy of 2 would not be grabbed because there is no combination of energy levels for the atom that are an energy of exactly 2 apart.   Now, if we were farther away from this gas, looking back at the energy source, we would see missing energy at wavelengths of light corresponding to energies of 1, 3, and 4 but not 2 or 5.   This missing energy dip in the spectrum is called an absorption line.

For stars, absorption lines are the key for determining spectral type.   The absorption lines for stars are created in the star’s atmosphere, a layer of non-dense gas that surrounds the star’s photosphere (i.e. where the light from a star comes out).   If it wasn’t for the atmosphere of a star, the star’s spectrum would look like a perfect blackbody. 

In the very early years of the 20th century, Annie Jump Cannon at Harvard Observatory, began examining the spectra of different stars and realized that they could be arranged into groups based on the strength of certain absorption lines in their spectra.   She grouped stars into 7 groups and labeled these groups A, B, F, G, K, M, and O.   Each group could further be divided into smaller, more specific groups, so today spectral types for stars are not just a letter but a letter and a number, such as G2, which is the spectral type of our Sun.   Finally it was realized that different spectral types of stars represented different temperatures of stars.  The order of the spectral types was rearranged, now going O, B, A, F, G, K, and M from hottest (O stars) to coldest (M stars).  Within each spectral type, the smaller numbers correspond to warmer stars as well.  For example, an O3 star is hotter than an O5 star.   However, any O star is always hotter than any B star (for example, an O9 star is hotter than a B0 star).   Therefore, a second more precise way to determine the temperature of a star is to determine its spectral type and that will directly tell the temperature of the star at the surface.  

Mass

A third key property of a star is its mass.   While people commonly think of mass as weight and vice-versa, please keep in mind that there is a difference:  weight is an object’s response to gravity, while mass is a fundamental property of an object.   In other words, an astronaut in space might be weightless, but he or she still has the same mass as they did on Earth.   Mass is key because it is universal and does not change depending on the local gravity of a location, and mass is used in many key equations that determine the motion of objects, including Newton’s 2nd law, Force = mass x acceleration, and Newton’s law of universal gravity, where the force of gravity depends directly on the masses of the two objects.

Masses for stars are actually quite difficult to measure.  An isolated star by itself is almost impossible to determine the mass of.    However, stars in binary systems do lend themselves to having their masses measured.  A binary system is when two or more stars are in orbit around each other.   By examining the motion of the stars in the binary system, if we can measure the period (i.e. the time it takes the two stars to make one orbit around each other) and the distance between the two stars in the binary system, then we can calculate the mass of each star.  

Fortunately for astronomers, two thirds of stars are in binary systems, so there are many opportunities to measure the masses of stars.   There are three main types of binary systems that astronomers observe and then use the data of the stars’ orbits to calculate their masses.   Visual binaries are rare cases where we can actually see the two stars individually and watch them orbit around each other.   These situations are rare because most binary systems have the two stars close enough together that even with our best telescopes, we do not have the angular resolution to separate out the two stars. 

However, what is particularly amazing is that even when we cannot separate out the light into two individual stars, such as in a visual binary, we can still identify the binary system, find its period and the distance between the two stars, and calculate the masses of the stars in the system.   The second and third types of binary star systems fall into this “cannot see both stars separately” category.   Spectroscopic binaries are detected because as the stars orbit each other, there are time the stars are moving towards us here on Earth and times they are moving away from us here on Earth.   This motion toward and away from us shows up as a small shift in the spectral lines of the two stars.   This shift is called a Doppler Shift.   Doppler shifts are most famous on Earth for sound waves.   If an ambulance is driving toward us the siren will sound at a shorter wavelength or pitch than if the ambulance is moving away from us.   The same thing happens for light and in a spectroscopic binary, we can observe the spectral lines of each star shifting to shorter and then longer wavelengths and use this data to measure the masses of the stars.   

The third type of binary system is called an eclipsing binary.   Again, we are not able to individually resolve each star in the binary system for an eclipsing binary.   Instead, we measure the total light from the two stars put together.   However, if in its orbit one star happens to pass directly in between the other star and the Earth, then while it is in front and eclipsing the other star, the total light from the binary system will drop slightly since some of one of the stars is blocked.   We will also see a similar drop half a period later as the 2nd star now passes in front of the 1st star.  

Now that we’ve discussed the ways to use binary systems to measure the masses of stars, what range of masses for stars do we see?   Masses are normally measured in a unit called a solar mass, or Mo.  1 Mo, or 1 solar mass, is just defined as the mass of our Sun.   Using this unit makes the numbers for the masses of stars much more manageable and understandable.  For example, a 2 Mo star is simply two times the mass of our own Sun.    Star masses range from 0.08 Mo to at least 150 Mo.   The lower limit of star masses (0.08 Mo) is a physical limit.   It is impossible to have a star that has less mass than 0.08 Mo.   Objects need to be at least 0.08 Mo in order to get hot enough in the core for hydrogen to fuse into helium, one of the hallmarks of a star’s first stage of life, the main sequence.   Objects with less than 0.08 Mo do not get hot enough for fusion and instead live their lives as brown dwarfs.  The upper limit of star masses is much more debatable.   The heaviest star that astronomers are confident in their measurements of is around 150 Mo, although there have been reports of stars as heavy as 265 Mo.  These incredibly heavy stars have so much energy coming from them that they may not be stable and might quickly push all the outer gas in the star away, effectively ending the life of the star.   

Conclusion

In this article we have discussed key properties of stars that can be measured by scientists and which give insight into the life of a star.   These properties (luminosity, surface temperature, and mass) are true fundamental properties of a star, are interrelated, and determine so much about how a star will appear in the sky and more importantly how a star will live its life.   If you are faced with an assignment or project that involves measuring or analyzing the properties of stars, don’t go it alone.  Let us here at 24HourAnswers.com help you understand how the properties of stars are measured, and how to interpret them in important ways. 

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