Exploring the Variable Luminosity of Star Systems.

Damien Trinh

Exploring the Variable Luminosity of a Star System “...variable stars have attracted the interest of amateur and professional astronomers alike for many decades.” [1]

When we look at the Universe we find that there are a seemingly innumerate number of stars, which vary in size, colour and luminosity. These variations are often due to the mass of the star, or what stage the star is in its lifetime. As a star ages its mass and luminosity will change, over periods of millions of years. However, when we look at stars in the night sky we find that a minority vary their luminosity over a period of days to a few weeks. These particular stars are catalogued as Variable Stars i.e. stars which vary in brightness. This can then be measured and be given a numerical value, in which we can compare the data, over a period of a few nights. If a variable star is close enough, then it is actually possible to visually see the difference. Variable stars are classified into two main categories: extrinsic and intrinsic. It is classified as extrinsic if the variability is caused by external factors; often binary stars or large planets, which eclipse the light in the star system. The intrinsic classification is given to stars that physically change or where a stellar event occurs, such as a stellar flare. [2] Although these classes can then be further broken down into more subsets, all variable stars are unified by their inherent mystery that surrounds them. As time progresses so does our understanding of variable stars, but this is only due to the massive advances in technology, within the past decade. Understanding these variables stars has become much more relevant in the previous years. Although often seen as an esoteric topic, studying variable stars has led to the discovery of various extrasolar planets; fuelling the search for extraterrestrial life and attracting the interest of both the public and astronomers alike. Although not obvious, studying variable stars can often have other significant contributions to other fields. The purpose of this piece is to hopefully explore why the luminosity varies and also how understanding these variations can be used in other areas. Though certain variable stars differ in their behaviour, to ‘regular’ stars, they are still stars. This means that how they evolve in their lifetime is very similar to that of other stars (of similar mass). Although the situations may vary, the laws of physics, throughout the Universe, remain constant; and so understanding them becomes a test of mankind’s grasp of the fundamental laws of physics. The majority of extrinsic variable stars are in fact binary stars and so will be explored first in this essay, where we will explore various ways a binary star’s luminosity can vary. The stars in these systems can vary widely and are an excellent example for variable star systems. These binary stars can also often impose events on its partner star, causing stellar events, which also vary the luminosity. These stellar events, however, are not exclusive to binary stars and can also be observed with isolated stars. Certain changes in light, such as radio or x-rays can be attributed to neutron stars or Pulsars (where the light pulsates), which will lead on from binary star systems, where we will explore the various subtypes of neutron stars. Although these aren’t strictly classified as variable stars, the light from these systems do vary and so will also be investigated. From this we can then begin to develop the ideas behind intrinsic variable stars. Many of these stars can be grouped together and therefore condensed and so will allow us to give a general overview of these stars. This will then allow us to then make conclusions for their uses and furthermore, their importance in astrophysics. Within our Universe there are a large number of stars which are a part of a binary, or multiple, star system. They range from stars which are so distant, it is only their mutual gravity which has kept them together, from stars which can be extremely close to each other, such that mass transfers can occur [3]; looked later at in this section. However, the scale at which these binary stars are from Earth make it difficult to observe them separately. However, that is not to say that no binary systems can be viewed separately. They can be observed with powerful telescopes, but the correct orientation of the binary system is needed as well. These particular binary stars are known as ‘visual binaries;’ where the two stars are visible separately [5], as in figure 1. If two stars are extremely close, when observing the binary star system, it is often observed as a single light source and can be mistakenly taken as a single star. If these stars could not be observed our estimates for the number of stars, in our Universe, would be inaccurate, by a large factor. However, these systems are not static. They are dynamic systems, under the influence of their mutual gravity. As such, similar to a star and planet, these stars will orbit each other. As these stars move along their orbit, relative to us, they can pass in front of each other. As they pass in front of each other they inevitably block out the light from their partner star, which causes a decrease in the total light from the system. As an outside observer, we can observe this drop in luminosity. However, as we only view this as a single star, it seems as though the star has a decreased luminosity, when in actual fact it is due to the eclipsing, of its partner star. [6] As there are two stars, each star gets eclipsed by the other. As an observation, we see two periods of changes in luminosity. The rate at which this occurs is dependent on the orbital period. These are

known as ‘eclipsing binaries,’ where “the viewer sees a double eclipse along a single plane.” [7]

By observing these systems, over an indefinite time period, we can build up a picture of how these stars’ eclipses affect the system, as a whole. As the star system’s overall luminosity varies; we can plot this data on a graph with time on the x-axis, whose scale is determined by the orbital period (often days), and the luminosity on the y-axis. Figure 2 demonstrates what happens in the ‘Algol System.’ As the dimmer star eclipses the brighter star there is a large drop in luminosity. This is because the main contributor of light has now been blocked. As an observer we now only can view the light, coming from the dimmer star. This creates the primary eclipse. The highest intensity of light is observed when both stars are ‘side-by-side,’ in their orbits. As the brighter of the two stars eclipses the dimmer star there is a much smaller dip in luminosity. [9] Although the change is much less significant, it is still detectable with very sensitive instruments. If both stars are of similar luminosity then the relative variations in magnitude are much greater, as the light can halve or double; as opposed to one large drop in luminosity and a subsequent smaller drop. When observing similar systems, it is the second drop in luminosity from which we can determine whether we are observing a binary star or a different variable star, as only eclipsing binaries will provide us with the double eclipsing effect. Similar techniques can be used for extrasolar planetary detection; however the changes in luminosity are much more subtle. The stellar members, of the binary system, can often vary in mass and therefore where they are in their lifetime. If their lifetimes vary a large amount, one star can be at the end of its lifetime, while the other still burns hydrogen. This results in a binary system, consisting of a star and white dwarf (a collapsed core of a star). As these stars orbit each other, the gravity of the white dwarf can begin to distort the shape of its partner star. As the star begins to get distorted it can extend such that mass from the star is now gravitationally bound to the white dwarf. This area of the star’s gravitational influence, where it dominates, is called its Roche Lobe. [10] As the mass from the star stretches out, it becomes gravitationally bound, to the white dwarf star, and is said to have overflowed its Roche Lobe. This then allows stellar material to stream onto the white dwarf, which can then lead to Type 1a Supernovae, arising from Cataclysmic variables. [11] Cataclysmic variables are unique, such that they arise from a binary system, where the lifetimes of these stars vary greatly. This allows material to flow from star to star, creating various stellar events, such as flares and novae. [12] As material streams onto the white dwarf, it begins to surround it in a disk, similar to planetary rings. As more and more stellar material enters the ring the density increases greatly. Eventually, there comes a point where the conditions needed for nuclear fusion are present, due to the high densities and temperatures. Consequently, the disk of stellar material can begin the same processes as a star i.e. fusing hydrogen into helium. This creates a sudden rise in brightness, as the disk begins to flare up. The point at which the stream of material enters the disk, around the white dwarf, is called the ‘bright spot.’ This area has a greater density than the rest of the disk and so therefore appears brighter, hence the name. [13] As the stellar material falls onto the white dwarf, the disk begins to drop in density. Furthermore, the decreasing volume of hydrogen, which can be fused, decreases overtime. The combination of lower densities and less material causes fusion to come to a halt, causing the system to decrease in brightness. However, as material is continually streaming from the star, the hydrogen and densities build up again, forcing another period of fusion. These processes can continue for long periods of time, creating large variations in the binary system’s luminosity. Additionally, magnetic fields can play a part in the variable luminosity, of Cataclysmic variables. If the white dwarf, that has material streaming on to it, has a significantly strong magnetic field, it can interact with the stellar material. Stars too can have magnetic fields, similar to the Earth’s magnetic field, as shown in Figure 3. Although a stellar magnetic field is often more chaotic they will follow the same general shape. The stellar atmosphere is filled with unused hydrogen and helium. The heat of these stars causes the atoms to become ionised i.e. lose or gain an electron. This change in electron numbers causes the atoms to become electrically charged. This is important for interacting with magnetic fields, as uncharged particles will not be

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affected by magnetic fields. As the secondary star overflows its Roche Lobe material begins to stream onto the white dwarf. However, these charged particles will begin to interact, with the magnetic fields, and funnel along the magnetic field lines, to the magnetic poles. As these particles accelerate to the poles they can be ejected into space, creating columns of stellar material, at the poles. [15] If the rotational axis is not aligned to that of its magnetic poles, as it rotates, the ejected material will seem to revolve around the white dwarf and so the luminosity of the system would begin to gain and drop, as parts of the ejected columns come into and out of view. The ideas of material being ejected at the magnetic poles are not exclusive to Cataclysmic variables, where the white dwarfs have significant magnetic fields. This occurs throughout the Universe, with the most notable example being black holes. Black holes are remnants of large massive stars. Their gravity is so immense that even light cannot escape. As material begins to form a disk around the black hole large magnetic fields can begin to build up. This results in two massive jets of material being ejected, at the poles of the black hole. These massive jets accelerate the material, causing it to heat up greatly and emit light. They heat up so much that the light released can be as energetic as light from the x-ray region, of the electromagnetic spectrum. Events such as these can be easily found, when viewing the Universe in x-ray light, as they are often brighter than most other x-ray sources in the Universe. [16] This idea is also very similar to neutron stars can vary in luminosity. Cataclysmic variables can also contain neutron stars, rather than white dwarves, where the same processes will occur. Neutron stars also have various subtypes, which we are only just beginning to understand. Neutron stars are an intermediate object, which lie between white dwarfs and black holes. At the end of its lifetime, if the star is of sufficient mass, rather than forming a white dwarf, as in lesser mass stars, the core of the star can no longer withstand its own weight. Consequently, the core begins to collapse even further, forcing the subatomic particles to merge into neutrons. This process releases so much energy that it generates a supernova. The result is a collapsed core of a star, comprised of only neutrons. As these have collapsed down, their actual size is very small. Neutron stars are often found between the ranges of five to twenty kilometres. This decrease in radius has radical effects on the neutron star. As the core collapses, to conserve angular momentum, the neutron star must begin to rotate at a higher pace. This is similar to an ice skater; as they spin and bring their arms towards them their rotation increases in speed. However, these neutron stars have originated from stars many times larger than our sun, to a size of a small city. Consequently, some neutron stars can be rotating at a rate of 1000 times a second. [17] These neutron stars can also be extremely hot, as they will have retained the heat, from the stellar core, which would have reached into the many millions of degrees. This heat is then radiated into space, as x-ray light. When these are first born they are incredibly hot and can easily be observed, when viewing in x-ray light. However, neutron stars are, in essence, a sphere of neutrons. Within them, they have no processes which can generate energy, as in a star. Their temperature cannot be sustained, with the constant radiating of light. Over long periods of time they begin to cool down and subsequently radiate less energetic light. The luminosity of these neutron stars will decrease as they cool, until eventually they are the same temperature as deep space; a few degrees above absolute zero. However, this cooling down takes billions of years; a period such that the Universe is not yet old enough so that cool neutron stars exist and the existence of cool neutron stars would only be able to be inferred from their gravitational effects. Over their active lifetime, neutron stars can turn into Pulsars. The reason why this occurs has many theories, although it is though that it is an evolutionary process, where only specific neutron stars can become Pulsars. [18] Pulsars are a subtype of neutron stars. Similar to Cataclysmic variables, particles can get caught within the Pulsar’s magnetic field and stream out of the poles, creating powerful beams of light. Similar to white dwarfs, if the rotational axis is not aligned with the magnetic poles the Pulsar acts like lighthouse where we can only view the Pulsar if the beam of light is pointed directly at us, as in figure 1. As it rotates it seems as though it pulsates, hence the name. As stated previously, these can be rotating at rates up to 1000 time per second. The variations of luminosity in these systems are due to their orientation, relative to the observer. If the magnetic and rotational axes are aligned we can never view this pulsating effect and so can never deduce they are Pulsars; only when the orientation is correct can we observe the lighthouse effect. These variations of the ‘off and on’ light, from Pulsars, are too quick for human eyes to detect, but they can be detected with sensitive instruments. The variable luminosity of Pulsars are much more systematic and structured and so can be used a reference points. As neutron stars take billions of years to cool, the rotation periods of Pulsars are exceptionally consistent, over long periods of time, and so therefore the pulses of light provide a visual means of consistent timing. This allows Pulsars to become incredibly accurate astronomical ‘clocks,’ which we can then utilise. [20]

By measuring the pulses of light we can begin to define a second by the number of light pulses, of a particular Pulsar, which we can use to calibrate other clocks and time keeping instruments, to a universal standard. Without these accurate clocks, our measurement of time would slowly become unsynchronised, causing great inaccuracies with orbiting satellites and in space exploration, for example, where synchronisations of times are vital. As mentioned previously, neutron stars have very strong magnetic fields and are considered to have the strongest fields, in our Universe. A subtype of neutron stars, called Magnetars, have extremely strong magnetic fields and their fields are thought to be at the upper theoretical limit, which a neutron star’s magnetic field can be. For comparison, the magnetic field strength of the Earth is approximately 50 micro-Tesla, while a Magnetar can reach strengths of 1011 Tesla; that is ten followed by eleven zeroes. Their magnetic fields are so strong that at a distance of 1000 kilometres, due to the magnetic properties of water, it would begin to destroy human tissue and at the distance of the Moon, credit cards would stop functioning, due to their magnetic strip. [21] Magnetars are still relatively new discoveries; astronomically speaking. As such their understanding is still relatively premature, although our understanding has increased since their discovery. Although there are no ‘nearby’ Magnetars, their structure and lifetimes can be inferred, due to various events that they produce. As their magnetic fields are so intense, they can become tangled and chaotic. Eventually, there comes a point that the field lines become so tangled that they break and rearrange themselves, into a simpler configuration. However, this breaking and rearrangement of field lines releases a torrent of energy, that can dwarf the output of the world nuclear arsenal and even our Sun. [22] On the 27th December 2004, a catalogued astronomical object, previously unknown as a Magnetar, underwent a magnetic field line configuration. This particular object, catalogued SGR 1806-20, was 50000 light years away; approximately half the diameter of our Milky Way. However, despite its distance, the amount of energy released was so intense that they managed to cause a sizeable effect here, on Earth. Various satellites and detectors were blinded and damaged, due to the amount of gamma rays. Our atmosphere was also affected and bloated up, as it was hit. At a distance on ten light years, the Ozone layer would have been destroyed. Fortunately, no known Magnetars exist within our cosmological neighbourhood. [23] Unlike Pulsars, the luminosity of a Magnetar is not consistent and systematic, but rather a single event, which increases its luminosity exponentially, brighter than any Pulsar or star, with a duration of less than a second. These events are very rare and furthermore, Magnetars do not remain Magnetars for a long time, relatively speaking, as their magnetic field begins to weaken over time. Consequently, astronomers do not know if an object is a Magnetar, until it reconfigures its magnetic field, and so there are most likely many unknown Magnetars, as regular observations cannot differentiate between them and usual neutron stars. However, there are some variable stars which are instantly recognisable, given enough observations. Unlike certain variables stars, like Binary stars (looked at earlier on), some stars vary intrinsically and are hence classified as ‘Intrinsic Variable Stars.’ The luminosity in these systems varies due to some intrinsic factor that is inherent in their nature, as opposed to an external factor. A type of intrinsic variable star is known as an RR Lyrae Variable. These stars also vary their luminosity periodically, but by different means to that of binary systems. RR Lyraes are more strictly known as ‘Pulsating Variables.’ These variables change their luminosity which causes a pulsating effect, similar to a light beacon. This pulsation is also directly related to the magnitude of the changes in size, of the star. A normal, hydrogen fusing, star generates trillions of photons per second. The energy created at the core of these stars is so great that it forms a radiation pressure. The energy pushes on the outer layers, of the star. Left at its own accord, the star would eventually be destroyed, due to this light pressure. However, stars contain a colossal amount of mass, creating a large gravitational field. The stars own gravity pulls on the layers of the star, pulling it inwards, towards the centre. If this was left on its own accord the star would also eventually be destroyed. However, most stars find an equilibrium between these two factors, of gravity and radiation pressure, resulting in a relatively stable star. However, in pulsating variables, there is a loss of equilibrium. As gravity begins to pull on the layers, the star begins to contract under its own gravity. As a result, pressures and temperatures in the core begin to rise. This increases the rate of fusion and therefore increases the amount of energy formed. This, in turn, increases the radiation pressure until it overcomes gravity and begins to bloat back out. As it bloats out, the pressure decreases and gravity begins to take over, as the pulsating variable oscillates between these two stages. [24] This process only occurs for particular types of stars. A Hertzsprung-Russell diagram is a diagram which plots a star’s luminostiy against its temperature. On this diagram there is a strip, named the “Instability

Strip.” A star which falls in this strip will become a pulsating variable star. Matthew Templeton, from the American Association of Variable Star Observers, stated that “In all other stars, the energy that is created is dissipated and the pulsations die away.” [26] This means that for stars that don’t fall in this strip the energy, from the increase in temperatures and pressure, gets distributed out and the pulsations slowly diminish in amplitude and the star stops pulsating and an equilibrium is found. “All stars have this hydrogen ionization layer, but it is only in stars that lie along the instability strip where the layer is at the right depth that the pulsations are self sustaining.” [27] As Matthew Templeton said, for stars in this strip, the depths of the different layers in these stars allow the pulsations to become self-sustaining and hence forming a pulsating variable. However, not every single star becomes a pulsating variable. Antara R. Basu-Zych, from the High Energy Astrophysics Science Archive Research Centre, said that “Only sometimes, the star overshoots and becomes a little too large and pressure balance is disturbed.” [28] Not every single star, in this strip, will become a pulsating variable star; however they all have the ability to be. For these stars, when it has contracted, there is a great increase in the light produced and hence a greater increase in the luminosity. In its bloated stage, the radiation pressure is much less and therefore less light is also produced, creating a decrease in luminosity. Their pulsating periods range from a few hours to approximately a day. Subsequently, this variable luminosity is visible and apparent, over a period of a few days. [29] Another type of pulsating variable is known as a Cepheid Variable. The process is the same a RR Lyrae, but these stars are much larger and so their periods are much longer and can last many weeks. This means that the variations in luminosity are much greater as well. [30] However, not all intrinsic variables are pulsating variable stars. Some variable stars vary because they are young and beginning to form. These are known as T Tauri stars.

T Tauri stars are young, intermediate mass, stars. Stars will form from gas and dust clouds, where the necessary elements are present, for stellar formation. Many protostars can begin forming from the same dust cloud, creating stellar ‘nurseries,’ where many young stars can form. Consequently, the dust cloud, which surrounds the stars, can become heated by the new stars. As the luminosity of these stars varies, the amount of heating the dust cloud receives also varies and so the existence of T Tauri stars can be inferred from the effects they cause. However, as these stars are not particularly large, their luminosity is often quite low and so they are often quite faint. As a result, to view these, large telescopes are needed to observe and study them, in full detail. [31] When we look at our own Sun, it fluctuates between eleven year periods, known as the solar maximum and minimum. As the maximum, the Sun is at its most active, creating many coronal mass ejections (solar flares) and sunspots. At this maximum, the magnetic field is at its strongest and sunspots are places where the magnetic field lines protrude from the surface. The protrusions cause the surface to decrease in temperature and hence become darker, as shown in figure 5. T Tauri stars are young and energetic. As such, their magnetic fields are very complex. This causes many field lines to extend beyond the surface, causing many sunspots. As a result the total luminosity of the system decreases, due to the lower temperature of the sunspots. As the T Tauri star rotates various sunspots come in and out of view, varying the luminosity over time. Furthermore, the dust and gas can obstruct the view, of the star, causing even more changes in luminosity. The light curves of these stars are often quite asymmetric, due the rotation of the star and movement of gas and dust. [33] While T Tauri stars vary due to their infancy, other stars vary due to their massive size. Similar to pulsating variables, with some massive stars there is an imbalance between the radiation pressure and gravity. However, in these cases the radiation pressure takes over and gravity never overcomes this pressure. Massive stars that exhibit this effect are called Wolf-Rayet stars.

Wolf-Rayet stars can be in the region of twenty or more solar masses in size. [34] As a result their cores are very dense and so a lot of energy is created. The surface temperature of these can be 50000 degrees Centigrade; for comparison, the surface temperature of our Sun is 6000 degrees Centigrade. [35] The rate of energy production is so great that the pressure, pushing on the outer layers, overcomes gravity. Consequently, large amounts of stellar material are blown away in violent and energetic winds, causing the Wolf-Rayets to lose mass

at a regular rate. This process can continue indefinitely, until eventually the star tears itself apart, ending its life prematurely, in a supernova. Unlike other large stars, the product of this is not a neutron star or a white dwarf. The process is so energetic that nothing remains, leaving only a nebula. As stellar material is blown away, around its stellar neighbourhood, there can be large and irregular changes in luminosity, as fusion occurs within the material being ejected, before a final and dramatic increase in luminosity, in the form of a supernova. [36] This essay is by no means a complete list of all the variable stars. However, it demonstrates the various different processes by which a star system can change its luminosity, when viewed here on Earth. When we consider the variety of stars in our Universe, it is no surprise that there are also many different types of variable stars. The classification of variable stars is somewhat vague, as the word ‘variable’ can denote many things and it is inevitable that all stars, in some point in their lifetime, will vary. For example, neutron stars, looked at in this essay, are not strictly classed as variable stars, despite under examination we find that their luminosity does vary. This is, in part, the reasoning behind the choice of the title. Purely looking at stars which were classified as variable stars would have restricted greatly the range of celestial bodies explored. As we’ve seen throughout this essay, star systems can vary due to effects of other stars, such as Cataclysmic variables, or vary due to factor inherent in their own nature, as with Wolf-Rayet stars. In all cases, this has caused an alteration in luminosity. It has become evident that the term ‘variable luminosity’ is quite vague and can have a variety of definitions, determined by how it is looked at. As such, the sensible conclusion was to cover all the different ways what it could mean. Despite there being a large leap forward, with our understanding in variable stars, it is still incomplete. Matthew Templeton, from the American Association of Variable Star Observers, stated that “We also still have to build stellar models relatively simply usually making very simple approximations of stellar structure, since 3-dimensional models of stars still require an enormous amount of computational power.” [37] The largest limiter to our understanding is indeed money and finance; something that is unlikely to change, in the near future.

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