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Planetary Nebulae Luminosity Function (PNLF). 5
Astronomers have come up with many ways of measuring astronomical distances. These various methods have their strengths and weaknesses. Meanwhile, research is ongoing on how to make these methods more efficient. Astronomers are also engaged in efforts to determine the accuracy of the various methods used to measure the distance between the earth and other heavenly bodies found in the universe such as stars and steroids. Furthermore, different methods are appropriate for measure certain distances and not others, depending on the many factors. This paper discusses six main methods that are being used to measure these distances. They include parallax, Cepheid variables, Planetary Nebulae Luminosity Function (PNLF), supernovae, the cosmological redshift, and main-sequence fitting.
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Parallax
Stellar parallax refers to the apparent movement of a nearby star against the background of distant stars as the earth continues to revolve around the sun. This creates an exaggerated view that reveals how the movement of nearby stars can be revealed relative to that of others that are more distant. That movement is used to determine the distance of the nearby star.
According to Jacoby and Branch, the parallax works well in measuring the distance to stars that are close enough to the sun to show a parallax that is measurable (22). The distance to such stars is always proportional to the stellar parallax. According to this type of measurement, proxima centauri is the nearest star, whose parallax is 0.762 arcsec; therefore, it is 1.31 parsecs away.
Some of the most commonly known distance measurements by parallax include distance 3 parsecs, 61 Cygni which are equal to a third of an arcsec, and the Barnard’s Star, which, at 1.8 parsecs, is equal to 5.9 light years. The proper motion exhibited by Bernard’s Star is larger than that of well-studied stars. Space-based instruments such as the Hipparcos satellite have greatly extended the distance at which parallax can be used to measure astronomical distances reliably.
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According to Wang and Steinhardt, proper motion simply refers to changes in the position of the star in the sky because of its true motion in space (483). This motion is often distinguished from the apparent motion of the star in the sky as a result of earth’s orbit around the sun. It is the apparent motion that makes it possible for distance to be measured by parallax. At 10.3 arcseconds per year, Bernard’s exhibits the largest proper motion, taking only 200 years to cover an angular diameter of the moon across space.
There are three types of parallax: trigonometric, statistical and spectroscopic parallax. Trigonometric parallax effect was discovered through Copernicus theory of the solar systems in 1838. During this time, F.W. Bessel measured, for the first time, of a star by the name ’61 Cygni’. By 1952, measurements of parallaxes to more than 5,800 stars had already been determined. However, the distance accuracy often turned out to be questionable, mainly because it was of a similar order with the error. Trigonometric parallax that is earth-based is yet to reach far. For instance, distances to Cepheid variables or supergiants are yet to be measured.
Tegmar indicates that in statistical parallax, proper motion of the stars is related to the stars’ mean velocity in a region within the solar system that is referred to as the LSR (Local Standard of Rest) (212). It has been found out that the velocity of the sun can be determined relative to the LSR. Meanwhile, an assumption has to be made, whereby zero is the average velocity relative to the LSR, in which case the apparent motion of the stars in the sky yields their distance. This method is useful for all objects that are known to be within the same distance by virtue of belonging to a cluster, or known to be within calculable relative distances.
Spectroscopic parallax is useful when a star is being studied through assignment of an individual spectral type. The star’s absolute magnitude is then determined on the basis of its position within the H-R diagram. Through comparison with the star’s apparent magnitude, its distance modulus is calculated directly. However, the process of assigning a spectral type to an individual star is complicated, making this process rather inaccurate. The only exception is in the case of bright stars, where large distances can be easily determined.
Cepheid Variables
Riess notes that Cepheid variables were first used as distance measuring tools for a category of stars known as delta Cepheid (1009). These variables have emerged as crucial tools for measuring astronomical distances because it has been found out that their periods of variability are closely related to their absolute level of luminosity.
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Hughes reports that an analysis of Cepheid’s spectrum reveals that apart from variation in velocity, a velocity of about 20km/s is closely associated with its orbit, a change in diameter by 15% and a swing in temperature from 5500K-6600K (247). These findings have proved the importance of these variables in measuring astronomical distances.
Cepheid variables, says Garnavich, are used to create the Cephiad luminosity curve, which is plotted as magnitude versus period (76). The resulting smooth curve reflects an average behavior. In the resulting observations, there is always a considerable scatter about the ‘shark fin’ shaped curve. Nevertheless, the variables are a rather accurate indicator of astronomical distances when they are used as a standard module.
A distinction is often made between Type I Cepheids and Type II Cepheids. Type I Cepheids are used to measure distances involving Population 1 stars while Type II Cepheids are used to measure Population II stars. Unlike Population I stars, Population II stars, such as W. Virginis Cepheid, are 4 times less luminous.
In Stetson’s view, Cepheid variable stars remain highly valuable methods of astronomical distance determination because of their period of variability, which exhibits a period-luminosity relationship (851). A measurement of apparent luminosity facilitates a straightforward determination of their distance. These variables are visible and measurable within distances of 20 million years.
Planetary Nebulae Luminosity Function (PNLF)
The theoretical fundament of PNLF, according to Percival, was laid out in 1989 as a tool for establishment of cosmic distances (235). So far, this method has proved to be profoundly successful. The main reason for its success is the fact that it is useful for both spirals and elliptical, in spite of the fact that both of these systems have completely varying stellar populations. However, notes Sch¨onberner, despite being used for about two decades, PNLF’s physical basis remains largely mysterious and a subject of controversial interpretations (5).
According to Jacoby, the planetary nebular luminosity function is the only standard candle that is applicable in all the large Local Supercluster galaxies (p. 40). It is more accurate than the Cepheid variables approach with the internal error being as small as 3 per cent. In this method, planetary nebulae are assumed to eject a mass of ionized gas that is similar to the one that is observed as a shell that surrounds the star.
Statisinka & McCall observe that planetary nebulae (PN), when viewed in other galaxies, are simply point sources (675). The central stars of all bright PN are those that have already peeled off the asymptotic branch and are moving away from it. Shortly after this, they stop producing energy and end up becoming white dwarfs. However, in the meantime, they remain extremely bright and hot. In fact, they are often so hot that the surrounding traps the energy and reprocesses it, forming a series of emission lines.
According to Hajian et al, the theoretical basis of the PNLF technique arises from a combination of factors (21). First the luminosity of a nebula of PN is always directly proportional to its central star’s luminosity. However, like in stars on the main sequence, a mass-luminosity relation exists for all post-asymptotic stars. Secondly, the PN central star’s mass varies slowly as a function of the star’s initial mass. According to Mendez et al, Loss of mass on the asymptotic giant branch and the giant itself makes the final star to have substantially lower mass than that of the initial star (534).
Supernovae
Apart from Cepheids, supernovae are the other types of standard candles that are used to determine astronomical distances. They can be used to measure distances are up to hundreds of millions of light years away. They are simply huge explosions that some stars experience when they near the end of their lifetimes.
Stars possess different fates, depending on their masses. Small stars such as the sun, begin by growing bigger after all the hydrogen in the cores has been ‘burned’, then they get cooler, and finally turn into a red giant. After all their helium has been used up, they remain with no energy and start to shrink as they begin cooling off. However, notes Tout, heavier stars do not end up at the red giant phase (259). When helium burns, many elements become fused at the core, until iron, the most stable element is produced. Instead of providing energy, iron uses up energy during the fusing process. After all the fusing reactions that produce iron, the stars have no additional energy left and they collapse. The collapse turns the star’s core into a neutron star, and sometimes, a black hole. The material from the star’s outer shells is expelled, causing a huge explosion. In this instance, a sudden flash of brightness can be observed, and in some cases, the resulting neutron star as well. These explosions are referred to as supernova type II.
Unfortunately, since no universal relationship between easily observable parameters and the brightness of the supernova explosions exists, these supernovae are not accurate determinants of cosmic distances. However, the other type of supernova explosions, the Supernovae type I, are more accurate since they can only happen in binary systems (whereby two stars orbit each other). As the two stars draw gases from each other, the resulting brightness causes decay of nickel and cobalt, the two main radioactive substances produced during the explosion. Radioactivity in these substances decreases exponentially with time.
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Feldmeier, Ciardullo and Jacoby indicate that the most crucial thing to note in Supernova type I is that a universal relationship exists between the rate of decay of the light observed and the brightness of the explosion (231). When the light received from the explosion is observed and the rate at which it becomes dimmer recorded, one obtains the supernova’s absolute brightness. When this is compared to the supernova’s apparent brightness, one obtains an accurate distance of the supernova, and by extension, the galaxy within which it is located. Reiss observes that recent measurements of distant supernova indicated that the expansion of the universe continues to accelerate rather than decelerate, contrary to earlier expectations (1009).
The cosmological red shift
A close examination of galaxies situated millions light years away reveals well-known spectral lines of certain elements that have been shifted from their usual areas. They are shifted in that they appear at wavelengths that are slightly larger than usual. Eisenstein indicates that the larger wavelength corresponds to a ‘redder’ appearance, thus the use of the term ‘red shift’ (564). Furthermore, the resulting relative shift remains the same in all spectral lines.
Such shifts, according to Ballinger and Peacock,constitute well-known phenomena that apply for both sound and light (119). They occur whenever the object that is emitting waves continues to move with respect to the observer, a phenomenon known as the Doppler Effect. The natural interpretation applies to galaxies, which are always moving with respect to us. A blue shift would indicate that a galaxy is moving towards us, as can be seen in the Andromeda’s galaxy, which continues to approach our galaxy because of gravitational attraction between these two galaxies.
Using the cosmological red shift, it has been proven that galaxies that are further away recede faster than those that are much close. Today, this phenomenon is explained with the use of the Big Bang theory, which holds that the whole of the universe is continually expanding. The method of determining the distance of distant objects remains rather simple. It entails measuring its red shift and plugging the measured value into the formula provided in the Big Bang theory.
Unfortunately, notes Pierce, some of the cosmological parameters that are used in the Hubble parameter, as the red shift formula is known, are not yet known with precision (388). Therefore, the distances calculated using this method always turn out being not as reliable as those measured using other methods. Nevertheless, this method is essential for estimation of the distance for someone who is not conversant with sophisticated methodologies.
Main-sequence fitting
In this approach, a color-magnitude diagram is constructed using the Hertzsprung-Russel (H-R) method for the stars in a cluster. Then, it is set against specially designed theoretical diagram for stars belonging to a similar group. Ann reports that these stars are aligned by color and then adjusted in such a way that the main sequence curves overlap (1640). The cluster’s distance modulus is then derived from the difference between the theoretical and observed magnitudes on the diagrams. This approach is useful for measuring distances between open clusters in situations where most stars are aligned on the main sequence.
References
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