Measurement of the Hubble Constant - Essay Example

Astrophysics: Measurement of the Hubble Constant An American astronomer, Edwin Hubble, made an observation that every object that is observable in interstellar space has a relative velocity to the earth and to any other similar object, and this relative velocity is observable by Doppler shift. Also, he observed that the galaxies that move away from the earth’s surface and that have this relative velocity that can be observed by Doppler shift have a relative velocity that is proportional to their distance from the earth and from other objects in interstellar space. Edwin Hubble derived the Hubble law in 1929 after doing intensive study for almost ten years. v = HoD is the mathematical expression of the Hubble law, whereby Ho is the Hubble constant of proportionality between D (the distance of a galaxy or interstellar body) and the object’s velocity, v. The Hubble time is the reciprocal of the Hubble constant of proportionality (Liddle 2003). There are many methods used to measure the Hubble constant. These methods are the Cepheid Distance Scale, Tip of the Red Giant Branch, Maser Galaxies, Surface Brightness Fluctuations, Tully-Fisher Relation and the Type Ia Supernovae. These different methods have different levels of precision, and each method has its advantages and limitations. The Cepheid Distance Scale method, the Tip of the Red Giant Branch method and the Maser Galaxies method are the methods known for highest precision and accuracy in measurement of the distances of galaxies from the earth and in determination of the Hubble Constant. The Tully Fisher Relation, the Surface Brightness Fluctuations and the Type Ia Supernovae methods are good at measuring distant galaxies and interstellar bodies. The Type Ia Supernovae method is the best when the galaxies being studies have maximum luminosity (Weinberg 2008). The aim of this report is not to discuss in length every method used to measure the Hubble constant, but it will concentrate on one method though there will be overlapping with other methods. This report will discuss the Cepheid Distance Scale methods and a critical literature review of this method will be written. The strengths and weaknesses of this method will also be presented. The Cepheid Distance Scale Method Cepheid variables have become very useful in determining distances from the earth to galaxies and other interstellar objects. The importance of these variables began way back in 1912 when the Leavitt Law was discovered. As a result of this, the Cepheid relationship between time and luminosity is also known as the Leavitt Law. Cepheids are observed to have a pulsation frequency of between two to one hundred days. Also, the brightness of these Cepheids has direct correlation with the frequencies names above. This makes it easy for the bright interstellar objects to be seen on a distance scale (Keel 2007). There is a specific way through which the Cepheid Distance Scale works; the interstellar body being observed has to be located in a place where the stars in its background are dim, resolved and unresolved (Kutner 2003). These stars in the background help in the identification of the specific body by illuminating the galaxy. However, for the identification of the distance of a certain body to be successful, overcrowding needs to be avoided so as to avoid confusion. Unrest in the atmosphere interferes with the clarity of the images seen and causes the contrast to lessen. Beyond the earth’s atmosphere, in space, clarity of the images is determined by the quality of the telescope’s slits and the range of wavelengths which the telescope can be adjusted to (Madsen 1995). The Cepheid Distance Scale method has been able to accumulate data that is highly accurate. However, there are several complications associated with this method, the main ones being reddening and metallicity. These effects cause certain errors and uncertainties, both of which have a great effect on the distance scale results. There are different methods of correcting the impact of these complications o the results of the distance scale (Liddle 2003). Cepheids are located in a zone that is full of helium ionization, and it is this zone that produces heat. When the opacity in the earth’s atmosphere changes with temperature, the Cepheids pulsate. If the opacity is too high such that the helium ionization zone is fully blocked from radiation, the helium ionization zone contains within itself the energy it carries. When this energy is retained within the layer, internal pressure accumulates therein causing the layers of gas above this zone to be pushed up. This elevation of layers of gas is what is referred to as radial expansion. When the hot gases in the stars and interstellar bodies expand, it goes against gravitational pull and therefore results in cooling even as the surface to volume ratio increase (Avishai 1999). This cooling of the expanded gases causes the ionized helium zone to cease being opaque and to gain transparency. Decrease in opacity results in an increase in the amount of radiation allowed through. When this happens, internal pressure decreases and the stars become smaller. When this happens, the cycle starts all over again. What is seen here is an alternating cycle of retaining and releasing of energy from the helium ionization zone, and this result to temperature changes, and this determines how luminous an interstellar body is. The period-luminosity relation, when using this scale, is seen to become steeper as near-infrared bands are approached. The metallicity is seen to decrease as these bands are approached (Keel 2007). These changes result to a change in chemical composition of the stars and interstellar bodies. As a result, the color change of the bodies is expected to change as a function of the metallicity, but this does not accurately happen as expected. Therefore, prediction of the metallicity and period-luminosity is quite a challenge with the Cepheid Distance Scale. Because of this error, there has come up two proposed tests of the sensitivity of the scale to the metallicity of the interstellar bodies (Avishai 1999). The luminosity of a galaxy or interstellar body is seen to decrease with increase in interstellar extinction. Interstellar extinction causes as apparent increase in the distance of a galaxy, causing large errors to the results. In order for interstellar extinction corrections to be made, two methods are used; two observations, each at a different wavelength, are made and compared. This is because of the fact that interstellar extinction is mainly a function of wavelength. Another method is by doing the observation from a wavelength band that is the longest so as to ensure minimum effects of the interstellar extinction (Weinberg 2008). Despite all these complications and errors, the Cepheid Distance Scale stands out as the most accurate method when compared to the other methods listed above for determining the Hubble Constant. The sizes and periods of the interstellar bodies are determined mainly using the Hubble Space Telescope. The speed of galaxies is also determined thus. High luminosity galaxies fall above the Ho = 55 line. Redshifts that are intrinsic (those of low velocity or the stationary ones) are observed in a different method; using the Virgo Cluster. This is because the intrinsic bodies are known to form the majority of the bodies found in this cluster (Harrison 1992). However, it has been argued that the stars seen by this method are not really in the Virgo Cluster but they only coincidentally happen to be aligned to this cluster. However, various tests have proved with accuracy and precision that these stars are located within the cluster (Madsen 1995). Over the last twenty years, there has been notable progress in the Cepheid Distance Scale method of determining the Hubble Constant. The reason why measurement of this constant has been given so much attention is because accurate measurement of the same is of great importance. This method has had various systematic errors in determining the distances of various galaxies and interstellar bodies, but these errors have been minimized over time. The most accurate measurement that this method has so far given is about plus or minus two kilometers per second, which shows great precision and accuracy (Madsen 1995). The distance-velocity graphs for the galaxies are plotted on a simple plot, and the results are consistent in proving the same thing; the universe is in continuous expansion, a discovery that has become of significant importance in this twenty first century. It has been proved to be true because according to the Cepheids method and other methods, the galaxies are seen to have receding velocities. However, the Cepheids Distance Scale method has been seen to give more accurate results (Avishai 1999). The Hubble constant’s SI units are in kilometers per second per megaparsec. The redshift of a galaxy is in direct correlation to its distance from the earth, and the greater the redshift of a galaxy the more it relies on the galaxy’s dark energy and its density. This, in turn, is highly dependent on the energy content of the universe. The energy content of the universe determines the uniformity in its expansion, and in a uniformly expanding universe the Hubble constant changes in direct proportion to time (Kutner 2003). In the past, the correlation between the galaxy distance and velocity and the relationship between the Hubble constant and time were taken to be rather simple relationships, but the uncertainties therein had not been seen yet. Listing mathematically the principles needed to accurately measure the Hubble constant appeared to be very simple, but it was realized that practically meeting these requirements was a very hard task. However, measuring radial velocities of the galaxies in relation to the infrared ands is very easy, up to date. However, the main difficulty here is getting to measure the distance with the required accuracy and precision with minima (up to 2%) margin of error (Harrison 1992). The placement of the solid state detector has to be very accurate for the measurement to have precision in it. The solid state detector, say a telescope, should be place far away enough to capture a smooth period-luminosity figure, considering that the galaxy being aimed at is interfered with by the random velocities of the surrounding interstellar bodies it interacts with. Also, the solid state detector should be placed near enough for it to capture measurements that are absolute, because placing it far away causes the measurements to be relative, hence giving more room to errors. The objects being studies also need to be clustered together so that their lack of abundance will not cause an increase in uncertainties (Kutner 2003). Two other calibrations to the Cepheid Distance Scale were made to correct the two errors. However, the mentioned calibrations are not the only ones that were done to the Cepheid Distance Scale; many complex calibrations have been done so as to make the scale a more accurate one. According to Hubble, many of these calibrations and corrections attempted to complicate the scale further, but he was optimistic by 1935 that all the necessary major corrections had been done and that “Further revision is expected to be of minor importance.” References Avishai Dekel, J. & Ostriker P. 1999. Formation of Structure in the Universe. Cambridge: Cambridge University Press. Harrison, E. 1992. The redshift-distance and velocity-distance laws". Astrophysical Journal, Part 1, vol. 403, pp. 28–31. Keel, W. 2007. The Road to Galaxy Formation, 2nd Ed. Springer Publishers. Kutner, M. 2003. Astronomy: A Physical Perspective. New York: Cambridge University Press. Liddle, A.R. 2003. An Introduction to Modern Cosmology, 2nd Ed. New York: John Wiley and Sons Publishers. Madsen, MS. 1995. The Dynamic Cosmos. CRC Press. Weinberg, S. 2008. Cosmology. Oxford: Oxford University Press. Read More

However, for the identification of the distance of a certain body to be successful, overcrowding needs to be avoided so as to avoid confusion. Unrest in the atmosphere interferes with the clarity of the images seen and causes the contrast to lessen. Beyond the earth’s atmosphere, in space, clarity of the images is determined by the quality of the telescope’s slits and the range of wavelengths which the telescope can be adjusted to (Madsen 1995). The Cepheid Distance Scale method has been able to accumulate data that is highly accurate.

However, there are several complications associated with this method, the main ones being reddening and metallicity. These effects cause certain errors and uncertainties, both of which have a great effect on the distance scale results. There are different methods of correcting the impact of these complications o the results of the distance scale (Liddle 2003). Cepheids are located in a zone that is full of helium ionization, and it is this zone that produces heat. When the opacity in the earth’s atmosphere changes with temperature, the Cepheids pulsate.

If the opacity is too high such that the helium ionization zone is fully blocked from radiation, the helium ionization zone contains within itself the energy it carries. When this energy is retained within the layer, internal pressure accumulates therein causing the layers of gas above this zone to be pushed up. This elevation of layers of gas is what is referred to as radial expansion. When the hot gases in the stars and interstellar bodies expand, it goes against gravitational pull and therefore results in cooling even as the surface to volume ratio increase (Avishai 1999).

This cooling of the expanded gases causes the ionized helium zone to cease being opaque and to gain transparency. Decrease in opacity results in an increase in the amount of radiation allowed through. When this happens, internal pressure decreases and the stars become smaller. When this happens, the cycle starts all over again. What is seen here is an alternating cycle of retaining and releasing of energy from the helium ionization zone, and this result to temperature changes, and this determines how luminous an interstellar body is.

The period-luminosity relation, when using this scale, is seen to become steeper as near-infrared bands are approached. The metallicity is seen to decrease as these bands are approached (Keel 2007). These changes result to a change in chemical composition of the stars and interstellar bodies. As a result, the color change of the bodies is expected to change as a function of the metallicity, but this does not accurately happen as expected. Therefore, prediction of the metallicity and period-luminosity is quite a challenge with the Cepheid Distance Scale.

Because of this error, there has come up two proposed tests of the sensitivity of the scale to the metallicity of the interstellar bodies (Avishai 1999). The luminosity of a galaxy or interstellar body is seen to decrease with increase in interstellar extinction. Interstellar extinction causes as apparent increase in the distance of a galaxy, causing large errors to the results. In order for interstellar extinction corrections to be made, two methods are used; two observations, each at a different wavelength, are made and compared.

This is because of the fact that interstellar extinction is mainly a function of wavelength. Another method is by doing the observation from a wavelength band that is the longest so as to ensure minimum effects of the interstellar extinction (Weinberg 2008). Despite all these complications and errors, the Cepheid Distance Scale stands out as the most accurate method when compared to the other methods listed above for determining the Hubble Constant. The sizes and periods of the interstellar bodies are determined mainly using the Hubble Space Telescope.

The speed of galaxies is also determined thus. High luminosity galaxies fall above the Ho = 55 line. Redshifts that are intrinsic (those of low velocity or the stationary ones) are observed in a different method; using the Virgo Cluster.

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