The stars in the heavens have actually caused observers to ponder many different inquiries over the centuries. Wherein did they come from? exactly how did they concerned be? just how old room they? Fortunately, astronomical science has progressed to the allude where we can now carry out an answer come this last question. By measuring both the luminosity that a star, which is the brightness relative to the brightness of our sun, and also the shade spectrum the the star, which to represent the surface temperature that the star and the rate at which it is burn its nuclear fuel, scientists are now able to calculation the age of the stars that the cosmos (Dalrymple 2004).

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Luminosity and also effective temperature are closely related come one another, together both characteristics are a an effect of the forces at job-related within a star. Stars originate as soon as a cloud of gas collapses in upon itself due to gravitational forces. This please of the gas cloud releases large amounts that gravitational energy which consequently produces an massive internal temperature. This huge internal temperature is enough to reason the hydrogen gas in ~ the cloud come burn via nuclear fusion reactions that develop helium. This nuclear fusion reactions create a significant amount that heat and also light, thereby providing the fuel because that the star"s luminosity and high temperature because that the bulk of the life (Dalrymple 2004).

Luminosity deserve to be defined as the complete radiation emitted per 2nd in all directions by a star, and it is expressed in units of solar luminosity, where our sun has a luminosity value of one. In order to uncover the luminosity the a star, the distance from the earth to the star need to be known. This distance deserve to be calculated for the closest stars using 2 measurements and some straightforward algebra. To begin, an observer actions the place of a star against the lift of an ext distant stars at 2 times that are 6 months apart; the observer can then calculate the apparent shift of the star in the sky, known as the parallax that the star. This information deserve to be used, along with the recognized diameter that the earth"s orbit, to discover the distance from the planet to the star follow to the complying with equation:

By combine this details with the measured radiation emitted by a star, researchers are maybe to use the principle that the noticeable brightness the a star is decreased by the square that its distance to calculate the star"s stellar luminosity. Stellar luminosity values can be as small as 0.1 time the luminosity of our sun to as big as 60,000 times as luminous together our sun (Motz 1975).

The surface temperature the a star is much less complicated to determine, together it deserve to be evaluated using the observable color of the star. The color of a star is straight related come the wavelength that the radiation emitted by the star. Physicist Max Planck developed the following equation that straight related the radiation emitted by any type of hot body to the temperature of that body, where I(ν) is power per unit time every unit surface area per unit hard angle every unit frequency, h is Planck"s constant, ν is the frequency, c is the rate of light, c/ν is the wavelength the the light, k is Boltzmann"s constant, and T is the temperature of the black body:

 (1)

Using this equation, scientists have calculated the surface ar temperatures for plenty of stars, v values ranging from 3,000 K for the colder red stars to 40,000 K because that the sexy blue-white stars (Motz 1975).

In reality, however, the period of any kind of given star is not estimated simply by evaluation of its very own luminosity and surface temperature values. In practice, the period of a star is evaluated by determining an age for the globular cluster of stars come which the star belongs. A globular swarm of stars is a team of gravitationally attractive stars the can selection in number from 10s of stars to more than a million stars per cluster. Each swarm of stars is unique, and all of the stars that a cluster were created at the very same time. As a an effect of this simultaneously formation, every stars within an separation, personal, instance cluster space the same age (Bolte 1998). The should also be noted that the luminosity and also surface temperature that a star are only provided by researchers to identify the expectation of a star - they perform not specify the actual period of a star. The expectancy of a star is just a role of just how much nuclear fuel that contains and the price at which that is burning the fuel. Larger, name is stars contain much more fuel than smaller, chillier stars, however they space burning their fuel at much higher rates than the smaller stars. As such, the larger stars burn out an ext quickly and exist for a shorter duration of time than smaller sized stars (Dalrymple 2004). This burn of nuclear fuel specifies the lifespan and also therefore the stellar advancement of a star, which we deserve to observe utilizing the luminosity and also surface temperature that the star.

In reality, however, the age of any type of given star is not approximated simply by review of its own luminosity and surface temperature values. In practice, the age of a star is evaluate by determining an er for the globular cluster of stars come which the star belongs. A globular cluster of stars is a team of gravitationally attractive stars that can range in number from 10s of stars to an ext than a million stars per cluster. Each cluster of stars is unique, and every one of the stars of a cluster were developed at the same time. As a an effect of this simultaneously formation, all stars within an individual cluster room the same age (Bolte 1998). The should additionally be listed that the luminosity and surface temperature that a star are only supplied by researchers to recognize the expectancy of a star - they perform not define the actual period of a star. The lifespan of a star is merely a role of just how much nuclear fuel that contains and the price at which the is burning the fuel. Larger, hotter stars contain much more fuel than smaller, cooler stars, however they are burning their fuel at much higher rates than the smaller stars. As such, the bigger stars burn out much more quickly and exist because that a shorter duration of time than smaller sized stars (Dalrymple 2004). This burn of nuclear fuel specifies the lifespan and also therefore the stellar evolution of a star, i m sorry we deserve to observe utilizing the luminosity and surface temperature the the star.

Using these luminosity and surface temperature worths of the stars in ~ a solitary cluster, scientists are able come establish period of the cluster (and therefore the stars within the cluster) utilizing a Hertzsprung-Russell (H-R) diagram. In one H-R diagram, luminosity is plotted together a function of temperature, as displayed in Fig. 1 below:

Figure 1: A Hertzsprung-Russell diagram of Globular swarm M5

As is noticeable in Fig. 2, the bulk of stars in a cluster lie follow me a consistent line the slopes diagonally indigenous the top left part of the diagram to the lower right part of the diagram, i m sorry is known as the key sequence (labeled ms in the diagram). In this main sequence, the upper best contingent of the succession is composed of the many massive, hottest, and brightest burning stars, while the reduced right portion is consisted of of much less massive, cooler, and least luminous stars. Every stars in ~ the main sequence count on the nuclear blend of hydrogen gas together the fuel for their light and heat production (Dalrymple 2004).

The section of the H-R diagram the is provided to determine the age of the star swarm is the turnoff point, significant TO in the over diagram. Together a star grows older, the will eventually exhaust all of its hydrogen fuel, resulting in a dramatic expansion in size coupled with a diminish in luminosity to end up being a red giant. Together this transformation occurs, the star will leave the key sequence and also move towards the top right corner of the H-R diagram. This stellar advancement is represented in Fig. 23 below, which diagrams the transforms that occur in one H-R diagram of a cluster over time.

Figure 2: one H-R diagram Highlighting Turnoff from the main Sequence

At the genesis of a star cluster, every stars autumn upon the main sequence (shown in the an initial chart of Fig. 2 - yellow line put for recommendation to initial problem of diagram). However, the large, glowing stars of the upper main sequence burn your fuel much more quickly and transform into red giants sooner 보다 the smaller sized stars that the lower main sequence. Thus, in a younger star cluster, the turnoff point will type at the height of the main sequence, whereby the more massive stars are start to become red giants (represented in the second chart of Fig. 2). As a swarm ages, less substantial stars will deplete their hydrogen fuel, and the turnoff point will move down follow me the main sequence. Eventually, in the oldest clusters, the turnoff allude will be close to the bottom ideal of the main sequence (chart 3 the Fig. 2). This migrate of the turnoff point over time is what allows scientists to recognize the age of a star cluster - they simply need to identify the fixed of the stars leaving the key sequence come predict the period of the whole cluster. Due to the fact that scientists know the initial problem of any type of cluster (all stars reside on the key sequence) and the price at i m sorry the stars that the cluster will certainly evolve into red giants and also move the turning point under the main sequence (determined utilizing volume of atom fuel that the stars and also the price at i beg your pardon the stars are burning that fuel), scientists can use the motion of the turnoff allude as a clock to screen the i of time within a swarm (Dalrymple 2004).

In enhancement to giving the age of the stars within the cluster, the period of globular clusters offered by H-R diagrams deserve to be provided to estimate the period of the galaxy castle inhabit. Due to the fact that globular clusters reside close to the center of a galaxy, their period is representative of the period of the galaxy, as they must have developed at nearly the exact same time.

By plotting the luminosity and also temperature worths of stars ~ above H-R diagrams, researchers have discovered the periods of globular swarm of stars within the Milky means galaxy to be in the selection of 11.5 come 14.0 exchange rate years, and also the age of the galaxy must therefore fall within this selection as well (Dalrymple 2004).

Another method of date globular swarm of stars requires measuring the age of white dwarf stars residing in a cluster. ~ a certain period of time, a red giant star will expel that is outermost material, creating a planetary nebula and leaving the hot core of the large in that is wake. This warm core that the star is well-known as a white dwarf. White dwarf stars are extremely dense, and they perform not make use of nuclear reactions to create light and heat. Instead, they operation on residual warm from the previous phase of their existence (Dalrymple 2004).

Since they room not creating any new heat, white dwarfs cool with time until they successfully die. The temperature that a white dwarf deserve to be measured using its brightness, and also the amount of light developed by a dwarf will decrease as the temperature decreases. Also, the price of cooling of a white dwarf slows together the temperature diminishes - a aspect that should be accounting for when dating a white dwarf. Using the recognized initial condition of the dwarf, its current brightness (and as such its temperature), and also the rate of cooling, one can extrapolate the data to recognize the period of a white dwarf. Scientists have utilized the Hubble an are Telescope to observe white dwarfs in the M4 globular cluster of the Milky means galaxy, and their observations indicate that the white dwarfs have period of 12.7 ± 0.7 exchange rate years, which can additionally be taken together an approximate period of the galaxy. This age is in good agreement with the period given by the H-R diagram method, and the agreement between the 2 methods says that the age of the stars and the Milky means galaxy is better than 11 billion years (Dalrymple 2004).

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Sources:Dalrymple, G.B. 2004. Old Earth, old Skies. Stanford college Press, Stanford, Ca.Motz, Lloyd. 1975. The Universe: its Beginning and End. Charles Scribner"s Sons, brand-new York.