IB+DP+Option+D+Astrophysics

[|Parsec] - [|Sixty Symbols] Published on 25 Jun 2010 Why do astronomers use parsecs instead of light-years? And what is parallax? || media type="youtube" key="dY7s7Zq4zDQ" width="560" height="315" [|Where to find the nearest rocky planet] Uploaded on 30 Jul 2015 [|NASA Jet Propulsion Laboratory], [|Explanet Exploration] www.nasa.gov || media type="youtube" key="CWMh61yutjU" width="560" height="315" [|Distances Astronomy#25], [|CrashCourse] Published on 16 Jul 2015 || media type="youtube" key="Op3AYaJc0Xw" width="560" height="315" [|How to measure extreme distance]s - Yuan-Sen Ting TED-Ed Published on 9 Oct 2014 || [|The Uncertainty Principle Documentary] [|The Uncertainty Principle Documentary] BY BBC TWO from youtube.com Published on 16 Oct 2016 [|Cosmic Portals] [|Cosmic Portals] =Core 16 hours= =** D.1 – Stellar quantities **= **//Essential idea://** One of the most difficult problems in astronomy is coming to terms with the vast distances between stars and galaxies and devising accurate methods for measuring them
 * media type="youtube" key="bJv55ebJbhs" width="560" height="315"

Reality: The systematic measurement of distance and brightness of stars and galaxies has led to an understanding of the universe on a scale that is difficult to imagine and comprehend. (1.1)
 * //Nature of science: //**

Objects in the universe The nature of stars Astronomical distances Stellar parallax and its limitations Luminosity and apparent brightness
 * //Understandings: //**

Identifying objects in the universe Qualitatively describing the equilibrium between pressure and gravitation in stars Using the astronomical unit (AU), light year (ly) and parsec (pc) Describing the method to determine distance to stars through stellar parallax <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Solving problems involving luminosity, apparent brightness and distance
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Applications and skills: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">For this course, objects in the universe include planets, comets, stars (single and binary), planetary systems, constellations, stellar clusters (open and globular), nebulae, galaxies, clusters of galaxies and super clusters of galaxies <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Students are expected to have an awareness of the vast changes in distance scale from planetary systems through to super clusters of galaxies and the universe as a whole
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Guidance: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">The vast distances between stars and galaxies are difficult to comprehend or imagine. Are other ways of knowing more useful than imagination for gaining knowledge in astronomy?
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Theory of knowledge: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Similar parallax techniques can be used to accurately measure distances here on Earth
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Utilization: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aim 1: creativity is required to analyse objects that are such vast distances from us <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aim 6: local amateur or professional astronomical organizations can be useful for arranging viewing evenings <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aim 9: as we are able to observe further into the universe, we reach the limits of our current technology to make accurate measurements
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aims: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">d (parsec) = 1 / p (arc–second) <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">L= σAT 4 <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">b = L/4 πd 2
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Data booklet reference: //**

Units we use in measuring anything are usually just for convenience. You don’t give the distance between countries in inches, or your age in seconds, or your height in kilometres.
 * Units**

Prior reading (5 minutes): [|The Cosmic Distance Scale] from nasa.gov


 * Activities :**
 * 1. In pairs, make a mind map including words below on a A3 paper. The title is Astrophysics. Only one labtop is allowed for each group** **(20 minutes)****.**
 * Words to include: //Parsec, A.U., Light year, Astronomy, Asteroids, Meteoroids, Meteorites, Comets, Stella cluster, Luminosity, Apparent brightness, Nebulae, Supernovae, Constellations, Galaxies, Globular, Palanets, Moons, Parallax, Arc-second, etc.// ||
 * 2. You will also PRESENT and display a diagram describing what Parsec and Arc-seconds are at the back of your mind map by the end of the class.**

Three different (much larger) length measuring units in the Universe: > > [|Parsec] (from britannica.com): unit for expressing distances to [|stars] and [|galaxies], used by professional astronomers. It represents the distance at which the radius of [|Earth]’s [|orbit] subtends an angle of one [|second] of arc. Thus, a [|star] at a distance of one parsec would have a [|parallax] of one second, and the distance of an object in parsecs is the [|reciprocal] of its parallax in seconds of arc.(1 Parsec: Distance of an object, a nearby star relative to the Sun, that has a parallax angle of 1 arc second.) > 1 Parsec = 206,264 A.U. = 3.08 x 10 16 m = 3.26 ly > [|Image] from star.pst.qub.ac.uk > [|Light-year] (from britannica.com): the distance traveled by light moving in a vacuum in the course of one [|year]. > A light-year equals about __ 9.46073 × 10^12 __ km ( __ 5.87863 × 10^12 __ miles), or __ 63,241 __ astronomical units. About __ 3.262 __ light-years equal one [|parsec].
 * 1) Astronomical Unit (AU) : The distance from the Sun to Earth ( = 1.5 x 10 11 m)
 * 1) Parsec (pc) :<span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">A <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">unit <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> of <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">astronomical length based <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> on <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">the distance from Earth <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> at <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">which stellarparallax <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> is <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">one second <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> of <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">arc and equal <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> to <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">3.258 light-years, 3.086 <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> × 10^16 meters.
 * 1) Light year (ly) : Distance light travels in 1 Earth year ( = 9.46 x <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">10^15 meters),
 * **//Stellar parallax//**

As you move from one position to another objects change their relative position. Eg) Close one eye and look at the tip of your finger. When you move it, it ‘appears’ to move further than an object in the distance. This apparent movement is called parallax and the effect can be used to measure the distance to some stars in our galaxy.
 * near objects appear to move when compared to far objects
 * closer stars will have an apparent movement when compared to more distant stars.
 * The closer the star is to Earth, the greater the parallax shift

Parallax angle is normally given in seconds (“), not degrees. As all stars are very distant, the parallax angle is always very small. 1 o = 60 ' = 3600 " 1 rad = 360/2<span style="font-family: Symbol,sans-serif;">p = 57.295 o

Distance in pc = 1 / parallax angle in seconds (expressed in radians) as1 pc = 1 A.U. / (1/206,264") <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 13.3333px;">d (parsec) = 1 / p (arc–second) [|Hawaii edu Ast 110: Class 9]

EXAMPLE 1 The star alpha Eridani is 1.32 x 10 18 m away. Calculate its parallax angle. SOLUTION 1: Refer to IB STUDY GUIDES page 193 parallax angle = 1 / parsec parallax angle = 0.02 "

Parallax p is measured in radians, The factor of 2 <span style="background-color: #f5efef; font-family: Symbol,sans-serif;">p /360 converts degrees to radians. 1 " = (2 <span style="background-color: #f5efef; font-family: Symbol,sans-serif;">p /360) x (1/3600 ) 1 pc = 1 AU / 1 " = 3.09 x 10 16 m || Parallax from [|ibphysicsnotes.wordpress.com] || || How far away are the stars and galaxies? [|How are these distances calculated?] from sciencemeetsreligion.org

media type="youtube" key="t31lVCPMEZc" width="560" height="315" [|Seven Sisters or Pleiades (M45)] - [|DeepSkyVideos]
 * //Objects in the universe//**
 * //Task 1://** Watch the Pleiades video clip for 6 minutes and write down all the terminoloy in your notebook.
 * Every known mass that has been viewed/witnessed in the Universe could include (in increasing magnitude):
 * comets
 * planets
 * stars (single and binary)
 * planetary systems (such as our solar system)
 * constellations
 * nebulae (clouds of dust and gases)
 * stellar clusters (open and globular)
 * galaxies
 * clusters of galaxies
 * super clusters of galaxies

Stars can be grouped together in stellar clusters:
 * open group contains 10^3 stars
 * globular group contains 10^5 stars || [[image:universe objects.PNG width="584" height="380"]] || Image left from [|www.as.utexas.edu/astronomy]

media type="youtube" key="kIiJZINJFiw" width="560" height="315" [|Size comparison of the universe 2016] [|Times Infinity] Published on 31 Dec 2016 ||

Many stellar clusters make u p a galaxy. Our galaxy (the Milky Way) rotates with a period of approx 2.5 x 10^8 years. Beyond the Milky Way, there are billions of other galaxies. Many are grouped together in clusters or super clusters. [|Celestial Objects] from www.seasky.org

//**The nature of stars**// Have you spotted the Earth in the solar system? Can you describe nuclear fusion?How does fusion power the Sun? media type="youtube" key="W1ZQ4JBv3-Y" width="560" height="315" || [|Where does the Sun gets its energy from?] by Veritasium Published on 6 May 2012 media type="youtube" key="Ux33-5k8cjg" width="560" height="315" || 12 minutes [|The Death of the Sun] | Space Time <span style="font-family: Roboto,Arial,sans-serif; font-size: 10px;">[|PBS Space Time] Published on 21 Feb 2018 <span style="display: block; font-family: Roboto,Arial,sans-serif; font-size: 10px;"><span class="date style-scope ytd-video-secondary-info-renderer" style="color: var(--ytd-video-publish-date-color); font-size: 1.3rem;">media type="youtube" key="iJY3y5_k0do" width="560" height="315" || ** [|How close are we to nuclear fusion] from forbes.com ** [|What is nuclear fusion] from www.iter.org
 * [|How does fusion power the Sun?] [|Science Channel] Published on 4 May 2015

[|Stars] emit an enormous amount of energy through the nuclear fusion of hydrogen into helium. The released energy reaches Earth in the form of electromagnetic radiation. The Sun is losing mass at a rate of 4.3 x 10 9 kg s-1 (3.9 x 10 26 W of energy). The Sun has been radiating this energy for around 4.5 billion years.

//**Task 2:** Take notes after reading the text page 643 - 644 and include the answers of the questions below.// //QUESTIONS)// 1. Describe what **Nuclear Fusion** is: H ydrogen nuclei collide and fuse resulting in a heavier helium nucleus releasing a tremendous amount of energy.

2. Complete the balanced nuclear reaction equation in a star. The major [|fusion reactions] between the deuterium ( 2 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H ) and tritium ( 3 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H ) include (from https://nuclear-energy.net/what-is-nuclear-energy/nuclear-fusion): 1) Merging a nucleus of deuterium with tritium nucleus of a helium nucleus consisting of two [|neutrons] and two [|protons], releasing a 1 [|neutron] and 17.6 MeV of energy.

2 <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; border: none; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px; margin-bottom: 1.4em;"> + 3 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; border: none; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px; margin-bottom: 1.4em;">=> 4 <span style="background-color: #ffffff; border: none; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px; margin-bottom: 1.4em;">He + n + 17.6 MeV

2) Merging Two Deuterium nuclei a Helium nucleus consisting of two [|protons] and one neutron, releasing a 3.2 MeV [|neutron] and obtaining energy. 2 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px;"> + 3 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px;">=> <span style="border: none; font-size: 70%; letter-spacing: 1px; margin: 0px; padding: 0px; vertical-align: super;">3 <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px;">He + n + 3.2 MeV

3) Merging Two Deuterium nuclei, we obtain a nucleus of tritium, a [|proton] and 4.03 MeV. 2 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; border: none; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px; margin-bottom: 1.4em;"> + 2 <span style="background-color: #ffffff; font-family: &#39;Roboto Condensed&#39;,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; border: none; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px; margin-bottom: 1.4em;">=> 3 <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px;">H <span style="background-color: #ffffff; font-family: Roboto Condensed,sans-serif; font-size: 14.4px; letter-spacing: 1px;"> + p + 4.03 MeV

3. Describe why this enormous amount of energy radiating outwards does not tear the outer layers of the Sun apart? The enormous amount of energy radiating outwards, the outward __p ressure __ of the fusion reaction, balances the inward pull of __g ravity __ of all stars. The star is in **equilibrium.**

4. What does it mean by a) binary stars and b) describe the three different categories of binary stars. a) B**inary stars**: Two stars that__ rotate __ about a common __c entre __ of __ mass __. b) **Three different categories of binary stars**: 1) **Visual**: These are binary systems that can be distinguished as two separate stars using a telescope. 2) **Spectroscopic**: Identified from the analysis of the spectrum of light coming from the ‘star’. Over time the wavelengths show a periodic shift or splitting in frequency due to the Doppler Effect: -Due to their orbit, sometimes the stars are moving towards the Earth, sometimes away. -When moving towards the Earth, the spectrum will be blue shifted, when moving away it will be red shifted.

Useful Applets: [|www.astro.cornell.edu] [|Java Astrophysics applets] and [|Other Java Sites] Image from [|phyzx.info] and [|abyss.uoregon.edu]

3) **Eclipsing**: Identified from the analyses of the light from the ‘star’. Over time, the brightness show a periodic variation. The reason for the ‘dip’ in brightness is that as a result of its orbit, one star gets in front of the other. Eg) If the stars were of equal brightness, it would cause the total brightness to drop by 50%.

[|Eclipsing Binary Stars] Lab from the University of Nebrask-Lincoln
 * [|Spectral Types of Stars]
 * [|Luminosity]
 * [|Eclipsing Binary Simulator] ([|swf])

**//Luminosity and Apparent brightness of stars//** [|Star temperatures] from hyperphysics

Recall the intensity as the pewer emitted by a source divided by the area of the sphere over which the energy is equally spread. I = P / 4<span style="font-family: Symbol,sans-serif;">p r 2 This **'Power'** for a star is called **'Luminosity (//L//)'** of the star and **'I'** is the '**apparent brightness (//b//)**'.

b = L/4 <span style="color: #ff0000; font-family: Symbol,sans-serif;">p d 2 Two stars can have the same apparent brightness even if they have different luminosities.
 * Apparent brightness (//b//)**: The power of a star received per unit area. The SI units are W m -2 . (= The amound of energy per second received per unit area.) The brightness of star is inversely proportional to the distance squared. //b// = //L///4<span style="font-family: Symbol,sans-serif;">p r 2

[|Example] 1) The luminosity of the sun is 3.839 x 10^26 W. Calculate the apparent brightness received at Earth. Solution 1) Distance between Earth and the Sun is 150,000,000,000 m (1.5 x 10^11 m). The apparent brightness (//b//) is given by: //b// = //L///4 <span style="color: #ff0000; font-family: Symbol,sans-serif;">p d 2 //b// = 3.839 x 10^26 / 4<span style="font-family: Symbol,sans-serif;">p (1.5 x 10^11)^2 = 1365 W/m 2

cf) **Absolute magnitude**: The luminosity of stars.

//**Task 3:**// Solve Worked example a), b) and c) on page 647 in your text. [|Distance to Cepheids example questions] from astro.unl.edu/classaction/questions/binaryvariablestars/ca_binaryvariablestars_distcepheids.html


 * Luminosity (//L//)**: The total power radiated by a star. The SI units are watts. (= The total amount of energy emitted by the star per second.) The Sun has a luminosity of 3.839 x 10 26 W

Luminosity is a measure of a total power radiated. A black body absords all wavelengths of light and reflects none but it is also a perfect emitter of radiation. Stars can be considered perfect black body radiators. As a result, the luminosity of a star can be calculated using the Stefen - Boltzmann Law: L = σAT 4 L = Luminosity (W) σ (sigma) = Stefen - Boltzmann Constant = 5.67 x 10 -8 W m -2 K -4 A = Surface area of the emitter/star (m 2 ) T = Absolute temperature of the emitter/star (K)

//**Task 4:**// Solve Worked example a), b) and c) on page 648 in your text. <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">**<span style="color: #939698; font-family: arial,helvetica,sans-serif; font-size: 13px;">D.2 – Stellar characteristics and stellar evolution ** media type="youtube" key="jjy-eqWM38g" width="560" height="315" [|Light: Crash Course Astronomy #24] [|CrashCourse] Published on 9 Jul 2015
 * Homework:** Go to IB STUDY GUIDES page 190-194, complete the glossary of new Astrophysics termology in your notebook.
 * media type="youtube" key="zWrttrTFv1I" width="560" height="315" || media type="youtube" key="R30ratQanWw" width="560" height="315" || media type="youtube" key="KNqn5HUP5ME" width="560" height="315" ||
 * [|Apparent Brightness, Luminosity, and Distance] [|Carrie Fitzgerald] Published on 27 Mar 2015 || [|The Age of the Universe] - Sixty Symbols [|Sixty Symbols] Published on 2 Feb 2018 || IB [|Astrophysics distances to stars] [|Studynova] Published on 2 Apr 2015 ||

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">**//Essential idea://** A simple diagram that plots the luminosity versus the surface temperature of stars reveals unusually detailed patterns that help understand the inner workings of stars. Stars follow well-defined patterns from the moment they are created out of collapsing interstellar gas, to their lives on the main sequence and to their eventual death. **//<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Nature of science: //** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Evidence: The simple light spectra of a gas on Earth can be compared to the light spectra of distant stars. This has allowed us to determine the velocity, composition and structure of stars and confirmed hypotheses about the expansion of the universe. (1.11) **//<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Understandings: //** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Stellar spectra <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Hertzsprung–Russell (HR) diagram <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Mass–luminosity relation for main sequence stars <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Cepheid variables <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Stellar evolution on HR diagrams <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Red giants, white dwarfs, neutron stars and black holes <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Chandrasekhar and Oppenheimer–Volkoff limits <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">**//Applications and skills://** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Explaining how surface temperature may be obtained from a star’s spectrum <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Explaining how the chemical composition of a star may be determined from the star’s spectrum <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Sketching and interpreting HR diagrams <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Identifying the main regions of the HR diagram and describing the main properties of stars in these regions <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Applying the mass–luminosity relation <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing the reason for the variation of Cepheid variables <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Determining distance using data on Cepheid variables <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Sketching and interpreting evolutionary paths of stars on an HR diagram <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing the evolution of stars off the main sequence <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing the role of mass in stellar evolution **//<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Theory of knowledge: //** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">The information revealed through spectra needs a trained mind to be interpreted. What is the role of interpretation in gaining knowledge in the natural sciences? How does this differ from the role of interpretation in other areas of knowledge? **//<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Utilization: //** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">An understanding of how similar stars to our Sun have aged and evolved assists in our predictions of our fate on Earth **//<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aims: //** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Aim 4: analysis of star spectra provides many opportunities for evaluation and synthesis <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Aim 6: software-based analysis is available for students to participate in astrophysics research <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">**//Guidance://** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Regions of the HR diagram are restricted to the main sequence, white dwarfs, red giants, super giants and the instability strip (variable stars), as well as lines of constant radius <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">HR diagrams will be labelled with luminosity on the vertical axis and temperature on the horizontal axis <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Only one specific exponent (3.5) will be used in the mass–luminosity relation <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">References to electron and neutron degeneracy pressures need to be made //**<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Data booklet reference: **// <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 11pt; text-align: justify;">λ max T = 2 .9 × 10 −3 m K <span style="color: #ad13da; display: block; font-family: Symbol,sans-serif; font-size: 10pt; text-align: justify;"><span style="font-family: Arial,sans-serif;">L µ M <span style="color: #ad13da; font-family: Symbol,sans-serif; font-size: 70%; vertical-align: super;">3.5 Spectroscopy allows us to analyse colors of celestial objects and determine an object’s temperature, density, spin, motion, and chemical composition. The radiation from stars is NOT a perfect continuous spectrum - there are particular wavelengths missing. The missing wavelengths correspond to the **absorption spectra** of the elements found in that star (although the absorption happens in the outer layers so we can only determine the elements towards the surface of the star). A star that is moving relative to Earth will show a Doppler shift in its absorption spectrum. - Light from stars **receding** from Earth will be red shifted - Light from stars **approaching** Earth will be blue shifted
 * Stella spectra**

As different stars give out different spectra of light, we can use this to classify stars into a **spectral class** (stars that emit the same type of spectrum are assigned to the same spectral class). Each spectral class is denoted by a different letter, with the letter corresponding to the star’s **surface temperature**. The main spectral classes (in order of decreasing surface temperature) are: media type="youtube" key="R6_dZhE-4bk" width="560" height="315" [|Star Classification] - Sixty Symbols [|Sixty Symbols] Published on 12 Oct 2010
 * Classification of stars**
 * O, B, A, F, G, K, M**
 * **Class** || **Surface Temp (K)** || **Colour** ||
 * O || 30,000 - 50,000 || blue ||
 * B || 10,000 - 30,000 || blue - white ||
 * A || 7,500 - 10,000 || white ||
 * F || 6,000 - 7,500 || yellow - white ||
 * G || 5,200 - 6,000 || yellow ||
 * K || 3,700 - 5,200 || orange ||
 * M || 2,400 - 3,700 || red ||

The relationship between the peak wavelength and temperature is given by the Wien displacement law: <span style="font-family: Symbol,sans-serif;">λ max T = 2 .9 × 10 −3 m K
 * Wien displacement law**

If we know the distance to a star we can analyse the light from the star to work out: 1) The chemical composition (by analysing the absorption spectrum) 2) The surface temperature (using a measurement of λmax and Wein’s Law) λmaxT = 2.9 x 10 -3 m K 3) The luminosity (using measurements of the brightness and the distance away) 4) The surface area of the star (using the luminosity, the surface temperature, and the stefan-Boltzmann Law). Total Power Radiated = <span style="font-family: &#39;Cambria Math&#39;,serif;">𝞂 AT 4
 * [|Blackbody Simulator] [[|swf]] from the University of Nebraska-Lincoln

=** Hertzsprung-Russell Diagram **= == <span style="background-color: #ffffff; color: #333333; font-family: Verdana,Verdana,Arial; font-size: 11px;">[|The Hertzsprung diagram where the evolution of sun-like stars is traced.] Credits:ESO Simulator: [|HR Diagram Explorer] ([|swf]) [|Hertzsprung-Russell Diagram Lab] from the University of Nebraska-Lincoln
 * Various Type of Star**
 * **Type of Object** || **Description** ||
 * Red Giant Stars || Red (relatively cool) and large in size. Star in its later stages of life. Source of energy is the fusion of elements other than hydrogen. **Red Supergiants** are even larger. ||
 * White Dwarf Stars || White (relatively hot) and small in size. Final stages of smaller mass star’s life. Fusion is no longer taking place, it is just hot remnants that are cooling down. Eventually, it will be too cold to give out light (**brown dwarf)** ||
 * Cepheid Variables || Unstable stars so they have a regular variation in brightness and luminosity. This is due to oscillations in the size of the star. Quite rare but very useful as the link between the period of brightness and luminosity can be used to calculate distances to galaxies. ||
 * Neutron Stars || Post-supernova remnants of larger mass stars. The gravitational pressure has forced a total collapse and the mass of the neutron star is not composed of atoms (essentially only neutrons). They have enormous density. A rotating neutron star is called a **pulsar**. ||
 * Black Holes || Post-supernova remnants of larger mass stars where gravitational collapse is not stopped. The result is the escape velocity is greater than the speed of light. ||
 * [|Spectral Classification]
 * [|Luminosity]
 * [|Hertzsprung-Russell Diagram]

‘Normal’ stars that are created through **nucleosynthesis** (fusion of different elements). For this to occur, two positively charged particles need to come close enough for interactions to take place. They must be at high temperature (energy) to overcome their repulsion. If a large hydrogen cloud is hot enough, these reactions occur spontaneously creating the outward power of a star (balanced by the inward gravitational pull). As a cloud of gas condenses, the loss of GPE must mean a gain in KE and hence temperature. If the temperature increases enough, the gas will ignite and a star is born. For main sequence stars, there is a correlation between the stars mass (M) and its luminosity (L) - the brighter the star, the more massive: L <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ M 3.5
 * Main sequence star**

<span style="display: block; font-family: Roboto,Arial,sans-serif; font-size: 10px;">**<span style="font-family: arial,helvetica,sans-serif; font-size: 13px;">Cepheid variables ** Very small parallax angle can be measured using satellite observations but even these are limited to stars that are about 100 kpc away. The problem is that when we observe light from very distant stars, we can’t tell the difference between a bright source that is far away and a dimmer source that is closer. When we observe a distant galaxy, all the stars are approximately the same distance away. If we know the luminosity of a source in that galaxy, we could compare this source to other stars to judge their luminosity. This known source is called a **standard candle**.

Cepheid variables are used as standard candles as their periodic compression and contraction produce a periodic variation in luminosity. This variation in luminosity is related to the average absolute magnitude of the Cepheid. From this, the luminosity of the Cepheid can be calculated by observing the variations in brightness.

To estimate the distance to a galaxy, the following process can be used: 1) Locate a Cepheid variable in the sky 2) Measure the variation in brightness over a given period of time 3) Use the luminosity-period relationship for Cepheids to estimate the average luminosity 4) Use the average luminosity, the average brightness and the inverse square law to estimate the distance to the star.
 * __Calculations:__**

PRACTICE QUESTION 1: A Cepheid variable star has a period of 10.0 days and apparent peak brightness of 6.34 x 10 -11 Wm-2. The luminosity of the Sun is 3.8 x 1026 W. Calculate the distance to the Cepheid variable in pc. The peak luminosity is radiated 103.7 times of the Sun with 10 days of period. SOLUTION 1: b = L /4πd2 d2= 3.8 x 1026 x 103.7 / 4 x 3.14 x 6. 34 x 10-11 m distance in pc = 4.88 x 1019 m / 3.08 x 1016 m So, the distance is 1587 pc = 1590 pc

PRACTICE QUESTION 2 (Worked example D13 from K. A. Tsokos): Estimate the distance of the Cepheid whose light curve is shown as below. SOLUTION 2: 740 pc

The mass-luminosity relationship can be used to compare the amount of time different mass stars take before the hydrogen fuel is used: Eg) A star that is 10 times more massive than the Sun will have a luminosity (10) 3.5 = 3,162 times greater than the Sun.
 * Red giant stars**

As the source of the luminosity is the mass of the hydrogen in the star, the larger star, that has 10 times more ‘fuel’ of the Sun is using it at a rate more than 3000 times faster than the Sun (the larger star will use its fuel in 1/300 of the time).

//A star that has a **larger** mass will exist for a **shorter** amount of time.//

A star cannot continue its main sequence forever as at some point the hydrogen fusing into helium will run out and become rare (the reactions take place less often). This causes the star to become no longer in equilibrium and the gravitational force will once again cause the core to collapse. This collapse again causes a rise in temperature of the core allowing the fusion of helium which results in the star massively increasing in size.

If the star has sufficient mass, a red giant can continue to fuse higher and higher elements and the process of nucleosynthesis can continue. <span style="background-color: #ffffff; color: #333333; font-family: Verdana,Verdana,Arial; font-size: 11px;">[|The most metallic layers are in the most internal part of the stars.] Credits:Astro Edu.

<span style="background-color: #ffffff; color: #333333; font-family: Verdana,Verdana,Arial; font-size: 11px;">[|The evolution of a star along its life depend on its original mass.] Credits:students.um.edu
 * Stellar Evolution (possible fates after Red Giant phase)**

There are essentially two (2) possible routes for a red giant to take as its life comes to an end. The path it takes depends on the __ **initial** **mass** __ of the star (and therefore the mass of the remnants that star leaves behind). With no further nuclear reactions taking place gravitational forces continue the collapse of the remnants. An important ‘critical’ mass is called the **Chandrasekhar Limit** and is equal to approximately 1.4 times the mass of the Sun. The fate of the star depends on whether the mass of its remnants is above or below the Chandrasekhar Limit.

If a star has a mass **less than 4 Solar masses**, its remnants will be **less than 1.4 Solar masses** and so is below the Chandrasekhar Limit. Here, a process called **[|electron degeneracy pressure]** prevents the further collapse of the remnants. In this case the red giant forms a **planetary nebula** and becomes a **white dwarf** which ultimately becomes invisible. [|What would the sun look like if all of its fire was somehow extinguished?] [|Khush Bhavsar] , Professor of Astronomy at Fiction [|Answered Mar 13, 2017] If a star is **greater than 4 Solar masses**, its remnants will have a mass **greater than 1.4 Solar masses** and so is above the Chandrasekhar Limit and electron degeneracy pressure is not sufficient to prevent collapse. In this case, the red supergiant experiences a **supernova**. It then becomes a **neutron star** or collapses to a **black hole**. The final stages again depends on mass. Whether a red supergiant turns into a neutron star or a black hole depends on the **Oppenheimer-Volkoff Limit** which is 2 - 3 Solar masses. Remnants **above** this limit turn into a black hole.
 * __Fate 1 - [|White Dwarf]:__**
 * media type="youtube" key="hSHf-0aNd2o" width="560" height="315" || media type="youtube" key="6-fbpMwK-eA" width="560" height="315" ||
 * Helium Fusion and [|Degenerate Electron Pressure] [|Video physical science] Published on 5 Oct 2015 || [|What are neutron stars?](Astronomy) <span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|Socratica] Published on 4 Jan 2015 ||
 * __Fate 2 - Neutron Star or Black Hole:__**

//NOTE :// White dwarfs and neutron stars do **not** have a source of energy to fuel their radiation so they must be constantly losing temperature. The fact that these stars can still exist for millions of years shows that the temperatures and masses involved are enormous.

[|Gallery of astronomical objects and astrophysical phenomena] from cronodon.com

All of the possible evolutionary paths for stars can be represented on a H-R diagram. A common mistake is that stars move along the line that represents the main sequence. However, once a star is formed, it stays at a stable luminosity and spectral class. Class task: Construct H-R diagram, Luminosity (Solar units) vs Temperature (K), including Spica, Sirius A, Sirius B, Sun, Betelgeux, Deneb, Proxima Centuri, Aldebaran, etc. [|gcseastronomy.co.uk]
 * H-R Diagram interpretation**

<span class="view-count style-scope yt-view-count-renderer" style="color: var(--yt-metadata-color);">media type="youtube" key="S-7S98epdmo" width="560" height="315"
 * HOMEWORK)** Take notes on Stellar Evolution for a Star like our Sun while watching the viedoclip of [|Hertzsprung-Russell Diagram and Stellar Evolution below.] Published on 17 Jun 2015<span class="view-count style-scope yt-view-count-renderer" style="color: var(--yt-metadata-color);"> <span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|Bartholomew Science]

media type="youtube" key="nCUS2uNGw7k" width="560" height="315" [|Types of Stars Song] by Mr.Parr <span style="background-color: #ffffff; color: rgba(17,17,17,0.6); font-family: Roboto,Arial,sans-serif;">Published on 20 Aug 2012

=** D.3 – Cosmology **= Article from [|www.sciencemag.org] <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">**//Essential idea://** The Hot Big Bang model is a theory that describes the origin and expansion of the universe and is supported by extensive experimental evidence.

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Occam’s Razor: The Big Bang model was purely speculative until it was confirmed by the discovery of the cosmic microwave background radiation. The model, while correctly describing many aspects of the universe as we observe it today, still cannot explain what happened at time zero. (2.7)
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Nature of science: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">The Big Bang model <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Cosmic microwave background (CMB) radiation <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Hubble’s law <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">The accelerating universe and redshift (z) <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">The cosmic scale factor (R)
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Understandings: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Describing both space and time as originating with the Big Bang <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Describing the characteristics of the CMB radiation <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Explaining how the CMB radiation is evidence for a Hot Big Bang <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Solving problems involving z, R and Hubble’s law <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Estimating the age of the universe by assuming a constant expansion rate
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Applications and skills: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">CMB radiation will be considered to be isotropic with T ≈ 2.76K <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">For CMB radiation a simple explanation in terms of the universe cooling down or distances (and hence wavelengths) being stretched out is all that is required <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">A qualitative description of the role of type Ia supernovae as providing evidence for an accelerating universe is required
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Guidance: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Contributions from scientists from many nations made the analysis of the cosmic microwave background radiation possible
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">International-mindedness: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Doppler effect (see Physics sub-topic 9.5)
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Utilization: //**

<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aim 1: scientific explanation of black holes requires a heightened level of creativity <span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aim 9: our limit of understanding is guided by our ability to observe within our universe
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Aims: //**

Task: These are the formulae that you will use today. As a group, I need you to explain the following: Anybody who wants extra credit can explain to the class, the Doppler effect. You have 40 minutes to complete this task and Ms. Lee expects your presentation during the second half of this class. People at your table must discuss amongst themselves. You are allowed to use any resources you like except wekipedia! I would wish you good luck but all you need is good researching and communicating skills. <span style="color: #58646d; font-family: &#39;Helvetica Neue&#39;,&#39;Lucida Grande&#39;,&#39;Segoe UI&#39;,&#39;Trebuchet MS&#39;,Verdana,Arial,Helvetica,sans-serif; font-size: 14px; vertical-align: baseline;">For LOs 1 & 2, Check [|this link] and do Not miss watching the video clip at last slide. <span style="color: #58646d; font-family: &#39;Helvetica Neue&#39;,&#39;Lucida Grande&#39;,&#39;Segoe UI&#39;,&#39;Trebuchet MS&#39;,Verdana,Arial,Helvetica,sans-serif; font-size: 14px; vertical-align: baseline;">Click these links for LOs [|3 & 4], <span style="color: #58646d; font-family: &#39;Helvetica Neue&#39;,&#39;Lucida Grande&#39;,&#39;Segoe UI&#39;,&#39;Trebuchet MS&#39;,Verdana,Arial,Helvetica,sans-serif; font-size: 14px;">[|LOs 2& 5], [|LOs 3 & 4] <span style="color: #58646d; font-family: &#39;Helvetica Neue&#39;,&#39;Lucida Grande&#39;,&#39;Segoe UI&#39;,&#39;Trebuchet MS&#39;,Verdana,Arial,Helvetica,sans-serif; font-size: 14px; vertical-align: baseline;"> and do questions in each document. <span style="color: #58646d; font-family: Helvetica Neue,Lucida Grande,Segoe UI,Trebuchet MS,Verdana,Arial,Helvetica,sans-serif; font-size: 14px;">For LOs 1 & 5, click <span style="font-family: Helvetica Neue,Lucida Grande,Segoe UI,Trebuchet MS,Verdana,Arial,Helvetica,sans-serif; font-size: 14px;">[|here] <span style="color: #58646d; font-family: Helvetica Neue,Lucida Grande,Segoe UI,Trebuchet MS,Verdana,Arial,Helvetica,sans-serif; font-size: 14px;">to try out the fun of Kahoot and calculations. <span style="color: #58646d; font-family: &#39;Helvetica Neue&#39;,&#39;Lucida Grande&#39;,&#39;Segoe UI&#39;,&#39;Trebuchet MS&#39;,Verdana,Arial,Helvetica,sans-serif; font-size: 14px; vertical-align: baseline;">Thank you all for your hard work!
 * //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Data booklet reference: //**
 * # Describing both space and time as originating with the Big Bang
 * 1) Describing the characteristics of the CMB radiation
 * 2) Explaining how the CMB radiation is evidence for a Hot Big Bang
 * 3) Solving problems involving z, R and Hubble’s law
 * 4) Estimating the age of the universe by assuming a constant expansion rate ||

Use the applet in the webpage to make measurments of all the galaxies. Measure their angular size and their observed redshift recovering [|Hubble's Original Data] from jersey.uoregon.edu [|Cosmic Microwave Background Explained] Space Time | PBS Digital Studios <span class="view-count style-scope yt-view-count-renderer" style="color: var(--yt-metadata-color);"><span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|PBS Space Time] Published on 25 Mar 2015 || media type="youtube" key="1kqWWLpyMpY" width="560" height="315" Exploring the Dark Universe: [|Cosmic Microwave Background] <span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|American Museum of Natural History] Published on 19 Dec 2013 || media type="youtube" key="QXfhGxZFcVE" width="560" height="315" [|How do you measure the size of universe?] | Space Time | PBS Digital Studios [|PBS Space Time] Published on 25 Feb 2015 || media type="youtube" key="3NTAS3k78OQ" width="560" height="315" [|From the Big Bang] to Now [|DrPhysicsA] Published on 4 Feb 2012 || <span style="background-color: #ffffff; color: rgba(17,17,17,0.6); font-family: Roboto,Arial,sans-serif;">[|The nearest star] <span style="background-color: #ffffff; font-family: Helvetica,Arial,sans-serif; font-size: medium;">[|Proxima Centauri] from nasa.gov media type="youtube" key="nhhdkYFmd7A" width="560" height="315" [|Creating the Elements - Sixty Symbols] Published on 16 Nov 2009 How do stars and supernovae create the elements. [|Sixty Symbols] [|IB Physics Astrophysics Definitions and Concepts] Google document [|Combined IB SL Physics Astro option qs 09-10.pdf] - THESE ARE QUESTIONS FROM RECENT SL PAPERS [|Combined IB SL Physics Astro option qs 09-10 MS.pdf] - AND THE SOLUTIONS - QUESTIONS ON HL ASTRO OPTION - The solutions to the above questions <span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 8587.5px; width: 1px;"> <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;">Stars emit an enormous amount of energy through the nuclear fusion of hydrogen into helium: Through analyses, the mass of the products is less than the mass of the reactants. Using E = mc <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: super;">2 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;">, we can work out the Sun is losing mass at a rate of 4.3 x 10 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: super;">9 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;"> kg s <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: super;">-1 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;"> (3.9 x 10 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: super;">26 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;"> W of energy). These reactions take place in the core of the star.
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