IB+DP+Option+D+Astrophysics+AHL

=AHL 10hours= = D.4 – Stellar processes = **//Essential idea://** The laws of nuclear physics applied to nuclear fusion processes inside stars determine the production of all elements up to iron. **//Nature of science: //** Observation and deduction: Observations of stellar spectra showed the existence of different elements in stars. Deductions from nuclear fusion theory were able to explain this. (1.8) **//Understandings: //** The Jeans criterion Nuclear fusion Nucleosynthesis off the main sequence Type Ia and II supernovae **//Applications and skills://** Applying the Jeans criterion to star formation Describing the different types of nuclear fusion reactions taking place off the main sequence Applying the mass–luminosity relation to compare lifetimes on the main sequence relative to that of our Sun Describing the formation of elements in stars that are heavier than iron including the required increases in temperature Qualitatively describe the s and r processes for neutron capture Distinguishing between type Ia and II supernovae **//Guidance://** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Only an elementary application of the Jeans criterion is required, ie collapse of an interstellar cloud may begin if M > Mj <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Students should be aware of the use of type Ia supernovae as standard candles <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">**//Aims://** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Aim 10: analysis of nucleosynthesis involves the work of chemists How do stars and supernovae create the elements. [|Sixty Symbols] || [|M1 - Crab Nebula] - Deep Sky Videos <span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|DeepSkyVideos] Published on 19 Jan 2012 The remnant of a Type II supernova observed by Chinese in 1054. It was visible for weeks even during the daytime. || [|Type II Supernova] - Sixty Symbols <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);">[|Sixty Symbols] Published on 29 Mar 2012 || [|Stellar Nucleosynthesis] [|matus1976] Published on 24 Apr 2012 || [|Why is the Solar System Flat?] [|minutephysics] Published on 9 Jan 2014 || The Jeans Criterion Stars form out of nebulae, interstellar clouds of dust. Such clouds might exist for millions of years in stable equilibrium. Eventually, a collision with another cloud or a shock-wave given out by a supernova exploding in the vicinity of the cloud disturbs it. This could result in the cloud becoming unstable and it could start to collapse. It is known that they are often very cold, just a few kelvin above absolute zero, by examining the spectra. At any given point in time, the total energy associated with the gas cloud can be thought of as a combination of: 1) the negative GPE (EP), which the cloud possesses as a result of its **mass** and **density** 2) the positive random KE (EK), that the particles in the cloud possess as a result of its **temperature**
 * media type="youtube" key="nhhdkYFmd7A" width="560" height="315" || media type="youtube" key="lBfCQt6TTms" width="560" height="315" || media type="youtube" key="LXUdRGw8UP4" width="560" height="315" || media type="youtube" key="ZWL0whGjopU" width="560" height="315" || media type="youtube" key="tmNXKqeUtJM" width="560" height="315" ||
 * [|Creating the Elements - Sixty Symbols] Published on 16 Nov 2009

When the gravitational energy of a given mass of gas exceeds the average kinetic energy of the random thermal motion of its molecules, the gas becomes unstable and tends to collapse: The cloud will remain gravitationally bound together if: E P + E K < 0 //**T**// is temperature //**R**// is the radius of the gas cloud //**M**// it its mass || Using this information allows us to predict that the collapse of an interstellar cloud may begin if it’s mass is greater than a certain critical mass called the **Jeans criterion (M J ).** For a given cloud of gas, M J is dependent on the cloud’s density and temperature and the cloud is more likely to collapse if it has: Large Mass Small Size Low Temperature
 * [[image:Jeans criterion derivation 1.PNG width="122" height="50"]] || [[image:Jeans criterion derivation 2.PNG width="376" height="50"]] ||
 * where //<span style="font-family: Comic Sans MS,cursive;">k // is Boltzmann's constant
 * //N//** is the number of particles

The Jeans criterion states a collapse can start if: M > M J

Main sequence stars fuse hydrogen nuclei to form helium nuclei by the proton-proton chain reaction. This is the process for small stars (masses just above 1 Solar Mass). However, an alternative process called **CNO (carbon-nitrogen-oxygen)** can take place at higher temperatures in larger mass stars. In this reaction, carbon, nitrogen and oxygen are used as catalysts to aid the fusion of protons into helium nuclei. [|Image from www.atnf.csiro.au]
 * //Nuclear fusion//**

__//Time spent on the main sequence//__ For the entire time a star is in the main sequence, hydrogen ‘burning’ is the source of energy that allows the star to remain in hydro-static equilibrium and have a constant luminosity. A time that a star exists on the main sequence ( TMS ) is determined by its mass: As L <span style="font-family: Symbol,sans-serif;">µ M 3.5, E/t <span style="font-family: Symbol,sans-serif;">µ M 3.5 => Mc 2 / t <span style="font-family: Symbol,sans-serif;">µ M 3.5 => t <span style="font-family: Symbol,sans-serif;">µ M - 2.5

PRACTICE 1: How long would a star with 100 times the mass of the Sun be expected to last in the main sequence? The Sun is expected to have a main sequence lifetime of approximately 10 10 years. SOLUTION: Time on main sequence for 100 solar mass star = 10 10 x (1 / 100 ) 2.5 = 10 5 years

PRACTICE 2: Explain why a star having a mass of 50 times the solar mass would be expected to have a lifetime of many times less than that of the Sun. SOLUTION: The more massive stars will have much more nuclear material, initially hydrogen. Massive stars have greater gravity so equilibrium is reached at a higher temperature at which the outward pressure due to radiation and the hot gas will balance the inward gravitational pressure. This means that fusion proceeds at a faster rate than in stars with lower mass - meaning that the nuclear fuel becomes used up far more rapidly. PRACTICE 3: By referring to the mass-luminosity relationship, suggest why more massive stars will have shorter lifetimes. SOLUTION: As the luminosity of the star is the energy used per second, stars with greater luminosity are at higher temperatures and will use up their fuel in shorter periods of time. The luminosity of a star is related to its mass by the relationship L <span style="color: #ffffff; font-family: Symbol,sans-serif;">µ M 3.5. Therefore, increasing the mass raises the luminosity by a much larger factor which in turn means the temperature is much higher. At the higher temperature the fuel will be used in a much shorter time. //**Nucleosynthesis off the main sequence**// As the main sequence continues, the star's hydrogen centre will eventually all fuse into helium. When this happens, the star no longer produces the core energy required to combat the gravitational forces of the star. This will cause the core to compress. This compression increases the core temperature, which increases the temperature of the surround hydrogen, causing the hydrogen to begin to fuse. When fusion of carbon starts the star swells into what is called a Red Giant.

For as long as a star is in the main sequence, hydrogen burning is its source of energy. For high mass stars, helium burning can take place where a new equilibrium state is reached (Red Giant or Red Supergiant phase). A common process by which helium is converted is a series of nuclear reactions called the **triple alpha process** in which carbon is produced:
 * [[image:triple alpha process equation.PNG width="129" height="57"]] || 1) 2 helium nuclei fuse into a beryllium nucleus and gamma ray

2) The beryllium nucleus fuses with another helium nucleus to produce a carbon nucleus and gamma ray || Some of the carbon produced in the triple alpha process can go on to fuse with another helium nucleus to produce oxygen and again release energy. In very high mass stars, gravitational contraction means that the temperature of the core can continue to rise and more massive nuclei can continue to be produced: <span style="font-family: Times New Roman,serif;">- Carbon burning can produce neon, magnesium and oxygen <span style="font-family: Times New Roman,serif;">- Oxygen burning can produce sulphur. Many reactions are possible and other heavy nuclei (silicon and phosphorous) can be produced. Fusion cannot produce elements heavier than iron, since the binding energy per nucleon peaks near iron and further fusion is not energetically possible as it requires more energy to fuse. <span style="background-image: url(/i/a.gif);">[|The most metallic layers are in the most internal part of the stars.] Credits:Astro Edu. Some of these alternative nuclear reactions also produce neutrons which can easily be captured by other nuclei to form a new isotope in a process called **neutron capture**. <span style="display: block; font-family: Roboto,Arial,sans-serif; font-size: 10px;">Stars can forge elements using two important methods - the slow and rapid processes of adding neutrons to an atomic nucleus || 45 minutes [|Nuclear Fusion In Stars] [|DrPhysicsA] Published on 7 Nov 2014 || [|Triple alpha process] from hyperphysics || Lecture 15 - [|Stellar Evolution] [|AST102IN Spring 2014] Published on 30 Mar 2014 || Many of the reactions that take place in the core of stars also involves neutrons as it is very easy for them to interact with other nuclei due to their lack of charge. When a nucleus captures a neutron, it is said to be **neutron rich**. Given enough time, most of these neutron rich nuclei would undergo beta decay where the neutron changes into a proton, emitting an electron and an antineutrino: This is known as **slow neutron capture (s-process)**. The overall result is a new heavier element. An alternative process, **rapid neutron capture (r-process)**, takes place when neutrons are present in vast numbers so there is not enough time for neutron rich nuclei to undergo beta decay before several more neutrons are captured. The result is for very heavy nuclei to be created. The r-process generally occurs during supernova where elements that are heavier than iron (uranium and thorium) can be created at these very high temperatures and densities. NOTE - for elements larger than iron to be formed, energy needs to be added to the system which generally only happens during a supernova explosion. Type Ia supernovae result from accretion of matter between two stars in a binary star. One of the stars is a white dwarf and the other is either a giant star or a smaller white dwarf. The formation of these supernovae show up as a rapid increase in brightness followed by a gradual tapering off. Type II supernovae consist of single massive stars in the final stages of their evolution. These classes of supernovae produce light curves with different characteristics.
 * media type="youtube" key="KlBG_A4Djp4" width="560" height="315" || media type="youtube" key="TtIeozyQ3Is" width="560" height="315" || [[image:triple alpha process.PNG width="349" height="319"]] || media type="youtube" key="hbF_ELJ0Ues" width="560" height="315" ||
 * [|The s-Process] - Sixty Symbols <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);">[|Sixty Symbols] Published on 25 Oct 2016
 * //Neutron Capture - synthesis of heavy elements//**
 * //[|Supernovae]//** from Britannica.com
 * **Type II supernovae** || **Type Ia supernovae** ||
 * After approximately 10 million years, for stars of 8 - 10 solar masses, all the hydrogen in the core has converted into helium and hydrogen fusion can now only continue in a shell around the helium core. the core undergoes gravitational collapse until its temperature is high enough for fusion of helium into carbon and oxygen. This phase lasts for about a million years until the core's helium is exhausted; it will then contract again under garvity, causing it to heat up and allowing the fusion of carbon into heavier elements. It takes about 10 thousand ears until the carbon is exhusted. This pattern continues, with each heavier element lasting for successively shorter lengths of time, until silicon is fused into iron 56 taking a few days. At this point the star is not in hydrostatic equilibrium because there is now little radiation pressure to oppose gravity. On reaching the Chandrasekhar limit of 1.4 M,[| electron degeneracy] [|pressure] is insufficient to oppose the collapse and the star implodes producing neutrons and neutrinos. The implosion is opposed by a [|neutron degeneracy] pressure that causes an outward shock wave. This passes through the outer layers of the star causing fusion reactions to occur. Although this process lasts just a few hours it results in the heavy elements being formed. As the shock wave reaches the edge of the star, the temperature rises almost instantly to 20000 K and the star explodes, blowing material off as a supernova. || These are very useful to astrophysicists as they always emit light in a predictable way and behave as a standard candle for measuring the distance of the galaxy in which the supernova occurs. Given the immense density of the material within a white dwarf, the gravitational field is unimaginabley strong and attracts matter from the companion star. When the mass of the glowing white dwarf eceeds the Chandrasekhar limit of 1.4 solar masses, the star collapses under gravity. The fusion of carbon and oxygen into nickel generates such radiation pressure that the star is blown apart, reaching a luminosity of 10 10 times that of the Sun. Because the chin reaction always occurs at this mass we know how bright the supernova actually is and, by comparing ti with the apparent brightness observed on Earth, we can estimate the distance of the supernova's galaxy up to distances of 1000 Mpc. After the explosion the ejected material continues to expand in a shell around the remant for thousands of years until it mixed with the interstellar material, giving the potential to form a new generation of stars.

[|Chandrasekhar limit for white dwarfs] from hyperphysics.phy-astr.gsu.edu || [|Type Ia supernova Image] (left) from wikipedia, Tycho's Supernova Remnant (right) NASA'S Chandra Finds New Evidence on Origin of Supernovas NASA/CXC/Chinese Academy of Sciences/F. Lu The explosion happened in 1572.
 * [[image:supernova-space.com width="741" height="832"]] || [[image:Type Ia supernova.png width="701" height="737"]]

Source to the right [|SPACE.com: All about our solar system, outer space and exploration] || [|Eclipsing Binary Stars] Lab from the University of Nebrask-Lincoln
 * [|Light Curves]

The two types of supernova are based on their **light curves** - a plot of how their brightness varies with time. Type Ia and Type II supernovae can be distinguished by observers on Earth from the manner in which the stars emit light. The type Ia emits light up to 10 10 times the luminosity of the Sun; this rapidly reaches a maximum and then gradually tails off over six months or so. The Type II emits light up to 10 9 times the luminosity of the Sun; however, the burst falls a little before reaching a slight plateau where it stays for some days before falling away more rapidly. The light curves for class Ia and II supernovae are shown in figure below. Graph from [|www.physics.byu.edu] PRACTICE 5: Outline the difference between a Type Ia and a Type II supernova.

PRACTICE 6: a) What is meant by a standard candle? A standard candle is a star of known luminosity that can be used to calculate its distance when compared with its apparent brightness. b) Explain how a Type Ia supernova can be used as a standard candle? As all Type Ia supernova occur when the mass reaches the Chandrasekhar mass they are all of the same peak luminosity. By measuring the apparent brightness, the distance of the supernova can be calculated. ( b = L / 4<span style="font-family: Symbol,sans-serif;">p d 2 )

** D.5 – Further cosmology ** <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Essential idea: <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">The modern field of cosmology uses advanced experimental and observational techniques to collect data with an unprecedented degree of precision and as a result very surprising and detailed conclusions about the structure of the universe have been reached.

//<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;">Cognitive bias: According to everybody’s expectations the rate of expansion of the universe should be slowing down because of gravity. The detailed results from the 1998 (and subsequent) observations on distant supernovae showed that the opposite was in fact true. The accelerated expansion of the universe, whereas experimentally verified, is still an unexplained phenomenon. (3.5) //<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;">The cosmological principle <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Rotation curves and the mass of galaxies <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Dark matter <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Fluctuations in the CMB <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">The cosmological origin of redshift <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Critical density <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Dark energy <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;">Describing the cosmological principle and its role in models of the universe <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing rotation curves as evidence for dark matter <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Deriving rotational velocity from Newtonian gravitation <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing and interpreting the observed anisotropies in the CMB <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Deriving critical density from Newtonian gravitation <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Sketching and interpreting graphs showing the variation of the cosmic scale factor with time <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Describing qualitatively the cosmic scale factor in models with and without dark energy <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;">Students are expected to be able to refer to rotation curves as evidence for dark matter and must be aware of types of candidates for dark matter <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Students must be familiar with the main results of COBE, WMAP and the Planck space observatory <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Students are expected to demonstrate that the temperature of the universe varies with the cosmic scale factor as T R1 _ <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">//International-mindedness:// <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">This is a highly collaborative field of research involving scientists from all over the world <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;"> <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">//Theory of knowledge:// <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Experimental facts show that the expansion of the universe is accelerating yet no one understands why. Is this an example of something that we will never know? //<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 2: unlike how it was just a few decades ago, the field of cosmology has now developed so much that cosmology has become a very exact science on the same level as the rest of physics <span style="color: #ad13da; display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: justify;">Aim 10: it is quite extraordinary that to settle the issue of the fate of the universe, cosmology, the physics of the very large, required the help of particle physics, the physics of the very small //<span style="color: #ad13da; font-family: Arial,sans-serif; font-size: 10pt;">Data booklet reference: // 1) **Isotropic** - the Universe looks the same in every direction from all positions. Eg) If you look in any direction from any position, the Universe will consist of random distributions of galaxies and galaxy clusters. 1) **Homogenous** - local distributions of galaxies that exist in one region of the Universe turns out to be the same distribution in all regions. Eg) Providing a large enough volume of space is considered, the number of galaxies and galaxy clusters in that volume will effectively be the same in all regions of the Universe.
 * media type="youtube" key="1loJTy6bOu8" width="560" height="315" || media type="youtube" key="QAa2O_8wBUQ" width="560" height="315" ||
 * [|Cosmic Microwave Background Radiation] <span style="font-family: Roboto,Arial,sans-serif; font-size: var(--yt-formatted-string-endpoint_-_font-size);">[|Sixty Symbols] P ublished on 26 Mar 2013 || [|What is Dark Matter and Dark Energy?] <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);">[|Kurzgesagt – In a Nutshell] Published on 6 Aug 2015 ||
 * The** **cosmological principle** is a pair of assumptions about the structure of the Universe upon which current models are based (providing only large scale structures are considered).

CMB radiation is essentially **isotropic** implying that the matter in the early Universe was uniformly distributed with no random temperature variations. If this was true, we would expect the development of the Universe to be identical everywhere and matter would still be uniformly distributed. However, this is not the case as matter is concentrated into stars and galaxies. Further analyses of CMB reveals tiny fluctuations (**anisotropies**) in the temperature distribution - usually a few <span style="font-family: &#39;Cambria Math&#39;,serif;">𝜇 K. The anisotropies in the CMB are crucial in understanding the formation of structures. There are small variations <span style="font-family: Symbol,sans-serif;">D T in temperature, of the order of <span style="font-family: Symbol,sans-serif;">D T/T <span style="font-family: Symbol,sans-serif;">µ 10 -5, where T = 2.723 K. These variations in temperature are related to variations in the density of the universe. With perfectly uniform temperature and density in the universe, stars and galaxies would not form.
 * CMB anisotropies**

Variation in CMB is observed by the **W**ilkinson **M**icrowave **A**nisotropy **P**robe (WMAP). The minute differences in temperature implies minor differences in density, which allow structures to be developed as the Universe expands. A map from the Plank satellite observatory, showing CMB fluctuations in temperature below displays minor observed variations in CMB throughout the visible Universe. [|Fluctuations in temperature of the CMB] according to ESA's Plank satellite observatory <span style="background-color: #ffffff; display: block; font-family: Georgia,Cambria,"Times New Roman",Times,serif; font-size: 21px;"> COBE, the first CMB satellite, measured fluctuations to scales of 7 º only. WMAP was able to measure resolutions down to 0.3 ° in five different frequency bands, with Planck measuring all the way down to just 5 arcminutes (0.0 8° ) in nine different frequency bands in total. ([|Images credit]: NASA/COBE/DMR; NASA/WMAP science team; ESA and the Planck collaboration) The stars in a galaxy rotate around their common centre of mass. Different models can be used to predict how the speed varies with distance from the galactic centre. A simple model to explain the different speeds of the rotation of stars near the galactic centre assumes that the density of the galaxy near the centre (<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ ) is constant. A star of mass (//m//) feels a resultant force of gravitational attraction towards the centre. The value of this resultant force is the same as if the total mass (//M//) of all the stars that are closer to the galactic centre were concentrated in the centre. An important point to note is that the net effect of all the stars that are orbiting at a radius that is greater than (//r//) sums to zero. The star at a given distance (//r//) from the centre will orbit in circular motion because its centripetal force is provided by the gravitational attraction: GMm / r 2 = mv 2 / r The total mass of stars that orbit closer than this star (//M//) is given by: //M// = volume x density = 4/3 πr 3 x //<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ // v 2 = ( 4/3 Gπr3//<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ // ) / r = 4/3 πG//<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ // //r// 2 v ∝ r
 * Rotation curves and the mass of galaxies**
 * 1.** **Near the galactic centre**

Galaxies rotate around their centre of mass and the speeds of this rotation can be calculated for individual stars from an analysis of the star’s spectra. A **rotation curve** for a galaxy show how this orbital speed varies with distance from the galactic centre. Most galaxies show:
 * 1) an initial linear increase in orbital velocity with distance within the galactic centre
 * 2) a flat or slightly increasing curve showing a roughly constant speed of rotation away from the galactic centre.

Far away from the galactic centre, observations of the number of visible stars show that the effective density of the galaxy has reduced so much that individual stars at these distances can be considered to be freely orbiting the centre mass and to be unaffected by their neighbouring stars. In this situation: v 2 = GM / r where M is the mass of the galaxy v <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ 1/r Try out [|Spiral Galaxy Rotation Curve Builder] applet by Bethany Baldwin-Pulcini and Steven Hyatt
 * 2. Far away from the galactic centre**
 * [[image:The rotation curve for the spiral galaxy M33.PNG width="552" height="317"]] || media type="youtube" key="o_0oB9CHvjc" width="560" height="315" ||
 * Image credit: Oxford IB Diploma by David Homer and Michael Bowen-Jones || [|Introductory Astronomy: Dark Matter] [|P.E. Robinson] Published on 19 Apr 2013 ||

Comparisons with observations of real galaxies show agreement with model 1 (near galactic centre) but no agreement with model 2 (far from galactic centre). Image from [|Nasa's cosmic times] [|Edge on galaxy NGC 4565]. This is a galaxy that is what the Milky Way would look like from a distant vantage point. (Image courtesy of Canada-France-Hawaii Telescope / Coelum) Image from www.kcvs.ca

Observed rotation curves for real galaxies agree with theoretical models within the galactic centre but is **not** observed to decrease with distance away from the centre as would be expected. Instead, the orbital velocity is roughly constant whatever the radius: v 2 = GM / r M/r = constant or M <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ r Thus the total mass that is keeping the star orbiting in its galaxy must be increasing with distance from the galactic centre. The thought that mass can increase due to distance is certainly not true for a visible mass (i.e. star) so the suggestion is that there must be **dark matter**. In this situation it would have to be concentrated outside of the galactic centre forming a halo around the galaxy. Further evidence suggests that only a very small amount of this matter could be made up of ordinary matter (protons and neutrons).
 * Evidence for dark matter**

__//Dark matter://__ 1) gravitationally attracts ordinary matter 2) does not emit radiation and cannot be inferred from its interactions 3) is unknown in structure 4) makes up the majority of the Universe with less than 5% of the Universe made up of ordinary matter.

Astrophysicists are trying to come up with theories to explain why there is so much dark matter and what it consists of. These theories include: 1) The matter could be found in Massive Astronomical Compact Halo Objects (MACHOs). There is some evidence that lots of ordinary matter exists in these groupings (low mass ‘failed’ stars, high mass planets, black holes). These would produce little or no light. Evidence suggests these could only account for a small portion of the dark matter. 2) There could be new particles that we do not know about called **W**eakly **I**nteracting **M**assive **P**articles (**WIMPs**). 3) Another thought is that our current theories of gravity are incorrect. Some theories try to explain the missing matter as simply a failure of our current theories to consider everything.

The expansion of the Universe means that the wavelength of any radiation (CMB) that has been emitted in the past has been ‘stretched’. The spectrum of CMB radiation received corresponds to black-body radiation at a temperature of 2.73 K The calculation uses Wein’s law to link the peak wavelength ( λ max ) of the radiation to the temperature (T) of the black body: λ max = (2.9 x 10 -3 ) / T λ max <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ 1/T When the radiation was emitted, the temperature of the Universe was much hotter, the cosmic scale factor (R) was much smaller and λmax was also proportionally much smaller. Since the stretching of the Universe is the cause of the change in wavelength, then the ratio of cosmic scale factors at two different times must be the same as the ratio of peak wavelengths: λ max <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ R 1/T <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ R or T <span style="font-family: &#39;Cambria Math&#39;,serif;">∝ 1/R Worked example D.24) The protons of CMB radidation observed today are thought to have been emitted at a time when the temperature of the universe was about 3000 K. Estimate the size of the universe then compared with its size now. from K.A. Tsokos Physics for the IB Diploma text page 41: SOLUTION: T ∝ 1 / R, T 0 / T = R / R 0 = 3000 / 2.7 =1100, so the universe then was about 1100 times smaller.
 * Cosmic Scale Factor (R) and Temperature**

The theoretical value of density that would create a **flat** Universe is called the **critical density (****<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ c )**. Its value is not certain because the current rate of expansion is not easy to measure but is estimated to have an order of magnitude around 10 -23 kg m -3 (a few proton masses every cubic metre). The density of the Universe is not easy to measure as the majority of the mass in the Universe is dark matter however, it can be estimated using Newtonian gravitation. The total energy of a galaxy (E T ) is given by: E T = E K + E P Kinetic Energy (E K ) = ½ mv 2 where Hubble’s Law states v = H o r E K = ½ m(H o r) 2 Potential Energy (E P ) = -GMm / r but M = Volume x density = (4/3) π r 3 <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ E P = - G4πr 3 <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ m / 3r = - 4Gπr 2 <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ m / 3 If E T is positive, the galaxy would escape the gravitational attraction - the Universe is **open**. If E T is negative, the galaxy will eventually fall back in - the Universe is **closed.** If E T is exactly zero, the galaxy will take an infinite time to be bought to rest - the Universe is **flat**. This will only occur when the density of the Universe is equal to the critical density (<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ c ). ½ m(H o r) 2 = 4 G π r 2 <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ m / 3 <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ c = 3H o 2 / 8πG Critical density:
 * Critical Density (****<span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ c )**

There is no Big Bang in the static universe. The universe always has the same size. Before Hubble discovered the expanding universe, Einstein missed the great chance of theoretically predicting an expanding universe. He later adding the cosmological constant which is related to a vacuum energy that is present in all space. It is now referred to as dark energy. As a result of the Big Bang, other galaxies are moving away from us. If there were no forces between them, this expansion would be constant. The expansion of the Universe however, cannot have been uniform. The force of gravity acts between all masses. This means that if two masses are moving apart from one another there is a force of attraction pulling them back together. This force must have slowed the expansion down in the past. What it is going to do in the future depends on the current rate of expansion and the density of matter in the Universe. 1) **Open Universe** - continues to expand forever. The force of gravity slows this expansion a little bit but is not strong enough to stop the expansion entirely. This would happen with a **low density** Universe. 2) **Closed Universe** - expansion stops and then the Universe collapses back on itself. This would happen in a **high density** Universe. 3) **Flat Universe** - the mathematically possible event between open and closed. The force of gravity keeps on slowing the expansion but will take an infinite time to come to rest. This would only occur if the Universe had a singular **specific density**.
 * Class Task :** //Research on a static universe and describe what it is.//


 * The cosmic scale factor and time**
 * Density parameter <span style="font-family: Symbol,sans-serif;">W



...... CLOSED SPACE ( <span style="font-family: Symbol,sans-serif;">W > 1; <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ > ⍴ c ) ..................... FlLAT SPACE ( <span style="font-family: Symbol,sans-serif;">W <span style="font-family: &#39;Cambria Math&#39;,serif;">= <span style="font-family: Symbol,sans-serif;">1; <span style="font-family: &#39;Cambria Math&#39;,serif;">⍴ = ⍴ c ) ................................. OPEN SPACE <span style="font-family: &#39;Cambria Math&#39;,serif;">( <span style="font-family: Symbol,sans-serif;">W < 1; <span style="font-family: &#39;Cambria Math&#39;,serif;"> ⍴ c <span style="font-family: &#39;Cambria Math&#39;,serif;">< ⍴ c ) || ||  || Observations using type Ia supernovae as standard candles has provided evidence that the Universe’s rate of expansion is increasing. Currently, there is no accepted explanation for this observation however the name given for the Universe’s accelerating expansion is called **dark energy**. Experimental evidence implies the existence of both dark matter and energy but physicists are yet to agree a theoretical basis that explains their existence. The existence of dark energy counteracts the attractive force of gravity. This will cause the cosmic scale factor to increase over time. The graph below compares how a flat Universe is predicted to develop with and without dark energy. Effect of dark energy on the cosmic scale factor. ( Credit: IB Oxford Study Guide page 212.)
 * <span style="background-color: #ffffff; color: #006699; font-family: Arial,Helvetica,Geneva,verdana,SunSans-Regular,sans-serif; font-size: 11px;"> [|Space curvature of the Universe] Credit: Lumen Astronomy || [|Variation of R for different density parameters] Image credit:http://www.nat.vu.nl/~wimu/FundConst-Notes.html || Credit: Oxford IB Diploma by David Homer and Michael Bowen-Jones ||
 * [|Dark energy]**
 * Dark matter** is hypothesized to explain the ‘missing matter’ that must exist within galaxies. Dark matter **adds to the attractive force of gravity acting within galaxies** implying more unseen mass than had been previously expected.
 * Dark energy** is hypothesized to explain the accelerating Universe. Dark energy **opposes the attractive force of gravity between galaxies**. The resulting increase in energy implies an unseen source of energy.

Three recent experiments that have studied the CMB in detail have together added a great deal to our understanding of the Universe: 1) NASA’s **Co**smic **B**ackground **E**xplorer (COBE) 2) NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) 3) ESA’s Planck space observatory
 * Current observation**

Together, these experiments have: In conclusion, the Universe: 1) is flat 2) has a density that is, within experimental error, very close to the critical density 3) has an accelerating expansion 4) is composed mainly of dark matter and dark energy
 * mapped the anisotropies of the CMB in great deal with precision
 * discovered that the first generation of stars to shine did so 200 million years after the Big Bang, much earlier than previously expected
 * calculated the age of the Universe as 13.75 __+__ 0.14 billion years old
 * calculated the Hubble constant to be 67.15km s -1 Mpc -1
 * showed that their results were consistent with the Big Bang and specific inflation theories
 * showed that the Universe is flat (E T = 0)
 * calculated the Universe to be composed of 4.6% atoms, 23% dark matter and 71.4% dark energy.

Interesting article to read from sci-news.com ( June 2017) 1. [|The mass of the white dwarf star Stein 2051B] determined by observing the changing position of another closely aligned star ('The bending of light by gravitation'). 2. Dr. Kailash Sahu 3. Albert Einstein’s theory of general relativity. 4. May 29, 1919, Arthur Eddington’s observations 5. [|Chromoscope]

<span style="background-color: #ffffff; color: #236cbf; font-family: Lora,serif; font-size: 16px; vertical-align: baseline;">[|Frequently asked questions for Astronomy] www.astro.cornell.edu [|Cosmic Microwave Background] [|Animations for Understanding Astrophysics] from wittman.physics.ucdavis.edu/Animations/index.html [|Astronomy Simulations and Animations] from astro.unl.edu/animationsLinks.html [|Quizzes on Astrophysics] from astro.unl.edu Astro [|Project groups] from cse.unl.edu/~astrodev/flashdev2/

Published on 17 Dec 2016 ||  ||
 * media type="youtube" key="V1JuWufdoxw" width="560" height="315" || media type="youtube" key="p1KdGItgPhg" width="560" height="315" || media type="youtube" key="gE9aFOF-Od8" width="560" height="315" ||  ||
 * 30 mins BBC - The Sky at Night - [|The Invisible Universe 2018] Documentary [|Anand Singh] Published on 15 Jan 2018 || 45 minutes [|Dark Matter and Dark Energy] HD [|ScienceNET] Published on 23 Jan 2014 || 55 minutes [|Hidden Universe - Dark Matter] [|Wisdom Land]

<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 2818px; width: 1px;"> <span style="direction: ltr; language: en-AU; line-height: 115%; margin-bottom: 16.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0pt; text-align: center; unicode-bidi: embed;"><span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;">How long would a star with 100 times the mass of the Sun be expected to last in the main sequence? The Sun is expected to have a main sequence lifetime of approximately 10 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: super;">10 <span style="font-family: Arial; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal;"> years.