Spring 2018 ASTR 1200-001 Homepage

  Spring 2018 ASTR 1200-001 General Astronomy: Stars & Galaxies: Weekly Summaries

Week 1 (Jan 17): Our Place in the Universe

• Register your clicker online.
• Read Chapter 1 of “Cosmic Perspective”.
• Appendix C of Cosmic Perspective reviews powers of ten, scientific notation, units, and ratios, all of which are needed to do the homeworks.
• Our cosmic address.
• Did you know that Baseline Road in Boulder is at exactly longitude 40° North? The view at 40°N 105°W.
• The Sun is a star.
• An Astronomical Unit (au) is the distance between the Earth and the Sun. First measured reliably by Cassini (1672) using a measurement of the parallax of Mars.
• The nearest star beyond our Sun, Proxima Centauri, is almost 10⁴ times more distant than Neptune, the outermost planet. Bessel (1838) was the first to measure successfully a parallax of a star, 61 Cyg, and hence deduce a reliable measurement of its distance.
• The center of the Milky Way is almost 10⁴ times more distant than the nearest star.
• Our Galaxy, the Milky Way, is the second largest member of the Local Group of about 100 galaxies. The largest member of the Local Group is M31, the Andromeda Galaxy. Edwin Hubble first measured a reliable distance to M31 in 1923, using the method of Cepheid variables discovered by Henrietta Leavitt around 1907.
• The Local Group is on the outskirts of the Local Supercluster of galaxies, containing several thousand galaxies. At the center of the Local Supercluster is the Virgo cluster of galaxies.
• The Virgo cluster is part of a “Cosmic Web” of large scale structure. The redshifts (Doppler shifts) of the spectra of galaxies indicate that galaxies are moving away from us: the Universe is expanding (Hubble 1929). More distant galaxies are receding faster, suggesting there was a Big Bang.
• Because light has a finite speed, as we see deeper in space, we see further back in time. We can observe the Universe only out to how far light can travel during the 14 billion year age of the Universe, a distance of 14 billion lightyears.
• Our cosmic origins.
• The deepest optical image of the Universe so far taken by human beings is the Hubble Ultra Deep Field.
• The deepest image of the Universe at any wavelength of the electromagnetic spectrum is the Cosmic Microwave Background.
• Our motion in the cosmos.
• Go directly to Fiske Planetarium on Monday.
• Read Chapters 4 & 5 of Cosmic Perspective in preparation for Week 2.

Week 2 (Jan 22): Spectra

• On Monday we experienced “Our Place in the Universe” at the Fiske Planetarium.
• Astronomers cannot do experiments: they can only observe. What they observe is light.
• Light.
  • Light is a wave (Young 1800) as evidenced by interference and diffraction.
    CU PhET’s Wave interference applet.
  • Light is an electromagnetic wave (Maxwell 1864)
  • The electromagnetic spectrum
    
  • Light moves at the speed of light \(c = 299{,}792{,}458 ~ \textrm{m/s}\)
    

    \(c\)  =  \(\lambda\)   \(f\) Speed of light  =  wavelength  \(\times\)  frequency

    
    
  • Light is both a particle and a wave
    

    particle property       wave property \(E\) = \(h\)   \(f\) Energy  =  Planck’s constant  \(\times\)  frequency

  
  
• Atoms
  • H (hydrogen) is the simplest of all elements: its nucleus consists of just a single proton.
    Neutral hydrogen has one electron in orbit around the proton.
  • Electrons are also both particle and wave.
  • The wavelike nature of electrons means they can only occupy certain orbitals in an atom.
  • Every atom has a characteristic spectrum of lines, corresponding to transitions between different orbitals. These are some of the transitions in a hydrogen atom. The Lyman lines, connecting to the ground (\(n\) = 1) state, are in the ultraviolet.
    

    Emission		Absorption

  • The Rosette nebula glowing in the pink light of H\(\alpha\).
• Energy comes in a variety of forms, but total energy is always conserved (Cosmic Perspective pp. 119–123).
  • Kinetic energy of motions of particles
    • Radiation energy is the kinetic energy of photons
    • Thermal energy is the kinetic energy of random motions of particles
  • Potential energy associated with forces:
    • Gravitational
    • Electromagnetic
    • Fission (weak, or radioactive, force)
    • Fusion (strong, or nuclear, force)
    • Rest mass energy (\(E = m c^2\))
• Colors of stars and galaxies
  • Stars have different colors, according to their surface temperature.
    Mitchell Charity’s What color are the stars?
    Some webpages on color that I wrote some years ago.
  • The Sun’s visible spectrum approximates a thermal spectrum, modulated by absorption lines.
  • Galaxies are colored by their stars, modulated by absorbing dust.
• Spectra
  • A hot, dense substance emits a thermal (or blackbody, or Planck) spectrum
  • A hot, low density gas produces an emission line spectrum
  • A cold, low density gas seen against a bright background produces an absorption line spectrum.
  • The emission and absorption lines of an atom occur at the same characteristic wavelengths (energies)
    
• Temperature
  • Temperature is a measure of the mean energy per particle of random motions of particles.
  • Wien’s law

    \(\lambda_\max\)  =  \(\frac{\displaystyle 2{,}900{,}000~\textrm{nm}}{\displaystyle T \textrm{ in K}}\) Peak wavelength  =  \(\frac{\displaystyle 2{,}900{,}000 ~ \textrm{nm}}{\displaystyle \mbox{Temperature in Kelvin}}\)

    CU PhET’s Blackbody spectrum applet.
  • The power \(P\) (energy emitted per unit time) radiated by an object of area \(A\) and surface temperature \(T\) is given by the Stefan-Boltzmann law:

    \(P\)  =  \(A\)   \(\sigma\)   \(T^4\) Power  =  Area  \(\times\)  Stefan-Boltzmann constant  \(\times\)  Temperature4

  • Matter changes phase as its temperature changes.
  • Temperature worksheet.
• Doppler effect (Doppler 1842)
  • The doppler shift (redshift) of the quasar 3C273 shows it to be receding at 16% of the speed of light.
• Read Chapter 14 of Cosmic Perspective in preparation for Week 3.

Week 3 (Jan 29): Our Star

• National Solar Observatory’s Current images of the Sun.
• Images of the Sun at various wavelengths.
• The distance to the Sun was needed to infer:
  • Its luminosity (power output) \(L = 4 \times 10^{26} \, \textrm{Watts}\);
  • Its mass \(M = 2 \times 10^{30} \, \textrm{kg}\), from the orbital period-radius relation of planets in the solar system, coupled with Newton's universal law of gravitation.
• Arthur Eddington’s (1926) “Internal Constitution of the Stars”:
  • Gas pressure balances gravity (Cosmic Perspective calls this gravitational equilibrium).
  • Eddington estimated the temperature inside the Sun from
    

    mean particle velocity = gravitational escape velocity

    The gravitational escape velocity at the surface of the Sun is 620 km/s.
    This yields an estimate \(T \approx 10^7 \, \mbox{K}\) for the temperature of the interior of the Sun.
  • More detailed calculations indicate \(T \approx 1.5 \times 10^7 \, \mbox{K}\) for the temperature at the center of the Sun.
  • The high temperature implied that the interior of the Sun is a compressible, ionized plasma of electrons and nuclei.
  • Eddington did not understand how the Sun generates energy, but speculated it might come from conversion of mass to energy (specifically, hydrogen to helium).
  • Final sentence of “Internal Constitution of the Stars”:
    “At terrestrial temperatures matter has complex properties which are likely to prove most difficult to unravel; but it is reasonable to hope that in the not too distant future we shall be competent to understand so simple a thing as a star.”

• The Sun has a fairly sharp edge in visible light — the photosphere.
  • The photosphere is the boundary between (partially) ionized and (mostly) neutral gas.

• The Sun fuses hydrogen through a three-step process called the proton-proton chain (Bethe 1938).
  • The fusion rate increases rapidly with temperature.

• The first reaction converts a proton into a neutron. In so doing it releases a neutrino, a weakly interacting particle that passes freely through the entire Sun.
  • The Sun observed in neutrinos.
  • The Solar neutrino problem: Only about 1/3 as many neutrinos are observed from the Sun as are predicted by solar models.
  • The remarkable solution to the problem is that the electron type neutrinos emitted by the Sun are oscillating into the two other types of the neutrino, the muon and tauon type neutrinos. This is a deep insight into fundamental particle physics that is still not well understood.

• Helioseismology probes the interior structure of the Sun from the pattern of 5-minute solar oscillations.

• The Sun is a star.
  • A star is an object that is undergoing nuclear fusion at its core.
  • The smallest mass that can achieve nuclear fusion is about 0.08 solar masses.
  • Jupiter is not a star: it is not undergoing nuclear fusion.
    Jupiter’s mass is about 0.001 solar masses.

• The Sun has three principal layers.
  1. A core, in which hydrogen is fusing into helium.
  2. A radiative zone, in which photons carry energy outward from the core. It takes about \(10^7\) years for a photon to diffuse from the core through the radiative zone.
  3. A convective outer zone, in which large scale convective motions carry energy bodily upward, like water boiling in a pot.

• From the surface of the Sun upward are three regions.
  1. The photosphere is the visible surface of the Sun. It forms a fairly sharp edge. It has a temperature of about \(6{,}000 \, \mbox{K}\).
  2. Just above the photosphere is the chromosphere (“color sphere”). It is the principal source of the Sun’s ultraviolet radiation, and has a temperature around \(10{,}000 \, \mbox{K}\).
  3. Extending upward from the chromosphere to large distances is a hot, low density corona, with a temperature of about \(10^6 \, \mbox{K}\).

• Convective motions in the Sun’s convective zone act like a dynamo, generating magnetic fields. These magnetic fields are responsible for much of the action observed at and above the Sun’s surface.
  • Solar granulation delineates convective cells. Hot gas wells up at the center of a cell, and cooler gas descends at the edge.
  • Charged particles follow paths that spiral along magnetic field lines, so that hot gas is constrained to move only along magnetic field lines. The result is beautiful prominences and loops.
  • Bubbles of magnetic field bursting from the surface of the Sun cause flares, which accelerate particles to high speed and heat gas to high temperatures. The Sun in x-rays.
  • Powerful flares can lead to in coronal mass ejections. If directed towards Earth, these can cause aurorae and disrupt radio communications.

• Read Chapters 15, 16 of Cosmic Perspective in preparation for Week 4.

Week 4 (Feb 5): Stars

• Stars have different colors and luminosities (intrinsic brightnesses).
  • Young open star clusters
  • Old globular star clusters

• Astronomers classify stars mainly by two observable quantities: their Luminosity \(L\) (energy emitted per unit time), and their surface Temperature \(T\).
  • The classification was accomplished through the work of women astronomers around 1900.
  • Williamina Fleming (1890) originally classified stars according to the strength of their H lines
    \(\leftarrow\) stronger H lines   A B C ...   weaker H lines \(\rightarrow\)
  • Rearranged by Annie Jump Cannon (1900) into a sequence of spectral types:
    \(\leftarrow\) higher Temperature    OBAFGKM   lower Temperature \(\rightarrow\)
    Famous mnemonic: Oh Be A Fine Girl/Guy, Kiss Me
  • Spectral types were recognized as a sequence of surface Temperature by Cecilia Payne-Gaposhkin,
  • who also showed (1925) that stars are composed mainly of

    H (Hydrogen) 75% by mass He (Helium) 25% by mass

• Measuring Temperature and Luminosity.
  • A star’s surface Temperature \(T\) can be measured either from its spectral type, or from the peak wavelength \(\lambda\)_max of its blackbody spectrum using Wien’s Law (Cosmic Perspective p. 155):

    \(T\) (Kelvin)  =  2,900,000 nm \(\lambda\)max

    
    
  • A star’s Luminosity \(L\) can be deduced from its measured apparent brightness, or flux \(F\), and distance \(d\) using (Cosmic Perspective p. 523):

    \(L\)  =  \(4 \pi d^2\)   \(F\) Luminosity  =  \(4 \pi\) (distance)2  \(\times\)  Flux

    
    
  • For nearby stars, a star’s distance \(d\) can be measured from its parallax:

    distance (parsec)  =  \(\displaystyle \frac{1}{\mbox{parallax angle (arcsec)}}\)

• Given the star’s luminosity \(L\) and surface temperature \(T\), its radius \(R\) can be deduced from the Stefan-Boltzmann law (Cosmic Perspective p. 155):

  \(L\)  =  \(4 \pi R^2\)   \(\sigma\)   \(T^4\) Luminosity  =  Area  \(\times\)  Stefan-Boltzmann constant  \(\times\)  (Temperature)4

The HR Diagram

• The Hertszsprung-Russel (HR) diagram (Ejnar Hertzsprung, Henry Norris Russell 1912) was key to understanding the nature of stars. The HR diagram is a plot of Luminosity versus surface Temperature (or Spectral Type).

• Star clusters played an important role in filling in the HR diagram, because the stars in a cluster are all at about the same distance.
  • The stars in a cluster formed out of the same cloud of interstellar gas and dust, and therefore have approximately the same:
    • Distance;
    • Age;
    • Initial composition.
  • HR diagram of the Pleiades, an open star cluster.
  • HR diagram of M4, a globular cluster.
  • HR diagram of Omega Cen, the largest of the Milky Way's 200 or so globular clusters, containing about 10 million stars.

• A star's Luminosity can be deduced from measures of its Flux (apparent brightness) and distance. For nearby stars, the star’s distance can be measured from its parallax. Historically, only parallaxes of nearby stars, within about 50 parsec, could be measured.
  • The European Space Agency (ESA) Hipparcos satellite obtained parallaxes for 118,218 stars during 1989-1993. The HR Diagram from Hipparcos.
  • The European Gaia mission (2013-2019) is obtaining positions, motions, and parallaxes down to 10^–5 arcsec of 1.3 billion stars in the Galaxy and Local Group of galaxies. The HR Diagram from Gaia.

• The HR diagram shows that stars fall into four main categories:
  • Main sequence stars, from cool dim to hot bright;
    • Most stars are main sequence stars
    • The Sun is a main sequence star
    • Main sequence stars are burning hydrogen in their cores
  • Supergiants, the most luminous stars;
  • Red giants, cool bright;
  • White dwarfs, hot dim.

• The Radius of a star on the HR diagram can be deduced from the Stefan-Boltzmann law.
  • Main sequence stars from 0.1 to 10 times the radius of the Sun;
  • Red giants from a few to 1000 times the radius of the Sun, about the orbit of Jupiter;
  • White dwarfs about 0.01 the radius of the Sun, or about the radius of the Earth.

• The Masses of stars in a binary star system can be deduced from orbital dynamics.
  • The sum \(M = M_1 + M_2\) of the masses of a binary pair satisfy Kepler's third law (Cosmic Perspective p. 126)

    \(t^2\)  =  \(\displaystyle {4\pi^2 \over \displaystyle G M}\) \(r^3\) \(\mbox{(orbital period)}^2\)  =  \(\displaystyle {4\pi^2 \over \displaystyle \mbox{Newton's \(G\)} \times \mbox{Mass of binary}}\) \(\times\) \(\mbox{(average orbital radius)}^3\)

    
    
  • The Sirius A-B binary system (main sequence star and white dwarf), with masses 2.06 and 1.02 solar masses.
  • Eddington argued, correctly, that the main sequence was a sequence of stars of different Mass:
    • Hot bright — more massive, up to about 120 solar masses;
    • Cool dim — less massive, down to about 0.08 solar masses.
    (Hertzsprung & Russell had originally suggested, incorrectly, that the main sequence was an evolutionary sequence, with stars evolving from hot bright to cool dim.)

• The lifetime of a star on the HR diagram can be estimated from its Mass and Luminosity:

  Lifetime  =  Energy available Luminosity  =  Mass \(\times\) \(c\)2 \(\times\) efficiency Luminosity

• The age of a star cluster can be deduced from the “main sequence turnoff” point in its HR diagram — the age of the most massive stars still remaining on the main sequence.

Summary

• You have learned something about:
  • How astronomers estimate various properties of stars:
    • Distance;
    • Composition;
    • Surface Temperature;
    • Luminosity;
    • Radius;
    • Mass;
    • Age.
  • The history of how these properties were learned from hard observations and hard thought.
  • How the HR diagram played a central role in understanding the stars. In particular, the HR diagram shows that stars come in four main categories:
    • Main sequence stars;
    • Super giants;
    • Red giants;
    • White dwarfs.

A Secret of the Universe

• Gravity is the perpetual motion machine that drives the Universe.
  • When you remove energy from a gravitating system, it contracts, and gets hotter (particles move faster).
• Examples of gravity power in astronomy (we'll look at all these in due course):
  • Interstellar gas cools, contracts, heats up, forming protostars.
  • Protostars emit jets along their axes.
  • A protostar contracts, heats up to the point where it can fuse H (hydrogen).
  • When a main sequence star exhausts H at its center, the He (helium) core contracts and heats up, enabling H to burn in a shell around the core, and causing the star to bloat into a luminous red giant.
  • When the Fe (iron) core of an evolved massive star collapses, the gravitational energy released powers a supernova.
  • The gas in an accretion disk around a neutron star or black hole gets faster and hotter as it spirals inward. Near the central compact object, the disk reaches relativistic temperatures, and emits x-rays.
  • Twin jets, often relativistic, emerge from the vortical opening along the spin axis of the accretion disk of the neutron star or black hole.

• Star formation
  • Pillars of Creation.
  • Computer simulation of stars forming.

• Read Chapter 17 of Cosmic Perspective in preparation for Week 5.
• Go directly to Fiske on Monday.

Week 5 (Feb 12): Stellar Evolution

• On Monday there was a Star Talk at the Fiske Planetarium. You made connections between what you have been learning in class, and stars and star patterns that you have known on the sky your entire life.
  • We explored:
    • the winter hexagon, the Pleiades cluster, the Hyades cluster;
    • the Orion star-forming nebula;
    • the Milky Way;
    • star forming regions in the Milky Way;
    • globular clusters in the halo of the Milky Way.
  • You watched “Solar Superstorms”.

• How can we understand what happens inside stars that are far away and last for millions and billions of years? Laws of physics allow mathematical modeling that can be compared to observations.

• Both low and high mass stars are essential to our existence.
  • Low mass stars like the Sun last long enough (billions of years) to support the evolution of life on their planetary systems.
  • High mass systems burn furiously, synthesize elements heavier than helium, end their lives in supernova explosions that thrust those elements into the interstellar medium, available to form new stars and planetary systems.
    “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of star stuff.” — Carl Sagan.

• Whenever a star runs out of fuel, it contracts, and heats up.

The evolution of low mass stars

• When a star has converted all the H in its core to He, it continues to burn H in a shell.
• The luminosity starts to increase, causing the star to start expanding into a red giant
• The core contracts, heats, until at about 10⁸ K, Helium flash.
  • He ignites and burns explosively, being consumed in about 1 second. But the star does not explode.
  • Helium burns to carbon in the “triple alpha” reaction, \(3 \, {}^4\textrm{He} \rightarrow {}^{12}\textrm{C}\). This is where the carbon for life was created.
  • Triple alpha reaction requires high density, so carbon is made only in stars, not in the Big Bang.
  • Roughly half the carbon burns immediately to oxgen.
  • About 1952, astronomer Fred Hoyle predicted to nuclear physicist William Fowler that the triple alpha reaction required the \({}^{12}\textrm{C}\) nucleus to have an excited state near 7.68 MeV. A few months later, Ward Whaling in Fowler's lab confirmed a resonance near 7.65 MeV.
• The He flash heats the core, which expands and cools it, temporarily driving the red giant back towards the main sequence. The star continues to fuse H and He in shells, driving back to a red giant. Evolution in the HR diagram.
• Evolution of the radius of a Sun-like star.
• The red giant develops a powerful wind.
• In the last stages of losing its envelope, the star appears as so-called planetary nebula (nothing to do with planets).
• The envelope dissipates into space, the core cools, leaving a carbon-oxygen white dwarf.

The evolution of high mass stars

• A high mass star is hot enough in its core that when it has converted all H to He at its center, He starts to fuse non-explosively.
• The star is hot enough to fuse carbon and oxygen to heavier elements. Its core develops a complicated shell structure of fusing heavy elements.
• The star becomes a supergiant.
• Eventually the core burns all the way to iron, which contains no more nuclear energy.
• When the iron core reaches the Chandrasekhar limit, 1.4 solar masses, it collapses, in a fraction of a second.
• The envelope bounces off the core, producing a supernova. We'll explore supernovae next week.

• Read Chapter 18 of Cosmic Perspective in preparation for Week 6.

Week 6 (Feb 19): Stellar Death

White dwarfs

• White dwarfs in globular cluster NGC 6397.
• Eddington’s paradox: “If a gravitating system, whenever it runs out of energy, contracts and heats up, how can it ever cool down?”
  White dwarf stars, with a density of 100 tons per cubic inch, were a mystery to Eddington.
• Mystery of white dwarfs solved by Subrahmanyan Chandrasekhar (1930), aged 19, who realized that white dwarfs were held up by electron degeneracy pressure.
  • For the delightful history of what happened, read Ch 4 of Kip Thorne’s prize-winning book “Black Holes & Time Warps: Einstein’s Outrageous Legacy”.
• What is electron degeneracy pressure (Cosmic Perspective §4.4, page 456)? It’s a quantum mechanical effect.
  • Electrons cannot be pushed closer than their wavelengths.
  • The shorter the electron wavelength, the higher the electron energy.
  • When electrons are squashed smaller than an atom, they become free (have enough energy to be ionized).
  • Squashed electrons retain this quantum zero-point energy even at zero absolute temperature (so the pressure is non-zero even when the temperature is zero).
    
• What does electron degeneracy pressure do?
  • It’s what holds up white dwarfs, and the cores of red giants.
    
  • Also holds up cores of planets more massive than Jupiter.
  • The outer electrons of solid metals are electron degenerate, giving metals their special properties: high thermal and electric conductivity, high reflectivity.
  • Nuclear fusion of electron degenerate matter is explosive, because when the temperature increases, the matter does not expand, so the temperature sky-rockets.
    • Helium flash.
    • Thermonuclear supernovae.
• More massive white dwarfs have smaller radii
  
  
• The Chandrasekhar (1931) limit: if a white dwarf (an electron degenerate object) exceeds 1.4 solar masses, the Chandrasekhar limit, it will collapse.
  • Why? Because the squashed electrons become so energetic that they become relativistic (move at almost the speed of light). Since they cannot move faster than light, they cannot exert enough additional pressure to withstand collapse.

Supernovae

• Supernova. A star that for a while becomes comparable in brightness to its parent galaxy.

• History.
  • 1054. Chinese astronomer Yang Wei-te reported a “guest star” (supernova) in constellation Taurus, which was recorded in the Annals of the Sung Dynasty.
  • 1931. Fritz Zwicky points out that some novae (new stars) are exceptionally bright. He calls them “supernovae”. He begins a solo campaign to discover supernovae.
  • 1932. James Chadwick discovers the neutron.
  • 1933. Baade & Zwicky make their remarkable prediction that supernovae produce neutrons stars.
  • 1940s. Nicholas Mayall measures the expansion rate of Messier 1, the Crab nebula, and shows that it must have originated in an explosion around 1054. He concludes that the Crab nebula is the remnant of the Supernova of 1054.
  • 1967. Jocelyn Bell discovers a pulsar, with a precise period of 1.337301 seconds, then three more. The first few pulsars are given the name “LGM” (Little Green Men). Observations that pulsars pulse over a wide range of radio frequencies ruled out the possibility of the source being intelligent life.
  • 1968. American astronomers discover a 0.033 second pulsar in the Crab nebula. The period is too short and too regular to be anything other than a rotating neutron star.
    
    
  • 2002. Chandra and Hubble movies of the Crab nebula.
  • Today. Thousands of pulsars are now known in our Galaxy and other galaxies, with periods ranging from 0.0013959548 seconds (PSR J1748-2446ad) to several seconds.

• A pulsar is a rotating, magnetized neutron star.
  • Listen to the sounds of pulsars.
  • Pulsar animation by Paul Bourke, Swinburne Centre for Astrophysics and Supercomputing.
  
  
• There are two kinds of supernova:

  Type:	Core collapse supernova	Thermonuclear supernova
  Spectra:	Show H lines	Show no H lines
  Where:	In star-forming regions, spiral arms	Anywhere in a galaxy
  \(\Rightarrow\)	Young, massive star (> 8 solar masses)	Old white dwarf

  
  
  • The two types have characteristically different light curves.

Core collapse supernova

• Evolution of a massive star (> 8 solar masses).

• The iron core is held up by electron degeneracy pressure. When it reaches the Chandrasekhar limit, 1.4 solar masses, it collapses, in a fraction of a second.
  • Where can the squashed electrons go? Electrons and protons are pressed together into neutrons, releasing a burst of neutrinos, \(e + p \rightarrow n + \nu\).
    
    
  • The envelope bounces off the core, producing a supernova.
  • The supernovae is powered by the gravitational energy released by the collapse of the core.
  • computer simulation by Adam Burrows
  • The core left behind is a neutron star, or a black hole if the star is very massive (> 25 solar masses).
• Supernova 1987A in the Large Magellanic Cloud.
• Cassopeia A (Supernova 1658).

Thermonuclear supernova

• A carbon-oxygen white dwarf accretes matter from a companion star perhaps a red giant or supergiant.

• The accreted hydrogen-rich gas forms an electron degenerate layer on the white dwarf. From time to time the hydrogen explodes, producing a nova (new star), as luminous as the most luminous stars (a million solar luminosities).

• Eventually the mass of the carbon-oxygen white dwarf may build up to the Chandrasekhar limit, 1.4 solar masses. At this point, the white dwarf begins to collapse.
  • Carbon ignites under pyconuclear (cold, dense) conditions close to the center.
  • Because the pressure is electron degeneracy pressure, the increase in temperature does not initially change the pressure. The temperature skyrockets, causing the nuclear burning to be explosive.
  • The nuclear burning front is extremely sensitive to the precise conditions, and develops in a complicated way: computer simulation of a thermonuclear supernova explosion.
  • In a fraction of a second, the center of the white dwarf is incinerated to ⁵⁶Ni. The white dwarf explodes, leaving nothing behind.
  • The supernova is powered by nuclear energy from the fusion of carbon (C) and oxygen (O) to nickel (Ni).
  • Nickel-56 is radioactive, decaying to cobalt (Co) then to iron (Fe):

    6 days   111 days   56Ni \(\rightarrow\) 56Co \(\rightarrow\) 56Fe

  • The energy released by this radioactive decay is what produces the characteristic light curve of a thermonuclear supernova.
• Tycho (Supernova 1572).

Week 7 (Feb 26): Gravitational waves

• General relativity predicts that masses that accelerate non-uniformly will produced gravitational waves, which propagate at the speed of light.

• Indirect detection of gravitational waves.
  • The gradual decrease in the orbital period of the Hulse-Taylor binary pulsar is consistent with the loss of energy by gravitational waves predicted by general relativity.
  • Russell Hulse and Joe Taylor won the 1993 Nobel prize for their discovery.

• Direct detection of gravitational waves from merging black holes.
  • The first ever direct detection of gravitational waves was from by the US Laser Interferometer Gravitational-Wave Observatory (LIGO) on 2015 September 14: GW150914. LIGO has two detectors, one in Hanford, Washington State, the other in Livingston, Louisiana.
  • Two black holes of 36 and 29 solar masses merged into a single black hole of 62 solar masses, radiating 3 solar masses in gravitational waves. Observed versus fitted waveform.
  • The Caltech-Cornell group's visualizations of black holes merging.
  • Rainer Weiss, Barry Barish, and Kip Thorne won the 2017 Nobel Prize in Physics “for decisive contributions to the LIGO detector and the observation of gravitational waves.”
  • As of Fall 2017, LIGO had detected 5 binary black hole mergers, and 1 binary neutron star merger. The last black hole merger, GW170814, and the neutron star merger, GW170817, were also detected by the European Virgo collaboration.
  • Both LIGO and Virgo are currently being upgraded. India and Japan will join the collaboration in the future.
  • It is anticipated that in the near future the international collaboration will detect one black hole merger per day, and even more neutron star mergers.

• Direct detection of gravitational waves from merging two neutron stars.
  • First detection of gravitational waves from the merger of two neutron stars 2017 Aug 17: GW170817.
  • Two seconds later, the Fermi and Integral gamma-ray telescopes detected a Gamma-Ray Burst (GRB).
  • The coincidence of gravitational and wave signals implies that gravitational waves move at the speed of light (to an accuracy of 10^–16), as predicted by general relativity.
  • A glitch in the original LIGO-Livingston data delayed a precise location on the sky.
  • 11 hours later, astronomers discovered a kilonova in the galaxy NGC 4993, 40 Mpc (130 million lightyears) away.
  • The kilonova provoked an unprecedented campaign of astronomical observations. More than 70 telescope and 3000 astronomers contributed.
  • The spectrum of GW170817 showed a characteristic signature very heavy elements. Kilonovae resulting from neutron star mergers probably produce most of the very heavy elements in the Universe, such as gold.

• A passing gravitational wave produces an oscillating tidal force, which can be detected by an oscillation in the distance between freely-falling masses.

• NASA's ambitious possible future mission LISA (Laser Interferometer Space Antenna), consisting of three spacecraft in a triangle a million kilometers on a side, should detect gravitational waves from merging supermassive black holes.

• Census of black hole and neutron star masses.

• Brian Greene talking about gravitational waves with Stephen Colbert.

• Review and Midterm.

Week 8 (Mar 5): Special Relativity

• On Monday we visited the Fiske Planetarium.
  • We contemplated the summer sky, when the Milky Way rises highest at Northern latitudes. We looked at the summer triangle (Vega, Altair, and Deneb), of which Deneb forms the tail of Cygnus the Swan, flying down the Milky Way towards its center.
  • To find black holes, look in x-rays or gamma-rays. X-rays and gamma-rays are the most energetic kinds of electromagnetic radiation; if you want to find something violent going on in the cosmos, then look in high energy radiation.
  • About half of the brightest x-ray sources on the sky are concentrated to the plane of the Milky Way. These are mostly x-ray binaries consisting of a neutron star or black hole accreting from a companion star, but there are also a number of supernova remnants. The other half of the brightest x-ray sources are distributed all over the sky. These are mostly Active Galactic Nuclei, bright objects found at the centers of galaxies, powered by supermassive black holes.
  • Some ot the brightest x-ray objects:
    • Sco X-1, the brightest x-ray source in the sky aside from the Sun. Sco X-1 is an x-ray binary system containing a 1.4 solar mass neutron star accreting from a low mass (0.4 solar mass) subgiant companion.
    • Cyg X-1, half way down the neck of Cygnus. This was the first source recognized to be a black hole accreting from a companion star.
    • M87, the huge ellipictical galaxy at the center of the Virgo cluster of galaxies at the center of the Local Supercluster of galaxies. M87 contains a supermassive black hole of 6 billion suns, the most massive black hole whose mass has been measured directly.
  • Astronomers identify two distinct types of black hole:
    • Stellar sized black holes (three to several tens of solar masses), seen in x-ray binary systems.
    • Supermassive black holes (millions to billions of solar masses), seen at the centers of galaxies.

  • We watched “Black Holes: The Other Side of Infinity”.

Special Relativity

• Special Relativity website.

• Postulates of Special Relativity
  1. Spacetime is a 4-dimensional continuum (3 dimensions of space, 1 of time).
  2. There exist “globally inertial” spacetime frames: frames with respect to which unaccelerated objects move in straight lines at constant velocity.
  3. The speed of light is the same in any inertial frame.
  4. The Principle of Special Relativity: the laws of physics are the same in any inertial frame (in other words, there is no absolute spacetime).

• How can the speed of light be the same in any frame?
  • Isn't this a paradox?
  • Einstein’s solution to the paradox is that observers in relative motion measure space and time differently.

    Are these boxes the same?

• Time dilation

• How a scene actually appears seen at close to the speed of light
  • Aberration: ahead appears fisheyed, behind zoomed.
  • Color: blueshift (higher energy photons) ahead, redshift (lower energy photons) behind.
  • Brightness: brighter ahead, dimmer behind.
  • Time: faster ahead, slower behind.

• The rules of 4-dimensional perspective: An observer moving to the right sees the “celestial sphere” distorted into a “celestial ellipsoid” with self at the focus of the ellipse.
  

• MIT's A Slower Speed of Light game.

• Nothing can move faster than light:
  • It would take an infinite energy to accelerate to faster than the speed of light.
  • If you could travel faster than light, you could also travel backwards in time.

• Nevertheless, time dilation allows you to travel effectively “faster than light”.
  • A relativistic trip across the Universe.

Week 9 (Mar 12): Black Holes and General Relativity

• Falling into a Black Hole.
• Inside Black Holes.
  • What happens when you watch someone else fall into a black hole?
  • What happens when you fall into a black hole?
• The Waterfall Model of Black Holes.
• Collapse to a Black Hole.
• No hair theorem: An isolated black hole rapidly (on few light crossing times) evolves to a state characterized by just 3 properties:
  • Mass
  • Electric charge
  • Angular momentum (spin)
  It loses its “hair” by gravitational radiation.

Observational evidence for Black Holes

• Astronomers see evidence for two kinds of black hole:
  • Stellar-sized black holes (5 to 30 solar masses) in x-ray binary systems;
  • Supermassive black holes (10⁶ to 10¹⁰ solar masses) at the centers of galaxies.

• X-ray binary systems
  • Jeffrey E. McClintock et al.'s 2011 drawings of 21 of the 23 known X-ray Binaries containing a Black Hole (pdf).
  • X-ray binaries consist of a low or high mass main sequence losing gas on to an accretion disk around a neutron star or black hole.
  • Simulation of a binary star produced from Rob Hynes' binsim sofware.
  • If the mass of the neutron star or black hole is more than 3 solar masses (the maximum theoretical mass of a neutron star), then it is inferred to be a black hole. Cygnus X-1, a 5.6 day x-ray binary, is the most famous example.
  • In some cases the compact object is an x-ray pulsar. Hercules X-1 is the most famous example.
  • John Hawley's magnetohydrodynamic computer simulation of a jet from an accretion disk.

• Kormendy & Gebhardt's 2001 census of Black Holes in Galactic Nuclei (pdf).
  • Observations of the centers of nearby galaxies indicate the presence of a large unseen gravitational mass in a small region — it must be a black hole.
  • Every galaxy large enough to have a bulge appears to have a central black hole.
  • M87, the huge galaxy at the center of the Virgo cluster, at the center of the Local Supercluster of galaxies, contains the most massive black hole known in the local Universe, 6 × 10⁹ solar masses.

• The supermassive black hole at the center of the Milky Way
  • Observations of the motions of stars, both angular motions on the sky, and radial motions from spectroscopy (redshifts and blueshifts), indicate the presence of a 4 × 10⁶ solar mass black hole at the center of our own Galaxy, the Milky Way.

Week 10 (Mar 19): Milky Way

History of understanding of our Galaxy, the Milky Way

• On Tuesday there was a Fiske Planetarium show on the Milky Way. The show was mostly about the history of the discovery that the Milky Way is a galaxy of stars, and that there are many other galaxies in the Universe.
  • My favorite book on the subject is Leila Belkora’s “Minding the Heavens: The Story of Our Discovery of the Milky Way”.
  • The ancients had various imaginative ideas about the Milky Way. Our word galaxy comes from Greek galaktikos = milky.
  • Galileo was the first person to use a telescope in astronomy. He found (1610) that parts of the Milky Way resolved into numerous stars.
  • Philosopher Kant proposed (1755) that some nebulae were “Island Universes”, comparable to the Milky Way in size, rotating according to Newton’s laws of gravity and motion.
  • William Herschel, discoverer of the planet Uranus, with the aid of his sister Caroline, undertook a laborious “star-gauging” enterprise to map the size of the Milky Way with his 19 inch telescope. He concluded (1785) that the Milky Way was roughly elliptical, with the Sun at the center.
  • William Parsons, 3rd Earl of Rosse, built a huge telescope with a 72 inch speculum mirror. With this he discovered (1845) spiral structure, whence the term “spiral nebulae”.
  • J. C. Kapteyn, during 1906-1920, organized a major international co-operative effort to repeat Herschel’s star-gauging exercise using observations from 40 observatories. He concluded (1922), sadly incorrectly, that the Milky Way is elliptical with the Sun at center.
  • Henrietta Leavitt discovered (1907-1912) the Period-Luminosity relation for Cepheid variable stars, thereby providing a reliable way to measure distances to other galaxies.

    Leavitt's 1912 diagram:

  • Vesto Slipher successfully obtained spectra of spiral nebulae (1912-1914), and discovered that most galaxies were redshifted, some by as much as 1000 km/s, an unprecedentedly large redshift.
  • Harlow Shapley argued (1920) that the system of globular clusters marked the center of the Milky Way in Sagittarius, and that the Sun was a long way from the center.
  • Edwin Hubble discovered (1923-1924), with the 100 inch telescope, Cepheid variables in the Andromeda Nebula, thereby establishing an accurate distance that demonstrated that Andromeda was a galaxy well outside the confines of the Milky Way.
  • Following theoretical work by Bertil Lindlbad, by measuring redshifts of stars in the Galactic neighbourhood of the Sun, Jan Oort (1927) demonstrated that the Galaxy is rotating about a center in Sagittarius.

Our Galaxy, the Milky Way

• Structure of the Milky Way, a barred spiral galaxy
  • bulge
    • Barred bulge
    • A black hole at the center
  • disk
    • Gas
    • Stars
    • Spiral arms
  • halo
    • Globular clusters
    • Dark Matter

• Computer simulation of the evolution of the Milky Way. The Milky Way today is not quite as stately as you may have thought!

• Satellite galaxies in orbit around the Milky Way
  • The Large and Small Magellanic Clouds, each about 1/100 of the mass of the Milky Way
  • Several tens of “dwarf elliptical” and “dwarf spheroidal” galaxies, each about 1/10,000 of the mass of the Milky Way. Most of these dwarf satellites are quite diffuse (unlike globular clusters), and have been revealed only recently by computer scans of telesopic images.

• Most of the rest of the visible (at any wavelength) Galaxy is in a disk. The Milky Way at many wavelengths.
  • Star-gas-star cycle:
    stars
     → supernovae and stellar winds
      → hot gas
       → warm diffuse gas
        → cool dense molecular gas
         → stars
  • Notice the driving role of gravity

• The rotation of the Galaxy
  • The rotation curve of the Milky Way implies more matter than can be accounted for by stars and gas — dark matter.

Week 12 (Apr 2): Galaxies and Cosmology

Hubble expansion

• The Hubble expansion of the Universe is probably the single most important observational result about galaxies.
  • Hubble law:

    \(v\)  =  \(H_0\)   \(d\) Recession velocity  =  Hubble’s constant  \(\times\)  distance

  • Indicates that there was a Big Bang.
  • Yields the age of Universe = 1/\(H\)₀ = 14 billion years.

• The cosmological horizon: we can see no further than light can travel in the 14 billion year age of the Universe.

• The recession velocity \(v\) of a galaxy is measured, relatively easily and accurately, from its redshift \(z\)

  \(z\)  =  \(\displaystyle \frac{\lambda_{\rm obs} - \lambda_{\rm em}}{\lambda_{\rm em}}\) redshift  =  \(\displaystyle \frac{\mbox{observed wavelength} ~-~ \mbox{emitted wavelength}}{\mbox{emitted wavelength}}\)

  • The recession velocity is related to its redshift by (for velocities much less than the speed of light)

    \(v\)  =  \(c\)   \(z\) Recession velocity  =  speed of light  \(\times\)  redshift

• The distance \(d\) to a galaxy is much harder to measure precisely. The principal method is to use “standard candles”, objects whose luminosities are known precisely. There is no perfect standard candle in astronomy, but the best are:
  • Cepheid variable stars (visible out to the Virgo cluster)
  • Thermonuclear supernovae — standard bombs (visible to cosmological distances)

• Hubble diagram of thermonuclear supernovae

• At the January 1998 meeting of the American Astronomical Society, two independent groups announced that the Hubble diagram of thermonuclear supernovae at high redshift indicated that the Universe was accelerating. This implied that the Universe must be dominated by some gravitationally repulsive substance — Dark Energy. This revolution led to the “Standard Model of Cosmology”, in which the mass-energy of the Universe consists of the following:

  Substance	Properties	Fraction of the mass-energy of the Universe	Main observational evidence
  Dark Energy	Gravitationally repulsive. Could be quantum mechanical vacuum energy?	70%	Hubble diagram of high redshift thermonuclear supernovae; and the Cosmic Microwave Background (CMB).
  Non-baryonic Dark Matter (Cosmic Perspective calls it “exotic”)	Heavy, weakly interacting particles not yet discovered in the lab.	25%	The clustering of Galaxies; and the CMB.
  Baryonic Matter	Atoms. The kind of stuff that you and planets and stars are made of. From Greek baryos = heavy (referring to protons and neutrons).	5%	The primordial abundances of light elements (H, D, 3He, 4He, Li); and the CMB.
  Neutrinos	Light, weakly interacting particles, that fly freely through the Earth without stopping.	< 1%	Upper limits on neutrino masses; and the CMB.
  Photons	Mostly the Cosmic Microwave Background.	0.006 %	We see it!
  Total:		100%	CMB indicates that the Universe is geometrically flat.

  
  

Cosmic Microwave Background (Cosmic Perspective Chapter 22)

• The Cosmic Microwave Background (CMB) is the radiation remnant of the primeval hot Big Bang fireball.
• Observationally, the Cosmic Microwave Background:
  • Has an exquisite thermal (black body) spectrum, with a temperature of 2.725 Kelvin.
  • Is almost uniform on the sky.
  • Shows a “dipole” distortion from the motion of the Sun through the CMB, at 365 km/s.
  • After subtraction of the dipole distortion, the residual temperature fluctuations are tiny, a few parts in 10⁵.
  • The power spectrum of fluctuations shows a pattern of acoustic peaks in remarkable agreement with the predictions of the Standard Model of Cosmology.
• Theoretically, the Cosmic Microwave Background:
  • Supports the idea that there was a hot Big Bang.
  • The CMB cools as the Universe expands, the wavelengths of CMB photons being stretched (redshifted) by the expansion of the Universe.
  • Its uniformity and thermal (blackbody) spectrum tell us that the Universe used to be much simpler when it was young.
  • Comes to us from the Epoch of Recombination, when the Universe was 380,000 years old, and the temperature was 3000 Kelvin.
  • At Recombination, hydrogen and other elements combined from an ionized plasma of nuclei and free electrons to a neutral gas of atoms. As a result, the Universe changed from being opaque to transparent, allowing the CMB to propagate freely to us from that time.
    

    Before Recombination	After Recombination
    ionized	neutral
    opaque	transparent
    vibrating photon-baryon fluid	baryons start collapsing into galaxies

  • The peak in the power spectrum, about 1° on the sky, corresponds to the cosmological horizon size at Recombination, about 400,000 lyr.

• Schematic evolution of the Universe

Week 13 (Apr 9): Galaxies

• On Tuesday there was a Fiske Planetarium show on “Galaxies”.

• The Hubble expansion is not perfect. Small ripples in the initial smooth distribution of matter in the Universe grew by gravity, collapsing into galaxies and groups of galaxies.
  • Redshift surveys of galaxies reveal a “cosmic web” of structure.
  • The large scale structure shows a characteristic scale of about 100 Mpc (300 million lightyears). This is the imprint of the scale of the cosmological horizon at Recombination.
  • Computer simulation of galaxy clustering by Volker Springel (2011) using Gadget computer code.

• The Local Group of galaxies is the local region of the Universe that has turned around from the general Hubble expansion, and is beginning to collapse for the first time.
  • The Local Group is about 1 Mpc across.
  • The Local Group contains about 100 galaxies:
    • M31, the Andromeda galaxy;
    • The Milky Way;
    • M33, the Triangulum galaxy;
    • various smaller irregular and dwarf spheroidal galaxies.
  • Computer simulation of the Local Group of galaxies by Klypin et al. 2003.
  • M31 is approaching the Milky Way at 300 km/s, and we may collide in 5 billion years time. Simulation.

• The Local Supercluster of galaxies is our piece of the cosmic web.
  • The Local Supercluster is about 100 Mpc across.
  • It contains thousands of bright galaxies.
  • The Local Group is on its outskirts.
  • At the center of the Local Supercluster is the Virgo cluster of galaxies.
  • Computer simulation of the Local Supercluster of galaxies by Klypin et al. 2003.

• Galaxies routinely collide.
  • When galaxies collide, they feel each other’s gravity, but the stars do not collide.
  • A compilation of simulations versus observations.
  • The Antennae galaxy.
  • The Cartwheel galaxy.

Week 14 (Apr 16): The Birth of the Universe

• On Friday, Prof. Mitch Begelman lectured on “Active Galactic Nuclei”.

The size and geometry of the Universe

• The Cosmic Scale Factor \(a\)
  • a measure of the size of the universe, with the defining property that it expands with the Universe.

• Wavelengths of light stretch with the expansion of the Universe

  \(\lambda\) \(\propto\) \(a\) Wavelength is proportional to cosmic scale factor

  Given astronomers' definition of redshift \(z\), it follows that

  \( 1 + z = \displaystyle {\lambda_{\rm obs} \over \lambda_{\rm em}} = {a_{\rm obs} \over a_{\rm em}} \)

  • True in a full general relativistic description of the Universe.
  • Another way of thinking about the redshift of distant objects in the Universe.

• The Cosmological Principle
  • Asserts that the Universe is spatially uniform at large scales.
  • In particular, the Universe has no spatial center.
  • The chief observational evidence for this is the extraordinary uniformity of the CMB.
  • The distribution of galaxies at the largest scales also appears to be uniform.

• The geometry of the Universe
  • Einstein’s General Relativity (GR) relates the geometry of spacetime to its total mass-energy density (in all kinds).
  • Given the Cosmological Principle, GR allows just three kinds of geometry: closed, flat, open.
  • The critical density is the density required to make the Universe flat.
  • The density of the Universe is commonly expressed relative to the critical density:

    \(\Omega\) \(\equiv\) \(\mbox{actual density of the Universe} \over \mbox{critical density of the Universe}\)

    
    

    Geometry:	Closed	Flat	Open
    Spatial curvature:	Positive	Zero	Negative
    Density:	\(>\) critical	\(=\) critical	\(<\) critical
    \(\bf \Omega\)	\(> 1\)	\(= 1\)	\(< 1\)
    (Circumference/radius) of a circle:	\(< 2\pi\)	\(= 2\pi\)	\(> 2\pi\)
    Sum of interior angles of a triangle:	\(> 180^\circ\)	\(= 180^\circ\)	\(< 180^\circ\)

• The angular size of fluctuations in the CMB depends on geometry. The angular location of the peak in the power spectrum of CMB fluctuations, at 1°, implies that that the Universe is pretty much flat.
  • The Boomerang balloon-borne telescope revealed (2000) that the Universe is flat to an accuracy of about 10%.
  • The WMAP satellite showed (2003) that the Universe is flat to an accuracy of about 1%.
  • The Planck satellite showed (2015) that the Universe is flat to an accuracy of about 0.5%.
  • This implies that the total mass-energy density of the Universe in all forms, including Dark Matter and Dark Energy, equals the critical density.

• General Relativity relates the age and fate of the Universe to its mass-energy content.

• The horizon of the observable Universe
  • The edge from which a signal created at the Big Bang could just reach us.
  • The distance to the horizon is approximately the age of the universe times the speed of light.
  • The CMB is the most distant thing that we can see in electromagnetic radiation; but it was emitted just inside our horizon (not at our horizon).

• The horizon and the CMB
  • The horizon size at Recombination, when the Universe was about 400,000 years old, was about 400,000 lightyears.
  • Today, this corresponds to about 1 degree of angle on the CMB sky.
  • The horizon problem: How can regions of the Cosmic Microwave Background more than 1 degree apart, which were causally disconnected at the time of Recombination, know to have the same temperature today?

Inflation

• Problems of the Universe
  1. Why is the Universe expanding?
  2. Why is the Universe at large so smooth (CMB fluctuations are tiny)?
  3. Why is the Universe so flat (Boomerang, WMAP, Planck)?
  4. The horizon problem (see above).
  5. What caused ripples in the smoothness?
  6. Where did matter in the Universe come from?

  Remarkably, the theory of Inflation (Alan Guth 1981) offers a solution to all of these problems.

• Inflation is a hypothesized epoch in the very early Universe when the mass-energy of the Universe was dominated by vacuum energy.
  • Vacuum energy is the quantum zero-point energy of the vacuum.
  • Vacuum energy is gravitationally repulsive, according to General relativity.
  • Consequence: the Universe inflates, doubling in size each “tick of the clock”.
    If the vacuum energy was that of GUT (Grand Unified Theories; see below), then
    • each tick was a GUT time, about \(10^{-38}\) seconds, long;
    • inflation took place over perhaps \(10^{-35}\) seconds altogether;
    • the Universe grew from perhaps 1000 GUT lengths, about \(10^{-29}\) meters, to perhaps a meter in size;
    • the temperature was about \(10^{26}\) Kelvin;
    • the vacuum density was more than \(10^{80}\) times the density of water.

• Solution to Problem 1: Why is the Universe expanding?
  • The repulsion of the vacuum accelerated the Universe into tremendous exponential expansion — inflation.

• Solution to Problem 2: Why is the Universe so smooth?
  • Any initial fluctuations in density were stretched (redshifted) into smoothness.

• Solution to Problem 3: Why is the Universe so flat?
  • Inflation made the Universe so huge that today we see only a small patch of it, which looks flat. On a much huger scale, well beyond our horizon, the Universe might not be flat at all.

• Solution to Problem 4: The horizon problem.
  • Before inflation, the different parts of the Universe were causally connected.
  • Inflation caused different parts of space to accelerate away from each other, eventually faster than the speed of light, so that they became causally separated.
  • So the solution is: Causally disconnected regions of the CMB were once causally connected, before Inflation.
  • The peaks in the power spectrum of fluctuations in the CMB require that the fluctuations were initially synchronized (like the initial pluck of a guitar string) as predicted by inflation.
  • Probably the most compelling observational reason in favor of inflation.

• Solution to Problem 5: What caused ripples in the smoothness?
  • Tiny quantum fluctuations in the inflationary vacuum energy produced ripples,
  • which later grew by gravity into galaxies, stars, and you.
  • Inflation predicts a “scale-invariant” spectrum of fluctuations at the largest scales (larger than the horizon size at Recombination) in agreement with the observed power spectrum of fluctuations in the CMB at scales much greater than 1°.

• Solution to Problem 6: Where did matter in the Universe come from?
  • The observed vacuum energy today is tiny, about \(10^{-26}\) kg/m³, far less than the \(10^{84}\) kg/m³ GUT density.
  • Therefore, inflation must have ended at some point.
  • Theory:

    Vacuum energy \(\rightarrow\) Matter + radiation energy.

• What is this vacuum energy that drove inflation?
  • It’s energy associated with the Unification of forces — specifically, with the unification of the electroweak and strong forces into a hypothesized GUT (Grand Unified Theory) force.
  • The interactions of all particles appear to be governed by just four forces:
    • Gravity
    • Electromagnetism
    • The strong, or nuclear, or color force
    • The weak force
  • Weinberg and Salaam won the 1974 Nobel prize for their theory of the unification of the electromagnetic and weak forces into a combined electroweak force.
    • Electroweak unification appears only at high energy, above about 10¹⁵ Kelvin, which is about the highest energy accessible in particle accelerators today.
    • Electroweak unification correctly predicts various experimentally observed phenomena — such as that, at high energy, neutrinos (which interact only by gravity and the weak force) interact similarly to electrons (which interact by gravity, the weak, and electromagnetic forces).
  • Extrapolating, physicists predicted that at even higher energies the electroweak force may unite with the strong force into a single GUT force.
    • But the GUT energy is too high, about 10²⁸ Kelvin, to be reached in particle accelerators, so the theory is not well understood and is not experimentally tested.
  • The (de)unification of forces is like a phase transition (like steam \(\leftrightarrow\) water). Vacuum energy is the “latent heat” of the transition.

• In summary, inflation offers an enticing and observationally consistent picture that suggests how the Universe today could have come from almost “nothing”.

• Inflation does not explain how the laws of physics that govern our Universe were laid down, nor why those laws are so beautifully adapted to life.

• What happened before inflation? An unanswered mystery.

Week 15 (Apr 23): Dark Matter

• Dark Matter (as opposed to gravitationally repulsive Dark Energy) is unseen matter which is detected by its gravitational effects.
  • The composition of the Universe is measured from the Cosmic Microwave Background, galaxies, and other supporting evidence to be 70% Dark Energy, 25% Dark Matter, 5% Baryonic Matter.

• Most of the Dark Matter is thought to be some mysterious “non-baryonic” particle whose interactions are so weak as to have escaped detection in the laboratory (so far — go physicists!).
  • The most compelling evidence that Dark Matter is non-baryonic comes from comparing the amplitude of fluctuations in the CMB to those in galaxies today. How can tiny fluctuations in the CMB grow by gravity into today's galaxies and galaxy clusters in “only” the age of the Universe? Baryons are not enough because before Recombination, baryons were tightly coupled to photons, and could not start clustering gravitationally. But non-baryonic dark matter could start clustering before Recombination.
    

• Dark Matter in spiral galaxies. The rotation of the galaxy reveals the total mass of gravitating matter in the galaxy. The mass of dark matter relative to luminous matter grows more and more at greater distances from the center of the galaxy.

• Dark Matter in the Local Group of galaxies.
  • For the Andromeda galaxy (M31) to be approaching us (at 300 km/s) requires that the M31-Milky Way system (the Local Group) contain ten times as much matter as is visible in stars.

• Dark Matter in clusters of galaxies.
  • The temperature of x-ray emitting hot gas reveals the depth of the gravitational potential well, hence the amount of gravitating matter. Again, typically the total mass is ten times the luminous mass.
  • Gravitational lensing of background galaxies (bluish arcs) by a foreground cluster (yellowish galaxies). Once again, typically the total mass measured from lensing is ten times the luminous mass.

• The Bullet Cluster shows two colliding clusters whose dark matter halos have passed through each other while their hot gas has not.

Week 16 (Apr 30): Finals Week

• Review for final.

  Spring 2018 ASTR 1200-001 Homepage

Updated 2018 Apr 30