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February 18, 2003Lynn Cominsky - Cosmology A3501 Seeing Stars Physical characteristics (distance, luminosity, mass, temperature, etc.) Life Cycles Creation of Elements Supernovae and Gamma-Ray Bursts Topics for the Day Stars: From the Cradle to the Grave
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February 18, 2003Lynn Cominsky - Cosmology A3502 Case Study: The Stars, Like Sparks of Fire In this interactive exercise, we will examine a “case study” of how astronomers study stars We will use the scientific method to observe, ask questions, then re- observe, modifying our questions and knowledge as our investigation expands
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February 18, 2003Lynn Cominsky - Cosmology A3503 Step 1: The Mighty Hunter
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February 18, 2003Lynn Cominsky - Cosmology A3504 Case Study 1: The Lights in the Sky are Stars Stars are points of light Different brightnesses Different colors Different distribution (many along Milky Way, not many at 90 degrees from it) Need distances to get physics, more understanding of their nature
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February 18, 2003Lynn Cominsky - Cosmology A3505 Case Study 2: The Stars, My Destination Astronomers measured distance. Have people predict what they think is brightness versus distance. Are brighter stars closer?
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February 18, 2003Lynn Cominsky - Cosmology A3506 Mag Lights 0.12 0.5 1.6 2.1 4.7 6.0 10.1
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February 18, 2003Lynn Cominsky - Cosmology A3507 Case Study 3: Distances Master Ogden and using Rigel’s brightness to get distance
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February 18, 2003Lynn Cominsky - Cosmology A3508 Parallax Introduction How it works. Get them to do it on their own with their thumbs.
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February 18, 2003Lynn Cominsky - Cosmology A3509 Distances to Stars Parallax : determined by the change of position of a nearby star with respect to the distant stars, as seen from the Earth at two different times separated by 6 months.
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February 18, 2003Lynn Cominsky - Cosmology A35010 Parallax, parsecs and light years 1 parsec is defined as the distance at which a star would have a parallax angle of 1 arc-second 1 arc-second = (1 degree/3600) = (1 degree/3600) ( radians/ 180 degrees ) = 4.85 x 10 -6 radians 1 parsec = (1.5 x 10 8 km)/(4.85 x 10 -6 ) = 3.086 x 10 13 km = 3.26 light years 1 light-year is the distance light will travel in one year 1 light-year = (2.998 x 10 8 m/s)(86400 s/d)(365 d/y) = 9.46 x 10 12 km = 9.46 x 10 15 m A LIGHTYEAR IS A DISTANCE, NOT A TIME!
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February 18, 2003Lynn Cominsky - Cosmology A35011 Parallax movie
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February 18, 2003Lynn Cominsky - Cosmology A35012 The Nearest Stars Distance to Alpha Centauri system is ~4 x 10 11 km or ~4.2 light years Distance between Alpha and Proxima Centauri is ~23 AU
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February 18, 2003Lynn Cominsky - Cosmology A35013 The Solar Neighborhood Some stars within about 2 x 10 14 km (~ 20 light years)
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February 18, 2003Lynn Cominsky - Cosmology A35014 Distances 430 772 242 721 817 1342 915 343 89
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February 18, 2003Lynn Cominsky - Cosmology A35015 Absolute vs. Apparent magnitude Apparent magnitude - How bright does the star appear (from the Earth)? Uses symbol “m” Absolute magnitude - the apparent magnitude of a star if it were located at 10 pc. Uses symbol “M” Absolute and apparent magnitude are related to the true distance “D” to the star by: m – M = 5 log (D/10 pc) = 5 log (D/pc) – 5 OR D = 10 pc * 10 ((m-M)/5) Magnitudes seem backwards – the bigger the number, the fainter the star.
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February 18, 2003Lynn Cominsky - Cosmology A35016 Case Study 3: The Star at Night are Clear and Bright Ogden now has distances, and can measure temperatures. With distance, can get absolute magnitude. Plots one versus the other.
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February 18, 2003Lynn Cominsky - Cosmology A35017 Orion Heat B8I M2I B2III B0I K5III A5V
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February 18, 2003Lynn Cominsky - Cosmology A35018 Classifying Stars Hertzsprung-Russell diagram
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February 18, 2003Lynn Cominsky - Cosmology A35019 Main Sequence Stars spend most of their lives on the Main Sequence How do they get there? What happens when they leave?
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February 18, 2003Lynn Cominsky - Cosmology A35020 Stellar Spectral types OBAFGKMLT (Oh, Be A Fine Guy/Girl, Kiss My Lips Thoroughly) Describe spectral features of stars Linked to temperature (not necessarily mass!) Once understood, leads to stellar life cycles
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February 18, 2003Lynn Cominsky - Cosmology A35021 Properties of Stars Temperature (degrees K) - color of star light. All stars with the same blackbody temperature are the same color. Specific spectral lines appear for each temperature range classification. Astronomers name temperature ranges in decreasing order as: Surface gravity - measured from the shapes of the stellar absorption lines. Distinguishes classes of stars: supergiants, giants, main sequence stars and white dwarfs. O B A F G K M
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February 18, 2003Lynn Cominsky - Cosmology A35022 Classes of Stars Bigger stars are brighter than smaller stars because they have more surface area Hotter stars make more light per square meter. So, for a given size, hotter stars are brighter than cooler stars. White dwarfs - small and can be very hot (Class VII) Main sequence stars - range from hotter and larger to smaller and cooler (Class V) Giants - rather large and cool (Class III) Supergiants - cool and very large (Class I)
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February 18, 2003Lynn Cominsky - Cosmology A35023 Life Cycles of Stars
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February 18, 2003Lynn Cominsky - Cosmology A35024 Molecular clouds and protostars Giant molecular clouds are very cold, thin and wispy– they stretch out over tens of light years at temperatures from 10-100K, with a warmer core They are 1000s of time more dense than the local interstellar medium, and collapse further under their own gravity to form protostars at their cores Orion in mm radio (BIMA) Simulation with narration by Jack Welch (UCB)
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February 18, 2003Lynn Cominsky - Cosmology A35025 Logan’s Run Introduce Logan’s Protostar game
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February 18, 2003Lynn Cominsky - Cosmology A35026 Protostars Orion nebula/Trapezium stars (in the sword) About 1500 light years away HST / 2.5 light years Chandra/10 light years
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February 18, 2003Lynn Cominsky - Cosmology A35027 Disks around stars There is much evidence of disks with gaps (presumably caused by planets) around bright, nearby stars, such as Beta Pictoris, or HD141569 (shown here)
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February 18, 2003Lynn Cominsky - Cosmology A35028 Stellar nurseries Pillars of dense gas Newly born stars may emerge at the ends of the pillars About 7000 light years away HST/Eagle Nebula in M16
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February 18, 2003Lynn Cominsky - Cosmology A35029 Pleiades Star Cluster A star cluster has a group of stars which are all located at approximately the same distance The stars in the Pleiades were all formed at about the same time, from a single cloud of dust and gas Roughly 10 8 years old D = 116 pc
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February 18, 2003Lynn Cominsky - Cosmology A35030 HR Diagram again as a reminder Hertzsprung-Russell diagram
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February 18, 2003Lynn Cominsky - Cosmology A35031 Main Sequence Stars Stars spend most of their lives on the “main sequence” where they burn hydrogen in nuclear reactions in their cores Burning rate is higher for more massive stars - hence their lifetimes on the main sequence are much shorter and they are rather rare Red dwarf stars are the most common as they burn hydrogen slowly and live the longest Often called dwarfs (but not the same as White Dwarfs) because they are smaller than giants or supergiants Our sun is considered a G2V star. It has been on the main sequence for about 4.5 billion years, with another ~5 billion to go
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February 18, 2003Lynn Cominsky - Cosmology A35032 Nuclear Fusion ! At 15 million degrees Celsius in the center of the star, fusion ignites ! 4 ( 1 H) --> 4 He + 2 e + + 2 neutrinos + energy Where does the energy come from ? Mass of four 1 H > Mass of one 4 He E = mc 2
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February 18, 2003Lynn Cominsky - Cosmology A35033 How much Energy 4 ( 1 H) --> 4 He + 2 e + + 2 neutrinos + energy Energy released = 25 MeV = 4 x 10 -12 Joules = 1 x 10 -15 Calories But the sun does this 10 38 times a second ! Sun has 10 56 H atoms to burn !
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February 18, 2003Lynn Cominsky - Cosmology A35034 A Balancing Act Energy released from nuclear fusion counter-acts inward force of gravity. Throughout its life, these two forces determine the stages of a star’s life.
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February 18, 2003Lynn Cominsky - Cosmology A35035 A Red Giant You Know
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February 18, 2003Lynn Cominsky - Cosmology A35036 The Beginning of the End: Red Giants After Hydrogen is exhausted in core... Energy released from nuclear fusion counter-acts inward force of gravity. Core collapses, Kinetic energy of collapse converted into heat. This heat expands the outer layers. Meanwhile, as core collapses, Increasing Temperature and Pressure...
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February 18, 2003Lynn Cominsky - Cosmology A35037 More Fusion ! At 100 million degrees Celsius, Helium fuses: 3 ( 4 He) --> 12 C + energy (Be produced at an intermediate step) (Only 7.3 MeV produced) Energy sustains the expanded outer layers of the Red Giant
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February 18, 2003Lynn Cominsky - Cosmology A35038 Stellar evolution made simple Stars like the Sun go gentle into that good night More massive stars rage, rage against the dying of the light Puff! Bang! BANG!
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February 18, 2003Lynn Cominsky - Cosmology A35039 How stars die Stars that are below about 8 M o form red giants at the end of their lives on the main sequence Red giants evolve into white dwarfs, often accompanied by planetary nebulae More massive stars form red supergiants Red supergiants undergo supernova explosions, often leaving behind a stellar core which is a neutron star, or perhaps a black hole (more in later lectures about these topics)
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February 18, 2003Lynn Cominsky - Cosmology A35040 Red Giants and Supergiants Hydrogen burns in outer shell around the core Heavier elements burn in inner shells
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February 18, 2003Lynn Cominsky - Cosmology A35041 White dwarf stars Red giants (but not supergiants) turn into white dwarf stars as they run out of fuel White dwarf mass must be less than 1.4 M o White dwarfs do not collapse because of quantum mechanical pressure from degenerate electrons White dwarf radius is about the same as the Earth A teaspoon of a white dwarf would weigh 10 tons Some white dwarfs have magnetic fields as high as 10 9 Gauss White dwarfs eventually radiate away all their heat and end up as black dwarfs in billions of years
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February 18, 2003Lynn Cominsky - Cosmology A35042 Planetary nebulae Planetary nebulae are not the origin of planets Outer ejected shells of red giant illuminated by a white dwarf formed from the giant’s burnt-out core Not always formed HST/WFPC2 Eskimo nebula 5000 light years
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February 18, 2003Lynn Cominsky - Cosmology A35043 Fate of high mass stars After Helium exhausted, core collapses again until it becomes hot enough to fuse Carbon into Magnesium or Oxygen. 12 C + 12 C --> 24 Mg OR 12 C + 4 H --> 16 O Through a combination of processes, successively heavier elements are formed and burned.
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February 18, 2003Lynn Cominsky - Cosmology A35044 Heavy Elements from Large Stars Large stars also fuse Hydrogen into Helium, and Helium into Carbon. But their larger masses lead to higher temperatures, which allow fusion of Carbon into Magnesium, etc.
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February 18, 2003Lynn Cominsky - Cosmology A35045 Periodic Table 16 O + 16 O 32 S + energy 4 He + 16 O 20 Ne + energy Light Elements Heavy Elements 4 ( 1 H) 4 He + energy 3( 4 He) 12 C + energy 12 C + 12 C 24 Mg + energy 4 He + 12 C 16 O + energy 28 Si + 7( 4 He) 56 Ni + energy 56 FeC-N-O Cycle
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February 18, 2003Lynn Cominsky - Cosmology A35046 The End of the Line for Massive Stars Massive stars burn a succession of elements. Iron is the most stable element and cannot be fused further. Instead of releasing energy, it uses energy.
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February 18, 2003Lynn Cominsky - Cosmology A35047 Supernova !
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February 18, 2003Lynn Cominsky - Cosmology A35048 Supernova Remnants: SN1987A ab cd a) Optical - Feb 2000 Illuminating material ejected from the star thousands of years before the SN b) Radio - Sep 1999 c) X-ray - Oct 1999 d) X-ray - Jan 2000 The shock wave from the SN heating the gas
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February 18, 2003Lynn Cominsky - Cosmology A35049 Supernova Remnants: Cas A OpticalX-ray
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February 18, 2003Lynn Cominsky - Cosmology A35050 Elements from Supernovae All X-ray Energies Silicon Calcium Iron
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February 18, 2003Lynn Cominsky - Cosmology A35051 Composition of the Universe Actually, this is just the solar system. Composition varies from place to place in universe, and between different objects.
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February 18, 2003Lynn Cominsky - Cosmology A35052 “What’s Out There?” A classroom activity that demonstrates the different elemental compositions of different objects in the universe. Demonstrates how we estimate the abundances. (Developed by Stacie Kreitman, Falls Church, VA)
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February 18, 2003Lynn Cominsky - Cosmology A35053 Top 10 Elements in the Human Body Element by # atoms 10.Magnesium (Mg)0.03% 9.Chlorine (Cl)0.04% 8.Sodium (Na)0.06% 7.Sulfur (S)0.06% 6.Phosphorous (P)0.20% 5.Calcium (Ca)0.24% 4. Nitrogen (N) 1.48% 3.Carbon (C) 9.99% 2.Oxygen (O) 26.33% 1.Hydrogen (H) 61.56%
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February 18, 2003Lynn Cominsky - Cosmology A35054 Spectral Analysis We can’t always get a sample of a piece of the Universe. So we depend on light !
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February 18, 2003Lynn Cominsky - Cosmology A35055 Spectral Analysis Each element has a unique spectral signature: Determined by arrangement of electrons. Lines of emission or absorption arise from re-arrangement of electrons into different energy levels. Hydrogen
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February 18, 2003Lynn Cominsky - Cosmology A35056 Nickel-odeon Classroom Activity Spread a rainbow of color across a piano keyboard (Developed by Shirley Burris, Nova Scotia) Then, “play” an element Hydrogen
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February 18, 2003Lynn Cominsky - Cosmology A35057 More Musical Elements Now play another element Helium Carbon And Another
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February 18, 2003Lynn Cominsky - Cosmology A35058 Getting a Handle on Water Oxygen All together now... Hydrogen Water
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February 18, 2003Lynn Cominsky - Cosmology A35059 Supernovae Supergiant stars become (Type II) supernovae at the end of nuclear shell burning Iron core often remains as outer layers are expelled Neutrinos and heavy elements released Core continues to collapse Chandra X-ray image of Eta Carinae, a potential supernova
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February 18, 2003Lynn Cominsky - Cosmology A35060 Making a Neutron Star
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February 18, 2003Lynn Cominsky - Cosmology A35061 Neutron Stars Neutron stars are formed from collapsed iron cores All neutron stars that have been measured have around 1.4 M o (Chandrasekhar mass) Neutron stars are supported by pressure from degenerate neutrons, formed from collapsed electrons and protons A teaspoonful of neutron star would weigh 1 billion tons Neutron stars with very strong magnetic fields - around 10 12-13 Gauss - are usually pulsars due to offset magnetic poles
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February 18, 2003Lynn Cominsky - Cosmology A35062 Neutron Stars: Dense cinders Mass: ~1.4 solar masses Radius: ~10 kilometers Density: 10 14-15 g/cm 3 Magnetic field: 10 8-14 gauss Spin rate: from 1000Hz to 0.08 Hz
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February 18, 2003Lynn Cominsky - Cosmology A35063 Crab nebula Observed by Chinese astronomers in 1054 AD Age determined by tracing back exploding filaments Crab pulsar emits 30 pulses per second at all wavelengths from radio to TeV movie
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February 18, 2003Lynn Cominsky - Cosmology A35064 Crab nebula Radio/VLA Infrared/Keck
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February 18, 2003Lynn Cominsky - Cosmology A35065 Crab nebula Optical/HST WFPC2 Optical/Palomar
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February 18, 2003Lynn Cominsky - Cosmology A35066 Crab nebula and pulsar X-ray/Chandra
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February 18, 2003Lynn Cominsky - Cosmology A35067 Cas A ~320 years old 10 light years across 50 million degree shell Radio/VLA X-ray/Chandra neutron star
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February 18, 2003Lynn Cominsky - Cosmology A35068 Not all explosions are created equal
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February 18, 2003Lynn Cominsky - Cosmology A35069 Classifying Bursts In this activity, you will be given twenty cards showing different types of bursts Pay attention to the lightcurves, optical counterparts and other properties of the bursts given on the reverse of the cards How many different types of bursts are there? Sort the bursts into different classes Fill out the accompanying worksheet to explain the reasoning behind your classification scheme
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February 18, 2003Lynn Cominsky - Cosmology A35070 What makes Gamma-ray Bursts? X-ray Bursts Properties Thermonuclear Flash Model Soft Gamma Repeaters Properties Magnetar model Gamma-ray Bursts Properties Models Afterglows Future Mission Studies
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February 18, 2003Lynn Cominsky - Cosmology A35071 X-ray Bursts Thermonuclear flashes on Neutron Star surface – hydrogen or helium fusion Accreting material burns in shells, unstable burning leads to thermonuclear runaway Bursts repeat every few hours to days Bursts are never seen from black hole binaries (no surface for unstable nuclear burning) or from (almost all) pulsars (magnetic field quenches thermonuclear runaway)
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February 18, 2003Lynn Cominsky - Cosmology A35072 X-ray Burst Sources Locations in Galactic Coordinates burstersnon-burstersGlobular Clusters Most bursters are located in globular clusters or near the Galactic center They are therefore relatively older systems
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February 18, 2003Lynn Cominsky - Cosmology A35073 X-ray Burst Source Properties Weaker magnetic dipole: B~10 8 G NS spin period seen in bursts ~0.003 sec. Orbital periods : 0.19 - 398 h from X-ray dips & eclipses and/or optical modulation > 15 well known bursting systems Low mass companions L x = 10 36 - 10 38 erg/s Neutron Stars in binary systems
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February 18, 2003Lynn Cominsky - Cosmology A35074 X-ray Emission X-ray emission from accretion can be modulated by magnetic fields, unstable burning and spin Modulation due to spin of neutron star can sometimes be seen within the burst
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February 18, 2003Lynn Cominsky - Cosmology A35075 Soft Gamma Repeaters There are four of these objects known to date One is in the LMC, the other 3 are in the Milky Way LMC SGR 1627-41
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February 18, 2003Lynn Cominsky - Cosmology A35076 Soft Gamma Repeater Properties Superstrong magnetic dipole: B~10 14-15 G NS spin period seen in bursts ~5-10 sec, shows evidence of rapid spin down No orbital periods – not in binaries! 4 well studied systems + several other candidate systems Several SGRs are located in or near SNRs Soft gamma ray bursts are from magnetic reconnection/flaring like giant solar flares L x = 10 42 - 10 43 erg/s at peak of bursts Young Neutron Stars near SNRs
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February 18, 2003Lynn Cominsky - Cosmology A35077 SGR 1900+14 Strong burst showing ~5 sec pulses Change in 5 s spin rate leads to measure of magnetic field Source is a magnetar!
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February 18, 2003Lynn Cominsky - Cosmology A35078 SGR burst affects Earth On the night of August 27, 1998 Earth's upper atmosphere was bathed briefly by an invisible burst of gamma- and X-ray radiation. This pulse - the most powerful to strike Earth from beyond the solar system ever detected - had a significant effect on Earth's upper atmosphere, report Stanford researchers. It is the first time that a significant change in Earth's environment has been traced to energy from a distant star. (from the NASA press release)
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February 18, 2003Lynn Cominsky - Cosmology A35079 Gamma Ray Burst Properties Unknown magnetic field No repeatable periods seen in bursts No orbital periods seen – not in binaries Thousands of bursts seen to date – no repetitions from same location Isotropic distribution Afterglows have detectable redshifts which indicate GRBs are at cosmological distances (i.e., far outside our galaxy) L = 10 52 - 10 53 erg/s at peak of bursts A cataclysmic event of unknown origin
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February 18, 2003Lynn Cominsky - Cosmology A35080 The first Gamma-ray Burst Discovered in 1967 while looking for nuclear test explosions - a 30+ year old mystery! Vela satellite
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February 18, 2003Lynn Cominsky - Cosmology A35081 Compton Gamma Ray Observatory Eight instruments on corners of spacecraft NaI scintillators BATSE
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February 18, 2003Lynn Cominsky - Cosmology A35082 The GRB Gallery When you’ve seen one gamma-ray burst, you’ve seen…. one gamma-ray burst!!
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February 18, 2003Lynn Cominsky - Cosmology A35083 GRBs the Second: Angling for GRBs Using data from several satellites in the solar system, you will use a “light ruler” to figure out the direction to a gamma- ray burst This is similar to the way that the Interplanetary Network (IPN) really works See http://ssl.berkeley.edu/ipn3/
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February 18, 2003Lynn Cominsky - Cosmology A35084 GRB the Third: The Plots Thicken Introduce it
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February 18, 2003Lynn Cominsky - Cosmology A35085 CGRO/BATSE Gamma-ray Burst Sky Once a day, somewhere in the Universe
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February 18, 2003Lynn Cominsky - Cosmology A35086 Near or Far? Isotropic distribution implications: Silly or not, the only way to be sure was to find the afterglow. Very close: within a few parsecs of the Sun Very far: huge, cosmological distances Sort of close: out in the halo of the Milky Way Why no faint bursts? What could produce such a vast amount of energy? A comet hitting a neutron star fits the bill
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February 18, 2003Lynn Cominsky - Cosmology A35087 Breakthrough! In 1997, BeppoSAX detects X-rays from a GRB afterglow for the first time, 8 hours after burst
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February 18, 2003Lynn Cominsky - Cosmology A35088 The View From Hubble/STIS 7 months later
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February 18, 2003Lynn Cominsky - Cosmology A35089 On a clear night, you really can see forever! 990123 reached 9 th magnitude for a few moments! First optical GRB afterglow detected simultaneously
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February 18, 2003Lynn Cominsky - Cosmology A35090 GRB the Fourth: Beam me Up Introduce the activity Problem: with known distance, what could give off that much energy? Maybe nothing! Need beaming.
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February 18, 2003Lynn Cominsky - Cosmology A35091 The Supernova Connection GRB011121 Afterglow faded like supernova Data showed presence of gas like a stellar wind Indicates some sort of supernova and not a NS/NS merger
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February 18, 2003Lynn Cominsky - Cosmology A35092 Hypernova A billion trillion times the power from the Sun The end of the life of a star that had 100 times the mass of our Sun movie
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February 18, 2003Lynn Cominsky - Cosmology A35093 Iron lines in GRB 991216 Chandra observations show link to hypernova model when hot iron-filled gas is detected from GRB 991216 Iron is a signature of a supernova, as it is made in the cores of stars, and released in supernova explosions
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February 18, 2003Lynn Cominsky - Cosmology A35094 Catastrophic Mergers Death spiral of 2 neutron stars or black holes
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February 18, 2003Lynn Cominsky - Cosmology A35095 Which model is right? The data seem to indicate two kinds of GRBs Those with burst durations less than 2 seconds Those with burst durations more than 2 seconds Short bursts have no detectable afterglows so far as predicted by the NS/NS merger model Long bursts are sometimes associated with supernovae, and all the afterglows seen so far as predicted by the hypernova merger model
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February 18, 2003Lynn Cominsky - Cosmology A35096 Gamma-ray Bursts Either way you look at it – hypernova or merger model GRBs signal the birth of a black hole!
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February 18, 2003Lynn Cominsky - Cosmology A35097 Gamma-ray Bursts Or maybe the death of life on Earth? No, gamma- ray bursts did not kill the dinosaurs!
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February 18, 2003Lynn Cominsky - Cosmology A35098 How to study Gamma rays? Absorbed by the Earth’s atmosphere Use rockets, balloons or satellites Can’t image or focus gamma rays Special detectors: crystals, silicon-strips GLAST balloon test
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February 18, 2003Lynn Cominsky - Cosmology A35099 HETE-2 Launched on 10/9/2000 Operational and finding about 2 bursts per month
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February 18, 2003Lynn Cominsky - Cosmology A350100 Swift Mission Burst Alert Telescope (BAT) Ultraviolet/Optical Telescope (UVOT) X-ray Telescope (XRT) To be launched in 2003
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February 18, 2003Lynn Cominsky - Cosmology A350101 Swift Mission Will study GRBs with “swift” response Survey of “hard” X-ray sky To be launched in 2003 Nominal 3-year lifetime Will see ~150 GRBs per year
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February 18, 2003Lynn Cominsky - Cosmology A350102 Gamma-ray Large Area Space Telescope GLAST Burst Monitor (GBM) Large Area Telescope (LAT)
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February 18, 2003Lynn Cominsky - Cosmology A350103 GRBs and Cosmology GRBs can be used as standard candles, similar to Type 1a supernovae However, the supernovae are only seen out to z=0.7 (and one at z=1.7), whereas GRBs are seen to z=4.5, and may someday be seen to z=10 Schaefer (2002) has constructed a Hubble diagram for GRBs, using the cosmological parameters from supernova data. When more burst redshifts become available (e.g., from Swift), the parameters can be determined independently
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