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Home , Apparent magnitude, Compact star, Dwarf nova, Giant star, Hayashi track, Luminous blue variable

2014 Div. C (High School) Help Session and Variable Scott Jackson Mt. Cuba Astronomical Observatory

• SO competition on March 1 st . • Resources – two laptop computers or two 3 ring binder or one laptop plus one 3 ring binder – Programmable calculator – Connection to the internet is not allowed! – Help session on Feb 7 th before competition at Mt. Cuba Observatory •

1 2 things you need to know • Specific objects (later) • Stellar evolution, including – spectral features and chemical composition, , blackbody radiation, (B-V), and H-R diagram transitions, -stars, variables , Cepheid variables, semiregular variables, red supergiants, variables , RR Lyrae variables , stars , , , x- ray binary systems , dwarf & recurrent , variables, Type II and Type Ia . – Kepler’s Laws , parallax, , and the to calculate distances to Cepheids, RR Lyraes and Type Ia supernovas • Distance scales • Period-luminosity relationship (Cepheids & RR Lyrae) • A ’s color or spectral class or surface temperature

• Scientific notation 3 Study aid -1 • Google each object, – Know what the look like in each part of the electromagnetic spectrum – Understand what each part of the spectrum means – Have a good qualitative feel for what the object is doing or has done within the astrophysical concepts that the student is being asked to know.

4 Study aid - 2 • Know the algebra behind the physics – Just because you think you have the right “equation” to use does not mean you know how to use it!!! – Some 1 st college courses in astronomy or will have good study aids and problems to practice with.

5 The test – 2 parts • Part 1 – multiple choice and a couple fill in the blanks

• Part 2 – word problems for astrophysics there will be some algebra ‰Solve the equations symbolically first then put in numbers!!!! ‰Hint: most problems will not need a calculator if done this way

6 • Mira, ---- , component A is a • W49B --- remnant • Tycho’s SNR -- • SNR -- Supernova remnant • G1.9+0.3 -- the youngest Galactic supernova remnant • -- expected to be supernova in the “near” future. • SS Cygni -- prototype periodic dwarf • T Tauri -- Pre- star, • GRS 1915+105 - X-ray binary = a regular star and a hole • -- a located in the . • The Trapezium -- tight of stars in the heart of the • -- a recurrent nova and in the constellation • Adell 30 -- A • RX J0806.3+1527 -- X-ray binary star system • V1647 Ori -- a pre–main sequence star which displays an extreme change • V1 --- Var 1 in M33 -- a star in a nearby . • NGC1846 --- Globular Cluster in the Large Magellenic cloud • NGC3132 ---a bright planetary nebula in the constellation Vela 7 Mira or Omicron Ceti • A star estimated 200–400 light away in the constellation . Mira is a binary star, consisting of the red giant Mira A along with . Mira A is also a variable star and was one of the first non- supernova variable star discovered. Mira is one of the brightest periodic variable in the sky. It is not visible to the for part of its cycle. It is a star in the very late stages of stellar evolution, on the , It is expelling its outer envelopes as planetary nebulae and will become a dwarf within a few million years. is fusing in its core. However, it can be thousands of times more luminous than the due to its very large distended envelopes. It is pulsating due to the entire star expanding and contracting

8 W49B • Supernova remnent (SNR G043.3-00.2 or 3C 398) is a nebula resulting from a supernova. [1] If the supernova was visible from it would have been seen around 1000 AD (the remnant "is about a thousand years old") which may have produced a -ray burst [2] and may have produced a . • W49B is barrel-shaped and located roughly 26,000 light-years from Earth. Recent findings indicate "rings" (about 25 light-years in diameter) around the "barrel", and also indicate intense X-ray radiation coming from nickel and along its axis. The star that created this nebula is thought to have formed from a dense dust cloud before throwing off hot, gaseous rings, creating a bubble, and exploding

9 Tycho’s SNR • SN 1572 (Tycho's Supernova , Tycho's Nova ), "B Cassiopeiae" (B Cas), or 3C 10 was a supernova of Type Ia in the constellation Cassiopeia, one of about eight supernovae visible to the naked eye in historical records. It burst forth in early November 1572 and was independently discovered by many individuals. [2 The color image depicts the X-ray emission. Most of the bright regions correspond to clumps of metal enriched material ejected from the star that exploded as a supernova over 400 years ago. Most notable is the weak rim of emission seen clearly around the entire remnant, which is believed to be the blast wave propagating through the surrounding circumstellar (or interstellar) medium

10 VELA SNR • The is a supernova remnant in the southern constellation Vela. Its source supernova exploded approximately 11,000-12,300 years ago (and was about 800 light years away). The association of the Vela supernova remnant with the Vela , made by astronomers at the University of Sydney in 1968, was direct observational proof that supernovae form neutron stars. The Vela supernova remnant includes NGC 2736. It also overlaps the Supernova Remnant, which is four times more distant. Both the Puppis and Vela remnants are among the largest and brightest features in the X-ray sky. This is a visible light image.

11 G1.9+0.3 the youngest Galactic supernova remnant (SNR), The expansion is shown in the lower image. NASA's Chandra X-ray Observatory image obtained in early 2007 is shown in orange and the radio image from NRAO's (VLA) from 1985 is in blue. The difference in size between the two images shows the expansion, allowing the X ray time since the original supernova explosion (about 140 years) to be estimated. This makes the original explosion the most recent supernova in the Galaxy, as measured in Earth's time-frame (referring to when events are observable at Earth). Equivalently, this is the youngest known supernova remnant in the Galaxy (140 years old), X ray (2007) and radio image (1985 – light blue) Eta Carinae • The system contains at least two stars, of which the primary is a luminous blue variable (LBV) that initially had around 150 solar , of which it has lost at least 30. A hot supergiant of approximately 30 solar masses is in around the primary, although an enormous thick red nebula surrounding Eta Carinae makes it impossible to see this companion optically. The Eta Carinae system is enclosed in the , itself part of the much larger Nebula, and currently has a combined luminosity of over five million times the Sun's. Because of its and the stage of its life, it is expected to explode in a supernova or in the astronomically near future.

13 SS Cygni SS Cygni is a variable star in the northern constellation (the Swan). It is perhaps the prototype , meaning that it undergoes frequent and regular outbursts - every 7 or 8 weeks . SS Cyg, like all other cataclysmic variables, consists of a close binary system. One of the components is a -type star, cooler than our Sun, while the other is a . Studies suggest that the stars in the SS Cyg system are separated (from surface to surface) by "only" 100,000 miles or less. In fact, the stars are so close that they complete their orbital revolution in slightly over 6 1/2

Artists conception 14 T Tauri • T Tauri stars (TTS) are a class of variable stars named after their prototype – T Tauri. They are found near molecular clouds and identified by their optical variability and strong chromospheric lines. T Tauri stars are pre-main sequence stars in the process of contracting to the main sequence along the , a luminosity-temperature relationship obeyed by infant stars of less than 3 solar masses in the pre-main-sequence of stellar evolution. It ends when a star of 0.5 solar masses develops a radiative zone, or when a larger star commences on the main sequence

T Tauri stars are the youngest visible F, G, K, M spectral type stars (<2 Solar mass). Their surface temperatures are similar to those of main sequence stars of the same mass, but they are significantly more luminous because their radii are larger. Their central temperatures are too low for fusion. Instead, they are Artists conception powered by gravitational released as the stars contract, while moving towards the main sequence, which they reach after about 100 million years. They typically rotate with a period between one and twelve days, compared to a month for the Sun, and are very active and variable 15 T Tauri

16 GRS 1915+105 • GRS 1915+105 or V1487 Aquilae is an X-ray binary star system which features a regular star and a black hole. It was discovered on August 15, 1992 by the WATCH all-sky monitor aboard Granat [1] "GRS" stands for "GRANAT source", "1915" is the (19 hours and 15 minutes) and "105" is in units of 0.1 degree (i.e. its declination is 10.5 degrees). The NIR counterpart was confirmed by spectroscopic observations. The binary system lies 11,000 away in . GRS 1915+105 is the heaviest of the stellar black holes so far known in the Galaxy, with 10 to 18 times the mass of the Sun. It is also a , and it appears that the black hole may rotate at 1,150 times per second.

Artists conception 17 47 Tucanae • 47 Tucanae (NGC 104) or just 47 Tuc is a globular cluster located in the constellation Tucana. It is about 16,700 light years away from Earth, and 120 light years across. It can be seen with the naked eye, with a visual apparent of 4.9. • The cluster appears roughly the size of the full in the sky under ideal conditions. • It is the second brightest globular cluster in the sky (after ), and is noted for having a very bright and dense core. It is also one of the most massive globular clusters in the Galaxy, containing millions of stars. • 47 Tuc's dense core contains a number of exotic stars. Globular clusters efficiently sort stars by mass, with the most massive stars falling to the center. 47 Tuc contains at least 21 blue stragglers near its core. It also contains hundreds of X-ray sources, cataclysmic variable stars containing white dwarfs accreting from companion stars, and low-mass X-ray binaries containing neutron stars that are not currently accreting, but can be observed by the X- rays emitted from the hot surface of the .47 Tuc has 23 known millisecond pulsars, the second largest population of pulsars in any globular cluster. These pulsars are thought to be spun up by the of material from binary companion stars, in a previous X-ray binary phase . 18 47 Tucanae

19 Trapezium The Trapezium, or Orion , is a tight open cluster of stars in the heart of the , in the constellation of Orion. It is a relatively young cluster that has formed directly out of the parent nebula. The five brightest stars are on the order of 15-30 solar masses in size. They are within a diameter of 1.5 light-years of each other and are responsible for much of the illumination of the surrounding nebula.

Visible light Infared light

20 T Pyxidis a recurrent nova and nova remnant in the constellation Pyxis. It's a binary star system It contains a sun-like star and a white dwarf. Because of their close proximity and the larger mass of the white dwarf, it draws from the larger, less massive star which causes periodic thermonuclear explosions to occur. The usual of this star system is 15.5, but there occurred eruptions with maximal apparent magnitude of about 7.0 in the years 1890, 1902, 1920, 1944, 1966 and 2011. Evidence seems to indicate that T Pyxidis may have increased in mass despite the nova eruptions, and is now close to the when it might explode as a Supernova. When a white dwarf reaches this limit it will collapse under its own weight and cause a type 1a supernova.

21 Abell 30 A planetary nebula – number 30 in the Abell catalogue. Planetary nebulae are created at the end stages of evolution of many low and intermediate mass stars. The expanding nebula is really the outer layers of the "old star". Although Abell 30 has a very uniform "bubble" on the outside, the interior region shows a lot of structure, In this image, Abell 30 is "in the act" of actually shedding the star's -rich gas mantle. Eventually only the tiny core of the original star will be left behind as a white .

X-ray image 22 RX J0806.3+1527 an X-ray binary star system about 1,600 light-years (490 pc) away. It comprises two dense white dwarfs orbiting each other once every 321.5 seconds, at an estimated distance of only 80,000 kilometres (50,000 mi) apart (about 1/5 the distance between the Earth and the Moon). The two stars orbit each other at speeds in excess of 400 kilometres per second (890,000 mph). The stars are estimated to be about half as massive as our own Sun, yet only the size of the Earth, which contributes to their high and is typical of white dwarfs. Astronomers believe that the two stars will eventually merge, based on data from the Chandra X-Ray Observatory, which shows that the of the two stars is steadily decreasing at a rate of 1.2 milliseconds per year as they thus are getting closer by approximately 60 centimetres (2.0 ft) per day. it is proof of Albert Einstein's theory of . This theory predicts that the stars will lose orbital energy by creating gravitational waves.

X-ray Illustration 23 V1647 Ori a pre–main sequence star which displays an extreme change in magnitude and spectral type. the FU Orionis flare with abrupt mass transfer from an accretion disc onto a young, low mass ,. Mass accretion rates for these objects are estimated to be around 10−4 solar masses per year. The rise time of these eruptions is typically ~ 1 year, but can be much longer. The lifetime of this high accretion, high luminosity phase is on the order of decades. However, even with such a relatively short timespan, an FU Orionis object has yet to be observed shutting off. The cyclic X-ray changes represent the appearance and disappearance of hot regions on the star that rotate in and out of view. The model that best agrees with the observations, say the researchers, involves two hot spots of unequal brightness located on opposite sides of the star. Both spots are thought to be pancake- shaped areas about the size of the sun, but the more southerly spot is about five times brighter.

24 NGC 1846 Globular Cluster in the . It is a spherical collection of hundreds of thousands of stars in the outer halo of the Large Magellanic Cloud. Aging bright stars in the cluster glow in intense shades of red and blue. The majority of middle-aged stars, several billions of years old, are whitish in color. A myriad of far distant of varying shapes and structure are scattered around the image.

Hertzprung-Russell Diagram

25 NGC 3132 Eight-Burst Nebula, the Southern , is a bright and extensively studied planetary nebula in the constellation Vela. two stars close together within the nebulosity, one of 10th magnitude, the other 16th. The central planetary nebula nucleus (PNN) or white dwarf central star is the fainter of these two stars. This hot central star of about 100,000 K has now blown off its layers and is making the nebula fluoresce brightly from the emission of its intense radiation

26 S Doradus variables Luminous blue variables (LBVs) are massive evolved stars that show unpredictable and sometimes dramatic variations in both their spectra and their brightness. They are also known as S Doradus variables after S Doradus, one of the brightest stars of the Large Magellanic Cloud. They are extraordinarily rare with just 20 objects listed in the General Catalogue of Variable Stars as SDor, and a number of these are no longer considered to be LBVs. The LBV stars like and Eta Carinae have been known as unusual variables since the 17th century, but their true nature was not fully understood until much more recently. The term "S Doradus variable" was used to describe them as a group in 1974

27 Kepler’s laws – how astronomers “weigh” stars 1. are ellipses with sun at one focus 2. Equal areas swept out in equal time 3. Harmonic law: Square of the period (P) is proportional to the cube of the semimajor axis (a). -- Gold standard for determining star’s masses in a binary system. Kepler’s law

2 3 P = a / (m1 + m2) P = orbital period (years) A = Distance between the two bodies (expressed in astronmical units – average distance from earth to sun) m1, m2 = mass of the two bodies orbiting each other (solar

masses) 28 Y axis is always Hertzsprung-Russell Diagram brightness or relative luinosity X axis is always temperature, color or spectral class Each dot is a star A is the location of our sun on the main sequence B are red giant stars that are fusing helium in their core C are red supergiants with Helium and Hydrogen buring in http://outreach.atnf.csiro.au/education/senior/cosmicengine/stars_hrdiagram.html shells and in its core D are white dwarfs (super hot carbon stars) 29 Hertzsprung-Russell Diagram

• Stars on the main sequence fuse hydrogen to helium in their cores • Giants and supergiants are fusing hydrogen outside the core. They may be fusing heavier elements in the core. • White dwarfs do not have active cores – they are dead stars (mostly carbon) that are cooling off)

• http://outreach.atnf.csiro.au/education/senior/cosmicengine/stars_hrdiagram.html 30 31 Neutron stars • A type of stellar remnant that can result from the of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of , which are subatomic particles without electrical charge and with slightly larger mass than . Neutron stars are very hot and are supported against further collapse by quantum degeneracy pressure due to the Pauli exclusion principle. This principle states that no two neutrons (or any other fermionic particles) can occupy the same place and quantum state simultaneously. • A typical neutron star has a mass between about 1.4 and 3.2 solar masses [1][2][3] (see Chandrasekhar Limit), with a corresponding radius of about 12 km if the Akmal– Pandharipande–Ravenhall (APR EOS) is used. [4][5] In contrast, the Sun's radius is about 60,000 times that. The density of a neutron star is approximately equivalent to the mass of a Boeing 747 compressed to the size of a small grain of sand, or the population condensed to the size of a sugar cube. [9] • In general, compact stars of less than 1.44 solar masses – the Chandrasekhar limit – are white dwarfs, and above 2 to 3 solar masses (the Tolman–Oppenheimer–Volkoff limit), a star might be created; however, this is uncertain. Gravitational collapse will usually occur on any between 10 and 25 solar masses and produce a black hole. [10] Some neutron stars rotate very rapidly and emit beams of electromagnetic radiation as pulsars . 32 Type 1A Supernovae • “Normally”, the white dwarf explodes in a supernovae when it reaches the Chandrasekhar limit of about 1.38 solar masses. Degenerate pressure is exceeded and the collapse forms a neutron star. • The current view is that never reaches this limit. The “normal” core collapse never occurs. Instead, the increase in pressure and density due to the increasing mass sucked in from the companion raises the temperature of the core and the white dwarf approaches to within about 1% of the Chandrasekhar limit. A period of intense power production () occurs for as much as 1,000 years. is in this stage. • At some point an explosive shock front is created that is powered by carbon fusion and then Oxygen fusion. Once fusion has begun, the temperature of the white dwarf rises. The white dwarf is unable to regulate the burning process and there is run away fusion reactions. It is generally accepted that a substantial fraction of the carbon and oxygen in the white dwarf is burned into heavier elements within a period of only a few seconds. • This raises the internal temperature to billions of degrees releasing enough energy to make individual particles making up the white dwarf to fly apart from each other. The star explodes violently and ejects material at speeds on the order of 5,000 to 20,000 km/sec or roughly up to 6% of the speed of light. The energy released in the explosion also causes an extreme increase in luminosity. The typical visual of Type Ia supernovae is Mv = −19.3 (about 5 billion times brighter than the Sun). • Kepler’s and Tycho’s SNR were formed in this manner. • SNR 0509-67.5 appears to have been created by an object in excess of the Chandrasikhar limit. It was likely created from the merger of two white dwarfs. • Type II supernovaes are caused by the collapse of the star’s core. That is, are pushed into protons causing a huge of that blows the star apart leaving behind a neutron star or black hole.. 33 http://en.wikipedia.org/wiki/Type_Ia_supernova Hertzsprung-Russell Diagram

• Stars on the main sequence fuse hydrogen to helium in their cores • Giants and supergiants are fusing hydrogen outside the core. They may be fusing heavier elements in the core. • White dwarfs do not have active cores – they are dead stars (mostly carbon) that are cooling off)

• http://outreach.atnf.csiro.au/education/senior/cosmicengine/stars_hrdiagram.html 34 The birth of a 1 star going onto the main sequence. Before point 4 , contraction of intersteller gas cloud. The cloud heats up as it contracts, causing its luminosity to increase -- we don’t see it because the is hidden in dust. From point 4 to 6 , -- The cloud contracts more and its luminosity drops. Point 6, hydrogen starts to fuse to helium in the stars core. The heat generated from fusion balances . The star’s surface heats up slightly. This is the location of T Tauri stars Point 7. The star has reached a long lived equilibrium where the heat from fusing hydrogen to helium balances gravity. The star resides on the main sequence for most of its life (~10 billion years for a 1 solar mass star). 35 7 to 8 branch, Hydrogen burns in shell around He core 8 to 9 Red giant branch, ditto -- at 9, He starts to fuse in core () 9 to 10 He burns in core, H burns in moves to new equilibrium . New “equilibrium” position for the red where He burns in core. This is the location for Cepheid variables and RR Lyrae variables stars 10 to 11 Red supergiant branch. Star has exhausted He in its core, it continues to burn He in shell and H in an outershell. Carbon in its core collapses under gravity. 11 to 13. White dwarf is formed in a planetary nebula 36 Categorizing stars by their spectra 1. Spectra can tell you 2. Absorption (dark) the stars approximate lines in a star’s spectra temperature give a finger print of (blackbody radiation) elements that are seen in that spectral class of stars

BUT emission spectra spectra (bright lines against a dark background) are given off nebulae – glowing gas clouds

37 Stars appear to be radiators The wavelength at maximum radiation changes with temperature λ max = 550 nm ‰ 5300 K temperature

λ max x Temperature = constant = 2.9E06 nm-°K Or = 2.9E07 A-°K Nm[=] nanometers for wavelength Or A [=] Angstrom units for wavelength

°K [=] degrees Kelvin 38 Dark (absorption) lines in emission spectra (of stars) or bright lines in nebulea • Electron transition from a lower energy state to a higher energy state ‰ adsorption line • Electron transition from a higher energy state to a lower energy state ‰ emission line • Below is the of lines associated with electron transition in the hydrogen to and from the second lowest energy level • H-α (“hydrogen alpha”) is an important line in both emission and absorption spectra. It has a wavelength of 656.3 nm or 6563 Angstroms

39 More on stars spectral class

40 Spectral class of stars He+ lines

H Balmer lines (B,A & F stars)

Ca+ lines (F & G stars)

Fe and neural metals K & M stars)

TiO2 lines

41 λ • max = 4200 A ‰ Example of a star’s spectra 6900 K temperature • Strong hydrogen lines, ‰B, A, and F type star • No helium lines not a B star. • ionized calcium (the H and K lines), • ‰This is an F type star

42 Spectra of T Tauri Stars The spectra typically show strong emission lines from Ha (Balmer series), Ca II at 3933Å and 3968Å, and sometimes iron also. Absorption lines of lithium are typical.

Hα

Hβ

43 Full spectrum from gamma rays to very long radio waves

• Black body radiation is applicable across the whole spectrum • An object emitting radio waves is very cold • An object emitting xrays is very hot.

44 Measuring Distances…

First brightness of stars…

45 Brightness of a star: A star’s magnitude

• Magnitude is more often used to describe an objects brightness. • The higher the magnitude the dimmer the object. – The apparent magnitude of our sun is -26.7 – The apparent magnitude of a is -12.6 – The apparent magnitude of the is ~ -1 – Dimmest star you see (in Wilmington) ~+3.5 – Dimmest star you see in a dark sky location ~+5.5 • The absolute magnitude is the magnitude of the star / object if it was place a fixed distance away (10 parsecs -- later).

46 Brightness of Stars • Brightness measured as luminosity or magnitude – Luminosity is the total energy output of a star • Depends on size and surface temperature • Usually measure relative to our sun, e.g., 4 times our sun. – A star’s magnitude is the of its luminosity – Apparent magnitude (m) [what we see] – is determined by four factors • Its temperature or color (wattage of a light bulb) • Its size • How far away it is • If it is obscured by dust – Absolute magnitude (M) • Magnitude of a star when viewed from a fixed distance

• Most abs magnitudes will be a negative number (bright) 47 Luminosity • Stefan-Boltzmann Law (black body radiation) – Energy/time/area = σσσ T4 • .σσσ = a constant (Stefan Boltzmann constant) • T4 = absolute surface temperature (Kelvin) • The total surface area of a spherical star is = 4 πππR2 • The total energy output by a star, Stellar Luminosity (energy emitted per second) is: – L ~= 4 πππR2 σσσ T4 – Most are measured relative to the sun L(sun)=1 • BUT what we see is the light flux at the star’s distance (D). – This total energy output is “spread out” on a sphere that is 4 πππD2 in area – Light flux is L/4 πππD2 48 49 Distances • . Average distance between the earth and our sun. (AU = 1.496x10 11 meters or 97 million miles or about 8.3 light minutes) This is a small unit of measure. – Used for interplanetary measures and for distances between stars in binary star systems (Kepler’s Laws) • Light years. The distance light travels in a year – LY = 9.46x10 15 meters, 6.33x10 4 AU • [pc]. The distance to an object that has a parallax of 1 arc second (next slide) ‰ preferred unit by astronomers pc = 3.26 LY = 2.06x10 5 AU = 3.086x10 16 meters • Kiloparsecs (Kpc) ‰ 1000 parsecs (10 3 parsecs) • Megaparsecs (Mpc) ‰ 1 million parsecs (10 6 parsecs)

50 51 • Geometric parallax Ï Gold standard for distances – 1 Parsec = 3.09 × 10 16 meters • parsec - (pc): distance at which an object would have a parallax of one arc second. Equals approximately 3.26 light years or about 206,265 astronomical units

52 Relationship between absolute and apparent magnitude and distance ‰ Distance modulus is m-M

The larger the distance modulus the further away the object is. Little m is usually >+10 Capital M is usually negative, 53 Relationships between distance modulus, luminosity, distances in parsecs and absolute magnitude

Astronomical unit = average earth- sun distance

What is distance modulus for our sun? 54 55 Instability gaps on an H-R diagram for the pulsating class of variable stars ‰Period of pulses scale with absolute brightness of the star “Period-luminosity relationship”

• http://outreach.atnf.csiro.au/education/senior/astrophysics/variable_pulsating.html 56 7 to 8 Subgiant branch, Hydrogen burns in shell around He core 8 to 9 Red giant branch, ditto -- at 9, He starts to fuse in core 9 to 10 He burns in core, H burns in shell star moves to new equilibrium Horizontal branch . New “equilibrium” position for the red giant star where He burns in core. This is the location for Cepheid variables and RR Lyrae variables stars 10 to 11 Red supergiant branch. Star has exhausted He in its core, it continues to burn He in shell and H in an outershell. Carbon in its core collapses under gravity.

57 Semiregular

Instability gaps on an H-R diagram for the pulsating class of variable stars Star periodically changing size or He changing ionization state and changing the star’s transparency of its outer atmosphere (Cepheid)

• http://outreach.atnf.csiro.au/education/senior/astrophysics/variable_pulsating.html 58 Semiregular

P is period P=0.8 to 35 days, P=0.2 to 1 days, ∆M~0.3-1.2 ∆M is change ∆M~0.2-2.0 in magnitude P=80 to 1000 days, ∆ (apparent or M~2.5-5.0 absolute)

• http://outreach.atnf.csiro.au/education/senior/astrophysics/variable_pulsating.html 59 Period-Luminosity Relationship equation for type 1 Cepheid

For Type I, Type II Cepheids and RR Lyrae Cepheids named after the first star discovered in the constellation (up north) M = -2.81* log(P)-1.43 Note this is luminosity – these stars are much P is period in days brighter than our sun.

• http://outreach.atnf.csiro.au/education/senior/astrophysics/variable_cepheids.html

60 Light curve for

• Saw tooth curve for Type 1

61 RR Lyrae and Cepheid stars as standard candles • Find the period. • This gives the luminosity or its absolute magnitude • Measure the apparent magnitude. • Determine the distance from the apparent and absolute magnitude (distance modulus) The same applies to RR Lyrae variable stars. Once you know that a star is an RR Lyrae variable (eg. from the shape of its light curve), then you know its luminosity

M = -2.81* log(P)-1.43 Type 1. P is period in days

62 63 Supernovae, two types (Type Ia and Type II)

1a

This plateau from the radioactive glow of heavy elements

64 Type Ia supernovae is where a white dwarf Because the type 1a “blows collapses because it up” at the same mass limit has pulled too much (see earlier discussion) (Chandrasekhar limit ~1.4x material from a mass of our sun) they have nearby companion about the same absolute star onto itself. magnitude at its peak brightness ‰ Standard candle

65 Using Type Ia supernovae as a standard candle • Because a type Ia “explodes” at the Chandrasekhar limit, all type Ia SN are about the same brightness – Type 1a have an absolute magnitude of about M~ -19.5 (that is a negative sign) • Observed in distant galaxies. • Observe a supernovae as it occurs, • Construct its light curve • From the light curve determine if it is a type 1a and estimate is maximum apparent magnitude (m) • Distance modulus is then (m+19.5) for Type Ia supernovae (m is apparent magnitude)

66 67 Red shifting a star’s spectrum

Wavelength of light (nanometers, nm)

1 nm = 1x10 -9 meters

Increasing red shift 68 Hubble’s law (measurement to very distant galaxies) Fundamental parameter ‰ measure of the expansion of our

Hubble’s Law: d = Vr or for small distances d = z * c (z < 0.5)

Ho Ho d = distance in megaparsecs (millions of parsecs) Vr is recessional velocity (km/sec) Measure using red shift of the light spectrum of a galaxy

Ho is Hubble’s constant, ~75 km/sec / megaparsecs z is the red shift = wavelength of the observed light -1 wavelength of the emitted light

C is the speed of light (3x 10 5 km/sec)

Problem: if wavelength of the observed light is 440 nm and the wavelength of the emitted light is 400 nm

What is Z? What is recessional velocity? What is the distance using Hubble’s law? In mpc? In light years? 69 Answer to problem z = 440 -1 = 1.1 -1 = 0.1 400 Vr = 0.1 x 3x 10 5 (km/sec) = 3x 10 4 (km/sec)

What is the distance using Hubble’s law? D = 3x 10 4 km/sec / (75 km/sec/mpc [kilometers/second/megaparces]) = 3/7.5 x 10 3 megaparces (mpc) = 0.4 x 10 3 mpc = 400 mpc = 3.26 light year / pc x 10 6 pc/mpc x 400 mpc = 1304 x 10 6 light years or = 1.3 x 10 9 ly

70 71 Mass of the main sequence star is reduced as it evolves and dies.

Material is shed either during the formation of a planetary nebulea (white dwarf) or during a supernovae.

The supernovae in this diagram are meant to be Type II and not Type Ia.

72 73 More info… An star’s is named using its constellation and letter of multiple letter designation. So… RY Sagittarii is in the constellation Sagittarius (summer sky) and counting up using the alphabet (a, b, c, d, e… z, AA, AB,…. ) it is star RY in this constellation. A class of stars (like the Cepheid variables or RR Lyrae variables) are named after the first star discovered in that class of stars. So the first Cepheid variable was discovered in the constellation of Cepheus. The RR Lyrae variables are named after the RR Lyrae (in the constellation of [string instrument]). The T Tauri stars were named after T Tauri (a star in ). 74