Temperature, Blackbodies & Basic Spectral Characteristics.

Temperature, Blackbodies & Basic Spectral Characteristics.

Things that have one primary temperature but also exhibit a range of temperatures are known in physics as blackbodies. They radiate energy thermally. Humans are blackbodies, primarily glowing in the infrared. Candles (fire!) and Incandescent lightbulbs are blackbodies. Stars are blackbodies. The sun glows primarily in the visible light.

Basic spectral form of a blackbody. energy output peaks at a given wavelength that wavelength indicates the overall temperature of the blackbody trails off at long wavelengths this is called the Rayleigh-Jeans tail (i.e. cooler temperatures, lower energies than the peak) dives to near nothing at shorter wavelengths (higher energies, higher temperatures): Wien s approximation. wavelength

Property of a blackbody: If it s the same size but hotter then it s giving off more energy at all wavelengths Hotter energy output Cooler wavelength

While blackbodies seem to be the most fundamental form of thermal emission, or building block, and stars are all blackbodies, astronomical objects are not all blackbodies! energy output wavelength Energy output can be flat, spiked, sloped, etc. and there is a WEALTH of information in an object s spectrum.

Spectrum of the Sun

The plot below shows three different blackbodies (A, B, & C). 1. Which one outputs the most blue light? 2. Which one appears the most blue? 3. Which one outputs the most red light? energy output A C B 4. Which one appears the most red? wavelength

The plot below shows three different blackbodies (A, B, & C). 1. Which one outputs the most blue light? A 2. Which one appears the most blue? A 3. Which one outputs the most red light? energy output A C B B 4. Which one appears the most red? C wavelength

How gas interacts with light. Take a specific gas, like hydrogen. In chemistry class you learn that it requires a specific energy to move electrons from different orbitals. Those are very specific energies. Shining a white light through a gas cloud that is cold results in absorption of light of that specific energy. ABSORPTION LINES

How gas interacts with light. Shining a white light through a gas cloud that is cold results in absorption of light of that specific energy. ABSORPTION LINES energy output wavelength EMISSION LINES energy output wavelength

energy leaves the gas (cooling!) energy goes into the gas (heating!) ABSORPTION LINES energy output wavelength EMISSION LINES energy output wavelength

Spectrum of the Sun

What we have learned Wien s Displacement Law T / / 1 Planck Function B (,T)= 2h 3 c 2 1 e h kt 1 energy output Hotter Blackbodies! Cooler wavelength

Wien s Displacement Law T / / 1 Planck Function B (,T)= 2h 3 1 c 2 What we have learned e h kt 1 energy output Hotter Blackbodies! Cooler wavelength Now we want to apply these tools to objects in space!

STARS 1. Magnitude System 2. Luminosity vs. Flux vs. Temperature 3. Stellar Classification & Composition

Stars Brightness ~ it s energy output. How can we measure this? 2 2 3 1 1 1 3 1 3 2 3 3 2 2 1 2 3 Ancient methods of measuring stellar brightness: classifying them into different classes or magnitudes 2 3

Stars Brightness ~ it s energy output. How can we measure this? 2 2 3 1 1? 1 3 1 3 2 3 3 1 Using our new numbering 2system, 2 what number would you assign 2the star in the green circle here? 3 Ancient methods of measuring stellar brightness: classifying them into different classes or magnitudes 2 3

The magnitude system. m= 2.5log(Flux)+Const WHAT?! Why would this EVER make sense? But it s actually how our eyes see the world! Our eyes are LOGARITHMIC light detectors! Objects that we perceive to be ~5 times brighter than a reference object (e.g. glowing screen vs sky) are ACTUALLY 100 times brighter.

The magnitude system. m= 2.5log(Flux)+Const In astronomy, magnitudes computed relative to a reference star, for example: Vega. We assert that Vega has a magnitude of 0, all other magnitudes of objects in the sky are compared to Vega: m= 2.5log(Flux) 2.5log(Flux Vega ) or m= 2.5log( Flux Flux Vega )

We assert that Vega has a magnitude of 0, all other magnitudes of objects in the sky are compared to Vega: m= 2.5log(Flux) 2.5log(Flux Vega ) or m= 2.5log( Flux Flux Vega ) For example, if there is a faint star next to Vega that is ~10 times fainter (10 times less flux) what is its magnitude?

Comparing magnitudes and fluxes for two different stars: m 1 m 2 = 2.5 log( F 1 F 2 ) How much fainter is a 4th magnitude star than a 0th magnitude star? Discuss.

The Hubble Space Telescope can see stars/distant objects down to 28th magnitude. How much fainter is that than our naked eye limit at ~6th magnitude? ~6e8 times = 600,000,000 times fainter

What we have learned. remember!! F = L 4 r 2 Magnitudes m 1 m 2 = 2.5 log( F 1 F 2 ) Flux follows an inverse square law with distance. m= 2.5log( Flux Flux Vega )

How much does the luminosity of stars vary? Knowing their distance with parallax, and measuring solar luminosity flux, we can infer their luminosities. L = 3.8 10 33 erg s 1 = = 3.8 10 26 J s 1 3.8 10 26 W The least to most luminous stars: 10 4 10 6 L (1/10,000) (1,000,000)

Absolute magnitudes Much more analogous to luminosity than apparent magnitude: does not vary with distance to the star. It s a way of stating a star s luminosity in terms of a magnitude the magnitude that star would be on the sky if put at a distance of 10pc. 10pc

Absolute magnitudes Much more analogous to luminosity than apparent magnitude: does not vary with distance to the star. It s a way of stating a star s luminosity in terms of a magnitude the magnitude that star would be on the sky if put at a distance of 10pc. apparent mag. M = m 5(log 10 (D L ) 1) absolute mag. distance to star in parsecs 10pc

STARS PART 2: Stellar Classification & How stars work

How would you start to classify these stars? brightness ~ flux/luminosity color ~ temperature

Brightest Dimmest Hottest Coldest

The Hertzsprung-Russell Diagram: comparing stellar luminosity with color/temperature most stars sit on the main sequence stars that are at some other point in HR diagram: almost always dying or dead

The Hertzsprung-Russell (HR) Diagram: comparing stellar Brightest luminosity with color/temperature Smallest supergiants main sequence white dwarfs giants Largest by next class period you ll be able to explain all parts of this! Dimmest Hottest Coldest

Temperature of the Surface of the Sun Temperature hard to measure this way unless you have a very precise (modern) camera! From the overall shape of the spectrum.

The Computers of 1800s Harvard Observatory actual astronomers

Annie Jump Cannon (1863-1941) classified most stars in the entire sky down to 9th magnitude. Set classifications: O B A F G K M

Lines in a star's spectrum correspond to a spectral type. O B A F G K M

Strong evidence of elements like carbon, nitrogen, sodium, calcium in the spectrum of the sun & other stars: It was largely thought at the end of the 19th century that the stars were mostly made of the same elements that make up the Earth.

Cecilia Payne-Gaposchkin: asked, what are stars made of using Cannon s extensive catalog.

Cecilia Payne-Gaposchkin: asked, what are stars made of using Cannon s extensive catalog. The most important PhD thesis in modern astrophysics: the stars are MOSTLY hydrogen (and helium) with trace levels of other elements. We only see those strong lines from the trace elements when there are variations in stellar temperature.

Lines in a star's spectrum correspond to a spectral type that reveals its temperature. (Hottest) O B A F G K M (Coldest)

The ionization states of different elements in the sun give a very accurate temperature constraint! And was easy to measure by eye Meghnad Saha developed the Saha equation to explain the ionization of different elements as a function of temperature. Put together with the work of Annie Jump Cannon & Cecelia Payne, describes our understanding of stellar classification. Saha Eq. (you don t need to know!)

So we can basically thank these three lovely people for figuring out the difference between different types of stars for us by the 1920s (i.e. stellar classification) Annie Jump Cannon Cecelia Payne Meghnad Saha

Lines in a star's spectrum correspond to a spectral type that reveals its temperature. (Hottest) O B A F G K M (Coldest)

Chemical Composition From detailed spectral line structure (which also gives pressure/density of the gas.)

Luminosity ~ Energy Output Temperature has a relationship with Luminosity but this takes a particular form for blackbodies: Stefan-Boltzmann Law F / T 4 F = T 4 =5.67 10 8 Wm 2 K 4 Peak wavelength temperature