COSMOS: UCI – Part 1

COSMOS Cluster 2 as Saturn and Its Moons

COSMOS Cluster 2 as Higgs Boson

This past month (June 24, 2012- July 21, 2012), I attended the COSMOS (California State Summer School for Mathematics and Science) at the University of California, Irvine, with brilliant minds from Northern and Southern California, as well as other states. The 152 students were divided into 8 clusters. I was part of Cluster 2: Astronomy and Astrophysics. With 22 other COSMOS students, I ventured into the world of astronomy and astrophysics unraveled by UCI professors Dr. Tammy Smecker- Hane, Dr. James Bullock, Dr. Aaron Barth, Dr. Erik Tollerund, TAs John Phillips, Liuyi Pei, and Shea Garrison-Kimmel, and Teacher Fellow Lisa Taylor. I discovered that all students shared a strong passion for astronomy and high aptitudes for learning. It has been my honor to learn with the students, listen to the professors’ lectures, and follow the TAs’ instructions for CLEA (Contemporary Laboratory Experiences in Astronomy) Labs.

For a cumulative final, the TAs divided the class into 8 groups for Project Labs:

“Deriving the Mass of Saturn” (By: Angel Guan, Francisco Terrones, and Luis Loza; Directed By: Liuyi Pei)

1. Deriving the Mass of Saturn

“Finding the Angular Velocity of an Asteroid” (By: Rachel Banuelos and Luis Salazar; Directed By: John Phillips)

2. Finding the Angular Velocity of Asteroids

3. Properties of an Eclipsing Binary Star System

  • By: Carlin Liao, Matthew Thibault, Sara Sampson; Directed By: Shea Garrison-Kimmel

4. Determining Stars’ Properties Using Stellar Spectra

  • By: Tina Liu, Noemi Urquiza, John Cabrera; Directed By: John Phillips

“Determining the Properties of Open Cluster M11″ (By: Luzanne Batoon, Julian Rose, Janet Lee; Directed By: Tammy Smecker-Hane)

5. Determining the Properties of Open Cluster M11

“Determining the Properties of Globular Cluster M13″ (By: Dennis Feng, Maricruz Moreno, Collen Murphy; Directed By: Tammy Smecker-Hane)

6. Determining Properties of Globular Cluster M13

7. Dark Matter in the Universe: Measuring the Rotation of Spiral Galaxies

  • By: Emma MacKie, Danny Tuthill, Michael Cox; Directed By: Shea Garrison-Kimmel)

8. Number Counts of Distant Galaxies and the Shape of the Universe

  • By: David Wong, Thomas Purdy, Joshua Heck; Directed By: Liuyi Pei

“Determining Stars’ Properties Using Stellar Spectra” (By: Tina Liu, Noemi Urquiza, John Cabrera)

- The red, white, yellow, and blue dots in the background represent stars of the H-R Diagram, including main sequence stars, red giants, and white dwarfs.

My Project: Determining the Properties of Stars Using Stellar Spectra (By: Tina Liu, John Cabrera, and Noemi Urquiza; Directed By: John Phillips)

ABSTRACT: Stellar spectra are fundamental in understanding properties — temperature, spectral type, chemical composition, and mass — of stars.  A spectrum is the amount of light that a star emits through narrow slit about 1 Angstrom in width. With the UCI Observatory’s 24-inch telescope and its photograph and ST-8 CCD camera, images of stars’ spectra — those of Arcturus, Vega (HD172167), and HD142780— were taken. Using the software program IRAF, the spectra were extracted, calibrated, and analyzed. Since stars are classified by spectral types, stellar spectra help distinguish a more massive and hotter star from a less massive and cooler star. Analyzing the strengths of absorption lines shows the stars’ compositions of elements such as hydrogen, helium, and calcium. While hotter stars such as Vega are more massive and have strong hydrogen absorption lines, cooler stars such as Arcturus are less massive and have strong neutral metals lines. Understanding stars’ properties leads to a better grasp of the past, present, and future of the Universe.

QUESTION: How can we use stellar spectra to determine the properties of stars such as spectral type, temperature, mass, and chemical composition?

Spectra of different elements including hydrogen, helium, and neon

BACKGROUND INFORMATION: Stars, actually infinitesimally small points of light, appear to twinkle because light refracts at Earth’s atmosphere. Held by gravity, stars shine due to nuclear fusion, its source of fuel. Their lifetimes depend primarily on mass; for their prime of life, stars, travel along the main sequence on the Hertzsprung- Russell, or Color- Magnitude Diagram. A stellar spectrum is the amount of light a star emits at a narrow wavelength interval (about 1 Angstrom, or 10^-10 meters). Each element has a distinguishable pattern of absorption lines (dark bands along the spectrum). Spectral types are a classification scheme developed by Annie Jump Cannon in the late 1800s and early 1900s. The spectral types are ordered in decreasing surface temperatures: O, B, A, F, G, K, M. Originally the classification scheme was A, B, C, D, etc. and stars were ordered according to the strengths of their Balmer (hydrogen) lines. Since stars with the strongest Balmer lines are not necessarily the hottest stars (hotter temperatures caused electrons to be excited and the atom to be ionized- lose electrons), the scheme was rearranged. The two stars analyzed were two variable stars: Arcturus of the constellation Boötes and Vega of the constellation Lyra.

MATERIALS:

  • 24-inch telescope, ST-8 CCD camera
  • Needed Files on Linux (software):
    • uciobs_fear_lowres.dat (from observatory website): List of arc lines used for wavelength calibration
    • arc_red.jpg (from website): Plots of arc images, with wavelengths of prominent lines
    • plotspec.pro : Plots the reduced spectrum and marks absorption lines that are found in LINES.UCI file
    • wave : File containing wave limits of reduced spectra. Needed to run plotspec.pro
    • LINES.UCI : Input file for plotspec.pro that contains prominent absorption lines to be marked on the final, reduced spectrum

PROCEDURES: Independent Variable: Wavelength (Angstroms); Dependent Variable: Intensity

  1. Take pictures of stars using a 24 inch telescope and ST-8 CCD camera
  2. Use DS9 on Linux to analyze and crop the portion of the image planned on using
  3. Edit parameters
  4. Label absorption lines according to reference, with each element specific to its wavelength
  5. Graph the spectrum
  6. Change “pixel” on the x-axis to “wavelength”
  7. Analyze the star’s properties by comparing them to predetermined spectral types.

RESULTS:

Arcturus Spectrum

Arcturus: “K” type star, 4,290 K, 1.5 solar masses, absence of hydrogen lines and abundance of neutral metal lines

Vega spectrum

Vega: “A” type star, 9,600 K, 2.14 solar masses, strong hydrogen lines

HD142780 spectrum

HD142780: “M” type star, 3,000 K, 0.2 solar masses, absence of hydrogen lines and abundance of neutral metal lines.

CONCLUSION: By analyzing the absorption lines on the stars’ spectra, we determined the spectral types of each, thus allowing us to find their respective properties. The absence of hydrogen lines and prevalence of neutral metals in Arcturus’ spectrum allowed us to identify it as a K type star (Figure 1) . Vega’s spectrum contained strong hydrogen and ionized metal lines. Therefore we classified it as an A type star (Figure 2). Because the spectrum revealed absent hydrogen lines and visible neutral metals, we classified it as a M type star (Figure 3).

DISCUSSION: WHY DO STELLAR SPECTRA MATTER FOR THE FUTURE OF ASTRONOMY?

  • Map galaxies
  • Map the Universe
  • Learn about the lifetimes of different stars
  • Use information on old stars to learn about conditions after the Big Bang
  • Learn about what has happened in the Universe since the Big Bang

REFERENCES:

Blumenthal, G., Burstein, D., Greeley, R., Hester, J., Smith, B., & Voss, H. G. (2007). Light, The Tools of the Astronomer, Taking the Measure of Stars. In 21st Century Astronomy. (2nd ed.). (pp. 92-128, 134-158, 380-385). New York, New York, U. S. A.: W. W. Norton & Company.

Kaler, J. B. (2010, July 30). Spectra. University of Illinois. Retrieved July 13, 2012, from http://stars.astro.illinois.edu/sow/spectra.html

Special Thanks to: COSMOS, UCI Professors and Graduate Students, our Teacher Fellow, and Cluster 2: Astronomy and Astrophysics!

COSMOS: UCI – Part 2

Stars Under a Microscope

Stars are held by gravity and shine because of the nuclear fusion reactions (fusing light nuclei into heavier nuclei, e.g. hydrogen atoms –> helium atoms) occurring in their cores. Luminosity and lifetime depend entirely on the star’s mass. Stars are composed of mainly hydrogen and helium, with trace amounts of other elements. Stars end their lives when they have exhausted their available nuclear fuel. Their final end states of stellar evolution are different and depend on mass.

OBSERVING STARS: Stars are so far away that they appear as infinitesimally tiny “points” of light.

What Do Astronomers Measure in Stars?

  • Brightness: Is the star constant or variable over time?
  • Spectrum: temperature and chemical composition
  • Color: temperature
  • Motion and Doppler Shift
  • Distance (measuring can be very difficult)

HOW MEASURING DISTANCE TO STARS IS IMPORTANT: Distance and magnitude can determine the star’s luminosity, or how much energy it’s generating and emitting. Distance to stars also determines the structures of galaxies. Then, measuring distances to galaxies can also determine the structure of the universe.

Parallax

MEASURING DISTANCE USING PARALLAX: Parallax is the apparent movement of a distant object when viewing from two different lines of sight. For example, hold out your thumb at arm’s length and close your right eye. Now, open your right eye and close your left eye. See the difference? Astronomers use distance the object “moved” and the angle from Earth and the object’s two different locations to determine the distance to that object. Earth’s motion acts as a baseline to measure the distance of a nearby star. As Earth moves around the Sun, a nearby star will appear to move slightly relative to distant background stars.

  • the star’s parallax = 1/2 the angular shift of the star over one year
  • parsec = parallax second of arc
  • 1 parsec = the distance to a star whose parallax angle is one arcsecond
  • 1 parsec = 3.26 light years
  • 1 parsec = 3.08 x 1016 meters
  • distance (in parsecs) = 1/parallax angle (in arcseconds) –> d = 1/p
*Note: Parsec is NOT a unit of time, but a unit of distance! Arcminutes and arcseconds are NOT units of time, but units of rotation.

All stars have parallaxes smaller than 1 arcsecond. The nearest star, Proxima Centauri has a parallax of o.77 arcseconds and a distance of 1.3 parsecs. Parallaxes can be measures to 200 parsecs from ground-based telescopes. The GAIA Mission (2013), if launched successfully, will allow astronomers to measure 20 micro-arcseconds, or distances to 1 billion stars!

APPARENT MAGNITUDE: Apparent magnitude is how bright a star appears from Earth. On a logarithmic scale, a magnitude 1 star is 100 times brighter than a magnitude 6 star. Brighter stars have smaller magnitudes. The brightest star in the night sky is Sirius at -1.5. The faintest objects detected by the Hubble telescope are magnitude 30. Photometry is measuring the apparent brightness of an object.

Comparing Two Stars’ Apparent Magnitudes with an Equation

m2-m1 = -2.5 log10 (b2/b1)

  • m2 and m1 = apparent magnitudes of two stars
  • b2 and b1 = fluxes of two stars (flux is the amount of light energy received per unit of time per unit of area)

Apparent Magnitude Comparison

  • The Sun = -26.8
  • Full Moon = -12.6
  • Sirius = -1.5
  • Naked Eye (faintest objects) = +6
  • Hubble telescope (faintest objects) = +30

ABSOLUTE MAGNITUDE: Absolute magnitude is the actual luminosities of stars. The Sun has an absolute magnitude of 4.83.

Calculating Absolute Magnitude

m-M = -5 + 5 log10 (d/10 parsecs)

  • m = apparent magnitude
  • M = absolute magnitude
  • d = distance in parsecs

FILTERS & COLORS: Telescopes have filters that isolate specific wavelength regions of the wavelength. The most common filter is UBVRI. Different filters corresponds to different brightness. The ratio of brightness through two different filters correspond to the star’s color. The star’s color also determines the star’s temperature. The ratio between the star’s brightness through two different filters, such as the B and V filters, would be bB/bV.

(B-V) = (mB-mV) = -2.5 log10(bB-bV)

  • The B-V color index depends on the surface temperature of the star

The zeropoints are defined by the star Vega. Vega is 10,000 K and Vega’s color index for any filter combination is 0.

Stellar Spectra

STELLAR SPECTRUM: A star’s spectrum is close to a black-body (an ideal physical body that absorbs all electromagnetic waves) curve, with absorption lines imprinted on it by elements in the star’s photosphere. From the late 1800s to the early 1900s, Harvard College Observatory employed women to observe, map, and define all stars in the sky. When the observers disagreed on the classification of these stars, Annie Jump Cannon invented the spectral sequence base on the strength of stars’ Balmer absorption lines (Hα). Star with the strongest Hα lines were spectral type “A”, and the next strongest were type “B.” Later, however, some letters were removed. The astronomers discovered that the strength of Hα lines depends on the stars’ surface temperatures and stars with temperatures of 10,000 K have the strongest Hα lines. The sequence was then re-arranged in decreasing temperature, resulting in: O, B, A, F, G, K, and M. An acronym to remember the spectral types is “OBa Fine Girl/Guy, Kiss Me.” The subtypes range from 0 –> 9, with subtype 0 as the hottest and 9 the coolest.

Spectral Types and Corresponding Temperatures

  • O = >25,000 K
  • B = 11,000 K – 25,000 K
  • A = 7,500 K – 11,000 K
  • F = 6,000 K – 7,500 K
  • G = 5,000 K – 6,000 K
  • K = 3,800 K – 5,000 K
  • M = 2,200 K – 3,800 K
  • L, T = <2,200 K

* Spectral Types L and T are the recently discovered brown dwarfs, or stars too small for nuclear fusion

In addition to the spectral type and the subtype, each star also has a class. For example, the Sun is G2V (V means main sequence star). While a M0 main sequence star may have 0.6 R☉ and 0.06 L☉, a M0 red giant star will have 40 R☉ and 300 R☉.

RADIUS: The Sun’s radius is 696,000 km, or 1 R☉. A Red Giant is 50 – 100 R☉. A White Dwarf is about   0.01 R☉.

MASS: The Sun’s mass is 1.989 x 10³º kg, or 1 M☉. 1 M☉ is 330,000 times Earth’s mass. Masses of stars range from 0.08 M☉ to over 100 M☉.

H-R Diagram: Majority of Stars in the Main Sequence; Very Few Stars as Red Giants or White Dwarfs

H-R DIAGRAM: The Hertzsprung-Russell (Color-Magnitude) Diagram  organizes the stars into a plot graph, based on color (spectral type)/ temperature and luminosity/ absolute magnitude.

  • Main Sequence: normal stars in their prime of life fusing hydrogen into helium
  • Red Giants: late-stage stars swollen to enormous size, sued up all fuel
  • White Dwarfs: the “dead” star cores

* ☉ = solar units; L = luminosity; R = radius; M = mass

THREE THINGS TO CONSIDER FOR STAR CLASSIFICATION:

  1. Mass: star’s evolution, location on main sequence, where is it in its lifetime
  2. Age: different locations in the H-R Diagram
  3. Chemical Composition/ Metallicity: abundance of metals

Light and Black Body Radiation

Light is composed of mass-less infinitesimal particles called photons that travel at the speed of light (300,000,000 m/s).

Electromagnetic Spectrum

THE ELECTROMAGNETIC SPECTRUM: depicts the different wavelengths and energies of light

Radio Waves –> Microwaves –> Infrared Light –> Visible Light (ROYGBIV) –> Ultraviolet Radiation –> X-Rays –> Gamma Rays (longest –> shortest wavelengths, lowest –> highest energies)

  • The Electromagnetic Spectrum and Stellar Spectra = continuous spectrum (energy emission over a  broad range of wavelengths – curve)
  • Laser = line spectrum (energy emission at a narrow range of wavelength – peak)

Black-bodies at Different Temperatures

A “black-body” is an object which absorbs all light incident on it and doesn’t reflect or transmit any light. Black bodies are perfect emitters of light. Their classification depends only on temperature, and not other properties such as chemical composition; hence, black-body radiation is also “thermal” radiation. In 1900, Max Planck discovered that a black body emits an energy spectrum of light. Black body radiation includes lava flow (800 K), incandescent light bulbs – tungsten wire heated (2,800 K). Comparing two black bodies of different temperatures, the hotter black-body will: 1) emit more radiation (more luminous); 2) emit more photons; 3) peaks at shorter wavelengths; 4) have a bluer color. Measuring the shape of a star’s spectrum can reveal the star’s temperature.

Wien’s Lawγ peak = 2,900 μm K/ T; using the wavelength of the black-body’s spectrum’s peak to determining the star’s surface temperature

Luminosity: amount of energy radiated by an object per second, in Watts

Brightness: how bright an object appears as seen by an observer; also known as flux received from the star

Stefan- Boltzmann LawL = σT4 x surface area, where L = luminosity, T = temperature, and σ = 5.67 x 10-8 W/ (m²•K4), Stefan-Boltzmann constant; to determine a star’s luminosity

 Apparent Brightness: how bright stars appear to the observer; depends on luminosity and distance

  • considering a set of photons that emerge at the same moment from the star’s surface, the spherical shell of photons is 4∏r², where r = distance from the star
  • L/4∏r² (L = luminosity) = energy per second per surface area of photons
  • apparent brightness or flux: b = L/4∏r²

Absolute Brightness: considering temperature and mass and disregarding distance, how bright the stars actually are

PHOTONS AND THE ATOM

The Atom

The Atom and Its Subatomic Particles

  • Subatomic particles: Electrons (-), Protons (+), and Neutrons (neutral)
  • The mass of a proton is 1830 times the mass of an electron; the mass of a proton is approximately equal to the mass of a neutron
  • While protons and neutrons form the atom’s nucleus, electrons have discrete energy levels in atom
  • The electron can only be on energy levels, not in between
  • Outer orbits have higher energy than inner orbits
  • Most of the space within an atom is empty!

Absorption/ Emission: Photons

Photons: Emission and Absorption

  • Photons are emitted in random fashion (cascade from level to level or all at once – from current level to the ground state, or the lowest energy level, the closest to the nucleus)
  • Absorption of a photon causes the electron to a higher energy level
  • A photon can only be absorbed if its energy is equal to the difference in energy between two energy levels
  • An electron can only stay in a higher energy level for a very short time
  • Ionization: If a photon is large enough, it can kick the electron out of the atom
  • Recombination: When a free electron becomes bound to an atom
  • Electrons give up energy by emitting a photon

Emission Lines from Gas Clouds

Emission Line Spectrum

  • A dilute (non-opaque) gas cloud is not a back-body emitter
  • Atoms in a hot, dilute cloud of ionized gas will emit a characteristic pattern of spectra lines (Emission Line Spectrum)

Absorption Line Spectra

Absorption Spectrum

  • Normal stars have absorption lines
  • Black-body radiation originates from the star’s interior