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Reaching for the Stars
Observing and measuring the properties of pulsating variables—stars, light-years away, whose brightness varies periodically as they expand and contract—with the aid of a robotic global network of telescopes. The main goal is to refine the methods of measuring cosmic distances. The size of the observable universe is some 92 billion light-years. Accurate galactic distances and recession speeds ultimately help scientists to determine more precisely the expansion of the universe. Pulsating stars were discovered by astronomer Henrietta Leavitt in 1908. Her work was crucial in the work of Edwin Hubble when in 1929 he confirmed the expansion of the universe that was previously predicted theoretically by the field equations of Einstein’s general relativity.
A collaborative research project in observational astronomy with the goal to measure various properties of RR Lyrae stars. This is done with the aid of a robotic global network of 0.4m reflecting telescopes spread at various sites around the Earth including their International Headquarters and Data Center located at the Las Cumbres Observatory (LCO) in California. The team is linked through the Solar Sibling moodle and Slack.
Project Team: Dr. Michael Fitzgerald (Research Project Plan Instructor, Australia), Dr. Tim Slater (Facilitator and bridge), Dr. Brian Uzpen (Instructional Assessment, USA), Saeed Salimpour (computer software expert) and Dr. Demetris Nicolaides (student supervisor, USA). Dr Nicolaides' mentees are students Destiny King (Bloomfield College), Sandra Moreno Cristobal (Gardner-Webb University), and Diana Sanchez-Marcelo (Bloomfield College).
ASTRONOMY READINGS
Space Book (excellent first introduction to astronomy--relatively short)
Astronomy Textbook (a detailed astronomy textbook)
LCO captures the gravitational waves from merging neutron stars
ASTRONOMY PAPERS & STAR DATABASES
SAO/NASA Astrophysics Data System
astro-ph (astronomy related papers from arXiv)
Star Databases: SIMBAD, AAVSO, GCVS, IRSA, Vizier, Galactic Dust Reddening and Extinction
USEFUL ASTRONOMY TERMS & PROCEDURES
Images Credit: Astronomy Textbook
Telescope: "bucket" to gather light--visible, infrared, radio, etc.--sort it to its component wavelengths, and record permanently the observation.
Reflecting Telescope: uses lenses
Refracting Telescope: uses mirrors
Resolution: smallest distinguishable image feature
Luminosity: how bright a star really is--its true (intrinsic) brightness resulting from all the energy (of all wavelengths) emitted by it per second. Measured in j/sec=watts.
CCD (charge coupled device) simulator: its operation is based on the photoelectric effect.
Apparent Brightness: how bright a star appears to be as a result of its distance--section 17.1. The further away the fainter it appears. Measured in watts.
Apparent Magnitude: a measure of the apparent brightness of a star--section 17.1. The smaller the number the brighter the star.
Absolute Magnitude: the apparent magnitude of a star if it were moved to 10 parsecs.
Variable: a star whose brightness varies with time--section 19.3.
Pulsating Variable: a variable star whose brightness varies periodically as its diameter expands and contracts--as a person's chest in breathing.
Cepheids and RR Lyrae Stars: two types of pulsating variable stars. Delta Cephei was the first to be discovered in the constellation Cepheus; RR Lyrae is in the Lyra constellation. All pulsating stars, regardless of their constellation, are now grouped into one of these two types. Why Cepheids Pulsate
Star Naming: the letter/s in front of a star name indicates its apparent brightness--alpha being brighter than a delta star--section 19.2.
Magnitude and Color: the hotter the star the bluer its light is.
Parallax: the shifting in the direction of an object with respect to its background due to a change in the position of the observer--section 19.2. For example, observer at A sees tree at C in the direction AC. But observer at B sees tree at C in the direction BC.
Parallax Angle: ACB/2
Astronomical Unit (AU): The average of the closest and furthest distances of Earth to the Sun. AU = 1.50 x 1011 m
Light Year (LY): Distance traveled by light in one year. LY = 9.46 x 1015 m = 6.31 x 104 AU
Parsec: The distance of an object with observation baseline (AB in photo above) of 1 AU and parallax angle 1 arc-second.
1 arc-second = 1/(60 x 60) of a degree
1 parsec = 206,265 AU = 3.26 LY
Metallicity: (Search for Fe/H in Vizier to find metallicity data of a star) "Astronomers use the term “metals” to refer to all elements heavier than hydrogen and helium [although most of such elements are not really metals]. The fraction of a star’s mass that is composed of these elements is referred to as the star’s metallicity. The metallicity of the Sun, for example, is 0.02, since 2% of the Sun’s mass is made of elements heavier than helium." Fraknoi, Andrew; Morrison, David; Wolff, Sidney C. Wolff. Astronomy (Kindle Locations 14951-14953). Kindle Edition."
From LCO: Exposure Time Calculator" and a "Target Visibility Calculator"
Photometry: measures star brightness
Spectroscopy: study of the colors of light
USEFUL ASTRONOMY LAWS
Triangulation: using parallax to measure distances. This method is limited to distances within the Milky Way galaxy. Distances beyond that don't produce an observable parallax angle, p. d is the distance Earth-star/planet, p is in arc-seconds, and d is in parsecs--section 19.2.
d = 1/p
Proof:
tanp = 1AU / d => d = 1 AU / tanp Approximate for small parallax angles p (in radians): d = 1 AU / (p radians)
1 parsec = 206,265 AU => 1 AU = 1 parsec / 206,265
1 rad = 180/3.14 degrees
1 degree = 60 arc-min = 60 x 60 arc-seconds => 1 degree = 3600 arc-seconds
Thus 1 rad = (180 x 3600)/3.14 arc-seconds = 206,265 arc-seconds
Replace 1 AU by parsecs and radians by arc-seconds to get:
d = 1 AU / (p radians) = 1 parsec / (206,265 p radians) = 1 parsec / (p arc-seconds)
Thus, d = 1/p
Planetary Distances: (1) use triangulation with baseline the diameter of Earth--make two measurements (say, 12 hours apart from the equator)--section 19.2. Or, (2) send a radio wave from earth and bounce it off a planet. Measure the radio wave’s roundtrip time, divide it by 2, and use the formula, the speed of light, c = d/t to calculate d, how far the planet is.
Light Curve: a plot between a star's apparent brightness vs. time. The period of pulsation of its brightness is read from the graph. In the example below the period is about 6 days.
RR Lyrae stars have periods less than 1 day. RR Lyrae stars have smaller periods and luminosity than Cepheids.
How to Calculate Luminosity (M)--or average luminosity if a star is variable: (1) Measure a star's apparent brightness (m)--or average brightness if the star is variable. (2) Measure its parallax angle, p, and calculate its distance d using d = 1/p. (3) Use m and d and the formula below (derived from Inverse Square Law for Light, see next law, below), to calculate the star's luminosity*, M, (at say 10 parsec)--section/example 5.2, section/table 18.2. *Recall, we defined this as absolute magnitude.
distance modulus calculations: M = m + 5 - 5 log d
Or, (2) Compare the star's spectral class with one (say the Sun) which we know its luminosity. When the spectral classes of the two stars match, it is reasonable to expect the two stars have the same luminosity--section 19.4.
The Inverse Square Law for Light: the light intensity, I, (W/m2) is inversely proportional to the distance squared--section/example 5.2.
I = constant/d2
Think of one square area to be the area of your telescope. Then at 2 and 3 times the distance the I drops by 1/4 and 1/9 since less light crosses the area of your telescope
How many times brighter would a star appear to be if it is moved closer say at (a) 1/2 and (b) 1/3 its present distance?
(a) 1/22 = 4 (b) 1/32 = 9
Flux Simulator of Inverse Square Law
Period-Luminosity Relation (PLR): A relation between a pulsating variable's period and its average luminosity. The longer the period of luminosity variation, the greater the luminosity--a direct proportionality. It was discovered by astronomer Henrietta Leavitt in 1908. It allows for a new improved method of measuring cosmic distances that couldn't be measured by parallax and triangulation. Her work was seminal. It helped astronomer Edwin Hubble who measured the distances and recession velocities of distant galaxies and confirmed the expansion of the universe as was predicted by Einstein's general relativity.
Construct a PLR Curve: (1) Measure the period of a star. (2) Calculate its luminosity (see above how). (3) Plot a star's luminosity vs. its period. IMPORTANT: Once such graph is constructed for many stars, it can be used as a tool to read off the luminosity of any other star of unknown luminosity, simply by measuring that star's period.
Measure Distance Using the PLR Curve: (a) Measure the period of a pulsating variable star. (b) Use the period to calculate (read off) the star's luminosity (M) from the PLR curve. (c) Measure the star's apparent brightness, m. (d) Calculate the star's distance d (in parsecs) from its luminosity (at 10 parsec, its absolute magnitude) and apparent brightness (magnitude). Fig. 19.12.
distance = d = 10(m - M + 5)/5
m = apparent magnitude (brightness); M = absolute magnitude (luminosity)
Magnitude and Distance Measurement (excellent reading)
Eratosthenes (ca. 276 - ca. 195 BCE) Measured the Size of Earth from Pure Geometry
Blackbody Radiation: Object's own radiation, dependent on its temperature
Logarithmic Scale (click the upper right corner icon 10x)
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