Spectroscopy and Light Measurement
90 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula to calculate the magnitude of a star compared to a standard star with a known magnitude?

  • m = ms - 2.5 log F/Fs (correct)
  • m = ms + 2.5 log F/Fs
  • m = ms ÷ 2.5 log F/Fs
  • m = ms × 2.5 log F/Fs

    • What is the unit of Ephoton?

  • Electronvolts
  • Joules (correct)
  • Joules per second
  • Photons per second

    • What is the formula to calculate the monochromatic photon flux?

  • n dot λ = F/hc/ λ (correct)
  • n dot λ = F + hc/ λ
  • n dot λ = F ÷ hc/ λ
  • n dot λ = F × hc/ λ

    • What is the formula to calculate the uncertainty of counts?

    <p>δn = square root of n - standard error</p> Signup and view all the answers

    What is the Signal-to-Noise Ratio (SNR) of a detector?

    <p>SNR = n/δn</p> Signup and view all the answers

    What is the formula to calculate the uncertainty in magnitude?

    <p>δm = (2.5/ln 10)( δn/n)</p> Signup and view all the answers

    What is the definition of probability?

    <p>Number of events occurring divided by sample space</p> Signup and view all the answers

    What is the cardinality of a set?

    <p>The number of elements in a set</p> Signup and view all the answers

    What is a Random Variable (RV)?

    <p>An outcome that is not deterministic</p> Signup and view all the answers

    What is the probability of an event in the frequentist interpretation?

    <p>The number of desired outcomes divided by the total number of all possible outcomes</p> Signup and view all the answers

    What is the condition for two events to be mutually exclusive?

    <p>They cannot occur at the same time</p> Signup and view all the answers

    What is the formula for the probability of two events A and B that are not mutually exclusive?

    <p>P(A U B) = P(A) + P(B) - P(A ∩ B)</p> Signup and view all the answers

    What is the formula for the probability of two dependent events A and B?

    <p>P(A,B) = P(A) × P(B|A)</p> Signup and view all the answers

    What is the condition for two events to be independent?

    <p>P(A,B) = P(A) × P(B)</p> Signup and view all the answers

    What is the probability axiom that states the sum of probabilities of all possible outcomes is equal to 1?

    <p>Sum of probabilities = 1</p> Signup and view all the answers

    What is the term for the simplest case possible that is the truth?

    <p>Axiom</p> Signup and view all the answers

    What is the term for something that can be incorporated into a theory or system?

    <p>Postulate</p> Signup and view all the answers

    What is the range of probability values?

    <p>0 ≤ P ≤ 1</p> Signup and view all the answers

    What is the wavelength of the Ly α transition in the Lyman series?

    <p>121.6 nm</p> Signup and view all the answers

    Which of the following is NOT a factor influencing the magnitude of an object?

    <p>The object's chemical composition</p> Signup and view all the answers

    What is the difference between luminosity and brightness?

    <p>Luminosity is the energy emitted per unit time, while brightness is the energy emitted per unit solid angle.</p> Signup and view all the answers

    What is the significance of a blackbody in astrophysics?

    <p>Blackbodies are perfect absorbers and emitters of radiation, allowing us to model stellar spectra.</p> Signup and view all the answers

    What is the wavelength range used to measure an object's bolometric luminosity?

    <p>All wavelengths</p> Signup and view all the answers

    How does the magnitude scale relate to the amount of light received from an object?

    <p>A lower magnitude indicates more light received.</p> Signup and view all the answers

    Why is the Balmer series more prominent in visible light than the Lyman series?

    <p>The Balmer series transitions occur between higher energy levels, resulting in longer wavelengths.</p> Signup and view all the answers

    Why is it necessary to consider the transmission characteristics of the instrument when measuring an object's magnitude?

    <p>All of the above</p> Signup and view all the answers

    Why is the magnitude of an object dependent on the distance from the observer?

    <p>The further away an object is, the less light reaches the observer.</p> Signup and view all the answers

    What is the probability of rolling a sum of 7 when tossing two fair dice?

    <p>1/6</p> Signup and view all the answers

    In the context of the provided content, what is the most accurate description of a random variable?

    <p>A variable that can take on different values, each with a specific probability associated with it.</p> Signup and view all the answers

    Which of the following scenarios represents a discrete random variable?

    <p>The number of heads obtained when flipping a coin five times.</p> Signup and view all the answers

    What is the probability mass function (PMF) used to represent?

    <p>The probability of a specific outcome for a discrete random variable.</p> Signup and view all the answers

    Consider a random variable X representing the number of heads obtained when flipping a coin four times. What is the probability of getting exactly two heads (P(X=2))?

    <p>3/8</p> Signup and view all the answers

    What is the key distinction between a continuous random variable and a discrete random variable?

    <p>A discrete random variable can only take on whole number values, while a continuous random variable can take on any value within a range.</p> Signup and view all the answers

    Which of the following is NOT a characteristic of a random variable?

    <p>It must be a continuous variable.</p> Signup and view all the answers

    What does the notation "P(X = x)" represent in the context of a random variable?

    <p>The probability of a specific outcome 'x' for the random variable 'X'.</p> Signup and view all the answers

    What is the formula used to calculate the number of combinations, 'k' items selected from a set of 'N' items?

    <p>N! / (k! * (N-k)!)</p> Signup and view all the answers

    Which of the following statements about the 2MASS survey is TRUE?

    <p>It cataloged approximately 300 million stars.</p> Signup and view all the answers

    What is the main purpose of the NGC and IC Catalogue?

    <p>To identify and categorize non-stellar objects in the sky.</p> Signup and view all the answers

    Which of the following objects is NOT listed in the Upsala General Catalogue (UGC)?

    <p>NGC 224</p> Signup and view all the answers

    The Washington Double Star Catalogue includes information on:

    <p>The proper motion of each star in the pair.</p> Signup and view all the answers

    What is the main difference between the Henty Draper Catalogue (HD) and the General Catalogue of Variable Stars (GCVS)?

    <p>The HD focuses on spectral classification while the GCVS catalogues variable stars.</p> Signup and view all the answers

    Which of these catalogues is NOT maintained by the Centre de Donnees Astronomique de Strasbourg (CDS)?

    <p>The Washington Double Star Catalogue</p> Signup and view all the answers

    Which of the following statements about flux is CORRECT?

    <p>Flux density is always measured in units of power per unit area.</p> Signup and view all the answers

    Which of the following statements about the magnitude system is INCORRECT?

    <p>A larger B-V color index indicates a bluer star.</p> Signup and view all the answers

    Which of these astronomical databases primarily focuses on minor planets, comets, and natural satellites?

    <p>The Minor Planet Center</p> Signup and view all the answers

    Which transition corresponds to the line H𝛼 in the Balmer series?

    <p>3 to 2 transition</p> Signup and view all the answers

    What primarily affects the magnitude of an astronomical object?

    <p>The distance from the observer</p> Signup and view all the answers

    What is bolometric luminosity?

    <p>Luminosity or brightness across the entire spectrum</p> Signup and view all the answers

    Which characteristic is true about black body radiation in astronomy?

    <p>It follows Planck's Law as a perfect emitter.</p> Signup and view all the answers

    What is the definition of absolute magnitude?

    <p>Brightness of an object at a specific distance</p> Signup and view all the answers

    What is the relationship between flux and brightness?

    <p>Brightness is the integrated result of flux across a solid angle.</p> Signup and view all the answers

    What wavelength corresponds to the Ly β transition in the Lyman series?

    <p>102.6 nm</p> Signup and view all the answers

    How is the magnitude scale described?

    <p>A logarithmic scale introduced by Norman Pogson.</p> Signup and view all the answers

    Which statement accurately describes stellar spectra?

    <p>They can be modeled as perfect absorbers and emitters.</p> Signup and view all the answers

    What does the notation $< X >$ refer to in statistical analysis?

    <p>Mean or expectation value of variable X</p> Signup and view all the answers

    In a binomial distribution, what does the term $P(X = m)$ signify?

    <p>Probability of obtaining exactly m successes in N trials</p> Signup and view all the answers

    What is the primary purpose of a probability density function (PDF)?

    <p>To describe the likelihood of random variable values in a continuous space</p> Signup and view all the answers

    Which of the following is used to calculate the second moment about the mean for a dataset?

    <p>Sum of squares of deviations from the mean</p> Signup and view all the answers

    If the probability of obtaining heads in a biased coin toss is P, what is the probability of obtaining tails?

    <p>q = 1 - P</p> Signup and view all the answers

    How is the average of multiple measurements defined mathematically?

    <p>$x̄ = \frac{1}{N} \sum_{i=1}^{N} X_i$</p> Signup and view all the answers

    In statistical mechanics, when analyzing a random variable's momentum, what does the distribution often resemble?

    <p>Normal distribution</p> Signup and view all the answers

    How is variance mathematically defined for a discrete random variable?

    <p>As the expectation of the squared deviations from the mean</p> Signup and view all the answers

    When analyzing the outcomes of a biased coin flipped N times, what is true about the random variable representing the number of heads?

    <p>It represents a binomial distribution</p> Signup and view all the answers

    Which of the following statements about the nature of light is CORRECT based on the provided information?

    <p>Light exhibits both wave-like and particle-like properties, depending on the method of observation.</p> Signup and view all the answers

    Based on the content provided, which of the following statements regarding the relationship between energy and wavelength is CORRECT?

    <p>The energy of a wave is directly proportional to its frequency.</p> Signup and view all the answers

    According to the provided information, what is the primary reason for studying light in astronomy?

    <p>To understand the composition and evolution of the universe.</p> Signup and view all the answers

    Which of the following statements regarding the 2MASS survey is TRUE?

    <p>It has catalogued over 500 million stars.</p> Signup and view all the answers

    Which of the following discoveries paved the way for the development of infrared astronomy as a quantitative science?

    <p>William Herschel’s invention of a thermometer detecting warmth outside the visible spectrum.</p> Signup and view all the answers

    Based on the information provided, what is the fundamental difference between the classical and quantum mechanical perspectives on light?

    <p>Classical physics considers light as a wave, while quantum mechanics views it as a particle.</p> Signup and view all the answers

    Which of the following objects is NOT listed in the Upsala General Catalogue (UGC)?

    <p>M31</p> Signup and view all the answers

    What is the main difference between the Henty Draper Catalogue (HD) and the General Catalogue of Variable Stars (GCVS)?

    <p>HD catalogs stars based on spectral classification, while GCVS focuses on variable stars.</p> Signup and view all the answers

    The provided content emphasizes that light exhibits both wave-like and particle-like properties. Which of the following experiments provides the strongest evidence for the particle nature of light?

    <p>The Photoelectric Effect.</p> Signup and view all the answers

    The content describes various types of light, including infrared, ultraviolet, X-ray, and radio waves. What is the underlying principle that governs the classification of these types of light?

    <p>The difference in their wavelengths.</p> Signup and view all the answers

    Which of these astronomical databases primarily focuses on minor planets, comets, and natural satellites?

    <p>Minor Planet Centre</p> Signup and view all the answers

    Which of the following correctly describes the relationship between frequency (v), wavelength (λ), and the speed of light (c) as stated in the provided content?

    <p>c = vλ</p> Signup and view all the answers

    Which transition corresponds to the line H𝛼 in the Balmer series?

    <p>n = 3 to n = 2</p> Signup and view all the answers

    The content highlights the importance of light in astronomy. What is the primary reason why light is crucial for studying distant objects in the universe?

    <p>Light provides information about the composition, evolution, and motion of celestial objects.</p> Signup and view all the answers

    What primarily affects the magnitude of an astronomical object?

    <p>All of the above.</p> Signup and view all the answers

    What is bolometric luminosity?

    <p>The total energy emitted by a star over all wavelengths.</p> Signup and view all the answers

    Which characteristic is true about black body radiation in astronomy?

    <p>All of the above.</p> Signup and view all the answers

    What is the definition of absolute magnitude?

    <p>The magnitude of a star if it were located 10 parsecs away from Earth.</p> Signup and view all the answers

    What is the primary reason why the Sun exhibits bright emission lines, such as the Balmer and Lyman Series, despite its continuous emission spectrum?

    <p>The absorption of photons by the Sun's atmosphere creates absorption lines, leading to the observation of bright emission lines.</p> Signup and view all the answers

    According to the provided content, which of the following statements about the Sun's core is FALSE?

    <p>The Sun's core emits a spectrum primarily consisting of bright emission lines, such as the Balmer and Lyman series.</p> Signup and view all the answers

    What is the fundamental principle that governs the emission of photons in the context of energy state exchange?

    <p>Photons are emitted when an electron transitions from a higher energy level to a lower energy level, releasing the difference in energy as a photon.</p> Signup and view all the answers

    Which of the following research communities would likely refer to a photon with an energy of 10 keV?

    <p>X-ray astronomers</p> Signup and view all the answers

    Based on the provided content, what is the most likely reason for the differences in terminology used by different research communities within astronomy?

    <p>Different research communities focus on different regions of the electromagnetic spectrum, leading to distinct terminology.</p> Signup and view all the answers

    Which of the following statements best reflects the significance of the photoelectric effect as described in the content?

    <p>The photoelectric effect provided evidence for the quantum nature of light, showing that light can interact with matter in discrete packets of energy called photons.</p> Signup and view all the answers

    In the context of the provided content, what is the primary reason why the Sun exhibits a continuous emission spectrum despite its core primarily emitting free-bound transitions?

    <p>The Sun's atmosphere absorbs photons at specific wavelengths, leading to the observation of a continuous spectrum after re-emission.</p> Signup and view all the answers

    Which of the following statements accurately reflects the relationship between the quantization of energy and the emission of photons?

    <p>Quantization of energy means that energy can only be emitted in discrete packets, leading to the emission of photons with specific energies.</p> Signup and view all the answers

    Based on the provided content, what is the most accurate description of the 'Balmer and Lyman Series'?

    <p>The Balmer and Lyman series are specific types of spectral lines observed in the Sun's spectrum, representing transitions of electrons in hydrogen atoms.</p> Signup and view all the answers

    Study Notes

    Spectral Lines

    • Balmer series: Hα (656.3 nm), Hβ (486.1 nm)
    • Lyman series: Lyα (121.6 nm), Lyβ (102.6 nm)

    Measuring Light

    • Luminosity: total amount of energy emitted across a specific wavelength range
    • Brightness: amount of energy emitted through a specific wavelength range over a solid angle
    • Absolute Magnitude: brightness of an object as it would be at a set distance
      • Solar system objects: 1 AU
      • Extrasolar objects: 10 pc
    • Bolometric Luminosity: luminosity or brightness across the entire spectrum

    Black Body

    • Stellar spectra can be modeled as perfect absorbers and emitters
    • Output follows Planck's Law
    • Flux: energy per unit area per unit time
    • Astronomical bodies emit light isotropically (equal in all directions)

    Magnitude Scale

    • Instruments return raw observing results in counts per second (photon strikes on receiving area divided by time taken)
    • Magnitude is dependent on physical characteristics of the object, distance from the observer, and transmission characteristics of the instrument
    • Example: a star/galaxy may have a magnitude of 10 in R band but 12 in B band

    2MASS

    • 2 Microns All Sky Survey
    • Observes Near-Infrared (NIR) with two 1.3 m telescopes in Arizona and Chile
    • 300 million objects, including stars and galaxies

    Catalogues

    • NGC (New General Catalogue of Nebulae and Cluster of Stars): non-stellar catalogue sources
    • IC (Index Catalogues): additional 5386 objects
    • UGC (Uppsala General Catalogue): Northern hemisphere catalogue of bright galaxies to mag 14.5
    • Burnham, Aitken, and Washington Double Star Catalogue: double star catalogues
    • Henry Draper Catalogue: spectrally classified stars
    • General Catalogue of Variable Stars: variable and suspected variable stars
    • SIMBAD (Set of Identifications, Measurements, and Bibliography for Astronomical Data): astronomical database operated by CDS (Centre de Donnees Astronomique de Strasbourg) in France
    • Minor Planet Centre: data and orbital elements for minor planets, comets, and natural satellites
    • Infrared Science Archive: stores and distributes IR astronomical data
    • VIZIER: offers access to a vast collection of astronomical catalogs and data tables

    Measuring Light: Stars to Detector

    • Flux/Flux Density (F): brightness of a celestial object (irradiance)
    • Powerhouse of the source: luminosity/radial flux
    • Detectors: brightness of a star; power delivered to a sensor by EM radiation
    • Bolometric Flux (Fbol): integrated over all wavelengths
    • Monochromatic Flux: flux per wavelength; spectral irradiance
    • Attenuation: effective amount of light lost in aggregate for a number of sight lines
    • Standard photometric system: sets of agreed-upon response functions

    Magnitude System

    • Introduced by Hipparcus in 2nd century BC
    • Developed by Norman Pogson in 1856
    • Zero-point: Vega
    • Absolute Magnitude (10 pc): specifying abs mag = specifying luminosity
    • Distance Modulus: difference between an object's apparent and absolute magnitude
    • Magnitude (capital letter depending on band data)
    • Color Index: quantitative measure of color
    • Bolometric Correction (BC): Mbol - V

    Measuring Light Detectors

    • Photon counting: 1) photon counting, 2) power measuring
    • Compare a star to a standard star with a known magnitude (ms)
    • m = ms - 2.5 log F/Fs

    Counting Photons

    • Photon count rate: n dot
    • Photon response function: Rp(λ)
    • Monochromatic photon flux: n dot λ
    • Uncertainty of counts: δn = square root of n - standard error
    • Signal-to-Noise Ratio (SNR): inverse of fractional uncertainty
    • Detector noise + photon counting noise

    Estimating Exposure Time

    • Probability: number of events occurring divided by sample space
    • Events: all possibly mutual outcomes of a sample space
    • Example: coin toss, single die
    • Random Variable (RV): outcome is not deterministic
    • Frequentist Interpretation: only works in an ideal situation where we know everything

    Probability Axioms

    • 0 ≤ p ≤ 1
    • Sum of probabilities = 1 (all possible outcomes)
    • Probabilities for mutually exclusive events add
    • If A & B can't occur at the same time, they are mutually exclusive
    • Example: probability of liking basketball or volleyball

    Random Variables

    • Variable that is not fully deterministic
    • Several possible outcomes
    • Can be either discrete or continuous
    • Example: single die (Discrete), tossing two dice (Continuous)

    The Nature of Light

    • We study light because we can’t touch celestial objects themselves, and we study it through flux, magnitude, and color filters.
    • Light is a wave with an oscillating electric field and a perpendicular oscillating magnetic field in classical physics.
    • Energy of the wave is inversely proportional to its wavelength (c = vλ).

    Brief Historical Development of Light Study

    • 1800s: William Herschel discovered Uranus and measured the rainbow's temperature, also made a thermometer that detects warmth outside the visible spectrum (infrared light).
    • Mid-1800s: Infrared astronomy was used for quantitative science, and a cow was the first detected object in infrared.
    • 1940s: Radio astronomy began.
    • Late 1900s: Ultraviolet, X-Ray, Millimeter, and Submillimeter observations became possible, and Maxwell's Electromagnetic theory was developed.

    Quantum Nature of Light

    • Light is both a particle (photon) and a wave simultaneously, and the method of observation determines its features.
    • Photons have energy given by E = hv = hλ/c, where h is Planck's constant.
    • Photons are emitted when there is energy state exchange.

    Electromagnetic Spectrum

    • The electromagnetic spectrum is continuous but is divided into bands: Gamma Rays, X-Rays, UV, IR, and Radio.
    • Different bands are referred to depending on the research community.

    Idiosyncrasies of Research Communities

    • X-Ray astronomers characterize photons by energies.
    • UV to IR observers refer to them by wavelength.
    • Millimeter and Radio regimes describe things in terms of frequency.

    Measuring Light

    • Luminosity is the total amount of energy emitted across a specific wavelength range.
    • Brightness is the amount of energy it emits through a specific wavelength range over a solid angle.
    • Absolute Magnitude is the brightness of an object as it would be at a set distance.
    • Bolometric Luminosity is luminosity or brightness across the entire spectrum.

    Black Body

    • Stellar spectra can be modeled as perfect absorbers and emitters, and they reflect next to no light.
    • Astronomical bodies emit their light isotropically (equal in all directions).

    The Magnitude Scale

    • Instruments typically return raw observing results in the form of counts per second.
    • Magnitude is dependent on physical characteristics of the object, distance, material between the observer, detector used, and transmission characteristics of the instrument.

    Catalogues and Databases

    • 2MASS (2 Microns All Sky Survey) observes NIR with two 1.3m telescopes in Arizona and Chile.
    • NGC (New General Catalogue of Nebulae and Cluster of Stars) and IC (Index Catalogues) contain non-stellar catalogue sources.
    • UGC (Uppsala General Catalogue) is a northern hemisphere catalogue of bright galaxies to mag 14.5.
    • WDS (Washington Double Star Catalogue) contains double star catalogues.
    • HD (Henry Draper Catalogue) is a catalogue of spectrally classified stars.
    • GCVS (General Catalogue of Variable Stars) contains variable and suspected variable stars.
    • SIMBAD is an astronomical database operated by CDS in France.
    • MPC (Minor Planet Centre) provides data and orbital elements for minor planets, comets, and natural satellites.
    • IRSA (Infrared Science Archive) stores and distributes IR astronomical data.
    • Vizier offers access to a vast collection of astronomical catalogs and data tables.

    Stars to Detector

    • Flux/Flux Density (F) is the brightness of a celestial object (irradiance).
    • Bolometric Flux (Fbol) is integrated over all wavelengths.
    • Monochromatic Flux is flux per wavelength.
    • Attenuation is the effective amount of light lost in aggregate for a number of sight lines.

    Magnitude System

    • The magnitude system was developed by Hipparcus and Norman Pogson.
    • Zero-point is Vega, with an average of many stars per calibrating scale in absolute flux units.
    • Absolute Magnitude (M) is specified in luminosity.
    • Distance Modulus (m-M) depends on distance (r in pc).

    Measuring Light Detectors

    • Probability density function (f(Vx)) is used to measure the velocity component along the x-axis.
    • Average/Mean/Expectation Value () is calculated by performing an experiment/observation.
    • Variance and Standard Deviation are measures of deviation from the center.

    Binomial Distribution

    • The binomial distribution is used to calculate the probability of getting a certain number of successes in a fixed number of trials.
    • Examples include normalization, calculation of mean, 2nd moment, standard deviation, and probability calculation.

    Probability Density Function

    • A probability density function (f(x)) is associated with finding a particle around the position x.
    • Examples include sketching the graph and calculating the expectation value.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    AST14 Observational Astronomy II PDF

    Description

    This quiz covers spectroscopy, including the Balmer and Lyman series, and measures of light such as luminosity, brightness, and absolute magnitude.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser