Questions and Answers
What is the formula to calculate the magnitude of a star compared to a standard star with a known magnitude?
What is the unit of Ephoton?
What is the formula to calculate the monochromatic photon flux?
What is the formula to calculate the uncertainty of counts?
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What is the Signal-to-Noise Ratio (SNR) of a detector?
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What is the formula to calculate the uncertainty in magnitude?
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What is the definition of probability?
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What is the cardinality of a set?
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What is a Random Variable (RV)?
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What is the probability of an event in the frequentist interpretation?
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What is the condition for two events to be mutually exclusive?
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What is the formula for the probability of two events A and B that are not mutually exclusive?
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What is the formula for the probability of two dependent events A and B?
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What is the condition for two events to be independent?
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What is the probability axiom that states the sum of probabilities of all possible outcomes is equal to 1?
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What is the term for the simplest case possible that is the truth?
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What is the term for something that can be incorporated into a theory or system?
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What is the range of probability values?
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What is the wavelength of the Ly α transition in the Lyman series?
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Which of the following is NOT a factor influencing the magnitude of an object?
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What is the difference between luminosity and brightness?
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What is the significance of a blackbody in astrophysics?
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What is the wavelength range used to measure an object's bolometric luminosity?
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How does the magnitude scale relate to the amount of light received from an object?
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Why is the Balmer series more prominent in visible light than the Lyman series?
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Why is it necessary to consider the transmission characteristics of the instrument when measuring an object's magnitude?
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Why is the magnitude of an object dependent on the distance from the observer?
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What is the probability of rolling a sum of 7 when tossing two fair dice?
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In the context of the provided content, what is the most accurate description of a random variable?
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Which of the following scenarios represents a discrete random variable?
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What is the probability mass function (PMF) used to represent?
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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))?
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What is the key distinction between a continuous random variable and a discrete random variable?
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Which of the following is NOT a characteristic of a random variable?
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What does the notation "P(X = x)" represent in the context of a random variable?
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What is the formula used to calculate the number of combinations, 'k' items selected from a set of 'N' items?
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Which of the following statements about the 2MASS survey is TRUE?
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What is the main purpose of the NGC and IC Catalogue?
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Which of the following objects is NOT listed in the Upsala General Catalogue (UGC)?
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The Washington Double Star Catalogue includes information on:
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What is the main difference between the Henty Draper Catalogue (HD) and the General Catalogue of Variable Stars (GCVS)?
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Which of these catalogues is NOT maintained by the Centre de Donnees Astronomique de Strasbourg (CDS)?
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Which of the following statements about flux is CORRECT?
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Which of the following statements about the magnitude system is INCORRECT?
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Which of these astronomical databases primarily focuses on minor planets, comets, and natural satellites?
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Which transition corresponds to the line H𝛼 in the Balmer series?
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What primarily affects the magnitude of an astronomical object?
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What is bolometric luminosity?
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Which characteristic is true about black body radiation in astronomy?
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What is the definition of absolute magnitude?
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What is the relationship between flux and brightness?
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What wavelength corresponds to the Ly β transition in the Lyman series?
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How is the magnitude scale described?
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Which statement accurately describes stellar spectra?
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What does the notation $< X >$ refer to in statistical analysis?
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In a binomial distribution, what does the term $P(X = m)$ signify?
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What is the primary purpose of a probability density function (PDF)?
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Which of the following is used to calculate the second moment about the mean for a dataset?
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If the probability of obtaining heads in a biased coin toss is P, what is the probability of obtaining tails?
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How is the average of multiple measurements defined mathematically?
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In statistical mechanics, when analyzing a random variable's momentum, what does the distribution often resemble?
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How is variance mathematically defined for a discrete random variable?
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When analyzing the outcomes of a biased coin flipped N times, what is true about the random variable representing the number of heads?
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Which of the following statements about the nature of light is CORRECT based on the provided information?
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Based on the content provided, which of the following statements regarding the relationship between energy and wavelength is CORRECT?
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According to the provided information, what is the primary reason for studying light in astronomy?
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Which of the following statements regarding the 2MASS survey is TRUE?
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Which of the following discoveries paved the way for the development of infrared astronomy as a quantitative science?
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Based on the information provided, what is the fundamental difference between the classical and quantum mechanical perspectives on light?
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Which of the following objects is NOT listed in the Upsala General Catalogue (UGC)?
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What is the main difference between the Henty Draper Catalogue (HD) and the General Catalogue of Variable Stars (GCVS)?
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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?
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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?
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Which of these astronomical databases primarily focuses on minor planets, comets, and natural satellites?
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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?
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Which transition corresponds to the line H𝛼 in the Balmer series?
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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?
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What primarily affects the magnitude of an astronomical object?
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What is bolometric luminosity?
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Which characteristic is true about black body radiation in astronomy?
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What is the definition of absolute magnitude?
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What is the primary reason why the Sun exhibits bright emission lines, such as the Balmer and Lyman Series, despite its continuous emission spectrum?
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According to the provided content, which of the following statements about the Sun's core is FALSE?
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What is the fundamental principle that governs the emission of photons in the context of energy state exchange?
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Which of the following research communities would likely refer to a photon with an energy of 10 keV?
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Based on the provided content, what is the most likely reason for the differences in terminology used by different research communities within astronomy?
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Which of the following statements best reflects the significance of the photoelectric effect as described in the content?
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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?
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Which of the following statements accurately reflects the relationship between the quantization of energy and the emission of photons?
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Based on the provided content, what is the most accurate description of the 'Balmer and Lyman Series'?
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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.
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Description
This quiz covers spectroscopy, including the Balmer and Lyman series, and measures of light such as luminosity, brightness, and absolute magnitude.