Astrophysical Techniques

Instructor: Prof. Yicheng Guo

Lecture 1. 2019/01/22

Introduction & Light, Magnitude, and Flux

About Me• Yicheng Guo

Ph.D. — University of Massachusetts Assistant Professor — University of Missouri

• Working on observational astronomy Studying the formation and evolution of distant galaxies by using various telescopes

About Me

• Office: Room 222 Physics

• Email: guoyic@missouri.edu

• Mailbox (for late labs): Room 223 Physics

Syllabus

❖ Tuesday & Thursday, 9:30 – 10:45pm - 75min/class

❖ 28 lectures over 15 weeks; — No class in the following dates: 02/19 (travel) — Final exam on class time 05/09 (outside the final exam week)

❖ Office hours: by appointment

❖ Some questions can be answered by emails; you can send me emails at any time

❖ Approximately 4 sets of homework (each set a few problems); no quiz

❖ Grade: 40% HW, 25% Final Exam, 25% Project, 10% Attendance

Textbook & Course Objectives❖ No designated textbook

❖ Reference books: (1) “Observational Astronomy” (Cambridge, 2nd edition) by Birney, Gonzalez, & Oespar (2) “To Measure the Sky” (Cambridge Press) by Frederick R. Chromey (3) “Handbook of CCD Astronomy” (Cambridge, 2nd edition) by Howell (4) “Practical Statistics for Astronomers” (Cambridge, 2nd edition) by Wall & Jenkins

❖ This course aims to give you only a taste of the techniques of observational astronomy

❖ The course also aims to give you some hand-on experiences, so that it will prepare you for serious research should you desire

Topics to Cover

❖ Light, magnitude, and flux

❖ Coordinate systems, time, and motion

❖ Optics

❖ Telescopes

❖ CCD

❖ Softwares & database

❖ Photometry

❖ Spectroscopy

❖ Statistics

❖ etc.

Extremely Important!!!

❖ This class is data-oriented, and often requires work on computers during lectures

❖ You should learn to work in Unix/Linux OS (because every observational astronomer does)

❖ Linux OS (Redhat 7) has already been installed at the lab computers as virtual machine

❖ You’ll do most of your projects in Unix/Linux, which means you’ll need to use the lab computers (if you have a Linux machine or a Mac at home, talk to me)

❖ Get a USB stick (at least 4GB) - you might need it for data transfer

Introduce Yourself❖ Your major

❖ Why interested in astronomy

❖ Expectation from this course

❖ Astronomy experiences (courses, research, etc.)

❖ Computer/software/coding experiences

❖ Questions?

What Observational Astronomy Is About

❖ Key of observational astronomy: observations & measurements⎯ how bright an object is, and

⎯ where it is ⎯ and when

❖ All we can do is measuring the light - how bright it is, and where it is from

❖ By quantitative measurements, we are able to understand the physical properties of a celestial object (“what”), and the physical mechanisms that govern its behaviors (“why”)

❖ Observational astronomy offers a unique pathway to reveal new physics (because of the extreme scales and conditions of its subjects)

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Astronomy & Astrophysics (quote from NASA’s mission)

How does the universe work? • origin and fate of our universe • gravity, dark energy, dark matter • blackholes

How did we get here? • origin and evolution of galaxies, stars, and planets

Are we alone? • planets around other stars • habitability

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Milky Way: the Galaxy Milky Way: a typical

galaxy

What’s a galaxy? — star, star remanent, interstellar gas, dust — gravitationally bound by dark matters

How to study galaxy formation and evolution

— observe galaxies at various evolutionary stages — establish an evolutionary track — understand the physics — test the theory with more data

2x10^9 light years

100,000 light years Milky Way: a typical galaxy

What’s a galaxy? — star, star remanent, interstellar gas, dust — gravitationally bound by dark matters

Milky Way: a typical galaxy

SDSS

Cosmological Framework ΛCDM hierarchical formation

Precision Cosmology + hierarchical structure formation Dark matter cannot be directly observed Observational study on galaxy formation and evolution is needed

Dark Energy: 70%

Dark Matter: 25%

NASA

Merger Tree Lacy & Cole 1993

Free H, He

4%

Stars 0.5%

Neutrinos 0.3%

Heavy elements: 0.03%

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Putting All Known Physics Together

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Test TimeTwo-million-dollar picture

(XDF: the deepest view of the Hubble Space Telescope)

Twenty-million-CPU hour picture (ILLUSTRIS simulation)

Promising, but need to work more Theorists: improved physical recipes Observers: detailed measurements of individual galaxies

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Light, Magnitude & Flux

Textbook Reference:

❖ To Measure the Sky: Chapter 1 (in particular, 1.3–1.6)

❖ Obs. Astro.: Chapter 5

Light Radiation: Electromagnetic Wave❖ Electromagnetic wave representation of light

❖ Wavelength and frequency; c = λ⋅ν

❖ Nowadays in observational astronomy, “optical” generally refers to 300-1000nm, i.e., the range over which CCDs have response

Electromagnetic Spectrum

Astronomers are interested in the entire spectrum!

Electromagnetic Spectrum

Astronomers are interested in the entire spectrum!

Quantum Mechanical Representation

❖ Light as particles, i.e., photons

❖ Energy associated with light: E = h⋅ν = h⋅c/λ

❖ Unit of light:Gamma rays — MeV, GeVX-ray — keV Ultraviolet, optical —Å (angstrom), nm (nanometer)Infrared (near-IR, IR, far-IR) — microns (µm), mm, cm-1 Millimeter, microwave — mmRadio — cm, m, MHz, GHz

❖ 1 eV = 1.602 × 10-19 Joule = 1.602 × 10-12 erg

❖ 1 m = 103 mm = 106 µm = 109 nm = 1010 Å

Geometrical Representation: Light Rays

❖ Very useful in discussing optics of telescopes and instruments

(Optical/IR) Astronomy: Counting Photons

❖ Photometry: measures the amount of energy arriving from a source

❖ Spectroscopy: measures the distribution of photons with wavelength

Luminosity and Flux❖ Luminosity: L = E/t (energy emitted per unit time)

❖ Flux: F = E/(tA) = L/(4πr2) — depends on distance to source (r)

❖ Monochromatic flux: — fν = F(ν,ν+dν)/dν = Eν/dA/dt/dν unit: erg·s-1·cm-2·Hz-1

1Jy (Jansky) = 10-26W·m-2·Hz-1

= 10-23erg·s-1·cm-2·Hz-1

— fλ = F(λ,λ+dλ)/dλ = Eλ/dA/dt/dλ unit: erg·s-1·cm-2·Å-1

fν ≠ fλ, but fνdν = fλdλ

Vega

Spectral Energy Distribution (SED)

❖ Celestial objects are of different colors

❖ What does “color” mean in astronomy?

❖ The energies that they emit at different wavelengths are different

❖ Spectrum and Spectral Energy Distribution

Wavelength

Rela

tive

Flux

Magnitude & Photometric Systems

❖ Definition of magnitude

❖ Why we use magnitudes in UV/optical/IR astronomy

❖ Different photometric systems

❖ Different magnitude systems

Magnitude: its modern definition

❖ m = -2.5 log10(F) + C , where⎯ m : magnitude⎯ F : flux (or flux density or apparent brightness)⎯ C : zeropoint appropriate for the given system

❖ 1) magnitude is dimensionless 2) the larger the magnitude in number, the fainter the object

❖ To compare the brightness of two different objects⎯ m1 - m2 = -2.5 log(F1/F2)

Why on earth do we use magnitudes ??!!

❖ Brightness of an object is our perception of its energy output rate at the distance that we measure it - why don’t we use physical units, such as W/m2 or erg/s/cm2 ?

❖ Magnitudes are only used at optical, IR and UV wavelengths

❖ Astronomy started from optical, and we have a long, long history that we cannot/shouldn’t cut off

❖ The use of magnitudes is part of the history

❖ Other branches of astronomy that started in modern time (radio, high-energy) do not have this heritage, and the use of physical units there is natural

Brief History of Magnitudes

❖ Hipparchus first classified stars by magnitudes, but referred to “size” more than to “brightness” (and this misconception continued into 19th century)

❖ The biggest (actually the brightest) stars being the “first magnitude” or “first class”, … and so on, all the way to those barely visible to naked-eye as the “sixth magnitude” or “sixth class”

❖ In the 19th century astronomers realized that stars are point-like, began to understand diffraction and seeing, and began to be able to measure star lights (photometry)

Brief History of Magnitudes (cont.)

❖ N. R. Pogson noted that stars of the first magnitude were roughly 100 times as bright as those of the sixth magnitude

❖ In 1856 Pogson proposed to make it a standard that a 1st mag star is 1001/5 (~ 2.512) times as bright as a 2nd mag star, … and so on; i.e.,

Δm= m2-m1

B1/B2 = (1001/5 )Δm

❖ And hence our modern definition of magnitude (and is not limited to 1-6 mag anymore)

N.R. Pogson(1829-1891)

Magnitude Systems

❖ Early magnitudes were still on a visual system defined by naked-eyes, and were still crude

❖ By the time when photographic films began to be used for recording, discrepancies were noted for some stars between their brightness appeared on film and by eye: films are more sensitive to blue objects while human eyes are more sensitive to red objects

❖ Photographic magnitude system: mpg

❖ Different colors of celestial objects makes it necessary to separate emissions from different parts of the spectra

❖ Hence the use of filters, and the reference to passbands

Filters, Photometric & Magnitude Systems

❖ When speaking of a magnitude, one must specify which passband (filter) and in which magnitude system

❖ A photometric system is determined by 1) its filters, 2) the optical system response (telescope + detector), and 3) the standard stars that set the zeropoints and are used for calibration

❖ m = -2.5 log10(F) + C

❖ When defining a magnitude system using a standard star, in theory one can set an arbitrary constant to “C” so that this standard star has a magnitude of a desired value and fix this system. From then on every measurement is relative to the standard star.

Two Commonly Used Broad-band Sets

❖ Filters cannot be made exactly the same; optics and detector responses vary from site to site - one cannot make two identical systems

❖ Standard stars have to be used to calibrate and normalize

Johnson U, B, VJohnson R, I orCousin R, I

Sloan DigitalSky Survey

(SDSS)u’, g’, r’, i’, z’

Commonly Used Magnitude Systems❖ Vega system: Vega in any bands has 0 mag by definition;

measurements linked to physical fluxes of Vega⎯ Vega is a A0 V star (blue) ⎯ Johnson-Morgan UBV (and UBVRI) system is largely a

Vega system but not exact; Vvega = 0.03 and all colors = 0 ⎯ Vega’s spectrum is very complicated at IR.

❖ AB system (Oke 1974): an object of flat-spectrum per unit frequency has all colors = 0 ⎯ mAB = -2.5log10(f) - 48.60 , where

(1) f : flux density in units of erg/s/cm2/Hz (2) 48.60 is chosen such that mAB = VJohnson for a flat-spectrum object (mAB,V = mVega,V) ⎯ standard stars are still needed for calibration ⎯ advantages: easy to compare with theory and physical quantities

Bolometric Magnituden Monochromatic magnitude

n Bolometric magnitude: all the electronic magnetic radiation emitted by a source is included in the measurement

n Bolometric correct: BC_band = m_bol - m_band. (BC_V of the Sun is -0.07. How small! And why negative?)

n M_bol = 4.74 - 2.5⋅log10(L/L_Sun)

Absolute Magnitude▪ Absolute Magnitude is a way of representing

luminosity in the magnitude system▪ We need a reference: Distance▪ We define the absolute magnitude (M) as how

bright an object would look if it were a distance of 10 parsecs away (1 parsec = 3.086x10^(21) meters)

▫ Example: The Sun◾Apparent Magnitude: m = -26.7◾Absolute Magnitude: M = +4.83 (in V)

Absolute Magnitude▪ We can determine an object’s absolute magnitude

(M) if we know its apparent magnitude (m) and distance (d)

▪ The second is called the Distance Modulus Equation

Distance must be in units of parsecs!

M = m – 5⋅log10(d) +5 m - M = 5⋅log10(d) - 5

Surface Brightness

n For point-like objects, magnitude is adequate to describe its brightness

n For extended objects, surface brightness is used sometimes

n Surface brightness µ = m + 2.5⋅log10(A), where A is the angular area in unit of arcsec^2. (Why?)

Ln, Log, and Log10n Natural logarithm: to base of e (mathematical

constant), ln(x), loge(x). It is ln(x) in most calculators; but in computer languages, it is often log(x).

n Logarithm to base 10: log10(x). In most calculators, it is log(x); but in computer languages, it is often log10(x).

n In astronomy, the use of log10(x) is dominant (why?), so we often use log(x) and log10(x) for the same thing , and use ln(x) for loge(x) — but not always…

END

n 1 radian = (180/pi) degree

n 1 steradian = (180/pi)^2 degree^2

n full sphere: 4*pi steradian = 4*pi* (180/pi)^2 degree^2