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Introduction to Astronomy and Astrophysics I Lecture 4

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Introduction to Astronomy and Astrophysics I Lecture 4 Introduction to Astronomy and Astrophysics I Lecture 4 Yogesh Wadadekar Aug-Sep 2019 ncralogo IUCAA-NCRA Grad School 1 / 20 Computing HA HA = LST - α What is the hour angle of an object at RA=23:00:00 at 6 pm local time on 22 December (winter solstice)? ncralogo IUCAA-NCRA Grad School 2 / 20 86400=2:3 × 103 × 102 = 3800 million years tidal friction and longer days There is a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the Earth’s rotation by tidal friction. How much longer before we have 48 hour days? ncralogo IUCAA-NCRA Grad School 3 / 20 tidal friction and longer days There is a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the Earth’s rotation by tidal friction. How much longer before we have 48 hour days? 86400=2:3 × 103 × 102 = 3800 million years ncralogo IUCAA-NCRA Grad School 3 / 20 Ecliptic latitude and longitude ncralogo What is the ecliptic latitude and longitude of the summer solstice point? What is the ecliptic latitude of the north celestial pole? IUCAA-NCRA Grad School 4 / 20 Galactic Coordinates ncralogo IUCAA-NCRA Grad School 5 / 20 Milky way in galactic coordinates ncralogo IUCAA-NCRA Grad School 6 / 20 base 1001=5 inverted - brighter objects have lower magnitude measurements relative For small changes, a x fractional change in flux produces a x change in magnitude Apparent magnitude - flux measure m1 − m2 = −2:5 log10(f1=f2) logarithmic ncralogo IUCAA-NCRA Grad School 7 / 20 inverted - brighter objects have lower magnitude measurements relative For small changes, a x fractional change in flux produces a x change in magnitude Apparent magnitude - flux measure m1 − m2 = −2:5 log10(f1=f2) logarithmic base 1001=5 ncralogo IUCAA-NCRA Grad School 7 / 20 measurements relative For small changes, a x fractional change in flux produces a x change in magnitude Apparent magnitude - flux measure m1 − m2 = −2:5 log10(f1=f2) logarithmic base 1001=5 inverted - brighter objects have lower magnitude ncralogo IUCAA-NCRA Grad School 7 / 20 For small changes, a x fractional change in flux produces a x change in magnitude Apparent magnitude - flux measure m1 − m2 = −2:5 log10(f1=f2) logarithmic base 1001=5 inverted - brighter objects have lower magnitude measurements relative ncralogo IUCAA-NCRA Grad School 7 / 20 Apparent magnitude - flux measure m1 − m2 = −2:5 log10(f1=f2) logarithmic base 1001=5 inverted - brighter objects have lower magnitude measurements relative For small changes, a x fractional change in flux produces a x change in magnitude ncralogo IUCAA-NCRA Grad School 7 / 20 Vega magnitude The most widely used magnitude system through the year 2000 was based on a set of normalizing constants derived from the spectrum of the bright star Vega. We are now slowly moving to absolute systems based on calibrations in terms of physical flux units. ncralogo IUCAA-NCRA Grad School 8 / 20 The STMAG system - flux per unit wavelength mλ(λ) = −2:5 log10 Fλ(λ) − 21:1 where Fλ(λ) is the spectral flux density per unit wavelength of a source at the top of the Earth’s atmosphere in units of erg s−1 cm−2 Å−1 . This is also known as the STMAG system because it is standard for the Hubble Space Telescope. For more details, see the Synphot User’s Guide at STScI. ncralogo IUCAA-NCRA Grad School 9 / 20 AB magnitudes - flux per unit frequency The corresponding system based on flux per unit frequency is mν(λ) = −2:5 log10 Fν(λ) − 48:6 −1 −2 −1 where Fν(λ) is in units of erg s cm Hz . This is also known as the AB system. This system has been adopted by the Sloan Digital Sky Survey and GALEX. (The resulting magnitudes are therefore very different from the STMAG system in the UV, for example.) ncralogo IUCAA-NCRA Grad School 10 / 20 Jansky- used in FIR and radio astronomy 1 Jy = 10−23 erg/sec/Hz/cm2 The conversion between AB magnitude m and flux density f of a star in Janskies is: f = 3631 Jy ×10−0:4m ncralogo IUCAA-NCRA Grad School 11 / 20 Caveats narrow band fluxes measured using broad bands (UBVRIJHK - calibration problems calibration done not with laboratory standards, but with standard stars Many filter systems - Johnson UBVRI, Gunn ugriz ncralogo IUCAA-NCRA Grad School 12 / 20 Surface brightness is the magnitude or flux per unit solid angle - mag/arcsec2 (optical), Jy/beam (radio), MJy/str (IR) ncralogo IUCAA-NCRA Grad School 13 / 20 Absolute magnitude - luminosity measure M = m − 5((log10 DL) − 1) for cosmological distances, DL is the luminosity distance. m − M is referred to the distance modulus. An object with a distance modulus of 0 is exactly 10 parsecs away. If the distance modulus is negative, the object is closer than 10 parsecs, and its apparent magnitude is brighter than its absolute magnitude. If the distance modulus is positive, the object is farther than 10 parsecs and its apparent magnitude is less bright than its absolute magnitude. ncralogo IUCAA-NCRA Grad School 14 / 20 Color in astronomy B − V = mB − mV R − K = mR − mK Shorter wavelength filter is always placed first, by convention. What does a low value of color indicate? Can color be negative? Why is color important? ncralogo IUCAA-NCRA Grad School 15 / 20 How to find this car in space? ncralogo IUCAA-NCRA Grad School 16 / 20 How to find Musk’s roadster? ncralogo IUCAA-NCRA Grad School 17 / 20 What is a star? 1 it is bound by self-gravity 2 it is powered by an internal energy source If any of these conditions is violated, the star ceases to be a star. ncralogo IUCAA-NCRA Grad School 18 / 20 Why are stars in equilibrium? ncralogo IUCAA-NCRA Grad School 19 / 20 Hydrostatic equilibrium ncralogo IUCAA-NCRA Grad School 20 / 20.
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