Unformatted text preview: ‘ recitation will be on this Fri. and will
I estimation. I _ to keep up with the reading! NASA, NOAO, ESAand The Hubble Herliage Team (STSCI/AURA) Radiation (Kulner, Ch. 2; see also Kamunen, Ch. 4; Shu, Ch. 2) AST 203 (Spring 2011) Properties of Stars  How we can measure various properties of stars?
 What properties do you think that we can measure? AST 203 (Spring 2011) Units and Measurements  n astrophysics, we use the cgs system of units — Unit of length: centimeter (cm)
— Unit of mass: gram (g)
— Unit of time: second (5)  Some derived units — Force is measured in dynes: g cm s'2  Compare to Newtons: 1 N = 1 kg m s‘2 = 105 dyn
— Energy is measured in ergs: g cm2 s'2  Compare to Joules: 1 J =1 N m =1 kg m2 5'2 =107 erg
— Power is measured in erg s'1  Compare to Watts: 1 W: 107 erg s'1 AST 203 (Spring 2011) Fundamental Constants — Speed of light: c = 3.00 x 1010 cm s'1 — Gravitational constant: G = 6.67 x 10'8 g'1 cm3 s'2 — Planck's constant: h = 6.63 x 10'27 erg s — Electron charge: e = 4.80 x 10'10 esu (g“2 cm?"2 s")
— Electron mass: me = 9.11 x10'28 g — Proton mass: mp = 1.67 x1024 g — Boltzmann's constant: k = 1.38 x 10'16 erg K'1 — StefanBoltzmann constant: a = 5.67 x 10'5 erg cm'2 s'1 K'4 Temperature is measured in Kelvin, K, but as we will see, it usually
enters into equations as kT, which is measured in ergs. AST 203 (Spring 2011) Angles and Solid Angles For this course, it is often more
convenient to work in radians. There are 27r radians in a circle:
271' rad : 360° lf 6 (measured in rad) is subtended by r‘
an arc, and r is the radius, arc length
is l=7°0 Also useful are the small angle formulas. lf 6 << 1 then
sin0m0; taanH
How many degrees correspond to 1 radian? You should know how to sketch cos 6, sin6 AST 203 (Spring 2011) Angles and Solid Angles Solid angles describe a fraction of a
sphere. If an emitting source covers an area
A on a spherical surface of
radius 7“, then the solid angle is Q:A/r2 Solid angles are measured in
steradians How many steradians in a
hemisphere? AST 203 (Spring 2011) Useful Formulas from Geometry You should be comfortable with computing the area and volume
of objects. Circle 0 : 27w
A : 71'7'2
S
r
h —l : 47rr2 4 3
7 371'?" Sphere ‘ /
 T
Cylinder I V : 7W2h
What is the surface area of a
cylinder? . l—
AST 203 (Spran 2011) Astronomical Information  ln astronomy, we primarily get information in the form of
electromagnetic radiation (I'll frequently use light to mean the
entire electromagnetic spectrum).  To a lesser extent, we also get information from: — Meteorites — Neutrinos — Gravitational radiation (maybe someday...)
— Cosmic rays AST 203 (Spring 2011) Mag n itudes
 Look at the night sky: some stars are brighter than others
 Greek astronomers created the magnitude system. — Stars assigned brightness on a scale of 1 to 6
 1 = brightest, 6 = faintest. — Standardized: difference in 5 magnitudes = factor of 100 in
brightness  Logarithmic scale—our eye's response to light is also logarithmic
 By brightness, we really mean flux—energy/area/second AST 203 (Spring 2011) Equatorial Coordinate System p  Star chart gives the position of the
stars in equatorial coordinates.  Right ascension, oz  analogous to longitude — measures distance vernal equinox
in hours, minutes, seconds  Declination, 6 SCP — analogous to latitude — measures the angle in degrees
north or south of the celestial
equator. AsT 203 (Spl ing 2011) Mag nitudes
Mathematically, we can relate the brightness or flux of two
objects as
E : 100(m2im1)/5
f2 remember—the brighter an object, the smaller the magnitude. Originally, the magnitude scale went from 1 to 6 6 is the “nakedeye limit" Today: Large telescopes can see down to magnitude 30 and below
The brightest stars in the sky have negative magnitudes apparent magnitude refers to how bright something appears
when viewed from earth. AST 203 (Spring 2011) ecliptic celestial
equator Magnitudes Apparent Magnitudes of Known Celestial Objects App. Mag. Celestial Object
226 73 Sun
—12 6 full Moon
I—Q 5 Maximum brightness of an Iridium Flare
74.7 Maximum brightness of Venus
I—3 9 Faintest oblects observable during the day With naked eye
72 9 Maximum brightness of Mars
I—2 8 Maximum brightness ofjubiter
7]. 9 Maximum brightness of Mercury
I—l S Brightest star (except torthe sun! at Vlslble Wavelengths: Sirius
20.7 Second brightest star Canopus
0 The zero point by definition: This used to be Vega
(see references for modern zero point)
In 7 Maximum brightness of Saturn
3 Faintest stars Visible in an urban neighborhood With naked eye
.4 6 Maximum brightness of Ganymede
5.5 Maximum brightness of Uranus
'6 Faintest stars observable With naked eye
.7 7 Maximum brightness of Neptune
12.6 Brightest quasar
'13 Maximum brightness of Pluto
27 Faintest objects observable in visible light With Em groundbased telescopes
'30 Faintest oblects observable in Visible light With Hubble Space Telescope I
38 Faintest objects observable in visible light With planned OWL E2020! Ilsee also List of brightest stars] (from Vlﬁkipedia)
AST 203 (Spring 2011) Properties of Logarithms
. lfN = apthen p = loga N — a is the base of the logarithm
. loga MN = loga M + loga N . loga (MIN) = loga M — loga N
. loga Mp = p loga M . We'll use “In” to mean loge, and “log” to mean log10 Properties of Exponents
. ap aq = ap+q
 a'p = 1/ap
. (ap)q = apq AST 203 (Spring 2011) Magnitudes We can rewrite our magnitude equation f1 < e )/5
—:100m2 m1
f2 by taking the base10 logarithm: m2 — m1 : 2.510g 2 What magnitude difference corresponds to a factor of 10 million
in brightness? What brightness ratio corresponds to a 10 magnitude difference? The Sun is 26.73 and the faintest object visible in the HST is 30
—this corresponds to a brightness ratio of 5 x 1022! AST 203 (Spring 2011) Magnitudes (Kantunen el al.) Consider a binary star system consisting of a magnitude 1 star
and a magnitude 2 star. What is the total magnitude of the binary system? AST 203 (Spring 2011) Light Astronomers primarily gain information about distant objects by
looking at the light coming from them. Properties of light: /
i in / ﬂ \ \ / / my“ \ E
*2???+‘*<i;i;i,ii2?ffhi:i? WE SupehManu/Wikipedia)
Maxwell: light is an electromagnetic wave alternating electric and magnetic fields perpendicular to each other. Such a configuration can freely propagate through space. AST 203 (Spring 2011) Light
EM waves have a number of properties associated with them: Wavelength: the distance between successive wave crests
Polarization: the direction of oscillation of the electric field
Direction of propagation: normal to the E and B fields Regardless of the wavelength or polarization, propagation speed
of an EM wave is constant, and in vacuum has the value: C = 3.00 X 1010 cm (5—1 In addition to the wavelength,)\ , we can also consider
frequency, 1/ ,—the number of oscillations per second. Auzc AST 203 (Spring 2011) Light Names assigned to different parts of the EM spectrum. é .. E E Our eyes are only sensitive to a g 3 small portion of this spectrum, 5 8 but astronomical objects can "” C” emit across the entire spectrum. 1000MHZ : Note, frequency is measured In 500MHz; units of Hz. ’ 50 MHz : AST 203 (Spring 2011) Light 3 Frequency (Hz) 1015_ 1D”, 1015_ 101a 1012_ 1D“_ \\101u_ \ 1093.. .. .. 1DE_ /. 1D7_ / 105_ Gamma—rays _ Xrays Ultraviolet Microwaves Rm: Radio TV A Vi Longwaves E.
on
1:
2
m
i:
E
0.1 A
_{1A
01nm
— 1 nm
/ 400 rim
/
,/
*1Dnm/
/
/
/ 500nm 600nm
700 nm
710mm
_{1000 pm
1mm
— 1 cm
— 10cm
*1m
— 10m
—1DUm
—1000m
(\Mkipedia) Our atmosphere is not transparent across the whole EM 100%
.9
a
u
3 50%
me spectrum nlnm Imn Iﬂnm 100nm Vlliﬂh uam
MILI
mm.
Mal lam Gamml um, Ivay: IM unmiqu
Llnm W by m appr momu lum loum 100w" 1mm 1cm mom Im 10m 1mm 1km (NASA/JPL; http:/Igallery.spitzer.callech.edullmagegallerylimage.php?image_name=bgOO5) Note the window at the visible spectrum—our eyes developed
sensitivity to these wavelengths because of this window. AST 203 (Spring 2011) Light If we want to observe in the infrared, we need to get above the atmosphere. The James Webb Space Telescope (JWST) to be
launched in 2013 (or later) will do just this. (NASA) AST 203 (Spring 2011) Light The Spitzer Space Telescope is in orbit now and returning all
sorts of IR images—we'll see a lot of them in this class. Andromeda galaxy imaged in the IR by Spitzer (NASA/JPLCaltecth. Gordon (University of Arizona» SOFIA will put a telescope in a
747 and ﬂy high—above the water vapor in the atmosphere, to
image in the IR. AST 203 (Spring 2011) Colors of Stars Some stars are different colors. Astronomers describe the color of a star
by measuring the intensity of energy a
star gives off over some wavelength
interval, Cu, or frequency interval, 61,}. We call this the spectra of the star. (Mouser Williams) AST 203 (Spring 2011) Colors of Stars Spectra from normal stars
MW over a range of masses. KSV Notice: smooth part, called
the continuum + a number of
Gav absorption lines—we'll talk M about those later. W Right now, we are interested
in understanding the
A“ continuum. Relative brightness 35V 05V 3500 4500 5500 0500 7500 8500
Wavelength f Angstroms (Jodrell Bank Observatory; based on Pickles 1988)
AST 203 (Spring 2011) Intensity I(u)du = energy/unit time/unit surface area in the frequency
range 1/ to V + dz/ being emitted into a cone of solid angle d9 Radiation moves through a small area dA into the cone described
by d9 Energy moving through this area
into the solid angle dB is dEzIV COSQdAdI/dﬂdt Intensity is measured in units of erg s"1 cm"2 Hz"1 ster'1 AST 203 (Spring 2011) Intensity (.059 {Actor [Vt lVl‘l‘eL/lsl‘ly ciefmd‘wh AST 203 (Spring 2011) Intensity In terms of wavelength, I(A)d)\ = energy/unit time/unit area in
the wavelength range A to A + dA emitted into solid angle d9 Then
dE : I,\ cos QdA dA d9 dt It is important to remember that intensity has a direction. Note—your book is a bit sloppy here. It leaves out the solid
angle part. AsT 203 (spring 2011) Blackbody  We won't go deeply into what intensity means (AST 341 topic) — We'll use intensity to derive some important results.
 Important concept: blackbody (thermal radiator) — Object in thermodynamic equilibrium
— Emission = absorption
— Emitted light has wellknown intensity spectrum  Function ofT only
 Isotropic, unpolarized.  Blackbody emission spectrum can be very different than that it
absorbs — Only requirement is that the net energy gain is zero, is it is in
equilibrium. AST 203 (Spring 2011) Blackbody A blackbody absorbs ALL incident
radiation —> black. If emission ¢ absorption, then T
would change —> no equilibrium. Stellar interior: atoms opaque to
radiation—absorb and reemit it. We see the stellar surface —>
stars act as good blackbodies. (Fimoozwmema) AST 203 (Spring 2011) Thermal Radiation 1433.2?
mm
.123 .100 uﬂr Seeing in IR maritime 3520 NA Elﬁn"I P A C Ashttpwmnlopsmos.ipac.caltech .ed u/cosmic_kids/learn_ir/ind ex. html Blackbodies 10'5 infrared visibleUV Ximy Gammuiruy T the peak of the
10‘": emission moves to
3 higher frequencies
5— (shorter
iO —
: wavelengths)
? mo;
3 : Hotter objects
ml appear bluer.
10710——
10’”:— 105 10‘“ 10‘5 102” Notice that the higher temperature blackbody emits more radiation than the lower temperature blackbodies at all frequencies.
AST 203 (Spring 2011) ...
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