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Methods of Mathematical Physics – Spring 2010-11
Week 2 – Thursday 8 April 2011
Dr. E.J. Zita
Cosmology: Distance ladder
Texts: Astrophysics in a Nutshell, by Don Maoz
Universe, by Freedman and Kaufmann
 Universe online: http://www.whfreeman.com/Catalog/static/whf/universe/
 See Boxes 17.1, 2, 3, 4
Fig.24-14: The Distance Ladder
* Parallax accurate to ~ 100 pc (HIPARCOS):
Observe flux f and measure distance D → Find luminosity L = 4Dpar2f
Universe (Ed.8) Ch.4 p.69, Ch.19 p.410, #32, 33, 70 (p.439)
Universe (Ed.9) Ch.4 p.72, Ch.17 p.434, #34, 35, 73 (p.465)
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#34: Suppose that a dim star were located 2 million AU from the Sun. Find
(a) the distance to the star in parsecs and
(b) the parallax angle of the star. Would this angle be measurable with present-day
techniques?
#35: The star GJ 1156 has a parallax angle of 0.153 arcsec. How far away is the star?
#73: Access the Active Integrated Media Module “Using Parallax to Determine Distance” in
Ch.17 of the Universe website or eBook. Use this to determine the distance in parsecs and in
light-years to each of the following stars:
(a) Betelgeuse (parallax p=0.00763 arcsec); (b) Vega (p=0.129 arcsec);
(c) Antares (p=0.00540 arcsec); (d) Sirius (p=0.379 arcsec)
(* Main sequence fitting) Observe young open star clusters – identify MS – compare observed
fCL to known f(L,D)
L
2
2
Ex: Ltype  4 Dpar
f par  4 DCL
fCL  DCL 
4 f
Carroll & Ostlie #13.18 p.540, using Fig. 13.27 p.531 and 13.29 p.534
* Tully-Fisher relation:
See Carroll & Ostlie p. 1001 ff, 1049
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* Cepheids in clusters with DCL (only 12 standard candles close enough!)
2
observe near f, find LCeph  4 DCL
f → measure pulsation period  → calibrate  -L relation
→ observe distant f, measure pulsation period  → calculate L → find D =
Universe (Ed.8) Ch.21 p.478-481, #40-41, 43
Universe (Ed.9) Ch.19, p.514-516; 607,8; 637-8; 644-5
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(Z notebook p.22) Universe Ed.8 Ch.19 #45:
 -Ceph (type I) has period =  d = 5.4 days and
Apparent brightness = 5.1 x 10-13 * bSun. Find distance to  -Ceph .
Estimate absolute luminosity L from Period-Luminosity plot above: L ~ ___
 L 
d
Or calculate L from C&) (14.1): log10 
  1.15log10   2.47  ____
L
 Sun 
Average luminosity over a pulsation period = L =_____
Lceph
LCeph  4 D2b
D = ____
D

Dsun
LSun
bceph
bSun
D = DSun*__________
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Spectroscopic Parallax: Universe Ed 8, Fig 17-18 p.456
p.454-5: Spectrum -> (Luminosity class from spectral lines) Fig 17-16, 17
p.107: Spectrum -> T (Spectral type: Wien’s Law: max T = 3 x 10-3 (K.m)
HR diagram: L-class + T -> L
Box 17-2: L + b -> Distance
Choose problems from Ch.17.
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