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Calculating the Distance to a Supernova by the Expanding Photosphere Method ***
Problem: Use Doppler shifting and the "expanding photosphere method" to calculate the distance to the type II supernova remnant SN 1969L. (The calculations are based on extracts from Jasper (n.d.).)
Hints:
Calculate flux in janskys; convert to joules.
Calculate the frequency of the central wavelength of the B filter.
Calculate the Planck function for frequency.
Calculate the angular size of the supernova (θ) at 14 days.
Calculate the distance to the supernova in Mpc.
Data:
(Supernova data are from observations of the type II supernova SN 1969L reported in Kirshner and Kwan (1974).)
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| (1) |
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![v[obs] := 8.5*10^6](/view.aspx?SI=154323/6236ca9608d1e388d06af8d4706beda1.gif)
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![R := v[obs]*t](/view.aspx?SI=154323/189c09aae732d11b5fea8275b3097482.gif)
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| (10) |
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| (11) |
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Useful Equations:
 
# 
where
θ = angular size on the sky
D = distance to the supernova
fγ = observed flux density
ς = correction factor
Bν(T) = Planck function
R = radius of the supernova = vobs (t-t0) + R0 where
vobs = the observed velocity of expansion
t = time since t0
t0 = time of the explosion
R0 = the radius at t0
Solution:
  
Flux = 10^(-m/2.5)*zeropoint flux for the filter, where m is the visual magnitude (13.4 for SN 1969L). The zeropoint flux for the B filter is 4260 mJy, according to Bessel (1990).
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in janskys. Convert janskys to joules
![f[nu] := 0.1859557445e-1*10^(-26)](/view.aspx?SI=154323/bcb6b9f3c036c8bfffcc4664a1653d18.gif)
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The central wavelength of the B filter is 0.44 μm (Bessel, 1990). (See Table 2 in the text). Convert this to frequency.
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Planck's function for frequency:
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![B[nu] := proc (T, nu) options operator, arrow; 2*h*nu^3/(c^2*(exp(h*nu/(k*T))-1)) end proc](/view.aspx?SI=154323/c57ce8d691b321f192d1cf41c8736103.gif) 
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)](/view.aspx?SI=154323/51454e3b86f13280264d92c794d6b22d.gif)
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Calculate the angular size at 14 days.
))) end proc](/view.aspx?SI=154323/c4903aec789b129addbdfc2e8934ae53.gif)
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))) end proc](/view.aspx?SI=154323/daa5411a113322c6af23c5af71371762.gif)
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Distance in metres:
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In megaparsecs
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This is close to the accepted value of 21.3 Mpc, given by Schmidt (2013).
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References
Bessel, M. (1990). UBVRI Passbands. Publications of the Astronomical Society of the Pacific, 102, 1181-1199.
Jasper, S. (n.d.). Distance Computation of Supernovae. http://www.google.ca/search?hl=en-CA&source=hp&q=sushil+jasper+supernova&gbv=2&oq=sushil+jasper+supernova&gs_l=heirloom-hp.3...1662.6130.0.6427.23.12.0.10.10.0.425.1485.1j3j2j0j1.7.0....0...1ac.1.34.heirloom-hp..16.7.1485.rYZio6g6h1o (accessed: 2015-06-01).)
Kirshner, R. P., and Kwan, J. (1974). Distances to extragalactic supernovae. The Astrophysical Journal 193, 27-36.
Schmidt, B. (2013). The path to measuring an accelerating Universe. Physics-Uspekhi, 56(10).
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