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# Calculating the Distance to a Supernova by the Expanding Photosphere Method

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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).)

 (1)

 (2)
 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

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).

 (16)

in janskys. Convert janskys to joules

 (17)

The central wavelength of the B filter is 0.44 μm (Bessel, 1990). (See Table 2 in the text). Convert this to frequency.

 (18)

Planck's function for frequency:

 (19)

 (20)

 (21)

Calculate the angular size at 14 days.

 (22)

 (23)

Distance in metres:

 (24)

In megaparsecs

 (25)

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).