calculating distance of SN 1987A

CALCULATING DISTANCE of SN1987A

Neşever BALTACI
Ozel Kultur Science High School,Astronomy and Physics Supervisor Teacher-
Physics Teacher in Umraniye Anatolia I.H.High School-Istanbul/Turkiye
nesever@yahoo.com
SUMMARY
Views which are taken by Hubble telescop, ESA – ESO at Feb, 1994 for SN 1987A are used for calculating the distance(D) of SN1987A to Earth .Calculations are done for appear diameter ,inclination angle and period from the light curves on milimetric papers by using mathematical toolkit inversions.It’s found outside of the ringD = 57,63 kpc inside of the ring D = 68,59 kpc average of distances:D= 63,11 kpc

A ) Calculating from outer part of the ring
1.Step by using mm graphic paper on the image
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) avarage ratio ( arcs / mm)
2. star to 1. star 89 3,0 0,03371
3. star to 1. star 50 1,4 0,02800 0,03111
3. star to 2. star 136 4,3 0,003162
2.Step
Appear diameter (a)= 51 mm
a = ( 51 mm ) . ( 0,03111 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
a = 4,848 . 10-6 rad / arcs
a = 7,6915 . 10-6 rad
3.Step cos i = near side / hypothenous so;
cos i = small axis/ big axis
cos i = 37 mm / 51 mm
= 0,7591 rad = >
i= 43,49 degree
4.Step by using light –time graph that is given
the day that first light is taken: t1=85,36 days
the day that max light is taken : t2 =451,21 day t= t2 – t1
t1 = 85,36 days t2= 451,21 t= 451,21 – 85,36 = >
t = 365,85 days
5.Step
sin i = dp / d => d = dp / ( sin i )
c = light speed( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440 seconds
dp = c.t d = dp / (sin i ) = ( c.t ) / ( sin i )
d=( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 43,49 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 42,63 )
d = 9,41013028815 / 0,68822 . 10-1 =>
(in meters) d = 13,673143 . 1016
6.Step
D = d / a
D = 13,673143 . 1016 / 7,6915 . 10-6
D = 1,7776 . 1022 m = 1,7776 . 1019 km
D = 1,7776 . 1019 / 3,084 . 1013
D = 57,63 kpc
B) Calculating from inner part of the ring
1.Step
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) average ratio( arcs / mm)
2. star to 1.star 83 3,0 0,0361
3. star to 1.star 47 1,4 0,0297 0,0331
3. star to 2. star 128 4,3 0,0335

2.Step
Appear diameter:(a) = 42 mm a = (42 mm ) . ( 0,0331 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
(in radian) a = 6,7396 . 10-6

3.Step cos i = near side / hypothenous so;
cos i = small axis / big axis
cos i = 31 mm / 43 mm
= 0,0809 rad
i = 41,30 degree
4.Step
the first days that light is taken: 85,36 days
the days that max. light is taken : 451,21 days
t=t2 – t1 t t1 = 85,36 days t2 = 451,21 days
t= 451,21 – 85,36
t = 365,85 days

5 .Step c = speed of light ( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440seconds
sin i = dp / d => d = dp / ( sin i )
dp = c.t
d = dp / (sin i ) = ( c.t ) / ( sin i )
d = ( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 41,30 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 41,30 )
d = 9,41013028815 / 0,660001
d = 14,25775756 . 1017 m

6.Step D = d / a
D = 14,25775756 . 1017 / 6,7396 . 10-6
D = 21,1551 . 1024 m = 21,1551 . 1021 km
D= 21,1551 . 1021 / 3,084 . 1013
D = 68,59 kpc





CONCULATION:
Distance of SN 1987A to Earth is calculated as 68,59kpc and 57,63 kpc
so the average of two results is taken DISTANCE=63,11 kpc








SOURCES:
• Fransson, C.; Cassatella, A.; Gilmozzi, R.; Kirshner, R. P.; Panagia, N.; Sonneborn, G.; Wamsteker, W.., 1989, Ap.J., 336, 429-441: Narrow ultraviolet emission lines from SN 1987A - Evidence for CNO processing in the progenitor - PDF FILE (ADS - 2.1 MB) - PDF FILE (LOCAL - 2.1 MB).
• Gould, A., 1994, Ap.J., 425, 51-56: The ring around supernova 1987A revisited. 1: Ellipticity of the ring - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).
• Panagia, N., Gilmozzi, R., Macchetto, F., Adorf, H.M., Kirshner, R.P. 1991, Ap.J., 380, L23-L26: Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud - PDF FILE (ADS - 0.8 MB) - PDF FILE (LOCAL - 0.8MB).
• Jakobsen, P., Albrecht, R., Barbieri, C., Blades, J. C., Boksenberg, A., Crane, P., Deharveng, J. M.,Disney, M. J., Kamperman, T. M., King, I. R., Macchetto, F., Mackay, C. D., Paresce, F., Weigelt, G., Baxter, D., Greenfield, P., Jedrzejewski, R., Nota, A., Sparks, W. B., Kirshner, R. P., Panagia, N., 1991, ApJ, 369, L63-L66: First results from the Faint Object Camera - SN 1987A - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).