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Obtaining your PEP epsilon(V) coefficient

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Making Observations for Obtaining Epsilon-V Coefficient Using the Two-Star Method

Preliminaries

Assuming you have a suitable photoelectric photometry system (telescope and photometer), you will also need the following:

  1. The example calculation from Dr. D.S. Hall, available from the PEP Committee Chair, or from the NASA Abstract Data Service.
  2. AAVSO Transformation Star Charts (four are available at ftp://ftp.aavso.org/archival_charts/misc/PEP/) or your own finder charts for the stars listed below. (Use your favorite planetarium-type program.)

Procedure

This information sheet expands on the information in the paper by Dr. Hall.

Select a convenient star pair and observe the selected pair when it is near your meridian on a night of exceptional clarity. Make a series of measurements through your V filter in the following sequence: r, s, b, s, r, s, b, s, r, s, b, s, r, s, b, s, r, s, b, s, r, s, b, s, r, s, b, s, r, s, where r is a red star measurement, b is a blue star measurement, and s is a sky background measurement. Each measurement must be an average of 3 or more individual deflections. You should end up with 7 measurements of the blue star and 8 measurements of the red star. You can make additional readings of the pairs if you wish, as long as you end up with a red measurement bracketing each of the blue measurements.

If you use either a pulse counting system or an SSP-3, your integration time should be 10 seconds or longer.

If you are using a pulse counting system, no gain value is entered, but you must do your own compensation for dead time before recording in the readings. If you use an SSP-3, enter 1, 10, or 100 for the gain, whichever is used. (Depending on your telescope aperture, all stars can be measured with a gain setting of 10.) If you use a DC integrating system, enter the half magnitude gain step used.

Treat the blue star as a "variable" and the red star as a "comparison" and determine the differential magnitude. You can do this by hand, or, since the procedure is rather calculation intensive, use a spreadsheet to do the calculations. If you use a spreadsheet, save it for future determinations. The procedure can be found in any of the standard references, but is outlined here.

 

Then calculate your transformation coefficient following the method described in Dr. Hall's paper:

  1. For each star, calculate the net deflection by (r - s) or (b - s), where s is the sky measurement immediately following the star measurement. The result will be the net deflection for each star measurement.
  2. For each blue star measurement, calculate the instrumental differential magnitude Δv using
    Δv = -2.5 log10 (2*b/(r1 + r2))
    where b is the net blue deflection and r1, r2 are the net red deflections on either side of the blue measurement.
  3. Average the Δv values so determined to calculate a mean Δv(0). If you can, also calculate a standard deviation of the Δv's, Sv.
  4. Calculate your transformation coefficient, epsilon(V) or "ε(V)" using
    ε(v) = (ΔV - Δv(0))/Δ(B - V)
    where ΔV and Δ(B - V) are found from the table below for the pair you selected. Δ is always in the sense of blue star minus red star.
  5. Send your calculations to the PEP Committee Chair for review after your first determination, and then report your ε(v), the standard deviation, Sv, and the star-pair used for the determination.

Epsilon V must be determined for your own particular photometer and telescope combination. Due to the possibility of changes in the photometer detector and the telescope mirror coatings over a period of time, transformation calibration should be done periodically, every year or two

Star pairs for measuring transformation coefficients

The first of each pair is the Red star; treat it as the comparison star. Treat the Blue star as the variable star.

Constellation Yale R.A. Dec. Δ(B-V) Other
Star Pair Bright Star hh mm dd mm V (stars) Designation
And       Δ(B-V)=-0.71  
SAO 37434 HR 483 01 42 +42 37 4.95  
SAO 37418 HR 477 01 41 +40 35 4.94 τ And
Per       Δ(B-V)=-1.39  
SAO 38890 HR 1052 03 31 +48 00 4.36 σ Per
SAO 38893 HR 1051 03 31 +48 06 5.82  
Ori **       Δ(B-V)=-1.245  
SAO 112098 HR 1534 04 49 +03 35 6.03  
SAO 112096 - - - 04 49 03 59 7.32  
LMi **       Δ(B-V)=-1.03  
SAO 62019 HR 4081 10 24 +33 43 5.50 26 LMi
SAO 62010 HR 4075 10 23 +33 54 5.878 27 LMi
Ser       Δ(B-V)=-1.13  
SAO 121157 HR 5854 15 44 +06 26 2.65 α Ser
SAO 121170 HR 5859 15 45 +05 27 5.58  
Her       Δ(B-V)=-1.39  
SAO 65890 HR 6418 17 15 +36 49 3.16 π Her
SAO 65921 HR 6436 17 18 +37 18 4.65 69 Her
Oph **       Δ(B-V)=-1.23  
SAO 122686 - - - 17 44 +05 15 7.805  
SAO 122687 - - - 17 44 +05 43 8.315  
Aqr **       Δ(B-V)=-0.985  
SAO 145916 HR 8453 22 11 -04 16 6.01  
SAO 145914 HR 8451 22 10 -03 54 6.27  
Peg       Δ(B-V)=-0.44  
SAO 91253 HR 8905 23 25 +23 24 4.40 ν Peg
SAO 91186 HR 8880 23 21 +23 44 4.60 τ Peg
Scl       Δ(B-V)=-1.055  
SAO 193224 HR 471 01 38 -36 32 5.94  
SAO 193261 HR 498 01 42 -36 49 5.7  
Col       Δ(B-V)=-0.99  
SAO 196653 HR 2263 06 17 -37 44 5.54  
SAO 196659 HR 2265 06 17 -37 15 5.88  
Cen       Δ(B-V)=-1.52  
SAO 205871 HR 5485 14 44 -35 11 4.05  
SAO 205839 HR 5471 14 42 -37 48 4.00  

** Indicates star pair for which an AAVSO finder chart is available at ftp://ftp.aavso.org/archival_charts/misc/PEP/

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