# Obtaining your PEP epsilon(V) coefficient

### 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:

- The example calculation from Dr. D.S. Hall, available from the PEP Committee Chair, or from the NASA Abstract Data Service.
- 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,

*is a blue star measurement, and*

**b***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.*

**s**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:

- 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.
- 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. - 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.
- 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. - 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)=-0.709 |
||||

SAO 37434 | HR 483 | 01 42 | +42 37 | 4.955 Note 2 | |

SAO 37418 | HR 477 | 01 41 | +40 35 | 4.949 | τ And |

Per |
Δ(B-V)=-1.406 |
||||

SAO 38890 | HR 1052 | 03 31 | +48 00 | 4.357 | σ Per |

SAO 38893 | HR 1051 | 03 31 | +48 06 | 5.833 | |

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 | 28 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)=-1.394 |
||||

SAO 65890 | HR 6418 | 17 15 | +36 49 | 3.161 | π Her |

SAO 65921 | HR 6436 | 17 18 | +37 18 | 4.626 | 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 | Note 1 | |

SAO 145914 | HR 8451 | 22 10 | -03 54 | ||

Peg |
Δ(B-V)=-0.44 |
||||

SAO 91253 | HR 8905 | 23 25 | +23 24 | Note 1 | ν Peg |

SAO 91186 | HR 8880 | 23 21 | +23 44 | 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 |

Note 1: The Aqr and Peg pairs are not recommended for transformations due to inconsistencies reported by several observers. The V magnitudes have been deleted to prevent indadvertant use.

Note 2: The And pair is under evaluation and not recommended for use unless other pairs are unavailable.

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

change log:

11/27/2016 added notes 1 and 2 at end of the table, and within the body of the table. Deleted Aqr V magnitudes of 6.01 and 6.27, and Peg V magnitudes of 4.40 and 4.60.

11/20/2016 changed entries to agree with GCPD. **Andromeda** From: delta(B-V)=-1.39 to -1.406 From: SAO 37434 V=4.95 to V=4.955 From: SAO 37418 V=4.94 to V=4.949 **Perseus** From: delta(B-V)=-1.39 to -1.406 From: SAO 38896 V=4.36 to 4.357 From:SAO 38893 V=5.82 to V=5.833 **Hercules** From: delta(B-V)=-1.39 to -1.394 From:SAO 65890 V=3.16 to V=3.161 From:SAO 65690 V=4.65 to 4.626 **Leo Minor **SAO 62019 was identified as 26 LMi, corrected to 28 LMi