AB Andromedae / AB And
Light curves and phase diagrams of the EW type eclipsing binary AB Andromedae / AB And.
Please note that AB And has a period which is constantly changing (Kreiner), so the phase diagrams which follow which include observations made several years apart are not strictly accurate, and the 'best-fit' periods are more of an average over that time interval rather than the period. I have also combined results obtained from unfiltered images and images taken with a green filter, which is not good practice!.
Please note that AB And has a period which is constantly changing (Kreiner), so the phase diagrams which follow which include observations made several years apart are not strictly accurate, and the 'best-fit' periods are more of an average over that time interval rather than the period. I have also combined results obtained from unfiltered images and images taken with a green filter, which is not good practice!.
'Run 1' light curve and phase diagram constructed from 19 unfiltered images taken with the Bradford Robotic Telescope Cluster Camera between 2 July 2013 and 5 October 2013.
'Run 2' light curve and phase diagram constructed from 59 images taken with the Bradford Robotic Telescope Cluster Camera with the three colour green filter between 12 October 2014 and 29 September 2016.
Combining the above two sets of data - unfiltered (run 1, in black) and filtered (run 2, in red)! - results in the following light curve and phase diagrams.
The above phase diagram but with all the data points in black:-
A primary minimum was observed from Somerby Observatory with the 2" Titan on 29 November 2017. The 151 images were unfiltered.
Combining these with the BRT observations produces the following light curve and phase diagram, BRT in black, Somerby in red.
A visually observed primary eclipse in 1991, made with my unfiltered 10 inch / 254mm reflector from Leicester, is below.
When combined with the 2" Titan observations of 29 November 2017 we obtain the following light curve and phase diagram. The consistency of the visual and ccd results illustrates the usefulness of visual observations of such stars.
Although there is an apparent difference in the maximum brightness between the two BRT runs, this could well be due to run 1 being unfiltered and run 2 being filtered. However, other observers have suggested that the maximum brightness does actually vary from one cycle to another, possibly due to brightening of the connecting material between the two stars in the system. See, eg Hasanzadeh et al (2008).
There is o-c interest in this star (Kreiner).
There is o-c interest in this star (Kreiner).
AB And model
The following is a model binary system which fits the above observations, using Binary Maker 3 (BM3). It uses no other observations and does not include any radial velocity data so it is not a 'definitive' model by any means.
In this model the primary has a surface temperature of 5800 K while the secondary has a surface temperature of 5350 K. Note that the temperatures used here are not quite consistent with the catalogued spectral classes of G5 and G5V (ref AAVSO VSX). The best fit inclination of the perpendicular to the plane of the orbits to our line of sight is 83.5 degrees.
This results in the following light curve, in blue, compared to my observations.
In this model the primary has a surface temperature of 5800 K while the secondary has a surface temperature of 5350 K. Note that the temperatures used here are not quite consistent with the catalogued spectral classes of G5 and G5V (ref AAVSO VSX). The best fit inclination of the perpendicular to the plane of the orbits to our line of sight is 83.5 degrees.
This results in the following light curve, in blue, compared to my observations.
The following are some details of the model from BM3, showing the model from our viewpoint and the critical potentials together with the centres of mass of the two stars and the barycentre of the system.
Output from Binary Maker
mass ratio input = 2.036700 mass ratio < 1 = 0.490990
Omega 1 = 5.215999 Omega 2 = 5.205342
Omega inner = 5.303534 Omega outer = 4.705244
C 1 = 2.304154 C 2 = 2.300708
C inner = 2.332460 C outer = 2.138991
Fillout 1 = 0.146310 Fillout 2 = 0.164121
Lagrangian L1 = 0.572575 Lagrangian L2 = 1.579339
AG = r1(back) = 0.482101 AS = r2(back) = 0.360000
BG = r1(side) = 0.451226 BS = r2(side) = 0.321605
CG = r1(pole) = 0.423131 CS = r2(pole) = 0.306910
DG = r1(point) = 0.572575 DS = r2(point) = 0.427425
Surface area 1 = 2.593745 Surface area 2 = 1.384075
Volume 1 = 0.384217 Volume 2 = 0.147701
Mean radius 1 = 0.452153 Mean radius 2 = 0.329505
Mean radius 1 (vol) = 0.450985 Mean radius 2 (vol) = 0.327918
Eccentricity = 0.00000 Longitude of Periastron = 0.0000
Phase of periastron = 0.00000 Phase of conjunction = 0.00000
Angular Rotation F1 = 1.0000 Angular Rotation F2 = 1.0000
Normalization Phase = 0.25000 Normalization Factor = 0.87000
inclination = 83.500 wavelength = 5500.00
temperature 1 = 5350.00 temperature 2 = 5800.00
luminosity 1 = 0.5609 luminosity 2 = 0.4391
gravity coefficient 1 = 0.320 gravity coefficient 2 = 0.320
limb darkening 1 = 0.650 limb darkening 2 = 0.650
reflection 1 = 0.500 reflection 2 = 0.500
Third light = 0.0000 Period = 0.33189220
K1 = 115.700000 K2 = 235.700000
V0 = -24.600000
mass ratio input = 2.036700 mass ratio < 1 = 0.490990
Omega 1 = 5.215999 Omega 2 = 5.205342
Omega inner = 5.303534 Omega outer = 4.705244
C 1 = 2.304154 C 2 = 2.300708
C inner = 2.332460 C outer = 2.138991
Fillout 1 = 0.146310 Fillout 2 = 0.164121
Lagrangian L1 = 0.572575 Lagrangian L2 = 1.579339
AG = r1(back) = 0.482101 AS = r2(back) = 0.360000
BG = r1(side) = 0.451226 BS = r2(side) = 0.321605
CG = r1(pole) = 0.423131 CS = r2(pole) = 0.306910
DG = r1(point) = 0.572575 DS = r2(point) = 0.427425
Surface area 1 = 2.593745 Surface area 2 = 1.384075
Volume 1 = 0.384217 Volume 2 = 0.147701
Mean radius 1 = 0.452153 Mean radius 2 = 0.329505
Mean radius 1 (vol) = 0.450985 Mean radius 2 (vol) = 0.327918
Eccentricity = 0.00000 Longitude of Periastron = 0.0000
Phase of periastron = 0.00000 Phase of conjunction = 0.00000
Angular Rotation F1 = 1.0000 Angular Rotation F2 = 1.0000
Normalization Phase = 0.25000 Normalization Factor = 0.87000
inclination = 83.500 wavelength = 5500.00
temperature 1 = 5350.00 temperature 2 = 5800.00
luminosity 1 = 0.5609 luminosity 2 = 0.4391
gravity coefficient 1 = 0.320 gravity coefficient 2 = 0.320
limb darkening 1 = 0.650 limb darkening 2 = 0.650
reflection 1 = 0.500 reflection 2 = 0.500
Third light = 0.0000 Period = 0.33189220
K1 = 115.700000 K2 = 235.700000
V0 = -24.600000
[Latest update 27 June 2022]