MBCAA Observatory

GSC 318805 / V551 Vir: a Blazhko starObserved: 42 sessions from 2009 to 2015Michel Bonnardeau

Season  Nb of sessions  Nb of V measurements  Nb of B measurements 
2009  3  72  68 
2010  11  273  260 
2011  6  166  158 
2012  6  149  110 
2013  5  259  0 
2014  7  388  0 
2015  4  284  0 
Total  42  1591  596 
For the differential photometry, the comparison star is GSC 318984 with V=12.056 and B=13.182, computed from the CMC14 r' magnitude and the 2MASS magnitudes, owing to the transformations of Bilir et al (2008) and of Smith et al (2002).
An example of a light curve:
Green: GSC 318905, Black: the check star. The error bars are the 1sigma
statistical uncertainties (computed as the qsum of the uncertainties on the
variable and of the comparison).
The B measurements are not analyzed here.
The data are analyzed with the PERIOD04 software program (Lenz and Breger,
2005) which provides simultaneously sinewave fitting and leastsquares
fitting algorithms. This yields the pulsation frequency:
F_{P} = 2.2378261 ± 4.2*10^{6} day^{1}
or the pulsation period:
P_{P} = 0.4468622 ± 0.8*10^{6} day (0.07 s)
Owing to the PERIOD04 software program, the data are fitted with the
following sinewave function of the time t, with a number of harmonics
of up to 4, above which they lost their significance:
where t are the HJD  2,454,000 and:
Z = 13.4625 +/ 0.0039
i  F_{i}  A_{i}  Φ_{i} 
0  F_{P}  0.3778 ± 0.0054  0.5022 ± 0.0024 
1  F_{P}*2  0.1459 ± 0.0056  0.3653 ± 0.0060 
2  F_{P}*3  0.0571 ± 0.0056  0.279 ± 0.015 
3  F_{P}*4  0.0367 ± 0.0055  0.139 ± 0.023 
4  F_{P}*5  0.0162 ± 0.0055  0.052 ± 0.055 
The resulting phase plot and the residual of the observations from the
f(t) function are shown in the figures below:
The red dots are the observations, the blue line is computed from the
f(t) function. The phase origin is arbitrary.
The differences between the observed magnitudes and the ones computed
with the f(t) function.
The deviations around the f(t) function come from the Blazhko effect.
The Blazhko modulation is expected to show up as side peaks around multiples of the pulsation frequency F_{P} in the Fourier spectrum (Breger & Kolenberg (2006), Szeidl & Jurcsik (2009)).
The PERIOD04 program is used to compute the Fourier spectrum of the residuals
around the F_{P} frequency:
On the right side of F_{P} there are peaks at F_{P}+1/62,
F_{P}+1/52 and F_{P}+1/45, and on the left side there
are peaks (weaker than the ones on the right side) at F_{P}1/62,
F_{P}1/52 and F_{P}1/45.
Quite weaker, there are also peaks at F_{P}±2/62, F_{P}±2/52
and F_{P}±2/45.
The spectra of the residuals (observations  f(t)) around the frequency
F_{P}. 45++ is the peak at F_{P}+2/45, 62 at F_{P}1/62, and so on.
The spectra of the residuals around 2.F_{P, }3.F_{P} and 4.F_{P} also show peaks for ±1/62, ±1/52 and ±1/45.
The spectrum of the residuals around 5.F_{P} shows no clear signal.
These peaks are interpreted as a modulation with a period P_{B} around 52 days, and the signals at 62 and 45 days as due to the seasonal 1 year alias.
The data are then fitted with the following frequencies: F_{P}±1/P_{B},
F_{P}±2/P_{B}, 2.F_{P}±1/P_{B},
3.F_{P}±1/P_{B}
and 4.F_{P}±1/P_{B}. And the amplitudes and phases for
the main pulsation are optimized again. The results are given in the table
below:
i  Interpretaion  F_{i}  A_{i}  Φ_{i} 
0  F_{P}  F_{P}  0.3716 ± 0.0040  0.5067 ± 0.0018 
1  2*F_{P}  2*F_{P}  0.1328 ± 0.0041  0.3601 ± 0.0050 
3  3*F_{P}  3*F_{P}  0.0472 ± 0.0039  0.282 ± 0.013 
3  4*F_{P}  4*F_{P}  0.0239 ± 0.0040  0.149 ± 0.028 
4  5*F_{P}  5*F_{P}  0.0162 ± 0.0038  0.035 ± 0.034 
5  F_{P}+1/P_{P}  2.2566168 ± 8.7E6  0.0994 ± 0.0039  0.3890 ± 0.0063 
6  F_{P}1/P_{P}  2.218949 ± 1.2 E5  0.0704 ± 0.0041  0.3770 ± 0.0087 
7  F_{P}+2/P_{P}  2.274372 ± 1.9 E5  0.0459 ± 0.0039  0.611 ± 0.013 
8  F_{P}2/P_{P}  2.200179 ± 3.6 E5  0.0235 ± 0.0040  0.570 ± 0.027 
9  2.F_{P}+1/P_{P}  4.495133 ± 4.3 E5  0.0151 ± 0.0041  0.216 ± 0.029 
10  2.F_{P}1/P_{P}  4.456011 ± 2.5 E5  0.0364 ± 0.0043  0.449 ± 0.018 
11  3.F_{P}+1/P_{P}  6.732359 ± 1.3 E5  0.0684 ± 0.0040  0.8914 ± 0.0091 
12  3.F_{P}1/P_{P}  6.694009 ± 4.5 E5  0.0198 ± 0.0039  0.133 ± 0.032 
13  4.F_{P}+1/P_{P}  8.970207 ± 2.1 E5  0.0422 ± 0.0041  0.752± 0.015 
14  4.F_{P}1/P_{P}  8.931784 ± 4.1 E5  0.0179 ± 0.0041  0.935 ± 0.031 
In the above, there are 10 different evaluations of the Blazhko period
(i=5 to 14). The average value and standard deviation are:
P_{P} = 52.5 ± 1.2 days
The observations may then be fitted with the function:
where ZB=13.4618 ± 0.0029
The residuals of the observations and of the fB(t) function are:
The 42 timeseries are compared with the above fit. For most of them, the
observations are found to be in good agreement with the fB(t) function. For example:
An example of a low amplitude Blazhko modulation which comes earlier
than the short period pulsation. Red dots: the observations, Blue dotted
line: the f(t) function, Green solid line: the fB(t) function.
One month later the Blazhko modulation comes later and stronger than
the short period pulsation.
The Blazhko modulation is nearly in phase with the short period modulation
with a bump.
Less than a week later, the Blazhko modulation is much later, still
with a bump.
However, sometimes the model does not fit the data. The 2 worst discrepancies are:
Another iteration for the determination of the Blazhko period
is done by scanning all the periods in the previous interval (52.5 ± 1.2),
regrouping the data in the same Blazhko phase interval
(with an interval of 0.1 Blazhko period),
making a phase plot
with the short period for each of these intervals,
summing the lengths of these phase plots.
The right Blazhko period is expected to give the smallest total length.
This is done for all the data except the 4 more discrepant timeseries
(the 2 shown above and 2 others). The resulting total length as the function
of the Blazhko period is:
It has a sharp minimum at 52.93 ± 0.01 d.
By regrouping the data in the same Blazhko phase interval (of 0.1 Blazhko
period), phase plots at different Blazhko phase can be made:
The red and green phase plots are separated in Blazhko phase by 0.5 Blazhko period.
The Blue dotted line comes from the f(t) model.
To make the animation that follows better looking, 3 discrepant timeseries
were not taken into account (among the 4 that were not used for the derivation
of the period). Furthermore 7 timeseries were displaced from one phase
interval to the adjacent one:
The Blazhko phase origin is arbitrary.
At the time of my observations, GSC 318905 was found to have a Blazhko modulation with a period of 52.93 days, different from the 48 d reported by Wils et al (2006). However this Blazhko modulation cannot be described entirely by a periodic decomposition, it has irregularities. When compared with other RR Lyrae stars I observed, it is less regular than RV Cet but more than AR Ser (which has 2 Blazhko modulations).
Bilir S., Ak S., Karaali S., CabreraLavers A., Chonis T.S. and Gaskell C.M. (2008) MNRAS 384 1178.
Breger M. and Kolenberg K. (2006) A&A 460 167.
Lenz P. and Breger M. (2005) Comm. Asteroseismology 146 53
Smith J.A., Tucker D.L., Kent S. et al (2002) AJ 123 2121.
Szeidl B. and Jurcsik J. (2009) Comm. Asteroseismology 160 17.
Wils P., Lloyd C. and Bernhard K. (2006) MNRAS 368 175.
Telescope and camera configuration.
Computer and software configuration.









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