GSC 318-805 / V551 Vir: a Blazhko star
Observed: 42 sessions from 2009 to 2015
|Season||Nb of sessions||Nb of V measurements||Nb of B measurements|
For the differential photometry, the comparison star is GSC 318-984 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 318-905, Black: the check star. The error bars are the 1-sigma statistical uncertainties (computed as the q-sum 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 sine-wave fitting and least-squares
fitting algorithms. This yields the pulsation frequency:
FP = 2.2378261 ± 4.2*10-6 day-1
or the pulsation period:
PP = 0.4468622 ± 0.8*10-6 day (0.07 s)
Owing to the PERIOD04 software program, the data are fitted with the
following sine-wave 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
|0||FP||0.3778 ± 0.0054||0.5022 ± 0.0024|
|1||FP*2||0.1459 ± 0.0056||0.3653 ± 0.0060|
|2||FP*3||0.0571 ± 0.0056||0.279 ± 0.015|
|3||FP*4||0.0367 ± 0.0055||0.139 ± 0.023|
|4||FP*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 FP 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 FP frequency:
On the right side of FP there are peaks at FP+1/62, FP+1/52 and FP+1/45, and on the left side there are peaks (weaker than the ones on the right side) at FP-1/62, FP-1/52 and FP-1/45.
Quite weaker, there are also peaks at FP±2/62, FP±2/52 and FP±2/45.
The spectra of the residuals (observations - f(t)) around the frequency FP. 45++ is the peak at FP+2/45, 62- at FP-1/62, and so on.
The spectra of the residuals around 2.FP, 3.FP and 4.FP also show peaks for ±1/62, ±1/52 and ±1/45.
The spectrum of the residuals around 5.FP shows no clear signal.
These peaks are interpreted as a modulation with a period PB 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: FP±1/PB,
and 4.FP±1/PB. And the amplitudes and phases for
the main pulsation are optimized again. The results are given in the table
|0||FP||FP||0.3716 ± 0.0040||0.5067 ± 0.0018|
|1||2*FP||2*FP||0.1328 ± 0.0041||0.3601 ± 0.0050|
|3||3*FP||3*FP||0.0472 ± 0.0039||0.282 ± 0.013|
|3||4*FP||4*FP||0.0239 ± 0.0040||0.149 ± 0.028|
|4||5*FP||5*FP||0.0162 ± 0.0038||0.035 ± 0.034|
|5||FP+1/PP||2.2566168 ± 8.7E-6||0.0994 ± 0.0039||0.3890 ± 0.0063|
|6||FP-1/PP||2.218949 ± 1.2 E-5||0.0704 ± 0.0041||0.3770 ± 0.0087|
|7||FP+2/PP||2.274372 ± 1.9 E-5||0.0459 ± 0.0039||0.611 ± 0.013|
|8||FP-2/PP||2.200179 ± 3.6 E-5||0.0235 ± 0.0040||0.570 ± 0.027|
|9||2.FP+1/PP||4.495133 ± 4.3 E-5||0.0151 ± 0.0041||0.216 ± 0.029|
|10||2.FP-1/PP||4.456011 ± 2.5 E-5||0.0364 ± 0.0043||0.449 ± 0.018|
|11||3.FP+1/PP||6.732359 ± 1.3 E-5||0.0684 ± 0.0040||0.8914 ± 0.0091|
|12||3.FP-1/PP||6.694009 ± 4.5 E-5||0.0198 ± 0.0039||0.133 ± 0.032|
|13||4.FP+1/PP||8.970207 ± 2.1 E-5||0.0422 ± 0.0041||0.752± 0.015|
|14||4.FP-1/PP||8.931784 ± 4.1 E-5||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:
PP = 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 time-series 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 time-series
(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 time-series
were not taken into account (among the 4 that were not used for the derivation
of the period). Furthermore 7 time-series were displaced from one phase
interval to the adjacent one:
The Blazhko phase origin is arbitrary.
At the time of my observations, GSC 318-905 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., Cabrera-Lavers 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.
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