- Email: [email protected]
The Long-term Light Variation of BL Lac Object 1ES 1959+650
CHINESE ASTRONOMY AND ASTROPHYSICS
ELSEVIER
Chinese Astronomy and Astrophysics 38 (2014) 233–238
The Long-term Light Variation of BL Lac Object 1ES 1959+650 † YUAN Yu-hai
LIU Fu-qing
Center for Experiment, Guangzhou University, Guangzhou 510006
Abstract According to the data of optical observations of the Tuorla Observatory in Finland, using the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method, respectively, we analyzed the periodicity of the long-term light variation of the BL Lac object 1ES 1959+650, and obtained its light period to be P =1.4±0.3 yr. Assuming that the origin of the periodicity is concerned with the accretion disk, we obtained the region where the instability of this source occurs being R =9.65 Rg , here Rg represents the Schwarzschild radius. Key words: BL Lacertae objects: individual: 1ES 1959+650—methods: numerical
1. INTRODUCTION The observations of BL Lac objects indicate that the timescales of their light variations are in the orders of magnitude from minute to year[1−2], and accordingly, they are classified into two sorts: the short-timescale variability[3−4] and the long-term variability[5−6] . 1ES 1959+650 is an HBL (high energy peak BL Lac object) being studied quite frequently, its redshift is z =0.046. This source was first detected from the Slew probe of the Einstein satellite[7] . Based on the broad-band distribution of X-ray/radio/opical colors, this source was identified as a BL Lac object[8] . The optical observation of this source indicated that its host galaxy is an elliptical galaxy[9], its γ-ray detection was performed by EGRET (Energetic Gamma Ray Experiment Telescope)[10] , and further confirmed by Fermi[11] . †
Supported by National Natural Science Foundation (10633010) Received 2012–09–21; revised version 2013–05–30 A translation of Acta Astron. Sin. Vol. 54, No. 5, pp. 405–410, 2013 yh [email protected]
0275-1062/14/$-see front matter © 2014 B.V. AllScience rights reserved. c Elsevier 0275-1062/01/$-see front matter 2014 Elsevier B. V. All rights reserved. doi:10.1016/j.chinastron.2014.07.001 PII:
234
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
The structure of this paper is as follows: Sec.2 gives the data and the related calculation methods, as well as the corresponding results; Sec.3 is the discussion and conclusion.
2. DATA AND CALCULATION METHODS The observational data in this paper were obtained by the 1.03 m optical telescope of the Tuorla Observatory in Finland, the data to be used have been preprocessed (monthly averaged). And the observations were made in the period from 10th Aug. 2002 to 26th Apr. 2011 at the R-band, the smallest interval of the data is 30 d. The light curve shown in Fig.1 consists of 260 observational data, in which the brightest magnitude is 13.9 mag, the darkest is 14.9 mag, and the average is (14.48±0.22) mag. We have used, respectively, the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method to analyze the long-term light variation of 1ES 1959+650.
Fig. 1
The light variation of 1ES 1959+650 at the R-band
2.1 The Power Spectrum Method The power spectrum method is the method most commonly used for calculating the long-period variability, it calculates the periodicity of the equally-spaced or unequally-spaced discrete signal by using the frequency features of its power spectrum[12] . Lomb[13] has improved this method, correspondingly it can be described as follows: assume that the observational data x(n) at a certain waveband have N data points, define f to be the frequency, and τ to be the timescale of light variation. The mean value of x(n) and its N 1 N 2 standard deviation can be calculated by x ¯ = N1 ¯)2 , n=1 x(n) and σ = N n=1 (x(n) − x respectively. As a function of the angular frequency ω ≡ 2πf > 0, the power spectrum P L
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
235
is expressed as: N −1 N −1 1 [ n=0 (x(n) − x)cos[ω(tn − τ )]]2 1 [ n=0 (x(n) − x)sin[ω(tn − τ )]]2 P L (ω) = + , N −1 N −1 2 2 2σ 2 2σ 2 n=0 cos [ω(tn − τ )] n=0 sin [ω(tn − τ )] (1) tn is the time of the n-th data point, which can be obtained by the following formula: N −1 n=0 sin(2ωtn ) tan(2ωτ ) = N . (2) −1 n=0 cos(2ωtn ) Using the power spectrum method the long-term light variation of 1ES 1959+650 was analyzed, and the result was obtained as shown in Fig.2. Then HWHM (the half width at half maximum) was used to calculate the corresponding error, the obtained result indicates the light periods to be τ1 = 2.8±0.7 yr and τ2 = 1.4±0.4 yr.
π τ
π τ
π Fig. 2 The result of power spectrum analysis shows the two possible periods to be τ1 = 2.8±0.7 yr and τ2 = 1.4±0.4 yr
2.2 The DCF Method The DCF method can be used to study the time-lag characteristics between two observational data sets of different wavebands. This method can be described as follows. At first we calculate the set of unsegmented discrete correlations for the two data sets: UDCFij =
(ai − a) × (bj − b) , σa2 × σb2
(3)
here ai and bj are two data sets, a and b are the mean values of the two data sets, σa and σb are the corresponding standard errors. Then we take an average for the M values in
236
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
the interval τ − Δτ /2 ≤ Δtij < τ + Δτ /2 to obtain the corresponding discrete correlation function DCF (τ ): 1 DCF(τ ) = (4) UDCFij (τ ) , M for an interval without data points, DCF (τ ) takes no value. Finally the standard error of DCF (τ ) is 0.5 1 σ(τ ) = . (5) [UDCFij − DCF(τ )]2 M If ai and bj are the same, then this method can be used for the periodicity analysis of this data set[16] . With the DCF method, the long-term light variation of 1ES 1959+650 was analyzed, and the obtained result is shown as Fig.3. The vertical coordinate Am expresses the intensity of correlation between two correlated quantities. Then the corresponding error was obtained by using HWHM, the obtained periods are τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.5 yr, respectively.
τ τ τ
τ Fig. 3 The result of the DCF method shows the three possible periods to be τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.5 yr
2.3 The Jurkevich Method The Jurkevich Method can be described as follows: to segment the observational data according to certain bins, then to fold the segmented data, and to segment again the folded data, finally to calculate the mean standard error Vm2 for every segment. Kidger et al.[18] introduced a rating factor η = (1 − Vm2 )/Vm2 , in which Vm2 has been normalized, if Vm2 =1, then η =0, the result has no periodicity; if η ≥ 0.5, it indicates that a rather strong periodical signal exists; if η < 0.25, it implies that there is no or only a weak periodical signal. For the
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
237
period obtained by this method its error can be obtained from the value of HWHM at the place of Vm2 . With the Jurkevich method, the long-term light variation of 1ES 1959+650 was analyzed, and the obtained result is shown in Fig.4. The quasi-periods are, respectively, τ1 = 1.4±0.3 yr (η =0.55), τ2 = 2.8±0.3 yr (η =0.69), and τ3 = 4.3±0.4 yr (η =0.66), in which the corresponding error was obtained from the value of HWHM.
τ τ τ
τ Fig. 4 The result of the Jurkevich method shows the three possible periods to be τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.4 yr
The long-term light variation of 1ES 1959+650 at the R-band was analyzed with the power spectrum method, the DCF method, and the Jurkevich method, respectively. The light periods derived by the three methods are not completely coincident, among them we chose as usual the common solution of all the three methods, whose error is smaller than the others to be the period. Hence, the light period of 1ES 1959+650 at the R-band is P = 1.4 ± 0.3 yr, and 2.8 yr, 4.3 yr ought to be the multiples of P , and therefore ought to be deleted.
3. DISCUSSION AND CONCLUSION The short-period light variations of 1ES 1959+650 at multiple wavebands have been analyzed already[19−20], however its long-term light variation has not yet been discussed, the main reason is the late discovery (in 1992) of this source. But the long-term light variations of many blazars have been discussed, and obtained their quasi-periods, for example, OJ 287, PKS 1510-89, 3C390.3, etc. Based on the optical data of 1ES 1959+650, this paper obtained its quasi-period to be P = 1.4 ± 0.3 yr.
238
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
Wallinder et al.[21] proposed to analyze the long-term light variation in terms of the 1/2 thermal instability of thin disks, and gave P ≈ 3.2 × 10−4 α−1 (x − 1)M8 ] yr, here visc [x x = R/Rg is the region where the instability occurs (Rg is the Schwarzchild radius), M8 is the mass of central black hole in units of 108 M (M is the solar mass), αvisc is the viscosity coefficient. Falomo et al.[22] obtained the mass of central black hole for this galaxy to be M8 =8.12±0.13. With αvisc =0.05, P =1.4 yr, M8 =8.12, we obtained its region of instability occurrence being R =9.65Rg . This paper analyzed the long-term light variation of 1ES 1959+650 at the optical waveband, and obtained its possible light period to be P =1.4±0.3 yr. Finally, by this result and under the assumption that the origin of this periodicity is concerned with the accretion disk, we obtained the region of its instability occurrence being R = 9.65Rg . ACKNOWLEDGEMENT The observational data come from the 1.03 m telescope of the Tuorla Observatory in Finland, the website is http://users.utu.fi/kani/lm/. References 1
Carini M. T., Miller H. R., ApJ, 1992, 1385, 146
2
Gupta A. C., Banerjee D. P. K., Ashok N. M., et al., A&A, 2004, 422, 505
3
Burbidge G. R., Jones T. W., ApJ, 1974, 193, 43
4
Wagner S. J., Witzel A., ARA&A, 1995, 33, 163
5
Kunkel W. E., AJ, 1967, 72, 1341
6
Raiteri C. M., Vallata M., Aller H. D., et al., A&A, 2001, 377, 396
7
Elvis M., Plummer D., Schachter J., et al., ApJS, 1992, 80, 257
8
Schachter J. F., Stocke J. T., Perlman E, et al., ApJ, 1993, 412, 541
9
Heidt J., Nilsson K., Sillanp¨ a¨ a A, et al., A&A, 1999, 341, 683
10
Hartman R. C., Bertsch D. L., Bloom S. D., et al., ApJS, 1999, 123, 79
11
Abdo A. A., Ackermann M., Ajello M., et al., ApJ, 2010, 715, 429
12
Deeming T. J., Ap&SS, 1975, 36, 137
13
Lomb N. R., Ap&SS, 1976, 39, 447
14
Edelson R. A., Krolik J. H., ApJ, 1988, 333, 646
15
Hufnagel B. R., Bregman J. N., ApJ, 1992, 386, 473
16
Fan J. H., ChJAS, 2005, 5, 213
17
Jurkevich I., Usher P. D., Shen B. S. P., Ap&SS, 1971, 10, 402
18
Kidger M., Takalo L., Sillanpaa A., A&A, 1992, 264, 32
19
Tagliaferri G., Foschini L., Ghisellini G., et al., ApJ, 2008, 679, 1029
20
Bottacini E., Bottcher M., Schady P., et al., ApJ, 2010, 719, 162
21
Wallinder F. H., Kato S., Abramowicz M. A., A&ARv, 1992, 4, 79
22
Falomo R., Kotilainen J. K., Treves A., ApJ, 2002, 569, 35
ELSEVIER
Chinese Astronomy and Astrophysics 38 (2014) 233–238
The Long-term Light Variation of BL Lac Object 1ES 1959+650 † YUAN Yu-hai
LIU Fu-qing
Center for Experiment, Guangzhou University, Guangzhou 510006
Abstract According to the data of optical observations of the Tuorla Observatory in Finland, using the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method, respectively, we analyzed the periodicity of the long-term light variation of the BL Lac object 1ES 1959+650, and obtained its light period to be P =1.4±0.3 yr. Assuming that the origin of the periodicity is concerned with the accretion disk, we obtained the region where the instability of this source occurs being R =9.65 Rg , here Rg represents the Schwarzschild radius. Key words: BL Lacertae objects: individual: 1ES 1959+650—methods: numerical
1. INTRODUCTION The observations of BL Lac objects indicate that the timescales of their light variations are in the orders of magnitude from minute to year[1−2], and accordingly, they are classified into two sorts: the short-timescale variability[3−4] and the long-term variability[5−6] . 1ES 1959+650 is an HBL (high energy peak BL Lac object) being studied quite frequently, its redshift is z =0.046. This source was first detected from the Slew probe of the Einstein satellite[7] . Based on the broad-band distribution of X-ray/radio/opical colors, this source was identified as a BL Lac object[8] . The optical observation of this source indicated that its host galaxy is an elliptical galaxy[9], its γ-ray detection was performed by EGRET (Energetic Gamma Ray Experiment Telescope)[10] , and further confirmed by Fermi[11] . †
Supported by National Natural Science Foundation (10633010) Received 2012–09–21; revised version 2013–05–30 A translation of Acta Astron. Sin. Vol. 54, No. 5, pp. 405–410, 2013 yh [email protected]
0275-1062/14/$-see front matter © 2014 B.V. AllScience rights reserved. c Elsevier 0275-1062/01/$-see front matter 2014 Elsevier B. V. All rights reserved. doi:10.1016/j.chinastron.2014.07.001 PII:
234
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
The structure of this paper is as follows: Sec.2 gives the data and the related calculation methods, as well as the corresponding results; Sec.3 is the discussion and conclusion.
2. DATA AND CALCULATION METHODS The observational data in this paper were obtained by the 1.03 m optical telescope of the Tuorla Observatory in Finland, the data to be used have been preprocessed (monthly averaged). And the observations were made in the period from 10th Aug. 2002 to 26th Apr. 2011 at the R-band, the smallest interval of the data is 30 d. The light curve shown in Fig.1 consists of 260 observational data, in which the brightest magnitude is 13.9 mag, the darkest is 14.9 mag, and the average is (14.48±0.22) mag. We have used, respectively, the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method to analyze the long-term light variation of 1ES 1959+650.
Fig. 1
The light variation of 1ES 1959+650 at the R-band
2.1 The Power Spectrum Method The power spectrum method is the method most commonly used for calculating the long-period variability, it calculates the periodicity of the equally-spaced or unequally-spaced discrete signal by using the frequency features of its power spectrum[12] . Lomb[13] has improved this method, correspondingly it can be described as follows: assume that the observational data x(n) at a certain waveband have N data points, define f to be the frequency, and τ to be the timescale of light variation. The mean value of x(n) and its N 1 N 2 standard deviation can be calculated by x ¯ = N1 ¯)2 , n=1 x(n) and σ = N n=1 (x(n) − x respectively. As a function of the angular frequency ω ≡ 2πf > 0, the power spectrum P L
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
235
is expressed as: N −1 N −1 1 [ n=0 (x(n) − x)cos[ω(tn − τ )]]2 1 [ n=0 (x(n) − x)sin[ω(tn − τ )]]2 P L (ω) = + , N −1 N −1 2 2 2σ 2 2σ 2 n=0 cos [ω(tn − τ )] n=0 sin [ω(tn − τ )] (1) tn is the time of the n-th data point, which can be obtained by the following formula: N −1 n=0 sin(2ωtn ) tan(2ωτ ) = N . (2) −1 n=0 cos(2ωtn ) Using the power spectrum method the long-term light variation of 1ES 1959+650 was analyzed, and the result was obtained as shown in Fig.2. Then HWHM (the half width at half maximum) was used to calculate the corresponding error, the obtained result indicates the light periods to be τ1 = 2.8±0.7 yr and τ2 = 1.4±0.4 yr.
π τ
π τ
π Fig. 2 The result of power spectrum analysis shows the two possible periods to be τ1 = 2.8±0.7 yr and τ2 = 1.4±0.4 yr
2.2 The DCF Method The DCF method can be used to study the time-lag characteristics between two observational data sets of different wavebands. This method can be described as follows. At first we calculate the set of unsegmented discrete correlations for the two data sets: UDCFij =
(ai − a) × (bj − b) , σa2 × σb2
(3)
here ai and bj are two data sets, a and b are the mean values of the two data sets, σa and σb are the corresponding standard errors. Then we take an average for the M values in
236
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
the interval τ − Δτ /2 ≤ Δtij < τ + Δτ /2 to obtain the corresponding discrete correlation function DCF (τ ): 1 DCF(τ ) = (4) UDCFij (τ ) , M for an interval without data points, DCF (τ ) takes no value. Finally the standard error of DCF (τ ) is 0.5 1 σ(τ ) = . (5) [UDCFij − DCF(τ )]2 M If ai and bj are the same, then this method can be used for the periodicity analysis of this data set[16] . With the DCF method, the long-term light variation of 1ES 1959+650 was analyzed, and the obtained result is shown as Fig.3. The vertical coordinate Am expresses the intensity of correlation between two correlated quantities. Then the corresponding error was obtained by using HWHM, the obtained periods are τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.5 yr, respectively.
τ τ τ
τ Fig. 3 The result of the DCF method shows the three possible periods to be τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.5 yr
2.3 The Jurkevich Method The Jurkevich Method can be described as follows: to segment the observational data according to certain bins, then to fold the segmented data, and to segment again the folded data, finally to calculate the mean standard error Vm2 for every segment. Kidger et al.[18] introduced a rating factor η = (1 − Vm2 )/Vm2 , in which Vm2 has been normalized, if Vm2 =1, then η =0, the result has no periodicity; if η ≥ 0.5, it indicates that a rather strong periodical signal exists; if η < 0.25, it implies that there is no or only a weak periodical signal. For the
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
237
period obtained by this method its error can be obtained from the value of HWHM at the place of Vm2 . With the Jurkevich method, the long-term light variation of 1ES 1959+650 was analyzed, and the obtained result is shown in Fig.4. The quasi-periods are, respectively, τ1 = 1.4±0.3 yr (η =0.55), τ2 = 2.8±0.3 yr (η =0.69), and τ3 = 4.3±0.4 yr (η =0.66), in which the corresponding error was obtained from the value of HWHM.
τ τ τ
τ Fig. 4 The result of the Jurkevich method shows the three possible periods to be τ1 = 1.4±0.3 yr, τ2 = 2.8±0.3 yr, and τ3 = 4.3±0.4 yr
The long-term light variation of 1ES 1959+650 at the R-band was analyzed with the power spectrum method, the DCF method, and the Jurkevich method, respectively. The light periods derived by the three methods are not completely coincident, among them we chose as usual the common solution of all the three methods, whose error is smaller than the others to be the period. Hence, the light period of 1ES 1959+650 at the R-band is P = 1.4 ± 0.3 yr, and 2.8 yr, 4.3 yr ought to be the multiples of P , and therefore ought to be deleted.
3. DISCUSSION AND CONCLUSION The short-period light variations of 1ES 1959+650 at multiple wavebands have been analyzed already[19−20], however its long-term light variation has not yet been discussed, the main reason is the late discovery (in 1992) of this source. But the long-term light variations of many blazars have been discussed, and obtained their quasi-periods, for example, OJ 287, PKS 1510-89, 3C390.3, etc. Based on the optical data of 1ES 1959+650, this paper obtained its quasi-period to be P = 1.4 ± 0.3 yr.
238
Yuan Yu-hai and Liu Fu-qing / Chinese Astronomy and Astrophysics 38 (2014) 233–238
Wallinder et al.[21] proposed to analyze the long-term light variation in terms of the 1/2 thermal instability of thin disks, and gave P ≈ 3.2 × 10−4 α−1 (x − 1)M8 ] yr, here visc [x x = R/Rg is the region where the instability occurs (Rg is the Schwarzchild radius), M8 is the mass of central black hole in units of 108 M (M is the solar mass), αvisc is the viscosity coefficient. Falomo et al.[22] obtained the mass of central black hole for this galaxy to be M8 =8.12±0.13. With αvisc =0.05, P =1.4 yr, M8 =8.12, we obtained its region of instability occurrence being R =9.65Rg . This paper analyzed the long-term light variation of 1ES 1959+650 at the optical waveband, and obtained its possible light period to be P =1.4±0.3 yr. Finally, by this result and under the assumption that the origin of this periodicity is concerned with the accretion disk, we obtained the region of its instability occurrence being R = 9.65Rg . ACKNOWLEDGEMENT The observational data come from the 1.03 m telescope of the Tuorla Observatory in Finland, the website is http://users.utu.fi/kani/lm/. References 1
Carini M. T., Miller H. R., ApJ, 1992, 1385, 146
2
Gupta A. C., Banerjee D. P. K., Ashok N. M., et al., A&A, 2004, 422, 505
3
Burbidge G. R., Jones T. W., ApJ, 1974, 193, 43
4
Wagner S. J., Witzel A., ARA&A, 1995, 33, 163
5
Kunkel W. E., AJ, 1967, 72, 1341
6
Raiteri C. M., Vallata M., Aller H. D., et al., A&A, 2001, 377, 396
7
Elvis M., Plummer D., Schachter J., et al., ApJS, 1992, 80, 257
8
Schachter J. F., Stocke J. T., Perlman E, et al., ApJ, 1993, 412, 541
9
Heidt J., Nilsson K., Sillanp¨ a¨ a A, et al., A&A, 1999, 341, 683
10
Hartman R. C., Bertsch D. L., Bloom S. D., et al., ApJS, 1999, 123, 79
11
Abdo A. A., Ackermann M., Ajello M., et al., ApJ, 2010, 715, 429
12
Deeming T. J., Ap&SS, 1975, 36, 137
13
Lomb N. R., Ap&SS, 1976, 39, 447
14
Edelson R. A., Krolik J. H., ApJ, 1988, 333, 646
15
Hufnagel B. R., Bregman J. N., ApJ, 1992, 386, 473
16
Fan J. H., ChJAS, 2005, 5, 213
17
Jurkevich I., Usher P. D., Shen B. S. P., Ap&SS, 1971, 10, 402
18
Kidger M., Takalo L., Sillanpaa A., A&A, 1992, 264, 32
19
Tagliaferri G., Foschini L., Ghisellini G., et al., ApJ, 2008, 679, 1029
20
Bottacini E., Bottcher M., Schady P., et al., ApJ, 2010, 719, 162
21
Wallinder F. H., Kato S., Abramowicz M. A., A&ARv, 1992, 4, 79
22
Falomo R., Kotilainen J. K., Treves A., ApJ, 2002, 569, 35