耀变体的峰频估计

张丽霞, 林潮, 2, 3, 樊军辉, 2, 3, 杨江河



耀变体的峰频估计

张丽霞1, 林潮1, 2, 3, 樊军辉1, 2, 3, 杨江河4

(1. 广州大学物理与电子工程学院, 广东广州, 510006; 2. 广州大学天体物理中心, 广东广州, 510006; 3. 广东省教育厅天文科学与技术实验室, 广东广州, 510006; 4. 湖南文理学院物理与电子科学学院, 湖南常德, 415000)

收集了60个耀变体样本, 考察了有效谱指数(RO,OX和RX)与同步峰频(logps)之间的关系。斯皮尔曼秩检验的结果显示有效谱指数与同步峰频之间有很好的反相关。根据两者的相关给出了同步峰频与有效谱指数关联的经验公式。通过该公式用RO和OX估算了耀变体的同步峰频, 所得结果与文献的经验公式结果进行了比较, 发现本文公式的结果更精确。

活动星系核; 耀变体; 同步峰频

Active galactic nuclei (AGNs) have specially observational properties. The standard model of AGNs contains a supermassive central black hole surrounding by an accretion disk. At the perpendicular direction of the accretion disk, there is a relativistic jet, in which the emissions are beamed at the observer’s frame. From observational properties of radio and optical bands, AGNs can be divided into two major classes, namely radio-loud AGNs and radio-quiet AGNs. Blazars is the subclass of radio-loud AGNs, which have superluminal motions, high polarization, large and rapid variation, high energetic γ-ray emissions and core-dominated non-thermal continuum. Nonthermal continuum emissions often extend to X-ray and γ-ray frequency[1–11]. Blazars can be divided into flat spectrum radio quasars (FSRQs) and BL Lacertae objects (BL Lacs). BL Lacs show weaker emission line than FSRQs, but they have quite similar continuum emission properties. Radio selected BL Lacertae objects (RBLs) and X-ray selected BL Lacertae objects (XBLs) are subclasses of BL Lacs. However, this classification is based on surveys[12–13]. Abdo et al. (2010)[14]classified blazars using their spectral energy distributions (SEDs): low synchrotron peaked (LSP,peaks< 1014Hz), intermediate synchrotron peaked (ISP, 1014Hz 1015Hz) blazars. Some similar classifications have been obtained and discussed in some previous studies[15–17]. In our recent work[15], a large sample of blazars are collected and the SEDs of 1392 blazars are obtained, then we found the blazars can be separated into three subclasses by using the Bayesian classification method, namely,peaks< 1014Hz for LSP, 1014Hz 1015.3Hz for HSP.

The synchrotron peak frequencies in the spectral energy distributions of blazars can be estimated in theOXvsROplane[14, 18–19]. Abdo et al. (2010)[14]obtained an empirical relationship by using the 48 quasi-simultaneous SED and the correspondingOXandROvalues. In their empirical relationship,peakscan be estimated fromOXandRO:where= 0.565 − 1.433RO+ 0.155OX, and= 1 − 0.661RO− 0.339OX. Afterward, Fan et al. (2016)[15]obtained a new empirical relationship by using a larger sample of SEDs, namelywhere= 1 − 1.262RO− 0.623OX, and= 1 + 0.034RO− 0.978OX.

However, for the empirical relationship in Adbo et al. (2010)[14]and Fan et al. (2016)[15], the estimation differences between the fitted and the estimated peak frequencies are relatively larger for some HSP blazars. Some of the estimation differences are more than 2 or even 3 orders of magnitude. In this work, we will analyze the relationship between synchrotron peak frequency (logps) and effective spectral indexes (RO,OX, andRX), and propose a new empirical relationship based on SEDs of blazars from Sambruna et al (1996)[9], and compare the present empirical relationship with those in Abdo et al. (2010)[14]and Fan et al. (2016)[15].

1 Sample and results

Sambruna et al. (1996)[9]compared the continuum emission properties from the radio through the X-ray bands of 60 blazars. In order to estimate the peak frequency and bolometric luminosity for each source, they adopted a parabolic function to log(vL) versus log. From Sambruna et al. (1996)[9], we obtain 60 blazars with available logps,RO,OX, andRX, which listed in Table 1.

Table 1 SEDs properties of 60 blazars

The relationships between the effective spectral indexes and the synchrotron peak frequency are shown in Fig. 1. In Fig. 1, anti-correlations can be seen between the effective spectral indexes and the synchrotron peak frequency. Since those correlations do not follow linear correlations, we adopt a Spearman rank correlation analysis to those correlation analysis. The Spearman rank correlation gives a correlation coefficient= −0.731, and a chance probability= 3.34 × 10−11for logpsvsRO,= −0.490 and= 7.20 × 10−5for logpsvsOX, and= −0.687 and= 1.34 × 10−9for logpsvsRX. The Spearman rank correlation results indicate that the synchrotron peak frequency is highly associated with the effective spectral indexes. All the sources mainly follow a blazar sequence inRO—logpsandRX—logpspanels, since LSP BL Lacs and FSRQs locate at the top left area and HSP BL Lacs at the bottom right area, while ISP BL Lacs in the middle area (Fig. 1). However, in aOX—logpspanel, the scatter is larger, so that no clear evidence of the blazar sequence exist here.

Figure 1 Plot of the effective radio to optical (a), optical to X-ray (b), radio to X-ray (c) spectral indexes against synchrotron peak frequency.

In order to obtain a new empirical relationship, a binary linear regression is adopted to the correlation between logpsand bothROandOX, and a strong correlation is found with= 0.707 and= 2.64 × 10−9. However, logps—RO—OXrelationship is not close to a single plane, so we use a piecewise function to fit that correlation as did in Abdo et al. (2010)[14]and Fan et al. (2016)[15], so we propose a new empirical relationshipwhere= 1 − 1.054RO− 0.440OX, and= 1 + 1.864RO− 1.285OX.

To compare the present empirical relationship with those in Abdo et al. (2010)[14]and Fan et al. (2016)[15], we estimate synchrotron peak frequencies using the empirical relationships in Abdo et al. (2010)[14], Fan et al. (2016)[15]and this work. The corresponding estimated results of our sample are listed in Table 1, in which Col. (2) gives the source name, Col. (3) the effective radio to X-ray spectral index,RX, Col. (4) the effective radio to optical spectral index,RO, Col. (5) the effective optical to X-ray spectral index,OX, Col. (6) logarithm synchrotron peak frequency in unit of Hz fitted by Sambruna et al. (1996)[9], logps, Col. (7) logarithm synchrotron peak frequency in unit of Hz estimated by the empirical relationship in Abdo et al. (2010)[14], logpAbdo, Col. (8) logarithm synchrotron peak frequency in unit of Hz estimated by the empirical relationship in Fan et al. (2016)[15], logpFan, Col. (9) logarithm synchrotron peak frequency in unit of Hz estimated by the empirical relationship in this work, logpTW.

For comparison, we calculate the estimation differences of those three empirical relationships, namely logps− logpAbdo, logps− logpFan, and logps− logpTW. The results are shown in Fig. 2. We find that the present empirical relationship is more accurate than that of Abdo et al. (2010)[14]and Fan et al. (2016)[15], since the sum of squares of estimation differences is 57.94 for this work, 63.53 for Abdo et al. (2010)[14], and 83.16 for Fan et al. (2016)[15]. Particularly, for the sources whoseps> 1018Hz, the estimation differences are larger than 3 order of magnitudes for empirical relationships in Abdo et al. (2010)[14]and Fan et al. (2016)[15]. In summary, the estimation differences of 4 blazars are larger than 2 order of magnitudes for the present empirical relationship, while 5 blazars in Abdo et al. (2010)[14]and Fan et al (2016)[15]. Therefore, the present empirical relationship is more accurate than that in Abdo et al. (2010)[14]and Fan et al (2016)[15]for the SEDs in Sambruna et al. (1996)[9].

Figure 2 Plot of the estimation differences of synchrotron peak frequency for the empirical relationship in this work (a), for the empirical relationship in Abdo et al. (2010) (b), and for the empirical relationship in Fan et al. (2016) (c) against the fitting synchrotron peak frequency.

2 Discussion

In this work, we collect synchrotron peak frequency (logps) and effective spectral indexes (RO,OX,RX) from Sambruna et al. (1996)[9], investigate the relationship between the synchrotron peak frequency and the effective spectral indexes, propose a new empirical relationship between synchrotron peak frequency (logps) and effective spectral indexes (ROandOX) from the SEDs of 60 blazars, and compare the present empirical relationship with those in Abdo et al. (2010)[14]and Fan et al. (2016)[15]. The corresponding results are shown in Table 1 and Figs. 1 and 2.

From Fig. 1 and the Spearman rank correlation analysis results, strong anti-correlations are found between the synchrotron peak frequency and the effective spectral indexes with= −0.731 and p = 3.34 × 10−11for logpsvsRO;= −0.490 and= 7.20 × 10−5for logpsvsOX; and= −0.687 and= 1.34 × 10−9for logpsvsRX. InROvs logpsandRXvs logpspanels of Fig. 1, the sources follow the blazar sequence with LSP BL Lacs and FSRQs locating in the left hand top area and HSP BL Lacs in the right hand bottom area, while ISP BL Lacs in the middle area. In theOXvs logpspanel of Fig.1, the scatter of the sources is larger in the low peak frequency region. However, the strong anti-correlation betweenOXand logpsindicate that the blazar sequence maybe exist but not very clear inOXvs logpspanel. In our recent work[15], the correlation between synchrotron peak frequency and effective spectral indexes were studied for a large sample of blazars, and anti-correlations are found between logpsandRO(andOX). From Fig. 2, we find that the present empirical relationship is more accurate than that in Abdo et al. (2010)[14]and Fan et al. (2016)[15].

In this work, it is hard to estimate the accurate synchrotron peak frequencies of HSP blazars by usingROandOX, especially for the sources whoseps> 1018Hz. From the fitting results in Sambruna et al. (1996)[9], only two sources have peak frequency higher than 1018Hz, they are 1443.5+6349 (logps= 19.57 Hz) and 2005−489 (logps= 18.26 Hz). For these two sources, the multi-wavelength data which used to fit the SEDs are few or do not reach the synchrotron peak, and their logps− logpTWare larger than 2 order of magnitudes. In addition, logps= 16.26 Hz and logps= 15.95 ± 0.22 Hz are found for 2005−489 in Ackermann et al. (2015)[20]and Fan et al. (2016)[15]respectively. Those results indicate that logps> 18 Hz would be the results of the limit of multi-wavelength data. Thus, we need more multi-wavelength data to confirm the logpsfor HSP blazars.

In fact, for the sources whose peak frequencies are higher than 1018Hz, the X-ray flux at 1 keV would not reach the synchrotron peak, then the accurate peak frequencies are very hard to be determined by fitting with a parabolic function, when only the low energy bands (≤ 1 keV) are taken into account. Thus, the higher energetic bands need to be taken into account. However, when the higher energetic bands are taken into account, the inverse Compton emissions would be included, so that the fitting would be affected by the inverse Compton component. In Fan et al. (2016)[15], we found that the differences between the fitted and the estimated peak frequencies for blazars whoseps> 1017Hz are significantly larger than those for others. Therefore, it is hard to estimatepsof blazars whose logps> 18 Hz by using parabolic fitting orROandOX. We propose that we need to take hard X-ray band or even γ-ray band into account when we determinepsof blazars whoseps> 1018Hz (or even 1017Hz).

3 Conclusions

Our main conclusions are as follows:

1) There are strong anti-correlations between effective spectral indexes and synchrotron peak frequency, and those relations follow the blazar sequence;

2) We propose a new empirical relationship, which can be used to estimate the synchrotron peak frequency of blazars by using the effective spectral indexes (ROandOX);

3) It is hard to determine the synchrotron peak frequency of blazars with logps> 18 Hz by usingROandOX.

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Peak frequency estimations for blazars

Zhang Lixia1, Lin Chao1, 2, 3, Fan Junhui1, 2, 3, Yang Jianghe4

(1. School for Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China; 2. Center for Astrophysics, Guangzhou University, Guangzhou 510006, China; 3. Astronomy Science and Technology Research Laboratory of Department of Education of Guangdong Province, Guangzhou 510006, China; 4. Department of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China)

A sample of 60 blazars is collected to investigate the correlation between the effective spectral indexes (RO,OX, andRX) and the synchrotron peak frequency (logps). The Spearman rank correlation analysis results indicate that there are strong anti-correlations between the effective spectral indexes and the synchrotron peak frequency, and those relations mainly follow the blazar sequence. Then, a new empirical relationship between the synchrotron peak frequency (logps) and the effective spectral indexes (ROandOX) is obtained. The empirical relationship can be used to estimate logpsof blazars using the correspondingROandOX. Comparing of the peak frequency estimated by present empirical relationship with those of previous works, it is found out that present empirical relationship is more accurate than theirs.

active galactic nuclei; blazar; synchrotron peak frequency

10.3969/j.issn.1672–6146.2017.01.004

P 157.7

A

1672–6146(2017)01–0013–06

樊军辉, fjh@gzhu.edu.cn。

2016–09–12

国家自然科学基金(U1531245, U1431112, 11203007, 11403006, 10633010, 11173009); 广州大学创新基金(IFGZ); 广东省珠江学者项目(GDUPS)(2009); 羊城学者(10A027S); 广东省和广州市重点学科; 广东省创新团队(2014KCXTD014)。