The calculation method of AGN γ-ray emission flux

YANG JiangHe, NIE JianJun, YANG RuShu



The calculation method of AGN γ-ray emission flux

YANG JiangHe1, 2, NIE JianJun1, YANG RuShu1

(1. Department of Physics and Electronics Science, Hunan University of Arts and Science, Changde 415000, China; 2. Center for Astrophysics, Guangzhou University, Guangzhou 510405, China)

Based on a power-low spectrum of AGN γ-ray emissions, the calculation method by using the γ-ray integral photon fluxes to calculate total flux density of γ-ray,flux density atGeV,average flux density,total luminosity, average luminosity and luminosity atGeV were discussed, and their corresponding calculation equation were put forward. The γ-ray emission flux density, luminosity parameter etc. were calculated using those equations presented in this paper for 4 Fermi Blazars. In other bands as radio, X-ray etc., the calculation method of flux density and luminosity can use this method too, if their emissions are power-low.

Active Galactic Nuclei (AGN); γ-ray emissions; flux density; luminosity; calculation method

The integral photons flux of celestial body emission is measured[1—7], while the emission flux density and luminosity etc. are usually adopted in a lot of investigations[8—20]. Therefore, transforms the integral photons flux into other quantitative model is important to research γ-ray emissions. The conversion method will be presented in this paper. The units as cm, s, Hz, Mpc, erg, Jy and GeV are adopted, and some constants are adopted as Planck constant, h = 6.626 07 × 10-34J·s, circumference ratio, π = 3.141 59, luminosity distance, 1 Mpc = 3.085 68 × 1024cm, electron volt, 1 eV = 1.602 18×10-19J, and light velocity, c = 2.997 92×108m/s.

1 Emission model

We assume the γ-ray photon flux associated with γ-ray photon spectrum index by a power-low spectrum[14—15, 21](Fig. 1), namely,

here,is the observation γ-ray integral photon flux in units of photons·cm-2·s-1in the energy range ofL～U(GeV),the γ-ray photon spectrum index and0the initial flux. In Figure 1, dis the photon flux in the energy range of～+ d, dis the emission total flux density in the range of～+ d.

Figure 1 Emission spectrum of γ photon

Here, the units of GeV and Hz are for photon energyand photon frequencyrespecteviley.

2 Calculation method

2.1 γ-ray total flux, Ft

or

or

The units ofandare photons·cm-2·s-1and GeV respectively.

2.2 Average energy of γ-photon, Ea,ph

Because the γ-ray total flux (t) in range ofL～UGeV is presented by Equations (5) and (7) in units of GeV·cm-2·s-1, and the observation γ-ray integral photons in the energy range ofL～UGeVisphotons·cm-2·s-1. Therefore, the average energy of γ-photon (a, ph) can be calculated byt/.

2.3 Flux density at E GeV, f(E)

When Equation (2) is considered, then the flux density atGeV is

where, the units ofandare photons·cm-2·s-1and GeV respectively.

2.4 Average flux density and its corresponding energy

2.4.1 Average flux density,a

Take Equation (12) into Eq. (14), then

Take Equation (13) into Eq. (16), then

2.5 Luminosity

2.5.1 Total luminosityt

在话剧《松绑》试演之后，福建省文化厅组织召开第三十二期“火花茶会”。出席会议的有厅领导石建平厅长以及黄苇洲副厅长、林守钦副厅长和赵建宏副巡视员，同时邀请到北京的三位重量级专家，中科院文艺研究所研究员刘平、中国剧协《剧本》原主编温大勇、中国剧协《剧本》原主编黎继德，以及省内专家和包括上海人艺导演杨昕巍在内的主创人员。会议由福建省戏剧家协会主席、福建省文化厅艺术处处长吴新斌主持。现将与会者发言予以刊载，以飨读者。

The γ-ray total luminosity in the range ofL～UGeV is calculated by following formula,

Here,Lis luminosity distance,tis total flux. The units in Eq. (18) are considered, then

2.5.2 The luminosity atGeV,()

The γ-ray luminosity atGeV is calculated by following formula,

Here,Lis luminosity distance,() is the flux density atGeV. The units in Eq. (22) are considered, then

Take Eq. (11) into Eq. (23), then we have,

2.5.3 The average luminosity,a

Take Eq. (12) into Eq. (26), then

3 Example

The calculation results for 4 blazars are listed in Table 2. However,the results calculated in the example are not K-corrected.

Table 1 Sample of Blazars

In Table 2, the descriptions of all columns are as follows.

Table 2 Calculation results

4 Summary

In this paper, we have discussed the calculation method of γ-ray emissions flux density, γ-ray luminosity, and average energy of γ-photons etc. using γ-ray emissions integral photons flux. The relevant volumes of the Fermi blazars emissions in a given example are calculated by the method presented in this paper. The method is also suitable in other bands such as radio, X-ray etc., if their emissions are power-low.

[1] Abdo A A, Ackermann, M, Ajello M, et al. Fermi/Large Area Telescope Bright Gamma-Ray Source List [J]. Astrophys J Sup Ser, 2009, 183: 46—66.

[2] Abdo A A, Ackermann M, Ajello M, et al. Bright Active Galactic Nuclei Source List from the First Three Months of the Fermi Large Area Telescope All-Sky Survey [J]. Astrophys J, 2009, 700: 597—622.

[3] Abdo A A, Ackermann M, Ajello M. et al. The first catalog of active galactic nuclei detected by the Fermi large area telescope [J]. Astrophys J, 2010, 715: 429—457.

[4] Abdo A A, Ackermann M, Ajello M, et al. Fermi Large Area Telescope First Source Catalog [J]. Astrophys J Sup Ser, 2010, 188: 405—436.

[5] Ackermann M, Ajello M, Allafort A, et al. The Second Catalog of Active Galactic Nuclei Detected by the Fermi Large Area Telescope [J]. Astrophys J, 2011, 743: 171—207.

[6] Nolan P L, Abdo A A, Ackermann M, et al. Fermi Large Area Telescope Second Source Catalog [J]. Astrophys J Sup Ser, 2012, 199: 31—76.

[7] Hartman R C, Bertsch D L, Bloom S D, et al. The Third EGRET Catalog of High-Energy Gamma-Ray Sources [J]. Astrophys J Sup Ser, 1999, 123: 79—202.

[8] Dermer C D, Finke J D, Krug H, et al. Gamma-ray studies of blazars: Synchro-compton analysis of flat spectrum radio quasars [J]. Astrophys J, 2009, 692: 32—46.

[9] Fan J H, Adam G, Xie G Z, et al. Correlation between the gamma -ray and the radio emissions [J]. Astron. & Astrophys, 1998, 338: 27—30.

[10] Fan J H. Relation between BL Lacertae objects and flat-spectrum radio quasars [J]. Astronphys J, 2003, 585: 23—24.

[11] Fan J H, Yang J H, Liu Y, et al. The gamma-ray Doppler factor determinations for a Fermi blazar sample [J]. Research in Astron Astrophys, 2013, 13: 259—269.

[12] Fan J H, Yang J H, Yuan Y H, et al. The Spectral Index Properties of Fermi Blazars [J]. Astrophys J, 2012, 761: 125—136.

[13] Fan X L, Bai J M, Liu H T, et al. The connection between radio and γ-ray emission in Fermi/LAT blazers [J]. Research in Astron Astrophys, 2012, 12: 1475—1485.

[14] Fan J H, Cheng K S, Zhang L. Multi-Wavelength Variation Properties of γ-Ray-Loud Blazars [J]. Publ Astron Soc Japan, 2002, 54: 533—539.

[15] Fan J H, Yang J H, Zhang J Y, et al. Beaming Effect in Fermi Blazars [J]. Publ Astron Soc Japan, 2013, 65: 25—33.

[16] Gao X Y, Wang J C, Zhou M. External photon fields in Fermi bright blazers [J]. Research in Astron Astrophys, 2011, 11: 902—908.

[17] Singal J, Petrosian V, Ajello M. Flux and Photon Spectral Index Distributions of Fermi-LAT Blazars and Contribution to the Extragalactic Gamma-Ray Background [J]. Astrophys J, 2012, 753: 45—55.

[18] Yang J H, Fan J H, Nie J J, et al. The gamma-ray spectral index changes for blazers [J]. Science China: Physics, Mechanics & Astronomy, 2012, 55(11): 2179—2185.

[19] Yang J H, Fan J H. The correlation between gamma-ray and radio emissions in γ-ray loud blazers [J]. Chin J Astron Astrophys, 2005, 5: 229—237.

[20] Zeng H D, Yan D H, Sun Y Q, et al. γ-Ray Luminosity Function and the Contribution to Extragalactic γ-Ray Background for Fermi-detected Blazars [J]. Astrophys J, 2012, 749: 151—158.

[21] Abdo A A, Ackermann M, Ajello M, et al. Gamma-ray Light Curves and Variability of Bright Fermi-detected Blazars [J]. Astrophys J, 2010, 722: 520—542.

[22] Pedro R Capelo, Priyamvada Natarajan.How robust are the constraints on cosmology and galaxy evolution from the lens-redshift test? [J].New Journal of Physics, 2007, 9: 445(1—30).

活动星系核伽玛辐射流量的计算

杨江河*1, 2, 聂建军1, 杨如曙1

(1. 湖南文理学院 物理与电子科学学院, 湖南 常德, 415000; 2. 广州大学 天体物理中心, 广东 广州, 510405)

基于伽玛射线辐射的幂律谱规律, 讨论了将观测的伽玛辐射积分光子流量转换成γ辐射总流量、GeV处流量密度、平均流量密度、总光度、平均光度及GeV处光度的计算方法, 并给出了详细计算公式. 用得到的公式计算了4个Fermi Blazars的γ辐射流量、光度等参量. 如果在其他波段(如: 射电、X射线)的辐射也是幂律的, 则其流量和光度也可以用类似的方法计算.

活动星系核; 伽玛射线辐射; 流量密度; 光度; 计算方法

P 15

1672-6146(2014)02-0056-06

10.3969/j.issn.1672-6146.2014.02.012

通讯作者email: yjianghe@163.com.

2014-3-10

国家自然科学基金(NSFC 10633010, NSFC 11173009); 光电信息集成与光学制造技术湖南省重点实验室资助; 湖南文理学院重点学科建设项目资助-光学; 湖南文理学院重点科研究项目(JJZD201101).

(责任编校: 江 河)