The calculation method of AGN γ-ray emission flux

YANG JiangHe, NIE JianJun, YANG RuShu

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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

在話劇《松綁》試演之后，福建省文化廳組織召開第三十二期“火花茶會(huì)”。出席會(huì)議的有廳領(lǐng)導(dǎo)石建平廳長(zhǎng)以及黃葦洲副廳長(zhǎng)、林守欽副廳長(zhǎng)和趙建宏副巡視員，同時(shí)邀請(qǐng)到北京的三位重量級(jí)專家，中科院文藝研究所研究員劉平、中國(guó)劇協(xié)《劇本》原主編溫大勇、中國(guó)劇協(xié)《劇本》原主編黎繼德，以及省內(nèi)專家和包括上海人藝導(dǎo)演楊昕巍在內(nèi)的主創(chuàng)人員。會(huì)議由福建省戲劇家協(xié)會(huì)主席、福建省文化廳藝術(shù)處處長(zhǎng)吳新斌主持?，F(xiàn)將與會(huì)者發(fā)言予以刊載，以饗讀者。

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.

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活動(dòng)星系核伽瑪輻射流量的計(jì)算

楊江河*1, 2, 聶建軍1, 楊如曙1

(1. 湖南文理學(xué)院 物理與電子科學(xué)學(xué)院, 湖南 常德, 415000; 2. 廣州大學(xué) 天體物理中心, 廣東 廣州, 510405)

基于伽瑪射線輻射的冪律譜規(guī)律, 討論了將觀測(cè)的伽瑪輻射積分光子流量轉(zhuǎn)換成γ輻射總流量、GeV處流量密度、平均流量密度、總光度、平均光度及GeV處光度的計(jì)算方法, 并給出了詳細(xì)計(jì)算公式. 用得到的公式計(jì)算了4個(gè)Fermi Blazars的γ輻射流量、光度等參量. 如果在其他波段(如: 射電、X射線)的輻射也是冪律的, 則其流量和光度也可以用類似的方法計(jì)算.

活動(dòng)星系核; 伽瑪射線輻射; 流量密度; 光度; 計(jì)算方法

P 15

1672-6146(2014)02-0056-06

10.3969/j.issn.1672-6146.2014.02.012

通訊作者email: yjianghe@163.com.

2014-3-10

國(guó)家自然科學(xué)基金(NSFC 10633010, NSFC 11173009); 光電信息集成與光學(xué)制造技術(shù)湖南省重點(diǎn)實(shí)驗(yàn)室資助; 湖南文理學(xué)院重點(diǎn)學(xué)科建設(shè)項(xiàng)目資助-光學(xué); 湖南文理學(xué)院重點(diǎn)科研究項(xiàng)目(JJZD201101).

(責(zé)任編校: 江 河)