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        The calculation method of AGN γ-ray emission flux

        2014-05-13 10:02:56YANGJiangHeNIEJianJunYANGRuShu
        關(guān)鍵詞:冪律伽瑪文化廳

        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”。出席會議的有廳領(lǐng)導石建平廳長以及黃葦洲副廳長、林守欽副廳長和趙建宏副巡視員,同時邀請到北京的三位重量級專家,中科院文藝研究所研究員劉平、中國劇協(xié)《劇本》原主編溫大勇、中國劇協(xié)《劇本》原主編黎繼德,以及省內(nèi)專家和包括上海人藝導演楊昕巍在內(nèi)的主創(chuàng)人員。會議由福建省戲劇家協(xié)會主席、福建省文化廳藝術(shù)處處長吳新斌主持?,F(xiàn)將與會者發(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.

        [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).

        活動星系核伽瑪輻射流量的計算

        楊江河*1, 2, 聶建軍1, 楊如曙1

        (1. 湖南文理學院 物理與電子科學學院, 湖南 常德, 415000; 2. 廣州大學 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處光度的計算方法, 并給出了詳細計算公式. 用得到的公式計算了4個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算.

        活動星系核; 伽瑪射線輻射; 流量密度; 光度; 計算方法

        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

        國家自然科學基金(NSFC 10633010, NSFC 11173009); 光電信息集成與光學制造技術(shù)湖南省重點實驗室資助; 湖南文理學院重點學科建設(shè)項目資助-光學; 湖南文理學院重點科研究項目(JJZD201101).

        (責任編校: 江 河)

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