Spectral Variations of $γ$-rays in Mrk 421

Abstract

We present a comprehensive analysis of the 17-year Fermi-LAT observational data of Mrk 421 to investigate the spectral variations in the $γ$-ray bands. The light curve of the source in the 0.1--1000 GeV band with a 14-day time bin exhibits significant variability at a confidence level exceeding 5$σ$, which is accompanied by spectral variation, displaying a {\it harder-when-brighter} behavior. Moreover, its flux variation can reach up to one order of magnitude within one day, with a daily flux up to $(1.19\pm0.84)\times10^{-8}~{\rm erg~cm^{-2}~s^{-1}}$ on MJD 56152. The 17-year integrated spectrum of Mrk 421 necessitates a complex model for explanation, whereas its time-resolved spectra over one-day or several-day time intervals can be well fitted by a power-law model. We propose that the complex spectral shape of the 17-year integrated spectrum stems from the superposition of different spectral shapes in different flux states. By generating the GeV spectra that are simultaneously observed with the archived TeV observations and constructing the combined GeV--TeV spectra, we find that some combined GeV--TeV spectral shapes clearly imply different radiation origins for the GeV and TeV emissions, challenging the one-zone leptonic model. It is found that the flux follows a lognormal distribution, while the photon spectral index distributions can be well fitted by either a lognormal or a Gaussian functions. The possible nature of the $γ$-ray variability in Mrk 421 is discussed.

Figures (8)

• Figure 1: Panel (a): the 17-year integrated spectrum of Mrk 421 obtained by Fermi-LAT observations in the 0.1--1000 GeV band. The black solid line and gray dashed lines represent the spectral fitting result and the corresponding $1\sigma$ uncertainties, respectively. Panel (b): HR as a function of $F_{0.1-100~{\rm GeV}}$, where ${\rm HR}=\frac{F_{1-100~{\rm GeV}}-F_{0.1-1~{\rm GeV}}}{F_{1-100~{\rm GeV}}+F_{0.1-1~{\rm GeV}}}$ and $F_{0.1-100~{\rm GeV}}=F_{0.1-1~{\rm GeV}}+F_{1-100~{\rm GeV}}$. The values of $F_{0.1-1~{\rm GeV}}$ and $F_{1-100~{\rm GeV}}$ are derived using a 14-day time bin, consistent with the data in panel (b) and panel (c) of Figure \ref{['lc']}. Panels (c) and (d): the histogram distributions of the flux and $\Gamma_{\gamma}$ with the lognormal (red solid lines) and Gaussian (green dashed lines) fits, respectively. The values of the flux and $\Gamma_{\gamma}$ are derived from the 17-year Fermi-LAT observational data within the 0.1--1000 GeV band, using a 14-day time bin, consistent with the data in panel (a) and panel (e) of Figure \ref{['lc']}.
• Figure 2: The 17-year long-term light curves, derived with a 14-day time bin, in the 0.1--1000 GeV band (panel (a)), 0.1--1 GeV band (panel (b)), 1--100 GeV band (panel (c)), 100--1000 GeV band (panel (d)), as well as the curves of $\Gamma_{\gamma}$ (panel (e)) and HR (panel (f)). The red horizontal dashed lines represent the average values. If TS $<$ 9, an upper limit of flux (red or black open triangles) is provided for that time bin. The gray shaded area indicates the time interval during which the light curve on a daily timescale is derived, as depicted in Figure \ref{['lc_day']}.
• Figure 3: Panel (a): the light curve (black solid squares) derived with a 1-day time bin in the 0.1--1000 GeV band, along with the curves of $\Gamma_{\gamma}$ (magenta solid stars). The red horizontal dashed line represents the weighted average flux. If TS $<$ 9, an upper limit of flux (black open triangles) is provided for that time bin. Panels (b) and (c): the histogram distributions of the flux and $\Gamma_{\gamma}$ with the lognormal (red solid lines) and Gaussian (green dashed lines) fits, respectively. The values of flux and $\Gamma_{\gamma}$ are consistent with the data presented in panel (a).
• Figure 4: The 24 time-resolved spectra of Mrk 421 obtained through Fermi-LAT observations in the 0.1--1000 GeV band. The first 18 spectra were simultaneously obtained with the archived TeV observations, and they are consistent with the data presented in Figure \ref{['Spe_GeV-TeV']}. The three panels in the second row from the bottom correspond to the three lowest-flux points in panel (a) of Figure \ref{['lc']}, while the three panels in the first row from the bottom correspond to the three highest-flux points in panel (a) of Figure \ref{['lc']}. If TS $<$ 9, an upper limit (inverted triangles) is given for that energy bin. The black solid lines and gray dashed lines represent the spectral fitting results and the corresponding $1\sigma$ uncertainties, respectively.
• Figure 5: (Continued.)