Multiwavelength variability and correlation studies of Mrk 421 during historically low X-ray and $gamma$-ray activity in 2015$-$2016. (arXiv:2012.01348v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Collaboration_MAGIC/0/1/0/all/0/1">MAGIC Collaboration</a>: <a href="http://arxiv.org/find/astro-ph/1/au:+Acciari_V/0/1/0/all/0/1">V. A. Acciari</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Ansoldi_S/0/1/0/all/0/1">S. Ansoldi</a> (2, 5), <a href="http://arxiv.org/find/astro-ph/1/au:+Antonelli_L/0/1/0/all/0/1">L. A. Antonelli</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Asano_K/0/1/0/all/0/1">K. Asano</a> (5), <a href="http://arxiv.org/find/astro-ph/1/au:+Babic_A/0/1/0/all/0/1">A. Babi&#x107;</a> (7), <a href="http://arxiv.org/find/astro-ph/1/au:+Banerjee_B/0/1/0/all/0/1">B. Banerjee</a> (24), <a href="http://arxiv.org/find/astro-ph/1/au:+Baquero_A/0/1/0/all/0/1">A. Baquero</a> (8), <a href="http://arxiv.org/find/astro-ph/1/au:+Almeida_U/0/1/0/all/0/1">U. Barres de Almeida</a> (9), <a href="http://arxiv.org/find/astro-ph/1/au:+Barrio_J/0/1/0/all/0/1">J. A. Barrio</a> (8), <a href="http://arxiv.org/find/astro-ph/1/au:+Gonzalez_J/0/1/0/all/0/1">J. Becerra Gonz&#xe1;lez</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Bednarek_W/0/1/0/all/0/1">W. Bednarek</a> (10), <a href="http://arxiv.org/find/astro-ph/1/au:+Bellizzi_L/0/1/0/all/0/1">L. Bellizzi</a> (11), <a href="http://arxiv.org/find/astro-ph/1/au:+Bernardini_E/0/1/0/all/0/1">E. Bernardini</a> (12, 30), <a href="http://arxiv.org/find/astro-ph/1/au:+Bernardos_M/0/1/0/all/0/1">M. Bernardos</a> (13), <a href="http://arxiv.org/find/astro-ph/1/au:+Berti_A/0/1/0/all/0/1">A. Berti</a> (14), <a href="http://arxiv.org/find/astro-ph/1/au:+Besenrieder_J/0/1/0/all/0/1">J. Besenrieder</a> (15), <a href="http://arxiv.org/find/astro-ph/1/au:+Bhattacharyya_W/0/1/0/all/0/1">W. Bhattacharyya</a> (12), <a href="http://arxiv.org/find/astro-ph/1/au:+Bigongiari_C/0/1/0/all/0/1">C. Bigongiari</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Blanch_O/0/1/0/all/0/1">O. Blanch</a> (16), <a href="http://arxiv.org/find/astro-ph/1/au:+Bonnoli_G/0/1/0/all/0/1">G. Bonnoli</a> (11), <a href="http://arxiv.org/find/astro-ph/1/au:+Bosnjak_Z/0/1/0/all/0/1">&#x17d;. Bo&#x161;njak</a> (7), <a href="http://arxiv.org/find/astro-ph/1/au:+Busetto_G/0/1/0/all/0/1">G. Busetto</a> (17), <a href="http://arxiv.org/find/astro-ph/1/au:+Carosi_R/0/1/0/all/0/1">R. Carosi</a> (18), <a href="http://arxiv.org/find/astro-ph/1/au:+Ceribella_G/0/1/0/all/0/1">G. Ceribella</a> (15), <a href="http://arxiv.org/find/astro-ph/1/au:+Cerruti_M/0/1/0/all/0/1">M. Cerruti</a> (19), <a href="http://arxiv.org/find/astro-ph/1/au:+Chai_Y/0/1/0/all/0/1">Y. Chai</a> (15), <a href="http://arxiv.org/find/astro-ph/1/au:+Chilingarian_A/0/1/0/all/0/1">A. Chilingarian</a> (20), <a href="http://arxiv.org/find/astro-ph/1/au:+Cikota_S/0/1/0/all/0/1">S. Cikota</a> (7), <a href="http://arxiv.org/find/astro-ph/1/au:+Colak_S/0/1/0/all/0/1">S. M. Colak</a> (16), <a href="http://arxiv.org/find/astro-ph/1/au:+Colombo_E/0/1/0/all/0/1">E. Colombo</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Contreras_J/0/1/0/all/0/1">J. L. Contreras</a> (8), <a href="http://arxiv.org/find/astro-ph/1/au:+Cortina_J/0/1/0/all/0/1">J. Cortina</a> (13), <a href="http://arxiv.org/find/astro-ph/1/au:+Covino_S/0/1/0/all/0/1">S. Covino</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+DAmico_G/0/1/0/all/0/1">G. D&#x27;Amico</a> (15), <a href="http://arxiv.org/find/astro-ph/1/au:+DElia_V/0/1/0/all/0/1">V. D&#x27;Elia</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Vela_P/0/1/0/all/0/1">P. Da Vela</a> (18, 26), <a href="http://arxiv.org/find/astro-ph/1/au:+Dazzi_F/0/1/0/all/0/1">F. Dazzi</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Angelis_A/0/1/0/all/0/1">A. De Angelis</a> (17), <a href="http://arxiv.org/find/astro-ph/1/au:+Lotto_B/0/1/0/all/0/1">B. De Lotto</a> (2), <a href="http://arxiv.org/find/astro-ph/1/au:+Delfino_M/0/1/0/all/0/1">M. Delfino</a> (16, 27), <a href="http://arxiv.org/find/astro-ph/1/au:+Delgado_J/0/1/0/all/0/1">J. Delgado</a> (16, 27), et al. (186 additional authors not shown)

We report a characterization of the multi-band flux variability and
correlations of the nearby (z=0.031) blazar Markarian 421 (Mrk 421) using data
from Mets”{a}hovi, Swift, Fermi-LAT, MAGIC, FACT and other collaborations and
instruments from November 2014 till June 2016. Mrk 421 did not show any
prominent flaring activity, but exhibited periods of historically low activity
above 1 TeV (F$_{>1mathrm{TeV}}<$ 1.7$times$10$^{-12}$ ph cm$^{-2}$ s$^{-1}$)
and in the 2-10 keV (X-ray) band (F$_{2-10 mathrm{keV}}<$3.6$times$10$^{-11}$
erg cm$^{-2}$ s$^{-1}$), during which the Swift-BAT data suggests an additional
spectral component beyond the regular synchrotron emission. The highest flux
variability occurs in X-rays and very-high-energy (E$>$0.1 TeV) $gamma$-rays,
which, despite the low activity, show a significant positive correlation with
no time lag. The HR$_mathrm{keV}$ and HR$_mathrm{TeV}$ show the
harder-when-brighter trend observed in many blazars, but the trend flattens at
the highest fluxes, which suggests a change in the processes dominating the
blazar variability. Enlarging our data set with data from years 2007 to 2014,
we measured a positive correlation between the optical and the GeV emission
over a range of about 60 days centered at time lag zero, and a positive
correlation between the optical/GeV and the radio emission over a range of
about 60 days centered at a time lag of $43^{+9}_{-6}$ days.This observation is
consistent with the radio-bright zone being located about 0.2 parsec downstream
from the optical/GeV emission regions of the jet. The flux distributions are
better described with a LogNormal function in most of the energy bands probed,
indicating that the variability in Mrk 421 is likely produced by a
multiplicative process.

We report a characterization of the multi-band flux variability and
correlations of the nearby (z=0.031) blazar Markarian 421 (Mrk 421) using data
from Mets”{a}hovi, Swift, Fermi-LAT, MAGIC, FACT and other collaborations and
instruments from November 2014 till June 2016. Mrk 421 did not show any
prominent flaring activity, but exhibited periods of historically low activity
above 1 TeV (F$_{>1mathrm{TeV}}<$ 1.7$times$10$^{-12}$ ph cm$^{-2}$ s$^{-1}$)
and in the 2-10 keV (X-ray) band (F$_{2-10 mathrm{keV}}<$3.6$times$10$^{-11}$
erg cm$^{-2}$ s$^{-1}$), during which the Swift-BAT data suggests an additional
spectral component beyond the regular synchrotron emission. The highest flux
variability occurs in X-rays and very-high-energy (E$>$0.1 TeV) $gamma$-rays,
which, despite the low activity, show a significant positive correlation with
no time lag. The HR$_mathrm{keV}$ and HR$_mathrm{TeV}$ show the
harder-when-brighter trend observed in many blazars, but the trend flattens at
the highest fluxes, which suggests a change in the processes dominating the
blazar variability. Enlarging our data set with data from years 2007 to 2014,
we measured a positive correlation between the optical and the GeV emission
over a range of about 60 days centered at time lag zero, and a positive
correlation between the optical/GeV and the radio emission over a range of
about 60 days centered at a time lag of $43^{+9}_{-6}$ days.This observation is
consistent with the radio-bright zone being located about 0.2 parsec downstream
from the optical/GeV emission regions of the jet. The flux distributions are
better described with a LogNormal function in most of the energy bands probed,
indicating that the variability in Mrk 421 is likely produced by a
multiplicative process.

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