We present coordinated multiwavelength observations of the bright, nearby BL Lac object Mrk 421 taken in 2013 January-March, involving GASP-WEBT, Swift, NuSTAR, Fermi-LAT, MAGIC, VERITAS, and other collaborations and instruments, providing data from radio to very-high-energy (VHE) gamma-ray bands. NuSTAR yielded previously unattainable sensitivity in the 3-79 keV range, revealing that the spectrum softens when the source is dimmer until the X-ray spectral shape saturates into a steep power law with a photon index of approximately 3, with no evidence for an exponential cutoff or additional hard components up to 80 keV. For the first time, we observed both the synchrotron and the inverse-Compton peaks of the spectral energy distribution (SED) simultaneously shifted to frequencies below the typical quiescent state by an order of magnitude. The fractional variability as a function of photon energy shows a double-bump structure which relates to the two bumps of the broadband SED. In each bump, the variability increases with energy which, in the framework of the synchrotron self-Compton model, implies that the electrons with higher energies are more variable. The measured multi-band variability, the significant X-ray-to-VHE correlation down to some of the lowest fluxes ever observed in both bands, the lack of correlation between optical/UV and X-ray flux, the low degree of polarization and its significant (random) variations, the short estimated electron cooling time, and the significantly longer variability timescale observed in the NuSTAR light curves point toward in-situ electron acceleration, and suggest that there are multiple compact regions contributing to the broadband emission of Mrk 421 during low-activity states.
Figure 1: Count rates for NuSTAR in the 3-7 keV (blue) and 7-30 keV (green) bands. The legend given in the second panel from the top applies to all panels; for both bands FPMA count rates are plotted with a lighter color. The data are binned into 10-minute bins. The time axis of each row starts with the first day of the month and the UTC and MJD dates are printed above the light curves for each particular observation. Note that the data shown in the top panel represent two contiguous observations (broken up near MJD~56115.15). The intervals shaded in grey show times for which simultaneous data from MAGIC and VERITAS are presented in this paper. Both the horizontal and the vertical scales are equal in all panels.
Figure 2: Upper Panel: Light curve of the July 2012 observation (FPMA in black, FPMB in grey) shown as an example for the count rate modeling; the two models fitted to each orbit of data are represented by purple (constant model) and blue lines (linear model). Lower Panels: The colored histograms on the left-hand side (colors matching the upper panel) show the distributions of reduced Χ2 for the two models fitted to every NuSTAR orbit up to the end of March 2013. The number of degrees of freedom (d.o.f.) in each fit varies slightly due to the different duration of the orbits, but it is typically around 10. The right panel shows the distribution of the residual scatter after subtraction of the best-fit linear trend from the observed count rates in each orbit, in units of the median rate uncertainty within the orbit, (σR)orb. The colors reflect the mean count rate of the orbit: the lowest-rate third in red, the mid-rate third in orange and the highest-rate third in yellow, distributed as shown in the inset. The residual scatter distribution is slightly skewed to values greater than unity, indicating that ≤20% of orbits show excess variability on suborbital timescales. A Gaussian of approximately matching width is overplotted with a thick black line simply to highlight the asymmetry of the observed distribution.
Figure 3: Hardness ratio (defined as the ratio of the number of counts in the 7-30 keV band to that in the 3-7 keV band) as a function of the count rate in individual 30-minute bins of NuSTAR data is shown with colored symbols: FPMA plotted with squares, and FPMB with diamonds. The colors distinguish different observations and match those in Figure 4. The thick black error bars and symbols show median count rate and hardness ratio in bins (1 ct s-1 width), delimited by the vertical dotted lines. The vertical error bars denote standard deviation within each bin.
Figure 4: Unfolded NuSTAR spectra of Mrk 421 in each of the 12 observations. Colors are arranged by the 3-7 keV flux. Also shown are spectra of the single highest-flux orbit (grey symbols) and the stack of three lowest-flux observations (black symbols). Modules FPMA and FPMB have been combined for clearer display and the bin mid-points for each spectrum are shown connected with lines of the same color to guide the eye. The left panel shows the unfolded spectra in the νFν representation, while the right panel shows the same spectra plotted as a ratio to the best-fit model for the lowest-flux stacked spectrum (a power law with Γ=3.05). Note that the vertical scale is logarithmic in the left, and linear in the right panel.
Figure 5: Trends in the hard X-ray spectral parameters as functions of flux for three simple spectral models revealed by time- and flux-resolved analyses of the NuSTAR data. The values fitted to high-S/N stacked spectra separated by flux (see Section 3.4 in the paper for an explanation) are shown with black-lined empty circles. A linear function is fitted to each of the trends and the uncertainty region is shaded in grey. Parameters of the fitted linear trends are given in Table 8 of the paper. The filled grey circles in the background show spectral modeling results for spectra of 88 individual orbits.
Figure 6: Comparison of the spectral trends revealed in our data, shown with black symbols, with the ones published by Giebels et al. (2007), shown with grey symbols. For this set of fits to the NuSTAR data the break energy E<sub>b<\sub> was kept fixed at 7 keV. The uncertainties are given at the 68% confidence level in order to match the previous results. Note the smoothness of the trends covering nearly two orders of magnitude and the apparent saturation effects at each end. The dotted lines are median photon indices for 2-10 keV flux below 10-10 erg s-1cm-2, representing the apparent low-flux saturation values.
Figure 7: Light curves for Mrk 421 from MAGIC, VERITAS (both above 200 GeV, binned in roughly 30-minute intervals), Fermi-LAT (0.2-100 GeV, binned weekly), NuSTAR (3-30 keV, binned by orbit), Swift/XRT (0.3-10 keV, complete observations), Swift/UVOT (UVW1, UVM2 and UVW2 bands, complete observations), ground-based optical observatories (R band, intranight cadence), OVRO and Metsahovi (15 and 37 GHz, both with cadence of 3-4 days). The host-galaxy contribution in the R band has been subtracted out according to Nilsson et al. (2007). The dynamic range in all panels is 40. Vertical and horizontal error bars show statistical uncertainties and the bin width, respectively, although some of the error bars are too small to be visible in this plot. The vertical lines mark midpoints of the coordinated NuSTAR and VHE observations: dashed lines mark the epochs for which we discuss SED snapshots in Section 4.4, while the rest are shown with dotted lines. The horizontal lines in some panels show the long-term median values, as explained in Section 4.1 of the paper.
Figure 8: Optical polarization of Mrk 421 between 2013 January and March. The degree of polarization is shown in the upper panel and the position angle of polarization is shown in the lower panel. Measurement uncertainties are based on photon statistics and are often smaller than the data points plotted. As in Figure 7, the vertical lines mark midpoints of the coordinated NuSTAR and VHE observations: dashed lines mark the epochs for which we discuss SED snapshots in Section 4.4 in the paper, while the rest are shown with dotted lines.
Figure 9: Fractional variability amplitude, Fvar, as a function of frequency for the period 2013 January-March. The vertical error bars depict the statistical uncertainty, while the horizontal error bars show the energy band covered (with the markers placed in the center of the segments). We show Fvar computed in two ways: using the complete light curves acquired in the campaign (empty symbols), and using only the data taken within narrow windows centered on the coordinated NuSTAR and VHE observations (filled symbols). Note that the points overlap where only the coordinated observations are available. The Fermi-LAT point is based on the weekly-binned light curve shown in Figure 7.
Figure 10: Flux-flux correlation between the X-ray and VHE (>200 GeV) flux in three different X-ray bands: Swift/XRT 0.3-3 keV in the left panel, Swift/XRT and NuSTAR 3-7 keV in the middle, and NuSTAR 7-30 keV in the right panel. Swift/XRT and NuSTAR measurements are shown with black-filled and white-filled symbols, respectively. Orange symbols mark MAGIC measurements, while dark red mark VERITAS. In the upper panels we show only the data taken essentially simultaneously (within 1.5 hours). The lower panels show data averaged over the nights of simultaneous observations with X-ray and VHE instruments. The values given in each panel are the number of data points considered (N), the slope of the log-log relation (a), and the discrete correlation function (DCF). The best fit linear relation (dashed grey line) and its uncertainty region are shown with grey shading. The thin dotted line of slope unity is shown in all panels to aid comparison.
Figure 11: Flux-flux correlations between the UV band (Swift/UVOT filter UVW1) and the optical (R band; top), soft X-ray (Swift/XRT 0.3-3 keV; middle) and GeV gamma-ray (Fermi-LAT 0.2-100 GeV; bottom) bands. The green data points are based on flux measurements that are coincident within 6 hours. The blue data points are derived by averaging over 7-day intervals, i.e., integration times used for determination of the flux in the Fermi-LAT band. In the top and bottom panels we overplot the slope of one-to-one proportionality (not a fit) with a black dotted line. Note that the vertical scale is linear in all panels, but has a different dynamic range in each one.
Figure 12: Upper Panel: Examples of approximate localization of the synchrotron SED component peak for two orbits of simultaneous observations with Swift and NuSTAR. The Swift data are shown as black filled symbols (diamonds for the UVOT and squares for the XRT) and the NuSTAR data are shown as black empty squares. Empty diamonds represent R-band data. For each of the epochs we show a log-parabolic curve fit to X-ray data alone (yellow) and all data (purple). For each curve, we mark the SED peak with an empty circle of matching color. Lower Panel: Results of the SED peak localization based on data from strictly simultaneous Swift and NuSTAR orbits. The colored data points show the frequency of the SED peak and the flux at the peak. The assumption of the log-parabolic model connecting the UV/optical and X-ray data (purple empty circles) reveals a proportionality between these variables in log-log space; the dashed black line shows a linear fit best describing that relation. The other method (using only X-ray data) does not show a similar relation. In comparison with the observations published previously, shown here with different hatched grey regions, in 2013 January-March we observed a state in which the peak occurred at atypically low energy and high flux.
Figure 13: SED snapshots for four selected epochs during the campaign, assembled using simultaneous data from Swift/UVOT, Swift/XRT, NuSTAR, Fermi-LAT, MAGIC, and VERITAS. Most of the data were acquired over a period shorter than 12 hours in each case; the exceptions are the Fermi-LAT data and part of the radio data, which were accumulated over roughly one-week time intervals. The two left panels show low-state SEDs, while the two on the right show elevated states (not flaring, but among the highest presented in this paper). The grey symbols in the background of each panel show the SED of Mrk 421 from Abdo et al. (2011) averaged over a quiescent 4.5-month period. The solid blue lines show a simple one-zone SSC model discussed in Section 4.3 in the paper. To aid comparison, the model curve from the first panel is reproduced in the other panels with a blue dotted line. The dashed red lines show SED models with a time-averaged electron distribution discussed in Section 5.3 for comparison with previously published results.
Figure 14: Light curves for Mrk 421 around the gamma-ray flare detected by Fermi-LAT in 2012, from Fermi-LAT (0.2-100 GeV, binned weekly), NuSTAR (3-30 keV, binned by orbit; see the top panel of Figure 1 for greater time resolution), MAXI (4-20 keV, weekly bins) and OVRO (15 GHz, weekly-daily cadence). Vertical and horizontal error bars show statistical uncertainties and the bin width, respectively, although some of the error bars are too small to be visible in this plot. The colored horizontal lines show the long-term median flux calculated from publicly available monitoring data. The dynamic range in all panels is 40, as in Figure 7, so that the two figures are directly comparable.