2.1.

Occulted Data Extraction

The data used in this paper are extracted from the “cleaned” level 2 event files in the NuSTAR archive at the science operations center (SOC). These data have all of the standard NuSTARDAS filters applied to them and are separated into the standard observing “modes.” To remove the sky background, we only use data when the sky is occulted by the Earth. NuSTAR does not repoint when the Earth enters the FoV, so in its low-earth ($\approx 600\mathrm{km}$) orbit the Earth occults the FoV for roughly 30-min out of every 96-min orbit. The duration of this occultation period varies depending on the position of the source in the sky and the time of the observation. By default, the NuSTARDAS pipeline uses the prefilter FTOOL⁷ and the NuSTAR orbital ephemeris in the two-line element (TLE) file to derive a number of key orbital parameters such as the “elevation” (ELV) of the telescope bore-sight from the Earth limb, whether NuSTAR is in sunlight or not (SUNSHINE), and the time since the telescope last exited the SAA. For standard science operations, “occulted” NuSTAR data are defined to include all data where the ELV parameter is $<3\mathrm{deg}$. In general, this is a conservative estimate to avoid any atmospheric attenuation from the Earth influencing the light curves or spectra of observations. Since we are attempting to remove all source photons from our data sets, we need to be more aggressive.

To estimate the appropriate ELV cutoff, we select data from observations of an extremely bright high-mass x-ray binary (HMXB), $\mathrm{A}0535+26$ during outburst. In this state, the source was several times brighter than the Crab, resulting in incident count rates $>2500$ counts per second on the NuSTAR detectors. We make a plot of the count rate versus the elevation angle (Fig. 2) and see the excess source emission included in the occulted data ($\mathrm{ELV}<3\mathrm{deg}$).

Fig. 2

The livetime-corrected source count rate versus the angle to the Earth limb (ELV). The vertical line shows the standard cutoff for occulted science data, while the vertical dashed line shows the cutoff used in this analysis.

We also perform a simple check in this case to see if there a discrepancy between the ingress and egress from the Earth limb (which could occur if there was a systematic misalignment between the telescope angle being used by prefilter and the actual bore-sight of the telescope). Here it is more convenient to simply plot the instrument livetime (which is inversely proportional to the incident count rate) and the elevation angle versus time (Fig. 3). We do a coarse estimate of the time when the livetime plateaus at its “high” level (when the source is behind the Earth) and find that both the ingress and egress time periods reach peak livetime at roughly 1.3 deg of ELV. This confirms that there is no systematic uncertainty in the prefilter measurement and also that if we use an aggressive ELV cutoff of $<0\mathrm{deg}$ that we will have removed all of the source-related photons from the dataset.

Fig. 3

The data here show the instrument livetime (left axis, blue data points) and the ELV (right axis, purple data points) for (a) an ingress and (b) egress from Earth shadow. The vertical solid line is a by-hand estimation of when the livetime has plateaued, while the horizontal guide line shows the ELV where this occurs. This corresponds to the time when the source is 100% blocked by the Earth limb.

An interesting implication of this analysis is that the ELV cutoff of 3 deg used by nupipeline results in at most 40 s of exposure loss before the atmospheric attenuation removes a majority of the source flux. However, if there are impulsive events that are evolving on timescales of a few seconds it might be possible to extend the usable science data beyond the end of the “SCIENCE” mode data.

2.2.

Solar Contamination

X-rays from the Sun can be especially bright when the Sun is active or flaring. To achieve the cleanest data set for our analysis, we want to remove the solar spectrum as it is highly variable and contains x-ray emission lines below 10 keV. A separate analysis dedicated to modeling the solar component in a similar manner to the CXB components is underway.

To estimate the impact of contamination due to solar background we produce monthly-averaged background spectra with $\mathrm{ELV}<0\mathrm{deg}$. Prefilter also provides an estimate of the “orbit day” based on the TLE and solar system ephemeris (via the SUNSHINE column). Using these data we construct data sets where NuSTAR is “in Sun” and “in Earthshadow.” The solar flux is primarily at low energies, so we integrate the monthly spectrum from 3 to 6 keV to estimate the received source rate on “DET0” for FPMA as a proxy for solar activity. We can then look at the difference between the rates in sunlight and in Earthshadow to estimate the impact of solar activity (Fig. 4). The first few years of the NuSTAR mission correspond to the peak of the solar cycle, so we see a lot of evidence for enhanced solar activity. We expect to see this activity increase again in the mid-2020s during the next solar maximum. The SUNSHINE flag is only an approximate estimate of whether the observatory is in sunlight based on the TLE. To fully remove the impact of solar activity, we would likely need to “bias” the entry into Earthshadow, similarly to how we use a more conservative cut of the ELV angle above. A more detailed study is beyond the scope of this work; here, we mainly use this to demonstrate the presence of an additional solar background.

Fig. 4

(a) A comparison of the 3 to 6 keV “In Sun” (blue) and in Earthshadow (red) count rates for the first 100 months since launch showing the excess near solar maximum in 2014 (MJD 56700) and the relative quite during the recent solar minimum. (b) The ratio of the two rates, showing the high amount of solar activity in the first three years of the mission, as well as the enhanced activity in September 2017 (MJD 58000), during which there were multiple X- and M-class flares.

We find that up until roughly four years after launch (mid-2016) there is a significant rate of enhanced background that can be associated with solar activity. After that, there are sporadic instances when individual months can be affected (i.e., Month 62 is September 2017 when there were multiple X-class flares).

For individual observations, the enhanced background from solar activity can appear both as “prompt” contribution from the x-ray flares themselves as well as “delayed” emission due to space weather (i.e., particles from a coronal mass ejections, or CMEs, that populate short-lived radiation belts; see Sec. 3.2). For the prompt emission, the x-ray flares can be so bright that the emission can penetrate through all of the shielding surrounding the detectors, even when NuSTAR is not pointed near the Sun. An example of this shown in Fig. 5 from an x-class solar flare on March 11, 2015, when NuSTAR was pointed 64 deg from the Sun. For situations like this, the NuSTAR SOC typically recommends avoiding using any of the data during the flare for science analysis of the primary target; the GOES full-disk integrated x-ray count rates can typically be used to filter out the solar activity, though during peak solar activity it can be difficult to distinguish between NuSTAR background spikes due to solar x-ray activity (when GOES is useful) and enhanced radiation belt activity (when GOES is not).

Fig. 5

The enhanced background caused by the X2.1 flare on March 11, 2015, during NuSTAR SEQID 30002041014. The blue-filled histogram shows the NuSTAR count rate during the flare, while the red trace shows the GOES x-ray flux monitor. The vertical dashed line is the time of the flare. The “missing” NuSTAR data here are caused by the event selection criteria and/or when NuSTAR was behind the Earth.

The major difference between these two phenomena is that the solar x-ray events have a thermal spectrum (with emission lines associated with 10 to 100 MK gas in the solar corona), while the radiation belt events show enhancements in the apparent nonthermal background and can dominate the high-energy background spectrum for the entire month. Figure 6 shows representative spectra for each case.

Fig. 6

(a) The observed spectrum of the solar flare shown in Fig. 5 showing the predominantly thermal spectrum along with a Fe emission lines around $\sim 6.4$ to 6.7 keV as well as emission (presumably from S XXV) at $\sim 2.9\mathrm{keV}$. (b) The spectrum of an “orphan” spike in the background associated with a radiation belt enhancement from September 08, 2017 during NuSTAR SEQID 60301028002 showing the continuum spectrum as well as fluorescence lines associated with the material surrounding the detectors (vertical dashed lines).

Unfortunately, neither of these cases can be systematically mitigated. The SOC provides background maps and lightcurves to help identify cases where automated screening could be used, while the NuMASTER table includes a flag set during the quality assessment of observations to identify observations with enhanced backgrounds due to solar or space weather activity.

3.1.

SAA-Induced Radioactivity

There is spatial variation in a line emission near $\approx 25\mathrm{keV}$, which is apparently related to activation of material in the CdZnTe detectors during the passages through the SAA. If we isolate the period of time just after the SAA passages and compare this with the total average spectrum, we clearly see the line (Fig. 9). To define this region we define the “radioactive” region as locations where the geomagnetic cutoff rigidity is between 10.8 and $12\mathrm{GeV}/\mathrm{c}$ and the longitude of the satellite is above 320 deg. The “Non-SAA” spectrum shown in Fig. 9 is the average spectrum outside this geomagnetic and geographic location. The only other excess that we observe is a broad excess near 3.9 keV. There do not appear to be many (if any) other obvious SAA-induced activate lines. We checked with prelaunch simulations of activation in the NuSTAR instrument and cannot identify a likely counterpart for these line features (though these may possibly be related to isotopes of Cd). The orbital path through the SAA means that it is difficult to determine the decay timescale. For now, we simply note the presence of this line and that it can be time variable as an impact on empirical models of the NuSTAR background.

Fig. 9

(a) Spectrum extracted just after NuSTAR passes through the SAA (red) compared with the non-SAA spectrum (blue). (b) The residuals between the two spectra show a clear line at $\approx 25\mathrm{keV}$ and a broad excess at $\sim 3.9\mathrm{keV}$.

3.2.

“The Tentacle”

One of the more common enhancements in the NuSTAR background occurs when NuSTAR passes through a short-lived radiation belt, which has been dubbed “the tentacle” due to its morphology in the NuSTAR ground maps stretching away from the SAA itself. This radiation belt appears after a CME passes nearby the Earth and can last for up to a week.

This excess background is fairly well localized geographically and geomagnetically (Fig. 10). Since 2013, versions of the NuSTARDAS software pipeline have included filtering mechanisms (via the nucalcsaa FTOOL) to flag and remove excess background in this region. There are a number of filter options that can be examined observation-by-observation using the NuSTAR background maps available at the SOC.

Fig. 10

(a) The NuSTAR $>10\mathrm{keV}$ count rate, binned by the geographic sub-satellite point for a month’s worth of data. The blank area between 270 deg and 320 deg longitude is the SAA, while the region between the vertical red lines shows “the tentacle.” (b) The background rate (integrated over DET0) versus geomagnetic cutoff rigidity for the total data (blue) and the data in the geographic tentacle region (red). (c) The total NuSTAR spectrum (blue) and the spectrum for the selected geographic and geomagnetic “tentacle” region (red) from 2 to 120 keV. (d) The excess emission in the tentacle region appears to be a relatively featureless power-law spectrum across the entire band-pass and does not appear to excite any activation lines in the detectors or the surrounding material.

The spectrum [Figs. 10(c) and 10(d)] shows a uniform power-law excess across the band-pass, implying that this is also caused by an increase in the rate of charged particles. However, we do not see much excess emission near the CsI fluorescence lines (20 to 30 keV), or near any other radioactive lines across the band-pass.

NuSTAR passes through this region at most once per orbit, and during some orbits this may be when the primary NuSTAR target is occulted by the Earth. Fortunately, any apparent long-term (orbital timescale) periodic signals for astrophysical sources can be identified as spurious if they primarily occur in this region.

4.1.

Growth of Activation Lines

The high energy activation lines are dominated by the 88 and 92 keV lines, which we associate with isotopes of Cd. In particular, the 88 keV line shows growth on a yearly timescale (Fig. 11). However, this growth is non-monotonic and does show a plateau roughly during the period of solar maximum. This could be related to the changing particle background as the solar cycle interacts with the Earth’s magnetosphere. A similar trend is seen in the change in gain over time of the NuSTAR detectors.⁹ The time-dependent gain has already been accounted for in these data, but both effects may be related to the same underlying change in background particle flux.

Fig. 11

(a) Six-month integrated spectra for FPMA (all detectors) showing the growth of the 88 keV line over time (color indicates years since launch). All epochs have been normalized by the count rate in the 110 to 120 keV line-free band to emphasize the change in the line strength relative to the underlying continuum. (b) The strength of the 88 keV line relative (integrated over the vertical lines in the left panel), normalized to the line strength in 2012 to highlight the growth of the line over time.

4.2.

Detector-to-Detector Variation

The four CdZnTe detectors on each focal plane have slightly different thicknesses, ranging from 1.5 to 2.0 mm (Table 1). The difference in detector volume can result in a change in the overall count rate between the detectors. All of the FPMB detectors are roughly the same thickness, so we see little variation between the detectors on that FPM. The FPMA detector vary in thickness, resulting in more detector-to-detector variation. In the standard background model nuskybgd,² this variation is accounted for via a featureless power-law term with a normalization that varies by $\approx 5\%$ to 10% between detectors. We extract background spectra from 100 to 120 keV when the observatory is in orbital night and computed the monthly average count rate for all four detectors on each focal plane. We clearly see that beat frequency (not plotted) of the monthly integration windows with the precession period of the observatory; however, when we scale the count rates to be relative to DET0, we see no evidence for any time-dependence in the relative strength of the internal background continuum (Fig. 12).

Table 1

The CdZnTe thickness for the eight detectors flying on NuSTAR as measured during ground testing.

Fig. 12

Monthly average 100 to 120 keV count rate versus time for (a) FPMA and (b) FPMB relative to DET0 on both FPMs. No clear trends with time are see in the relative strength of the internal continuum.

4.3.

Variation in the Internal Continuum

The overall continuum shape has been relatively stable over time, with some deviations associated with high background periods associated with solar activity. We integrate the background in 6-month intervals to highlight the changes in the spectral shape (Fig. 13). While the shape is mostly stable, the overall normalization varies by roughly 50% between 6-month intervals.

Fig. 13

Background spectra for FPMA (all detectors) integrated over 6-month intervals. Color indicates years-since-launch.