A Catalogue of Forbush Decreases Recorded on the Surface of Mars from 2012 Until 2016: Comparison with Terrestrial FDs

Abstract

Forbush decreases (FDs) in galactic cosmic rays (GCRs) have been recorded by neutron monitors (NMs) at Earth for more than 60 years. For the past five years, with the establishment of the Radiation Assessment Detector (RAD) onboard the Mars Science Laboratory (MSL) rover Curiosity at Mars, it is possible to continuously detect, for the first time, FDs at another planet: Mars. In this work, we have compiled a catalog of 424 FDs at Mars using RAD dose rate data, from 2012 to 2016. Furthermore, we applied, for the first time, a comparative statistical analysis of the FDs measured at Mars, by RAD, and at Earth, by NMs, for the same time span. A carefully chosen sample of FDs at Earth and at Mars, driven by the same ICME, led to a significant correlation ($cc=0.71$) and a linear regression between the sizes of the FDs at the different observing points at the respective energies at Mars and Earth. We show that the amplitude of the FD at Mars ($A_{\mathrm{M}}$), for an energy of $E>150~\mbox{MeV}$, is higher by a factor of 1.5 – 2 compared to the size of the FD at Earth ($A_{\mathrm{E}}$), for a definite rigidity of 10 GV. Finally, almost identical regressions were obtained for both Earth and Mars as concerns the dependence of the maximum hourly decrease of the CR density ($\mathit{DM}_{\mathrm{in}}$) to the size of the FD.

1 Introduction

Galactic cosmic rays (GCRs) are omnipresent in the interplanetary (IP) space. As a result, their recorded intensity variations reflect their modulation by large structures propagating in the IP medium, like high speed streams (HSS) from coronal holes (Iucci et al., 1979; Kryakunova et al., 2013) and interplanetary coronal mass ejections (ICMEs) (e.g. Lockwood, 1971; Cane, 2000; Belov, 2009; Richardson and Cane, 2011). In the latter case, the leading shock wave of the ICME (if any) and the following ejecta could modulate GCRs, while, in the former case, HSS may form stream interaction regions (SIRs), as well as corotating interaction regions (CIRs), which affect GCRs. Both may result in a reduction of the cosmic ray (CR) intensity, known as the Forbush decrease (FD), as first discovered by Forbush (1938). For the past 60 years neutron monitors (NMs) have been recording the variation of GCRs at Earth and have shown that the transient GCR intensity decreases, i.e. FDs, demonstrate a depression on a time scale from several hours to several days (Lockwood, 1971; Cane, 2000; Belov, 2009; Papaioannou et al., 2010). FDs associated with ICMEs are known as non-recurrent, while FDs associated to CIRs as recurrent as they co-rotate with the Sun following the 27 day Carrington rotation period. This categorization is based on the sporadic or the recurrent nature of their causative interplanetary disturbance (Cane, 2000; Belov, 2009; Richardson and Cane, 2011).

Apart from ground-based NMs, several researchers have employed different datasets to study GCRs and the associated FDs: i) the anticoincidence guard data on Interplanetary Monitoring Platform (IMP) 8 (Cane, 2000; Richardson and Cane, 2011), ii) the anticoincidence shield (ACS) of the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) spectrometer (SPI), (Jordan et al., 2009, 2011), iii) the measurements of the Electron Proton Helium INstrument (EPHIN) detector onboard the Solar and Heliospheric Observatory and Chandra (Heber et al., 2015) and, recently, iv) Cassini’s Magnetosphere Imaging Instrument (MIMI)/ Low Energy Magnetospheric Measurement System (LEMMS) measurements (Roussos et al., 2017), among others. There have also been studies that attempted to track the evolution of large interplanetary structures within the heliosphere, using all observational evidence available. Although limited by the small number of spacecraft at remote heliospheric distances, such studies have provided important insight as concerns the variability of the FD characteristics and the response of GCRs to the dynamically evolving heliosphere at different radial and spatial distances (e.g. McDonald, Trainor, and Webber, 1981; Van Allen and Fillius, 1992; Witasse et al., 2017).

The observed properties of FDs within the heliosphere are extremely variant. This is due to: a) the complexity and the interplay of their solar sources as those propagate and interact with and within the dynamical heliosphere (Belov, 2009) and b) the differences between the observing points (Möstl et al., 2015). It is noteworthy that even at a radial distance of 1 AU (e.g. near-Earth IP space), the properties of FDs significantly vary. Belov et al. (2001) analyzed the factors and the dependencies that determine the magnitude of FDs. These included the intensity of the interplanetary magnetic field (IMF) and the velocity of the solar wind. From their analysis these authors introduced an index (e.g. the product of the maximal solar wind velocity and the maximal IMF intensity, $V_{\max} B_{\max}$) and showed that this index had a significant correlation with the average magnitude of the FDs. Moreover, even for a subset of non-recurrent FDs that are caused by ICMEs with magnetic clouds (MCs) it was possible to identify highly variable FD time profiles caused by fast, slow, and complex ICMEs (Belov et al., 2015). However, the study of FDs has been fundamental for the understanding of the heliospheric environment and the processes that take place in the IP medium. Up to now, FDs still provide crucial information from these environments (e.g. Papaioannou et al., 2005, 2009b; Abunina et al., 2013a,b; Abunin et al., 2013; Abunina et al., 2015; Kryakunova et al., 2015).

In this article we present a complete survey of FDs events that were identified on the surface of Mars using measurements from the Radiation Assessment Detector (RAD) (Hassler et al., 2012), onboard the Mars Science Laboratory’s (MSL) rover Curiosity (Grotzinger et al., 2012), observed during the maximum and declining phases of Solar Cycle 24, from 2012 to 2016. We also perform a parallel scanning of the FDs that were recorded at Earth by neutron monitors (NMs) during the same period. We select FDs identified by MSL/RAD and by NMs within the same time period and we perform a comparative statistical and correlation analysis, at the respective energies and at each observing point. In addition, we make an effort to identify the related ICMEs of the FDs (when possible) but we do not list the related HSS (if any) or the more complex interplanetary structures, which may result from the interaction of the solar sources, leading to the recorded FDs in this stage of our study.

2 Instrumentation and Data Description

2.1 Radiation Assessment Detector (RAD)

Since its landing on the Martian surface on 6 August 2012, RAD, being an energetic particle detector, has been identifying protons, energetic ions of various elements, neutrons, and gamma rays. A detailed description of the RAD instrument can be found in Hassler et al. (2012) and Zeitlin et al. (2016). On Mars, its recordings not only include direct radiation from space (i.e. GCRs or solar energetic particles (SEPs)), but also secondary radiation produced by the interaction of space radiation with the Martian atmosphere and ground that results on both charged and neutral particles (Ehresmann et al., 2014; Köhler et al., 2014; Guo et al., 2017). In addition RAD delivers dose¹ and dose equivalent rates, which have been analyzed to be concurrently modulated by the Martian atmosphere changes (both diurnally and seasonally) as well as the dynamic heliospheric conditions (Guo et al., 2015). On the surface of Mars, a thermal tide controls the diurnal pressure changes that in turn gives ground to a daily oscillation of the dose rate measured by RAD (Rafkin et al., 2014; Guo et al., 2017). In particular, there is an anticorrelation of the total dose rate measured at RAD with respect to the pressure: when the pressure increases (during the night), the total dose rate decreases and vice versa (during the midday). Additionally, the variation of GCRs at Mars results from Mars seasonal variations and heliospheric structure variability due to solar activity and rotation (Hassler et al., 2014; Guo et al., 2015). RAD measures doses in two detectors: the silicon detector B and the plastic scintillator E. The latter has a much bigger geometric factor and, thus, has much better statistics. Hence, the dose rate from E is a very good proxy for quantifying the time variation of GCRs (Guo et al., 2018).

2.2 Neutron Monitors (NMs)

Neutron monitors (NMs) are standard devices that measure cosmic rays (CRs) arriving at Earth. In particular, NMs provide the most stable long term dataset of GCRs for the past 60 years and, thus, are essential for studying GCRs and associated FDs. The Sun, occasionally, emits high-energy particles that result in a significant increase in the count rate of a NM. Such events are called ground level enhancements (GLEs) and occur almost once per year (Shea and Smart, 2012; Papaioannou et al., 2014). The flux of GCRs is mainly isotropic; however, the effect of the heliospheric environment leads to its solar modulation. A prominent event that signifies the effect of solar modulation on GCRs is the FD (Cane, 2000; Belov et al., 2001).

Using as many as possible NM recordings, the Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN) cosmic ray group has created a database of FDs and IP disturbances (http://spaceweather.izmiran.ru/eng/dbs.html). This database includes the results of the global survey method (GSM) (e.g. density, magnitude, decrement, recovery, 3D anisotropy, gradients of the CR) obtained by the data from the worldwide network of NMs throughout the period from 1957 (when continuous network observations began) up to the present (Belov, 1987; Asipenka et al., 2009; Belov et al., 2018). These variations of density and anisotropy of CRs are valuable and can be used effectively to study heliospheric processes, compared to the data of any single CR detector, since the GSM allows for deriving characteristics of CRs outside the Earth’s atmosphere and magnetosphere (Belov et al., 2018). In addition, this database includes GOES measurements (continuously updated), the Operating Missions as a Node on the Internet (OMNI) database IP data, the list of sudden storm commencements (SSCs) from ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUDDEN_COMMENCEMENTS/, the list of solar flares reported in the solar geophysical data (http://sgd.ngdc.noaa.gov/sgd/jsp/solarindex.jsp), as well as all relevant IP data and geomagnetic indices (Kp, which provides the deviation of the most disturbed horizontal component of the magnetic field; Dst, which that represents the axially symmetric disturbance magnetic field at the dipole equator on the Earth’s surface).

3 Compilation of the FD Catalog at Mars

3.1 FD Event Selection

3.1.1 Data Handling

First we imported the continuous RAD GCR dose rate data into a dedicated database. This covers the whole time span from 2012 to 2016. The RAD rate includes the original dose rate measurements of the MSL/RAD. It has been shown that the GCR dose rate measurements delivered by RAD exhibits a significant amount of periodic variation with a frequency of 1 sol (i.e. a Martian day of ≈ 24 h 40 min). This is due to the variation of the atmospheric pressure during the course of one Martian day, which leads to a clear anticorrelation between RAD measured dose rate and the surface pressure (Rafkin et al., 2014; Guo et al., 2018). However, the simple subtraction of the pressure effect during an FD event is not feasible, since this atmospheric effect is not constant but depends on solar modulation of GCRs (Guo et al., 2017). The reliable identification of FD events in the RAD dose rate measurements requires the application of a notch filter that suppresses the effect of the diurnal variation in the data but leaves other influences (including variations in a shorter time scale) intact (Guo et al., 2018). Figure 1 shows an example of the data stored in the database. In the top panel, the blue line corresponds to the hourly averaged RAD dose rate, whereas the red trace is the sol-filtered dose rate. The bottom panel (green line) depicts the diurnal variation of this period which seems to be about ${\approx}\,3.5\%$.

Figure 1

A sample of the RAD dose rate [$\upmu\mbox{Gy}/\mbox{day}$] for a two month period, namely 01 March – 30 April 2015, as those are stored in the dedicated database of FDs on the Martian soil. See text for explanations.

3.1.2 Selection

Next, we extracted FDs using hourly variations ($\delta(t)$) obtained from the sol-filtered data. Those are closest to the CR density variations obtained from the NM network data when applying the global survey method (GSM) (Belov et al., 2018). GSM takes into account the recordings of all NMs of the worldwide network and provides a continuous time series of 10 GV GCR density and anisotropy outside the atmosphere and the magnetosphere. These products are used as the basis for the terrestrial FD database (Belov, 2009; Papaioannou et al., 2010). We have, automatically, spotted all decreases in the RAD dose counting rate. This was a two step procedure. In the first step, we used a moving average function as follows: we applied a window centered on an hour of measurements, enforcing a width of 12 hours prior and 12 hours after this specific hour or measurement, resulting into a total of 25 hours. This time span (i.e. the 25 hours) was then used for the identification of the range of values for RAD. Consequently, a maximum ($\mathit{Max}$) and a minimum ($\mathit{Min}$) was identified in the count rate (within this window) as well as a time of maximum ($t_{\max}$) and a time of minimum ($t_{\min}$). The second step of this procedure was to calculate the difference $\delta= \frac{\mathit{Max}-\mathit{Min}}{\mathit{Max}}$ in % for each hour. If $\delta$ was ${\geq}\,1\%$, a candidate decrease was marked. Next, we identified the $t_{\max}$ and $t_{\min}$ for the count rate of a candidate event that was identified. It was further assumed that $t_{\max}$ was the actual start of the candidate FD, while the $t_{\min}$ was left open and was reevaluated at every hour. All these decreases were listed as possible candidates of FD events. The next and main step was to visually inspect and to cross-check the candidate FD event with respect to its solar origin (see Section 3.1.3) and the associated FD at Earth (if any). This procedure has led to a clear sample of 424 FDs identified in the measurements of RAD on the surface of Mars. Figure 2 depicts the long term behavior of the sol-filtered RAD data for the whole time span of the database. FDs with large amplitude ($A_{\mathrm{M}} > 4\%$) are noted with vertical red arrows. Red circles denote FD events that have been identified both at Earth and at Mars.

Figure 2

Long term behavior from 2012 to 2016 of the filtered Martian CR detector (e.g. RAD) count rate variations (blue line). Forbush decreases with a magnitude ${>}\,4\%$ on the surface of Mars are pointed with red arrows. The circles identify FDs observed on both Mars and Earth.

Given the fact that the most important parameter in FDs is the magnitude of the decrease, we have also identified the maximum difference of the variations in the selected period (i.e. FD duration time) as $A_{\mathrm{M}}=\delta$. For each of the 424 FD events we further determined a quality index ($q$), with respect to its identification with $q \in[1,5]$. The highest number, 5, was assigned to those FD events in which the $\delta(t)$ data were complete, diurnal variations (Rafkin et al., 2014) were reliably excluded, and there were no other difficulties in the selection of the FD and the correct determination of its size ($A_{\mathrm{M}}$). On the other hand, the lowest number, 1, was assigned to those periods in which the selection of the FD was practically impossible for a number of reasons (e.g. data gaps, the effect of solar CR, unfiltered diurnal or semidiurnal wave). The in-between ranking allocated number 2 to FD events for which it was possible to select the FD, but the size of the FD was unreliable due to data problems (e.g. data gaps, diurnal variation – especially prior and after a data gap). Intermediate cases with significant and minor data problems were marked cases 3 and 4, respectively.

3.1.3 Solar Origins of the Event

For each FD event recorded on Mars we tried to identify its corresponding solar source and when possible the related causative CME. For this purpose, we utilized the catalog of CMEs (Gopalswamy et al., 2009) based on recordings from the Large Angle and Spectrometric Coronagraph (LASCO: Brueckner et al. 1995) onboard the Solar and Heliospheric Observatory (SOHO) (Domingo, Fleck, and Poland, 1995), available at https://cdaw.gsfc.nasa.gov/CME_list/ and the ICME simulations from the Wang–Sheeley–Arge (WAS) ENLIL cone model (Arge and Pizzo, 2000; Arge et al., 2004) available at https://iswa.gsfc.nasa.gov/IswaSystemWebApp/. Furthermore, we included a quality index ($q_{\mathrm{S}}$), ranging from 1 to 5, based on the evaluation of the identified relation. The higher the number (i.e. 5) corresponds to the more concrete association. A similar index is also used in the database of terrestrial FDs maintained by IZMIRAN (Belov et al., 2018). The purpose of such an index is to provide a quantification on the estimations made during the identification of the solar sources. Naturally, there are straightforward as well as complex cases. This index (as any other one) provides different levels of such an evaluation and is subjective. Every effort has been made in order to identify the most likely situation as concerns the driving solar sources. The information tabulated in Table 1 (see the Appendix) further encourages the research efforts and paves the way for the identification of more complex situations.

Additionally, we established one more index: $q_{\mathrm{E}}$ also on a five-point scale, which characterizes the quality of the association of the Martian FD to the FD event at Earth. If the identified FD events (at Mars and at Earth) were driven by the same interplanetary disturbance and no other causative event could significantly affect CRs we assigned number 5. If factors that could mask the relation of the recordings at Mars and Earth were present but their influence turned out to be rather small then $q_{\mathrm{E}}$ was set to 4. In the cases the influence was distinguishable and/or rather clear $q_{\mathrm{E}}$ was 3 and 2, respectively. If the recorded variations at Earth and Mars are totally unrelated then $q_{\mathrm{E}}=0$, at the same time a very weak or even doubtful relation is marked with $q_{\mathrm{E}}=1$.

Table 1 (see the Appendix) includes the following information: column one provides the number of the FD event, column two gives the date and column three the start time of the FD at Mars. Next, column four provides the magnitude of the FD at Mars ($A_{\mathrm{M}}$), in %. The following three columns (i.e. five, six, and seven) show the assigned quality indices, $q$, $q_{\mathrm{S}}$, and $q_{\mathrm{E}}$. As a comparison, we also provide the magnitude of the FD at Earth ($A_{ \mathrm{E}}$), in %, in column eight. Note that when an FD was spotted in the RAD data but no FD was identified in the NM data – based on the solar origin of the events – we use $\mathit{NULL}$ as a flag. This flag is also used when no data or information are available, across Table 1. Column nine provides the time from the onset of the FD event until its density minimum, $t_{\min}$, in [hrs]. Columns 10 and 11 show the maximal hourly decrease (i.e. maximum steepness) in the CR density $D_{\mathrm{min}}$ in %, and the corresponding time of the maximal hourly density decrease during the main phase of the FD, $\mathit{tD}_{\mathrm{min}}$ in [hrs], respectively.² These FD characteristics are calculated for the FDs recorded on the surface of Mars. The final four columns (i.e. 12, 13, 14, and 15) give the associated solar event. In particular, the launch date and time of the CME as it first appeared in LASCO-C2 onboard SOHO (columns 12 and 13, respectively), the corresponding radial linear speed of the CME, in [$\mbox{km}/\mbox{s}$], as this was derived by the CDAW CME catalog (column 14), and the transit velocity of the ICME from the Sun to Mars, in [$\mbox{km}/\mbox{s}$] (column 15), calculated based on the aforementioned timing.

Figure 3 provides a compilation of several snapshots of the capabilities offered by the database of the RAD data.

Figure 3

A compilation of snapshots of the capabilities offered by the database of FDs at Mars. The top panel on the right shows a comparison of the RAD filtered dose rate (in blue) with the output of the GSM (in green) for an indicative time range. The top panelo on the right, demonstrates the related WSA ENLIL simulation with respect to the selected time range, which is also available through the database. The bottom panel on the right depicts the compiled FD database while the bottom panel on the left shows the statistics (e.g. regressions) that are possible to do in the implemented machinery.

3.2 Examples of FD Events at Mars and at Earth

3.2.1 Driven by the Same ICME

Multipoint simultaneous observations of GCRs on Earth and on Mars provide unprecedented opportunities for the analysis of the impact of the interplanetary counterparts of ICMEs on GCRs. Given the relative close radial difference between the Earth (1 AU) and Mars (${\approx}\,1.5~\mbox{AU}$), if an ICME passes over the Earth, there is a significant probability that this interplanetary disturbance will also arrive at Mars and vice versa provided that the planets have a small longitudinal separation. However, this is not a one-to-one relation and each case should be studied independently. ICMEs with large widths often affect at least one of the observation points, i.e. Mars and/or Earth. In this work, we are mostly interested in those ICMEs that resulted in a FD both on Earth and on Mars. Several examples of such events are presented in Freiherr von Forstner et al. (2018) and a similar example is illustrated in Figure 4.

Figure 4

WSA ENLIL model simulation of the ICME on January 2014 (top panel) and the resulting FDs at Mars and Earth (bottom panel). The top panel on the left hand side depicts the arrival of the ICME at Earth (highlighted by a green arrow), while the top panel on the right hand side presents the arrival of the ICME at Mars (highlighted by a blue arrow). The corresponding times of shock arrival are indicated in the bottom panel as green (Mars) and blue (Earth) arrows at the top of each of the respective time series.

Figure 4 shows the example of an ICME taking place in January 2014. Earth encountered the propagating ICME first and the recorded FD was recorded on 09 January 2014 at 20:00 UT. Almost 36 hours later, Mars also encountered the ICME and a FD was recorded on 11 January 2014 at 08:00 UT (see the vertical arrows in Figure 4, bottom panel). During this event, the longitudinal separation between Earth and Mars was ${\approx}\,50^{\circ}$, nevertheless the ICME affected both observational points. The causative of the FD at both Mars and Earth was a fast halo CME ($V_{\mathrm{CME}}=1830~\mbox{km}\,\mbox{s}^{-1}$) that was spotted by LASCO onboard SOHO on 07 January 2014 at 18:24 UT. In order to better understand the heliospheric variability of this period we further turned to the WSA ENLIL simulations. According to the space weather Database of Notifications, Knowledge, Information (DONKI) (https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/4364/2), this CME resulted into an ICME with a predicted shock arrival time at Earth on 09 January 2014 at 00:38 UT and at Mars almost 17 hours later at 17:55 UT. As illustrated in the top panel on the left hand side of Figure 4, Earth encounters the central part of the ICME while Mars was influenced mainly by its edge (top panel, right hand side). As a result, the FD at Earth is characterized by a relatively fast and sharp decrease, followed by a recovery period of several days.

3.2.2 Driven by Different ICMEs

In our catalog of FDs at Mars (see Table 1), we have identified examples of large ICMEs that resulted into FDs at both points in the heliosphere (e.g. Mars and Earth) at much larger longitudinal differences (in two cases this longitudinal difference is ${>}\,90^{\circ}$).

On the other hand, there are also examples when, although the longitudinal difference is relatively small and the FDs at Earth and Mars are closely related in time, those are triggered by different ICMEs. Such an example is presented in Figure 5.

Figure 5

The WSA ENLIL simulation of the first ICME on February 2014 (top left hand and middle panels), the resulted CR variations on Mars and Earth in February 2014 (bottom panel) and the WSA ENLIL simulation of the second ICME on February 2014 (top right hand panel) that resulted into the large FD at Earth on 27 February 2014. The red arrows indicate the extension of the ICMEs in the upper WSA ENLIL panels and the start of the related FDs in the bottom panel.

The FD started at Mars on 26 February 2014 at 09:00 UT. This was associated to a western (S15W73) relatively fast CME ($V_{ \mathrm{CME}}=948~\mbox{km}\,\mbox{s}^{-1}$) which did not encounter the Earth. At the same time a small but efficient ICME, driven by a partial halo CME of moderate velocity ($V_{\mathrm{CME}}=582~\mbox{km}\,\mbox{s}^{-1}$) – which apparently does not affect Mars – arrived at Earth earlier and resulted into a large FD that started on 20 February 2014 (Figure 5, upper panel on left hand and middle panels, depicts this ICME in the WSA ENLIL simulations). Additionally, the bottom panel of Figure 5 presents the time evolution of the RAD dose rate at Mars (in blue color) and the 10 GV GCRs variation at Earth (in green color). The evolution of this ICME spans up until the recovery of the FD at Earth. The flank of the ICME passing by Earth and not affecting Mars can also be seen in Figure 5 (upper middle panel). However, the most significant effect during this period begins on Earth at the end of 27 February 2014 at 16:50 UT. This is associated to a large and fast ($V _{\mathrm{CME}}=2147~\mbox{km}\,\mbox{s}^{-1}$) eastward halo CME (Figure 5, right hand panel), which occurred on 25 February 2014 at 01:25 UT, which was associated to an X4.9 flare at 00:39 UT, situated at S12E82. This ICME also passed by the east of Mars. It should be noted that February 2014 constitutes a special period, since it is one of the rare intervals for which identifications of the propagating ICME(s) were made in situ at different vantage points within the heliosphere (i.e. Mercury, Earth, Venus) (Wang et al., 2018; Winslow et al., 2018). These studies focus mostly on the period from 15 – 21 February 2014 (as concerns the ICME), which precedes the period discussed here but provides comprehensive background information for the complex conditions of the interplanetary space.

3.2.3 Complex Cases

Different combinations of structures propagating in the IP space resulted into noticeable short term GCRs intensity decreases at both Mars and Earth. In particular, interactions of: i) successive CMEs (Burlaga, Plunkett, and St. Cyr, 2002; Lugaz and Farrugia, 2014; Temmer et al., 2012), ii) CMEs with HSS and/or CIRs and iii) very complex cases with more than one of the aforementioned interactions taking place. Evidently, such interaction(s) imply a significant energy and momentum transfer with the interacting flux systems being merged (Burlaga et al., 2003; Liu et al., 2012) and with the CMEs being deflected from their initial propagation direction (Zhuang et al., 2017). The identification and interpretation of such complex events is not a trivial task since the resulting properties (e.g. FD amplitude) can be modified depending on relations between types and parameters of the participating structures. In our catalog of FDs at Mars, several such cases are present. For example, the events N^o 135 and 136 (see Table 1) on 17 and 19 February 2014, respectively. A very complex situation with a CME-CME interaction and an additional influence of a HSS took place (Figure 6). A series of slow partial halo and halo CMEs were ejected on 11 and 12 February 2014, respectively. The fastest partial halo CME on 11 February 2014 was the one registered at LASCO-C2 on 19:24 UT ($613~\mbox{km}\,\mbox{s}^{-1}$), while the fastest halo CME on 12 February 2014 was observed at 16:36 UT ($533~\mbox{km}\,\mbox{s}^{-1}$). This halo CME propagated under disturbed conditions. This halo CME seemed to interact with the preceding CMEs, forming a larger disturbance which propagated out until Mars. Finally, Mars was under the influence of this structure until 20 February 2014 (Figure 6). Table 1, lists the FD at Mars on 17 February 2014 at 07:00 UT with an amplitude of $A_{\mathrm{M}}=6.8\%$. This is associated to the halo CME of 12 February 2014 (which is, of course, part of the overall disturbance) and then lists for Earth an FD with amplitude $A_{\mathrm{E}}=4.3\%$. This corresponds to the FD at Earth that was registered earlier on 15 February 2014 (see Figure 6).

Figure 6

The WSA ENLIL and DONKI HELCATS simulation of the CME on 11 February 2014 (top left hand panel), the WSA ENLIL and DONKI HELCATS simulation of the second CME on 12 February 2014 (bottom left hand panel), their interaction as those propagate in the IP space (bottom middle panel), the WSA ENLIL and DONKI HELCATS simulation of the complex structure that occupied Mars up until 20 February 2014 (bottom right hand panel) and the resulted CR variations on Mars and Earth (top right hand panel). The red arrows indicate the extension of the CMEs and ICMEs in the WSA ENLIL and DONKI HELCATS panels and the start of the related FDs at Mars in the top right hand panel. The green arrow points to the relevant FD that was recorded at Earth.

Another complex case appears also for the events N^o 175 and 176 (see Table 1) on 05 and 06 July 2014. Interaction between each of the involved CMEs (see Table 1) and a propagating HSS took place, together with the interaction and merging of the CMEs at ≈ 0.8 AU.³ In particular, the CME on 01 July 2014 at 11:48 UT ($614~\mbox{km}\,\mbox{s}^{-1}$) seemed to overtake the propagating ICME. However, due to the relative position of Mars with respect to the Sun and the eastern direction of the CMEs, Mars only encountered their flanks. As a result, a series of small amplitude ($A_{\mathrm{M}}$) FDs were recorded at Mars.

4 Statistics

At a first glance, the FDs recorded on the surface of Mars and at Earth are surprisingly similar. Given the fact that Mars and Earth are very close, on the scale of the solar system, the interplanetary disturbances affecting both of them should be similar and there will be times that the same disturbance affects both planets. However, such similarity is still surprising, since the terrestrial and the Martian CR observations differ not less than two orders on the efficient energy of the recorded particles.

Before comparing FDs on Earth and on Mars, we need to discuss the specific features and the details of their selection per dataset. In principle, differences are essential. The GSM method provides as an output hourly variations of the CR density at Earth with an accuracy of ${<}\,0.1\%$. This feature makes it possible to select even very small (in terms of magnitude $A_{\mathrm{E}}$) FDs that sometimes appear to have an amplitude of 0.3%, with a potential unbiased selection starting at ≈ 1%. More important is that the GSM determines the CR characteristics separately for each hour, and this allows us to separate the density and the anisotropy variations. In addition, the near-Earth interplanetary space provides continuous measurements of all key solar wind (SW) parameters (SW velocity, intensity of the interplanetary magnetic field (IMF), and so on) and at the same time geomagnetic activity indices provide reliable identifications of the geomagnetic storms, especially the sudden storm commencements (SSCs). From the combined analysis of direct and indirect data, as a rule, it is possible to know the type of interplanetary disturbance and its arrival time at Earth. From this information one tries to get the response of the CRs (i.e. FD) for each interplanetary disturbance. As a result, it is possible not only to select FDs of small magnitude in the CR recordings at Earth but also to identify their solar drivers. However, this is practically impossible for the GCR data on Mars. Indeed, the smallest FDs, as concerns the magnitude ($A_{\mathrm{M}}$), in the catalog of FDs on the surface of Mars have a size of $A_{\mathrm{M}}= 1.1\,\mbox{--}\,1.2\%$. Moreover, the selection of FDs at RAD data that avoids biases starts at ≈ 3% (Guo et al., 2018). At the same time, RAD has given ground to the multipoint recordings of FDs on another planet, hence it provides the scientific community with unprecedented opportunities to study large scale magnetic structures (ICMEs, CIRs) propagating continuously through the interplanetary medium.

For the total time span of the Martian FD database studied here, that is, from 15 August 2012 to the end of 2016, we identified 424 FD events in the RAD dose data. During the same time period, at Earth a total of 541 events were identified. One should note that the larger number of FDs at Earth should not be misleading; if the capabilities to select the FDs from the Martian data would be similar, the number of FDs on Mars would be possibly higher compared to the relative number of FDs at Earth, because of the smaller energy of the registered CR at Mars. Furthermore, the Martian atmosphere shields away most of the GCR protons which have energies less than about 150 MeV (Guo et al., 2017). This cutoff is lower than the atmospheric cutoff at Earth, which is around 450 MeV (Clem and Dorman, 2000) and the definite energy of 9.1 GeV, which corresponds to the rigidity of 10 GV used in this study. If we could use the same energy for both Earth and Mars, the resulting FDs at Mars would be smaller than at Earth, given their distance difference. FDs can be considered as the disturbances in the GCR distribution caused by local variations and the presence of clouds of magnetized plasma that slowly fill (Cane, Richardson, and Wibberenz, 1995; Vanhoefer, 1996; Wibberenz et al., 1998; Cane, 2000; Dumbović et al., 2018), hence the size of the FD will get lower for larger distances from the Sun. Furthermore, recent studies based on observational evidence have shown that the amplitude of the FD drops as a function of the heliocentric distance (Witasse et al., 2017; Winslow et al., 2018). However, such a comparison is beyond the scope of this article.

Figure 7 provides the distribution of the magnitude of FDs that were recorded both at the Earth (orange color histograms) and at Mars (blue color histograms). There are $n=541$ FD events at Earth presented in this figure. However, the number of FD events at Mars is $n=410$. This is because we used only the events with a quality index $q \geq 2$. For these two distributions the mean and the median amplitude in % for the FDs at Earth was 1.43 and 1.10, respectively. For the FDs at Mars the mean and the median amplitude in % is 3.17 and 2.74, at the respective energies at each observing point.

Figure 7

Distribution of the size of FDs observed in the period 2012 – 2016 at Earth (orange color histograms) and at Mars (blue color histograms).

As a next step we compared the FDs at both planets with the same magnitude. In this comparison, the predominance of Mars is obvious: there are 341 FDs with a magnitude ${>}\,2\%$ recorded on the Martian surface but only 106 on Earth. At the same time, if we apply the same comparison to FDs with a magnitude of > 3% the corresponding quantities are 172 and 49 for Mars and Earth, respectively. Finally, the comparison between FDs with a magnitude of > 4% leads to 92 events for Mars and 22 for Earth. The largest FD in this period was ≈ 10% for the Earth, whereas on Mars the largest FD size was > 17%. Referring to Figure 7, it is evident that the FDs at Mars are noticeably larger in size at the respective energies (i.e. $E > 150~\mbox{MeV}$ for Mars and 9.1 GeV for Earth).

Analysis of the histograms Figure 7 reveals that the distributions of the magnitude of FDs at Earth and at Mars are highly skewed producing a long tail with large values. Distributions with such a form often follow a power law: $p(x)=C\mathrm{e}^{(-\alpha)}$. We have identified this power-law distribution by plotting the complementary cumulative distribution function (CCDF) on a log–log scale (Figure 8). The straight line asserts above some minimum values $X_{\min}$ both for Mars and for Earth which means that the tail of the distributions appears to be a power law (Newman, 2005). The method of a linear regression is used for the estimation of the power-law slope $\alpha$. The estimation of $X_{\min}$ is based on the Kolmogorov–Smirnov statistics (Clauset, Shalizi, and Newman, 2009). The distribution of FDs at Earth corresponds to a power law slope $-\alpha=-2.40 \pm0.19$ with $A_{\mathrm{E}}\geq1.1\%$ (284 FDs from 2012 to 2016). Similar results were obtained for terrestrial FDs from 1957 to 2016 (4692 events), $-\alpha=-2.31 \pm0.11$, $A_{\mathrm{E}} \geq1.4\%$ (2159 FDs). As for the distribution of $A_{\mathrm{M}}$, its power law slope is significantly steeper and the value from which the power law begins is noticeably larger than that for the distribution of $A_{\mathrm{E}}$ (Figure 8). For the magnitude of FDs at Mars $A_{\mathrm{M}}$, a power-law has been identified recently by Guo et al. (2018) who used FD recordings on the surface of Mars (by MSL) and outside the Martian atmosphere (by the Mars Atmosphere and Volatile Evolution Mission (MAVEN)). For their sample of 121 FD events registered by MSL, an $\alpha= -2.08 \pm0.32$ was obtained. However, for FDs that were registered by MSL but not by MAVEN the corresponding $\alpha$ was $-2.85 \pm0.57$, with the spectra being less of a power-law distribution with higher uncertainties of the fitting. Hence, the identification of a reliable slope is not a trivial task. In our work, although the correspondence of the tail of the $A_{\mathrm{M}}$ distribution to a power law follows from the CCDF, we do not have enough FDs at Mars with $A_{\mathrm{M}}\geq X_{\min}$, at present, to reliably estimate the slope with sufficient accuracy.

Figure 8

The logarithm of the complementary cumulative distribution functions (CCDFs) versus the logarithm of the magnitude of FDs at Earth and at Mars ($A_{\mathrm{F}}$ is the magnitude of the FDs).

Relations between different characteristics of FDs at Earth, such as the connection between the maximal hourly decrease in the CR density ($\mathit{DM} _{\mathrm{in}}$) and the total size of the FD ($A_{\mathrm{M}}$) have been studied by Belov (2009) and Abunin et al. (2012). This correlation has also been identified here for the FD events recorded on the surface of Mars (Figure 9). The circles depict the individual FD events. The diamonds of orange color represent the binned averaged intervals of the variation of $D_{\mathrm{min}}$ with the standard statistical errors overplotted.

Figure 9

The relation between the maximal hourly decrease in the CR density ($\mathit{DM}_{\mathrm{in}}$) and the total size of the Forbush decrease. Small circles represent individual episodes of FDs on Mars. Diamonds represent FDs on Mars averaged for equal intervals of the variation of $D_{\mathrm{min}}$ (standard statistical errors are also shown). Large blue circles are similarly averaged values of the FDs on Earth. In addition the linear regressions are presented for each sample, color coded as: red for FDs at Mars and blue for FDs at Earth. See text for details.

For comparison, Figure 9, also presents the binned averaged intervals of variation of $D_{\mathrm{min}}$ in the same time period for Earth. It can be seen that the Martian and the terrestrial FDs are surprisingly well matched. In particular, for Mars the linear regression yields the following relation:

$$ A_{\mathrm{M}} = (0.47 \pm0.07) + (-3.64 \pm0.32) \cdot D_{\mathrm{min}}. $$

(1)

At the same time, a similar regression is obtained for Earth:

$$ A_{\mathrm{E}} = (0.20 \pm0.03) + (-3.69 \pm0.16) \cdot D_{\mathrm{min}}. $$

(2)

It is most interesting to compare FDs observed at Earth and at Mars that are triggered by the same solar source (i.e. ICME). This is because it is possible to derive the propagation time of the ICME in the interplanetary space as well as its corresponding deceleration (or acceleration). Furthermore, multipoint observations of FDs at Earth and at Mars can be used to quantify the actual effect of the ICMEs on the radiation environment of each observing point. Such events constitute a rather small part over the whole sample of events. Nevertheless, in these four and a half years of continuous measurements at Mars several tens of events were identified. In particular, we applied the following criteria: $3 < q \leq5$ and $2 < q_{\mathrm{E}} \leq 5$ in our database of FD events at Mars. This is because we wanted to retrieve a sample of FD events with a high quality index for both the identification of the FD event ($q$) at Mars and its relation to FDs at Earth ($q_{\mathrm{E}}$). As a result, a sample of $n=20$ FD events recorded at both Mars and Earth was identified. For these events we compared the magnitude of the FD at Earth to the one at Mars (Figure 10). The correlation coefficient was $cc=0.71$.

Figure 10

Relation of the magnitudes for FDs caused by the same interplanetary disturbances on Earth and on Mars.

The linear regression overplotted in Figure 10, yields the following relation:

$$ A_{\mathrm{M}} = (1.07 \pm0.24) \cdot A_{\mathrm{E}} + (1.7 \pm0.3). $$

(3)

It appears (see Figure 10) that FDs at Mars are larger in size compared to terrestrial FDs, for the respective energies at each observing point. In particular, for small effects (${<}\,2\%$) this difference is about 2 – 3 times, while for the largest events in this comparison the difference is about 1.5 times.

According to Equation 3, an ICME with no FD at Earth would have an expected FD at Mars with the noticeable amplitude of 1.7 (${\pm}\, 0.3$)%. This is most probably due to the fact that numerous small interplanetary disturbances with weak magnetic fields can modulate CRs of low energy like those recorded by RAD on Mars, but their effect on GCR charged particles with a rigidity of 10 GV (${\approx}\,9.1~\mbox{GeV}$) (as those are derived by the application of the GSM on the neutron monitor data of the worldwide network) will be almost imperceptible. In general, FDs obtained from RAD dose rates at Mars obviously surpass the amplitude of the near-Earth FDs observed by neutron monitors (Figure 10), at the respective energies recorded at each observing point. If we, on top of this, consider the distinction of energies at the different observing points, we could expect significantly greater differences in the magnitudes of FDs. This is because the FDs observed at Earth are strongly dependent on the energy of the particles and their amplitude noticeably increases as a function of the decreasing energy. A recent extended study of a large number of FDs at Earth has shown that a typical (mean) index with a power-law spectrum ($\gamma$) of the dependence of the size of the FDs ($A_{\mathrm{E}}$) (caused by ICMEs) on the rigidity ($R$), assuming that the spectrum of the cosmic ray variations is defined as $A_{0}R^{-\gamma}$, is: $\gamma=0.6\,\mbox{--}\,0.7$. This estimation refers to a $R=10~\mbox{GV}$ (or equivalently to an energy of ${\approx}\,9.1~\mbox{GeV}$) and represents a mean value for FDs, taking into account the evolution of $\gamma$ within the different phases of a FD (Klyueva, Belov, and Eroshenko, 2017). Proton energies of ${>}\,150~\mbox{MeV}$ (similar to those recorded from RAD at Mars) would fall into a range of rigidities of ${>}\,0.55~\mbox{GV}$, hence, based on the aforementioned rigidity dependence, the expected size of the FD at Mars ($A_{\mathrm{M}}$) would be higher than the size of the FD at Earth ($A_{\mathrm{E}}$) not only by a factor of 1.5 – 2 (see above). However, this is not what we observe in the data. It should further be noted for completeness that, for RAD, located in Gale Crater, well below the mean Martian surface altitude, the atmosphere is effectively shielding against GCR particles below a cutoff energy of about $165~\mbox{MeV}/\mbox{nuc}$. However, this cutoff energy also changes as the Martian atmospheric depth changes diurnally and seasonally (Rafkin et al., 2014; Guo et al., 2015) up to 25%. Simulations of particle transport through the atmosphere have shown that the cutoff energy varies between 140 and 190 MeV depending on the atmospheric depth which may change between $18\mbox{ and }25~\mbox{g}/\mbox{cm}^{2}$ during different seasons (Guo et al., 2019). A possible explanation is that, during the propagation of the ICME from the Earth orbit to Mars, the efficiency of the ICME to modulate CRs decreases. At the same time, it is also likely that the energy (rigidity) dependence of the FD magnitude actually changes upon transition to lower energies. Perhaps this is due to the shape of the background energy spectrum of galactic CRs, which in the inner heliosphere has a maximum, due to the modulation of CRs by the solar wind, close to several hundreds of MeV. One should note that FDs are created at the expansion of the interplanetary disturbance (e.g. ICME), which is a quasitrap for the charged CR particles (Parker, 1965; Belov, 2009). During the expansion, GCR particles are cooling (i.e. lose energy). If the CR spectrum is decreasing (with increasing energy), i.e. CR flux drops as a function of energy, for CR particles with energies detected by neutron monitors (e.g. ${\geq}\,1~\mbox{GV}$), this leads to a decrease in the observed CR density of a given energy (rigidity). In the opposite case, if the CR spectrum is increasing (with increasing energy), i.e. the CR flux rises as a function of energy, for example in the energy range of up to a few hundreds MeV, the energy loss can only reduce the actual FD.

5 Conclusions

We have performed a systematic scanning of MSL/RAD dose rate recordings from 2012 to 2016. A total of 424 FDs were identified in this period, leading to a comprehensive catalog of FD events recorded on the surface of Mars. This is the largest database of FDs that has been observed away from Earth and also for measurements of relatively low energies (comparing to the observations retrieved by neutron monitors).

Furthermore, we performed a comparative statistical analysis between the FDs recorded at Mars (at $E>150~\mbox{MeV}$) and at Earth (at $E=9.1~\mbox{GeV}$) and we have shown that:

• FDs at Mars and Earth have almost identical dependencies on the values of the maximum hourly decrease of the CR density ($\mathit{DM}_{\mathrm{in}}$) to the size of the FD at the respective energies (see Figure 9 and Equations 1 and 2).

• The MSL/RAD data, at an energy of $E>150~\mbox{MeV}$, allow for the identification of FDs with a magnitude exceeding 1.5 – 2% while the mean amplitude of the identified FDs at Mars is 3.17%.

• When selecting a prime sample of FDs at Earth and at Mars, driven by the same ICME, a significant correlation ($cc=0.71$) and a linear regression between the sizes of the FDs at the different observing points, for the respective energies at each observing point, was obtained (see Figure 10 and Equation 3).

In addition, it was shown that the FDs observed at Mars, for protons with an energy of ${>}\,150~\mbox{MeV}$, have larger sizes ($A_{\mathrm{M}}$) compared with terrestrial FDs. This is in line with the findings of an independent recent study of FDs (Guo et al., 2018). However, it is noted that the observed differences in magnitude (Figure 10) are much smaller than what is expected from the differences in the energy ranges in both sets of observations. Most probably this is the result of the weakening of the energy dependence of the FD size at low energies, which provides evidence that the cooling of the CR particles, inside the ICME, plays an important role in the creation of FDs observed at Earth during its expansion.

Finally, we have tabulated all identified FDs at Mars from MSL/RAD in Table 1 (see the Appendix), where we also provide the start time and the magnitude of the FD ($A_{\mathrm{M}}$). Furthermore, in the same table we present the related (if any) FDs at Earth, their sizes ($A _{\mathrm{E}}$) and the characteristics of the FDs at Mars (i.e. $t_{\min}$, $\mathit{DM}_{\mathrm{in}}$, $\mathit{tD}_{\mathrm{min}}$), as well as three quality indices that quantify the degree of the uncertainty in the identification of the FD at Mars ($q$), the association to an FD at Earth ($q_{\mathrm{E}}$), and the obtained solar association ($q_{\mathrm{S}}$). Table 1 also includes the identification of the parent solar event (i.e. CME) together with the relevant information derived from the SOHO/LASCO CME catalog. It is noteworthy that a comparison of the catalog of FDs on the surface of Mars presented in this work to the one reported in Guo et al. (2018) has an overlap of 71%, which underlines a remarkable similarity considering the independent way of establishing the lists in these two articles. We also note that all of the large FD events are present at both lists. Given the fact that several of the events that are not identical in these two catalogs correspond in principle to the same event with a difference in the identified start time, the resulted similarity would be even higher. The results of our analysis (including Table 1) can be freely utilized in future studies.

Appendix

Table 1 The catalog of Forbush decreases at Mars. See text for details.