Time history of the Martian dynamo from crater magnetic field analysis

Authors


Abstract

[1] Large impacts simultaneously reset both the surface age and the magnetization of the entire depth of crust over areas comparable to the final size of the resulting craters. These properties make large impact craters (>300 km in diameter) ideal “magnetic markers” for constraining the history of the Martian core dynamo. However, the relationship between crustal magnetization and magnetic field measured in orbit is nonunique, making the measured magnetic field signature of an impact crater only a proxy for the magnetization (or lack thereof) below. Using Monte Carlo Fourier domain modeling of subsurface magnetization, we calculate probability distributions of the magnetic field signatures of partially and completely demagnetized craters. We compare these distributions to measured magnetic field signatures of 41 old impact craters on Mars larger than 300 km in diameter and calculate probabilities of their magnetization state. We compare these probabilities to cratering densities and absolute model ages and in this manner arrive at a robust time history of Martian large-crater magnetization and hence of the Martian dynamo. We conclude that the most likely scenario was a Mars dynamo active when the oldest detectable basins formed, ceasing before the Hellas and Utopia impacts, between 4.0 and 4.1 Ga (in model age) and not thereafter restarting. The Mars atmosphere was thereafter exposed directly to erosion by the solar wind, significantly altering the path of climate evolution. Further improvements to the history of the Martian dynamo will require better crater age estimates and lower altitude magnetic field data.

1 Introduction

1.1 Impacts and Crustal Magnetization

[2] Large impacts on Mars (which, for our purposes, form craters > ~300 km in diameter), alter the magnetization of the entire depth of crust over a geographic area comparable to the final size of the resulting crater [Hood et al., 2003; Shahnas and Arkani-Hamed, 2007]. Excavation removes and reorients magnetized material within the transient cavity [Melosh, 1989]. Further, shock heating causes thermal demagnetization [Mohit and Arkani-Hamed, 2004]. Following the impact, as the new crust cools, the melt sheet and any other crustal minerals heated above their Curie point can acquire a new thermoremanent magnetization (TRM) with a magnitude proportional to the strength of the local ambient magnetic field and the capacity of the rock to carry thermoremanence.

[3] In addition, shock from the impact can add or remove net magnetization, depending on this local magnetic field and prior magnetization state of the crust. Unmagnetized materials can be magnetized in an external magnetic field through shock remanent magnetization (SRM), and existing magnetization can be reduced or erased if the minerals are shocked in an ambient field too weak to induce a sufficient SRM. In addition, SRM may not be stable over geologic timescales [Cisowski and Fuller, 1978, Gattacceca et al., 2010].

[4] Brecciation and fluid circulation can combine to produce post-impact hydrothermal systems which can lead to the acquisition by crustal rocks of chemical remanent magnetization (CRM), the strength of which is controlled primarily by oxygen fugacity which controls the minerals that form and cooling speed which affects grain size [Grant, 1985]. It is important to note that essentially all magnetization in Martian impact structures is TRM, SRM, or CRM, comprising what is commonly referred to as natural remanent magnetization (NRM). This is in contrast to the case of terrestrial impact structures where a substantial component of magnetization induced by the geomagnetic field can account for anywhere from ~5% to >90% of total magnetization [Ugalde et al., 2005]. Mars' lack of a global magnetic field, and hence induced magnetization, thus removes a substantial complication from the interpretation of impact crater magnetic signatures.

[5] TRM tends to be the strongest and most stable of the types of NRM for the iron-bearing minerals likely responsible for Mars' remanent magnetism [Dunlop and Arkani-Hamed, 2005] and, if there exists a sufficiently strong ambient field, is virtually certain to occur in a substantial portion of large craters [Shahnas and Arkani-Hamed, 2007]. Although the magnetic mineral fraction in post-impact crust can be strongly affected by CRM processes like serpentinization [Quesnel et al., 2009], one can nonetheless argue that the magnetization contained within an impact crater is a reasonable proxy for the strength of the ambient magnetic field averaged over the crater cooling time (less than several million years [Ivanov, 2004]). Impact craters are thus useful in piecing together the history of Mars' ambient magnetic field.

1.2 The History of the Martian Dynamo

[6] Mars does not currently possess a global dynamo-driven magnetic field, but evidence of strong crustal magnetization implies that such a field is all but certain to have existed in the planet's early history [e.g., Acuña et al., 1999]. The dynamo may have started immediately following accretion/differentiation [Williams and Nimmo, 2004] or alternatively may have been inhibited for up to ~100 Ma (i.e., past initial crustal formation) by thermal stratification of the core resulting from collisions with large planetary embryos. This latter hypothesis is supported by the large extent of likely nonmagnetic primordial crust in the southern hemisphere [Arkani-Hamed and Boutin, 2012]. We have no solid evidence tying the start of the dynamo to any particular time before the formation of the oldest detectable impact basins (see below).

[7] Although the dynamo may or may not have started when the first Martian crust formed, the crustal strong magnetic fields detected by the Mars Global Surveyor (MGS) magnetometer (MAG), primarily over the heavily cratered crust of the southern highlands, can only be explained by large, coherently magnetized regions of crust (at least) hundreds of kilometers in scale [Acuña et al., 1999; Connerney et al., 2001], which in turn can only be adequately explained by the past presence of a dynamo-driven global magnetic field comparable in strength to that at the Earth's surface (i.e., ~10s of μT).

[8] Large-crater counts performed with crustal thickness and topographic data place younger bounds on ~20 impact basins in regions of moderate to strong crustal magnetic field [Frey, 2008, 2010; Lillis et al., 2008a], each larger than 1000 km in diameter, i.e., sufficiently large that magnetic field measured over the center of the crater is assuredly an adequate proxy for crustal magnetization [Lillis et al., 2010] and that they were formed when Mars had a global dynamo magnetic field. These magnetized basins are, by cratering densities, the oldest detectable structures, with N(300) crater densities greater than 2.6 (i.e., more than 2.6 craters greater than 300 km per 106 km2). The conversion from N(300) to model age suffers from systematic uncertainties in the lunar cratering rate earlier than 3.9 Ga and in the extrapolation of the cratering function from lunar maria to Martian conditions (discussed in sections 2.2 and 5.1). With these substantial caveats in converting to absolute model age, these magnetized basins were deemed to have model ages between 4.1 and 4.3 Ga.

[9] The only definitive thermochronometric data placing a younger bound on the life of the Martian dynamo comes from studies of Martian meteorite ALH84001. Its NRM resides primarily in single-domain magnetite- and pyrrhotite-bearing carbonates [Antretter et al., 2003; Rochette et al., 2005; Weiss et al., 2002]. The non-carbonate-hosted TRM was acquired at 4.1 Ga, while the carbonate-hosted TRM was acquired either at the same time (4.1 Ga) or possibly as late as 3.9 Ga [Shuster and Weiss, 2005; Weiss et al., 2002], in a paleomagnetic field with a magnitude of ~50 μT [Weiss et al., 2008].

[10] Thus, it is not seriously debated that the Martian dynamo was active sometime before 4.1 Ga, possibly for several hundred million years. Lillis et al. [2008a] noted that the large impact craters Utopia, Hellas, Isidis, and Argyre have diameters >1000 km, model ages ≤ 4.1 Ga and extremely weak crustal magnetic fields above them. Lillis et al. [2008a] thus concluded that Martian crustal magnetization underwent a rapid decrease around 4.1 Ga and that this was likely due to the cessation of the Martian dynamo. Some recent work on the magnetic field signature of Martian volcanic terranes with surface flow features younger than 4.0 Ga has suggested the possibility that the dynamo may have been subsequently active [Lillis et al., 2006, Hood et al., 2010; Milbury et al., 2012], though as discussed in the following section, we believe these interpretations to be insufficiently supported.

1.3 The Limitations of Using Volcanic Features to Constrain the Magnetic History

[11] The magnetic signatures of volcanic features offer another opportunity to further constrain dynamo history, in particular, the time period after the large craters formed. Hood et al. [2010] examined positive magnetic anomalies over Apollinaris Mons and Lucus Planum, concluding that substantial magnetization exists in the crust beneath both. Milbury et al. [2012] jointly used gravity and magnetic field data to separately model 29 magnetic sources in the Syrtis Major and Tyrrhenus Mons region. In both these cases, inferred magnetization beneath crust with a surface age in the Late Noachian/Early Hesperian (~3.7 Ga) was taken to support the idea of an active dynamo at this later time.

[12] However, for this line of reasoning to be valid, two assumptions must be true: (1) the surface age must represent the age at which all or most of the magma beneath the surface (which acquires a new magnetization when it cools below the magnetic blocking temperature(s) of its primary magnetic mineral(s)) was emplaced, i.e., no substantially earlier magmatic episodes can have occurred at that location which either did not produce significant intrusions and surface lavas or whose lavas were covered by later episodes; (2) the magnetization over the great majority of the magnetizable depth of crust (30–60 km [Voorhies, 2008; Dunlop and Arkani-Hamed, 2005]) and over an area large enough to influence orbital magnetic field data (i.e., > ~2 × 105 km2) must be reset at approximately the same time as the emplacement of the oldest visible lava flows on the surface, i.e., requiring magma chambers, sills and, dikes with cumulative thickness much greater than the 2.8–7.8 km inferred by Kiefer [2004a, 2004b] for several highland volcanoes (hydrothermal circulation does not significantly expand the region that experiences thermal demagnetization [Ogawa and Manga, 2007]). In other words, volcanoes we wish to utilize for constraining Martian dynamo history must be built and must reset the magnetization of ~10 million cubic kilometers of crust, both in a relatively short time (say, 100 Ma). This is not the case for any of the Martian highland volcanoes, many of which are too small (see Plescia [2004] for their sizes) and for which we cannot know the eruption history further back in time than the oldest visible flows. Criterion (2), however, may be satisfied by the largest Tharsis and Elysium volcanoes [Lillis et al., 2009], which have likely been completely thermally demagnetized by prolonged, pervasive magmatism, starting in the Noachian [Johnson and Phillips, 2005] and continuing well into the most recent Amazonian epoch [Robbins et al., 2011].

[13] For the reasons mentioned above, we argue there is a weak and uncertain link between the oldest visible surface age of a volcanic edifice and the age of the magnetization of the underlying crust. Therefore, the orbital magnetic field signatures of volcanoes are in general poorly suited to constrain dynamo history, and it is unwise to conclude from magnetic fields measured over highland volcanoes with surface ages <4 Ga that the Martian dynamo was active at these times. This is in contrast to the situation for large impact craters (the topic of this paper), where both the entire depth of magnetization and the surface crater retention age are reset almost simultaneously (in geologic terms). Impact craters (over volcanic features) offer a more definitive and reliable probe of the evolution of ambient magnetic field conditions over Martian history.

1.4 Is a Given Impact Crater Demagnetized?

[14] Section 4 of Lillis et al. [2010] demonstrated that magnetic field at 185 km altitude is a robust proxy for magnetization in the inner regions of craters greater than 1000 km in diameter. Examination of only the ~30 detected impact craters larger than 1000 km gives a consistent history of the Martian dynamo: cessation around a model age of 4.1 Ga, as mentioned earlier. However, none of these craters is younger than ~4.0 Ga in absolute model age. In order to investigate Mars' dynamo history over an extended time period, in particular to ages < 4.0 Ga, we must rely on smaller craters. However, as crater diameter decreases, the altitude of observation increasingly masks the magnetic signature of a demagnetized crater (which can be a local minimum or local maximum depending on the observation altitude, crater size, and coherence scale of the magnetization). To address this uncertainty, in this paper, we develop new statistical tools to calculate the probability distribution function of fractional crater magnetization for a crater of a given size and magnetic field signature. As an example, we intend to be able to answer questions like the following: if a 375 km crater displays a mean magnetic field magnitude at 400 km altitude in its central regions that is 75% of the mean field magnitude between 1.25 and 2 crater radii, what are the relative likelihoods of that crater being 90%, 50%, and 25% demagnetized, etc.? Coupled with improved crater retention ages, these tools should enable a more confident and comprehensive examination of the history of the Martian dynamo.

2 Data Sets

2.1 Crustal Magnetic Field Magnitude at Two Altitudes

[15] Orbital measurements of crustal magnetic fields are dominated by wavelengths of crustal magnetization comparable to the altitude of observation, with shorter wavelengths attenuating more with altitude and longer wavelengths causing relatively weaker signals [Blakely, 1995]. We use data sets at two different altitudes for quantitative comparison with magnetization modeling.

2.1.1 |B| at 185 km From Electron Reflectometry

[16] The first data set is the electron reflection (ER) map of the field magnitude |B|, due to crustal sources only, at 185 km altitude above the Martian areoid, hereafter referred to as B185. It is derived from pitch angle distributions of magnetically reflecting 100–400 eV solar wind electrons [Lillis et al., 2004; Mitchell et al., 2007; Lillis et al., 2008b] collected over the 7.5 year mapping orbit phase of MGS. Its altitude is determined by the mean altitude of unity scattering depth (akin to optical depth) for 100–400 eV electrons. Though it is binned at 0.5° resolution (30 km in latitude), its altitude limits the smallest features resolvable to ~200 km peak to peak. It has a regionally dependent detection threshold for crustal fields of ~1–4 nT, allowing us to examine the magnetic signatures of impact craters in greater detail than is possible with magnetometer data alone. Its main disadvantage is that data gaps exist wherever magnetic field lines at the 370–430 km mapping orbit altitude are topologically closed (i.e., attached to the crust at both ends), a common occurrence in regions of strong crustal fields such as Terra Sirenum (although such regions may still contain demagnetized zones within them). Uncertainties in B185 are well fitted by the following expression from Lillis et al. [2008a]:

display math(1)

[17] Figure 1a shows this map in orthographic projection for the hemisphere of Mars centered on 110°E, 8°N. The ER map relies on tracing magnetic field lines from ~400 km to 185 km, using the following approach. The noncrustal component of the magnetic field is taken to be the difference between the measured field spacecraft location and an evaluation at that location of the spherical harmonic magnetic field model mentioned in section 2.1. The crustal (evaluated from the model) and noncrustal components are added vectorally at each altitude as the field line is traced down to 185 km. Errors in locations are <50 km, depending on the strength and uncertain low-altitude geometry of the crustal field. To eliminate noncrustal noise, we subtract 3.0 nT from the entire map before comparing to modeled magnetic fields.

Figure 1.

Orthographic maps of the crustal magnetic field magnitude at (a) 185 km and (b) 400 km altitude used in this study (denoted B185 and B400; note logarithmic scale) overlaid on shaded MOLA topography [Smith et al., 2001]. The B185 map was adapted from Lillis et al. [2008a]. B400 is taken from a low-noise internal magnetic field model of Mars closely following the lunar work of Purucker [2008] and reported in Lillis et al. [2010]. Impact basins >1000 km in diameter are shown as solid circles [Frey, 2008]. Each ring in multiringed basins is shown. Demagnetized and magnetized basins are identified with blue and red lettering, respectively. The letters are abbreviations for the following basins: Hellas (He), Scopolus (Sc), Isidis (Is), Utopia (Ut), North Polar (NP), Amenthes (Am), Zephyria (Ze), Southeast Elysium (SE), and Amazonis (Az) [Frey, 2008].

2.1.2 |B| at 400 km From Internal-External Field Separation of Magnetic Field Measurements

[18] The second data set is an evaluation at 400 km of a degree-52 spherical harmonic representation of the internal magnetic field of Mars using a correlative technique on the 7 years (1999–2006) of mapping orbit magnetic field observations from Mars Global Surveyor (MGS). This internal dipole model exploits MGS's 88-orbit repeat geometry and incorporates radial and north-south vector component data from immediately adjacent passes. Field components of internal and external origin are separated using techniques developed for analysis of Lunar Prospector magnetic field observations by Purucker [2008]. We shall refer to values from this 400 km altitude map as B400. Its main advantage over other internal magnetic field representations at 400 km is its appreciably lower level of external (i.e., noncrustal) field contamination. Details of the technique, as well as uncertainties in the map, are provided in the appendix of Lillis et al. [2010]. Figure 1 shows B400 in orthographic projection for the hemisphere of Mars centered on 110°E, 8°N. To eliminate noncrustal noise, we subtract 4.0 nT from the entire map before to comparing to modeled magnetic fields.

2.2 Crater Databases

[19] To be useful in constraining dynamo history, a Martian impact crater must be greater than ~300 km in diameter. Smaller craters do not necessarily reset the crustal magnetization during their formation [Shahnas and Arkani-Hamed, 2007]. So that it will be useful in constraining dynamo history, a qualifying crater also must have a determined cumulative size frequency distribution (CFSD), or cratering density N(D), defined as the number of craters greater than a diameter D kilometers overlaid on the crater/basin in question, as determined in at least one of the following three published lists: Frey [2008], Werner et al. [2008], or Robbins et al. [2013] (based on the extensive database of Robbins and Hynek [2012]).

[20] Frey [2008] identified quasi-circular depressions (QCDs) in Mars Orbiter Laser Altimeter (MOLA) topography data [Smith et al., 2001] and crustal thin areas (CTAs) in crustal thickness data from MGS radio tracking [Neumann et al., 2004] as ancient, sometimes heavily degraded, impact craters. This data set has been augmented, rated, and revised [Frey and Mannoia, 2013] using higher-resolution gravity maps derived from Mars Reconnaissance Orbiter tracking data [Konopliv et al., 2011]. The minimum size for CTAs is ~300 km, as determined by the resolution of orbital gravity maps of Mars. N(300) was calculated by counting overprinted craters > 300 km in diameter over the entire basin in question. To achieve meaningful counting statistics, this database is limited to the 23 basins greater than 1000 km in diameter (see Table 1). Where basins are clearly multiringed, each ring is recorded (see Figures 1 and 6), though the most distinct is considered the main rim. The resulting N(300) values are necessarily minima since all old, degraded craters may not be detectable. These N(300) crater retention ages for ancient basins were converted to absolute model ages using the cratering chronology of Hartmann and Neukum [2001], although we and Frey [2008] acknowledge that such a conversion is fraught with difficult-to-assess systematic errors and therefore should be interpreted carefully, as discussed in section 5.1.

Table 1. A List of the 33 Craters Used in this Paper to Constrain the History of the Mars Dynamoa
Basic InformationCrater Retention InformationMagnetic Field Information
[Frey, 2008]Robbins et al. [2013]Werner et al., [2008]Angular Ranges Used (min, max) (deg)Magnetic Field, 185 km alt
NumberSymbolNameEast LongitudeLatitudeDiameter (km)Transient CavityN(300) (#/106 km2)ΔN(300)Model Age (Ga)N(50) (#/106 km2)ΔN(50)Model Age (Ga)N(10) (#/106 km2)Model Age (Ga)|B|, (r < 0.5R) (nT)|B|, (1.25R < r < 2R) (nT)Ratio Bin/Bout
  1. aThe columns are as follows: (1) number; (2) symbol; (3) name; (4, 5) position of center (east longitude, latitude); (6, 7) main topographic rim and theoretical transient cavity diameters; (8–10) crater retention information derived by Frey [2008]: N(300) (number of craters >300 km in diameter per 106 km2), error in N(300), and the estimated absolute model age derived from the cratering chronology of Hartmann and Neukum [2001]; (11–13) crater retention information derived by Robbins et al. [2013]: N(50) (number of craters >50 km in diameter per 106 km2), error in N(50) and the average of the absolute model ages derived separately from the cratering chronologies of Hartmann [2005] and Neukum et al. [2001], (14–15) crater retention information derived by Werner et al. [2008]: N(200) (number of craters >200 km in diameter per 106 km2), error in N(200) and the estimated absolute model age derived from the cratering chronology of Neukum [2001], (16) the angular range (s) used for calculating radial profiles of magnetization, (17–19) the average crustal magnetic field magnitude at 185 km altitude within 0.5 crater radii (B_in-185), between 1.25 and 2.0 radii (B_out-185) and the ratio between them.
1IsIsidis87.813.413528750--29.097.843.974093.9690-600.839.40.02
2AgArgyre317.5−48.913158531.470.584.0420.923.793.931823.8350-1751.456.10.02
3HeHellas66.4−42.2207012951.780.494.0734.813.904.024973.99340-1600.267.80.00
4HmHematite357.83.210657023.371.954.14-----0-36060.654.21.12
5ArAres343.94.0330019904.330.714.17-----0-36048.626.21.85
6SWSW Daedalia213.9−29.312788314.681.914.18-----0-36055.6137.60.40
7SiSirenum205.3−67.410697055.572.494.20-----0-36080.1191.10.42
8DaDaedalia228.3−26.4263916205.701.024.20-----75-1090.476.71.18
9ZeZephyria164.3−12.311937806.272.374.21-----0-36075.967.51.12
10AmAmenthes110.6−0.810707056.682.034.22-----0-36048.262.60.77
11SESE Elysium170.33.714039053.241.454.13-----160-3014.561.40.24
12UtUtopia115.545.0338020352.680.444.11-----80-2850.023.80.00
13NPNorth Polar197.080.4214513382.990.914.12-----60-1200.420.10.02
14AcAcidalia342.759.8308718723.210.654.13-----195-1003.913.60.29
15CrChryse318.025.0172510953.420.654.14-----225-5010.663.90.17
16AzAmazonis187.927.1287317523.860.774.15-----70-135, 220-34010.51.85.87
17SoSolis275.7−25.4176411183.681.234.15-----130-308.529.00.29
18ProPrometheus93.9−83.3924616---55.7820.734.04--290-301.3197.70.01
19LadLadon333.1−18.21097722---112.8337.564.18--315-27011.945.80.26
20ACT3-A181.6−36.710777104.392.204.17-----0-360171.8239.80.72
21CCT3-C138.8−72.112808327.782.464.24-----0-36050.746.21.10
22DCT3-D166.0−41.2288417584.750.854.18-----0-360303.468.14.46
23FCT3-F140.8−0.2158010104.081.444.16-----125-2021.659.20.37
24GCT3-G36.5−2.212458114.932.014.18-----0-360269.863.44.26
25HCT3-H7.928.514349248.672.324.25-----0-36041.634.11.22
26HuHuygens55.6−13.8467329---37.4815.184.004663.9820-16020.278.00.26
27CaCassini32.123.4408290---44.9317.204.066474.03155-11025.040.90.61
28AnAntoniadi60.821.4400285---30.5015.843.911443.7980-3014.252.80.27
29Epepsilon356.2−21.6358257---88.0044.254.11--260-15021.638.20.57
30TkTikhonravov35.913.3343247---68.8024.344.1610304.1090-36051.485.90.60
31Eteta53.223.5340245---97.9621.334.18--0-360103.765.81.57
32Ioiota28.9−0.3325235---84.7727.564.14--225-135, 175-28042.877.30.55
33HlHerschel129.9−14.4297217---49.0122.253.923833.95120-6022.850.10.45

[21] Robbins et al. [2013] used a different method from Frey [2008] to estimate the ages of large craters. They mapped the best preserved remnant rims of each large crater as an estimate for the surface that best dates to each large crater's formation. Craters from the Robbins and Hynek [2012] Martian crater database that were emplaced on the mapped rims were then extracted. (The Robbins and Hynek [2012] database lists a single diameter for each crater determined by tracing all remaining rim crest points in both visible images (THEMIS Daytime IR [Edwards et al., 2011]) and MOLA topography data [Smith et al., 2001].) These were binned into crater size-frequency distributions (CSFDs), normalized by surface area, and N(D) crater densities were extracted directly from the CSFDs. Model ages were also fit using both the systems of Neukum et al. [2001] and Hartmann [2005]; the regions of the CSFDs that best paralleled the different isochrons were used for fitting. To compare between craters in this paper, we use the N(50) ages and the mean of absolute isochron model ages derived separately from the Neukum et al. [2001] and Hartmann [2005] cratering chronologies, as shown in Table 1. Fifteen craters >300 km in diameter are taken from the database for use in this work.

[22] Werner [2008] used a technique similar to Robbins et al. [2013] though with different data sets. The author mapped large crater rims—though out to approximately one crater radius from the rim in many cases—and identified superposed craters in the mapping area. Mapping was done with Viking Mosaicked Digital Image Model 2 (MDIM 2), Mars Orbiter Camera Wide Angle (MOCWA), and MOLA data. The author identified craters D ≥ 1 km and then used craters D ≥ 16 km to fit to the Neukum et al. [2001] isochrons to derive absolute model ages and uncertainties. Differences compared with Robbins et al. [2013] are due to the differences in mapping methodology and the availability of the higher-resolution THEMIS mosaics since 2008. We use nine craters from this database in the present work.

[23] This leaves us with 41 suitable craters, ranging from Herschel at the small end (297 km) to Utopia as the largest (outer ring diameter of 4200 km). Only Hellas and Argyre are contained in all three databases. However, several of these craters are to some degree unsuitable for constraining dynamo history, either because they lack “pristine” rims (i.e., resurfacing has likely occurred and derived ages are therefore resurfacing ages and not formation ages) or because the magnetic field both inside and outside the crater is near the noise threshold of the magnetic maps and hence a quantitative judgment on impact demagnetization is not possible. The 33 suitable craters and the eight unsuitable craters (along with reasons for lack of suitability) are listed in Tables 1 and 2, and there is more discussion of specific unsuitable craters, and how they relate to dynamo history, in sections 5.2 and 5.3. Although the term “impact basin” commonly refers only to very large craters, both terms shall be used somewhat interchangeably in this paper.

3 Statistical Modeling of Impact Demagnetization Signatures in Magnetic Field Data

[24] Section 3 of Lillis et al. [2010] provide a detailed description of (1) the statistical Fourier domain technique of modeling crustal magnetization, (2) impact demagnetization thereof, and (3) the calculation of the resulting magnetic fields that would be observed at orbital altitudes. A statistical approach was chosen because inverting magnetic field measurements to calculate the three-dimensional distribution of subsurface magnetization in or around a given impact crater suffers from inherent nonuniqueness [e.g., Blakely, 1995; Biswas, 2005]. In this paper, we will follow very closely the model framework of Lillis et al. [2010], to which the interested reader is referred. We use this framework to calculate magnetic field signatures we expect over impact craters of different sizes and degrees of magnetization compared to their surroundings.

3.1 Magnetic Fields Above Demagnetized Craters

[25] We create a prism of magnetization with a characteristic horizontal and vertical coherence wavelength, then simulate impact demagnetization by reducing the magnetization in an azimuthally symmetric pattern of arbitrary size (Figure 2a). We calculate the resulting magnetic field at a given altitude (Figure 2b). In this modeling framework, we consider Dreset or Rreset, the diameter or radius of the modeled circular zone where the magnetization has been reset (to zero or some fraction of pre-impact demagnetization), instead of the topographic rim or ring radius of a crater. The relationship between topographic diameter and Dreset is discussed in section 4.1.

Figure 2.

Example of modeling of impact demagnetization. (a) A 48 × 256 × 256-element random magnetization distribution with characteristic horizontal and vertical wavelengths of 128 km and 12 km, respectively, with a Full Width at Half Maximum (FWHM) of 10 A/m, with a 300 km diameter cylinder of zero magnetization, with a linear magnetization increase from 125 km to 175 km radius. (b) The resulting magnetic field magnitude measured at 100 km altitude above the distribution shown in Figure 2a).

[26] Each instance of this procedure produces a different crustal magnetization distribution and corresponding magnetic field profile. Again, we do this because we cannot know the real subsurface magnetization distribution due to the aforementioned nonuniqueness of magnetic inversion [Blakely, 1995]. To illustrate the diversity of magnetic field signatures above a demagnetized impact crater, Figure 3 shows the circumferential averages of radial profiles of magnetic field intensity resulting from 150 of such simulation runs at 185 km and 400 km altitude above completely demagnetized circular zones of 200 km, 400 km, 600 km, and 1000 km diameter.

Figure 3.

The circumferential averages of magnetic field intensity at 185 km and at 400 km altitude above completely demagnetized circular zones of 200 km, 400 km, and 600 km in 1000 km diameter are plotted as a function of radius. The dominant coherence wavelength of pre-impact magnetization was assumed to be 1000 km. Red/blue solid lines and vertical error bars represent the mean and standard deviation of magnetic field profiles from 150 separate runs of our Monte Carlo in magnetization model, respectively. Light gray lines represent each of the 150 individual runs.

[27] According to potential theory, |B| varies linearly with magnetization strength. Also, Lillis et al. [2010] showed that for altitudes above 185 km, |B| also varies linearly with vertical coherence wavelength. Thus, since we will only be considering ratios of magnetic field magnitude inside and outside craters, our choice of either variable for magnetization modeling is unimportant.

[28] In our model, the region over which magnetization “ramps up” from zero to its pre-impact value is centered at Rreset and occurs over 10% of Rreset. Lillis et al. [2010] showed that it was not possible to distinguish between ramp-up distances in the range 0–800 km for large impact basins Utopia, Argyre, Hellas, and Isidis, i.e., such distinctions are effectively “smeared out” by our altitude of observation. Hence, we will adopt 10% as a nominal value.

[29] While a few isolated anomalies on Mars are, with necessary assumptions of source geometry, somewhat amenable to constraining the direction of subsurface magnetization [e.g., Hood et al., 2005], the distribution of magnetization directions is largely unknown. This is evidenced by the fact that the strong magnetic anomalies in Terra Cimmeria and Terra Sirenum have been successfully fit by assuming the crustal magnetization is entirely in the north-south direction [Hood et al., 2007], radial up-down direction [Connerney et al., 1999], and a combination of both [Sprenke and Baker, 2000].

[30] We choose a magnetization polar angle of 45°, thus limiting uncertainties in modeled field intensity to <15% [Lillis et al., 2010]. The azimuthal angle of magnetization axis does not affect the circumferentially averaged radial magnetic field profiles we analyze in this paper.

[31] In Figure 3 and all subsequent figures, we assume that the typical coherence wavelength of magnetization is 1000 km, i.e., that the typical lateral extent of a region of approximately uniformly magnetized crust on Mars is ~500 km. This is supported by the magneto-spectral analysis of Voorhies et al. [2002], Voorhies [2008] and the quantitative fitting of 185 km and 400 km altitude magnetic field data of Lillis et al. [2010]. There may be localized areas where smaller or larger magnetization coherence scales dominate, but Lillis et al. [2010] found ~1000 km to be the best fit in both a global-average sense and separately in the extensive regions surrounding the Utopia, Argyre, Hellas, and Isidis basins.

3.2 Magnetic Field In-Versus-Out Ratio

[32] Due to the great diversity of possible radial magnetic field profiles, particularly for smaller demagnetized craters (see Figure 3), it is not useful to fit specific measured radial profiles to the modeled mean profiles. Instead, we consider as our primary metric the ratio of the magnetic field measured within 0.5 crater radii to the field measured between 1.25 and 2 radii, which we call the in-versus-out ratio. Other limits were investigated. For the inner case, less than 0.4 radii resulted in very few data points for the smallest craters, while greater than 0.6 radii was affected by some of the surrounding magnetization. For the outer case, 1.25 radii was sufficient to avoid magnetic edge effects, while larger than 2.0 radii occasionally overlapped unrelated demagnetized regions. We shall refer to this ratio as Bin/out, or Bin/out-185 and Bin/out-400 for measurements at 185 km and 400 km altitude, respectively.

[33] To achieve sufficient statistical significance, 1000 Monte Carlo cases were run for each of 72 radii of demagnetization from 25 km to 1800 km and for 12 values of crater fractional magnetization, from 0% (i.e., completely demagnetized) to 110% (10% more magnetized than the surroundings). Probability distribution functions of Bin/out were calculated and are shown in Figures 4 and 5, providing us with important information about how likely a demagnetized crater is to display an obvious magnetic minimum and if so, how deep that minimum might be.

Figure 4.

(a–d) Distributions of modeled values of Bin/out for six different values of demagnetized diameter. Figures 4a and 4b plot Bin/out at 185 km altitude, while Figures 4c and 4d plot at Bin/out 400 km altitude. Figures 4e and 4f plot the mean and standard deviation of Bin/out as a function of demagnetized diameter at both altitudes, 185 km and 400 km. The top and bottom rows are for the cases of 0% and 10% remaining magnetization, respectively.

Figure 5.

Probability distributions of Bin/out are plotted for 12 values of fractional crater magnetization ranging from 0.0 (completely demagnetized) to 1.1 (10% more demagnetized than the surroundings). The left and right columns are for 185 km at 400 km altitude (i.e., Bin/out-185 and Bin/out-400), respectively, while each row is for a different diameter of reset magnetization Dreset.

[34] Figure 4 deals only with craters that are fully (0% remaining) or almost fully (10% remaining) demagnetized. The latter is included because demagnetized ejecta from other impacts or secondary TRM caused by nearby crustal fields could cause an impact crater formed in the absence of any global magnetic field to retain a small magnetization. Figure 4 shows that demagnetized craters require radii of at least > 400 km before we begin to see a substantial decrease in Bin/out-400, whereas 600 km and 1000 km craters show more pronounced minima. In contrast, demagnetized craters 200 km and larger always show values of Bin/out-185 below 0.9, while 400 km demagnetized craters always have Bin/out-185 < 0.45. The right-hand panels of Figure 4 also show how the mean and standard deviation of Bin/out-185 and Bin/out-400 vary with demagnetized diameter.

[35] As well as examining the probability distributions in Bin/out of different sized demagnetized craters, it is also useful to compare how these distributions differ for craters that are completely, mostly, partially, or not at all demagnetized, as shown in Figure 5. First, it is interesting to note that, for craters that are not demagnetized at all but whose size could allow for demagnetization diameters of 300 km and larger, the range of possible Bin/out ratios is remarkably wide, i.e., through just the natural undulations in magnetic field at altitude, a moderately deep magnetic field minimum can occur in magnetized regions (e.g., see Figure 2c for localized magnetic lows over magnetized crust).

[36] Conversely, at least at 400 km altitude, the range of Bin/out ratios over completely or almost completely demagnetized craters (i.e., black and indigo lines in Figure 5) is also quite wide; e.g., a demagnetized crater 400 km in diameter can display a range of values of Bin/out-400 between 0.2 and 1.0.

[37] Importantly, one can also use these probability distributions to pose the question (relevant to the overall issue of dynamo history): if one observes a particular crater with a given value of Bin/out measured at a known altitude, what are the relative likelihoods of the crust within the crater being demagnetized and to what degree? Here we find the 400 km altitude map does not constrain crater magnetization as well as we would hope. For example, a crater with Bin/out-400 = 0.83 with a diameter of reset magnetization Dreset = 400 km, has almost equal probabilities of having zero magnetization or the same average magnetization as its surroundings. Of course, if the same crater shows Bin/out = 1.3, then it is almost certain to contain some magnetization. Even at 600 km diameter, there is still a substantial amount of overlap between the probability curves for fractional magnetizations of 0.2 (the maximum one could argue is impact-demagnetized) versus 1.0 (not at all demagnetized). The situation is clearer at 185 km altitude, with more separation between the curves. For example, a hypothetical 400 km crater with Bin/out-185 = 0.83 at 185 km is extremely unlikely to be demagnetized and therefore very likely formed while the dynamo was still active. This is the logic we now apply to Martian craters with approximate ages derived from crater counting.

4 Assigning Demagnetization Probabilities to Martian Craters

[38] The family of probability curves shown in Figures 4 and 5 can now be used to estimate the relative likelihoods of a given crater being completely, mostly, partially, or not at all demagnetized; i.e., we wish to calculate relative likelihood as a function of the fraction of the original magnetization remaining after the impact. To apply this methodology to a real large crater or basin, we must identify a radius that encompasses the region where the magnetization would have been reset by the impact event.

4.1 Identifying a “Radius of Reset Magnetization” Rreset

[39] As mentioned in section 1, magnetization is reset through excavation of the transient cavity, thermal and pressure demagnetization, and (if an ambient magnetic field exists) remagnetization of the crust outside that cavity. Calculating the effective radius Rreset of these three effects requires knowledge of (A) the thermal and pressure-demagnetization properties of the crust, (B) the diameter of the transient cavity, and (C) the maximum pressure and temperature contours during the impact, which can be estimated using rough scaling laws or hydrocode simulations [e.g., Senft and Stewart, 2007].

[40] (A) can be estimated only roughly due to our lack of knowledge of the dominant Martian magnetic mineral [e.g., Dunlop and Arkani-Hamed, 2005] and the lack of measurements of published pressure demagnetization at pressures above 1.2 GPa [Louzada et al., 2011]. Determining (B) and (C) requires knowledge of the impact energy, along with reasonable estimates for mantle viscosity and the density and mechanical properties of the impactor and target material. Unfortunately, for impacts leaving craters >300 km in diameter (our minimum size), which puncture the entire depth of crust and involve mantle deformation, crustal collapse, and multiphase flow, laws relating impact energy to final crater size (derived for smaller craters [Melosh, 1989]) are generally unreliable at present [Stewart, 2011]. In addition, some large impact craters on Mars (and other planetary bodies) do not have one identifiable crater rim but rather several concentric rings, further confusing the issue of what constitutes the main rim.

[41] In other words, there exists no absolutely reliable formula we can use to convert topographic estimates of crater radius into estimates of Rreset, the radius inside of which the magnetization has been reset. Therefore, although we will choose a single value of Rreset (the main basin topographic rim) for each crater to establish a timeline for the Martian dynamo, for the purpose of examining the technique, it is prudent to calculate probability distributions of crater magnetization for a range of reasonable estimates of Rreset. These estimates fall into four categories. First, for craters in the database of Frey [2008] (all of which are >1000 km in diameter), each of the topographic rings is used for completeness. Second, all crater radius estimates from Robbins et al. [2013] are used. Third, for craters <500 km, an estimate of the diameter of the transient cavity by Melosh [1989] is also used, as it is a safe lower bound on the demagnetization diameter:

display math(2)

where Dc is the transition diameter from simple to complex craters (7 km for Mars) and Dfinal is the final diameter. Fourth, demagnetization radii derived by Lillis et al. [2010] for the obviously demagnetized basins Hellas, Isidis, Utopia, and Argyre are also used as a check of this method.

4.2 Calculating Bin/out for Martian Craters

[42] In order to more fully investigate how our estimate of demagnetization probability depends on our choice of Rreset, we calculate Bin/out for a wide range of values. For each Rreset we average each 0.5° × 0.5° pixel within 0.5 Rreset and divide by the average of all the pixels between 1.25 Rreset and 2.0 Rreset. However, for the latter average, we exclude pixels from angular ranges that are clearly nonmagnetic, whether or not crust in this angular range has been obviously subsequently demagnetized after the impact (e.g., Tharsis) or perhaps was never magnetic (e.g., southwest of Hellas [Arkani-Hamed and Boutin, 2012]). We do this so that we can get a “clean” ratio Bin/out of the magnetic field of pre-impact magnetized crust outside the crater/basin to post-impact crust inside it, with which to compare to our modeled impact demagnetization discussed in section 2. The angular ranges used are shown with dotted white lines in Figures 6-11 and are listed in Table 1.

Figure 6.

Magnetization probability of the Hellas Basin. (a–c) MOLA topography [Smith et al., 2001], |B| at 185 km altitude [Lillis et al., 2008], and |B| at 400 km [Lillis et al., 2010], respectively, over the same geographic area. The four colored rings represent four considered values of Rreset (i.e., the radius inside of which magnetization has been reset by the impact). The white lines show the boundaries of the angular ranges (listed in Table 1) used to calculate the radial profiles of magnetic field magnitude. (d) Azimuthally averaged magnetic field magnitude as a function of radius from the center of the basin at 185 km (black line) and 400 km (redline). (e and f) Relative probability as a function of Rreset and remaining magnetization fraction. The colored vertical lines in Figures 6d–6f are the same radii as the rings in Figures 6a–6c. (g) Relative probability as a function of remaining magnetization fraction inside the basin, plotted with the same color scheme for each of the considered values of Rreset, where solid and dashed lines are derived from 185 km and 400 km altitude magnetic field data, respectively.

Figure 7.

Same as Figure 6 but for Daedalia basin.

Figure 8.

Same as Figure 6 but for Prometheus Crater.

Figure 9.

Same as Figure 6 but for Ladon basin.

Figure 10.

Same as Figure 6 but for Antoniadi crater.

Figure 11.

Same as Figure 6 but for Tikhonravov crater.

4.3 Calculating Demagnetization Probability Distributions for Select Craters

[43] It is illuminating to assess our method for determining the likelihood of demagnetization on a few select craters to ensure that the results are consistent with previous conclusions. For a given crater, for every value of Rreset, we calculate Bin/out-185 and Bin/out-400. For each combination of Rreset and Bin/out, we can then calculate the relative probabilities of that value of Bin/out occurring if the fractional magnetization left within the crater was in the range 0.0, 0.1, 0.2, …, 1.1. In other words, we calculate the relative likelihood that the crater is totally, partially, or not at all demagnetized within each assumed value of Rreset. To illustrate this visually, we choose an abscissa (x axis) value of Bin/out in the appropriate panel of Figure 5 (or an interpolation between two panels depending on Rreset), then compare the ordinate (y axis) values for each of the curves representing values of fractional magnetization.

[44] Figures 6-11 show this calculation for a number of craters/basins, showing maps of topography and magnetic field magnitude at both altitudes, radial magnetic field profiles, and relative probability as a function of the remaining fraction of magnetization. While Figures 6e, 6f, 7e, 7f, 8e, 8f, 9e, 9f, 10e, 10f, 11e, and 11f show how the relative probability distributions change depending on the choice of Rreset, Figures 6g, 7g, 8g, 9g, 10g, and 11g contain the most relevant information, showing the relative likelihood of the observed value of Bin/out resulting from different magnetization fractions. The narrower the distribution, the smaller the uncertainty and the more confidence we have in the probable magnetization of the crater. Conversely, the wider and flatter the distribution, the larger the uncertainty in the crater magnetization. This can be seen intuitively by examining the dotted green curves in Figure 10g for a 300 km diameter zone, which was derived from the relative heights of the curves in Figure 5d at a value of Bin/out-400 = 1.0. This zone is as likely to have any range of magnetization fractions as any other between 0.0 and 1.1; i.e., from just the 400 km altitude magnetic intensity data, it is equally as likely to be magnetized as demagnetized.

[45] The Hellas and Daedalia basins (Figures 6 and 7, respectively) were chosen as examples of very large basins (>2000 km diameter). The former displays essentially zero probability that its magnetization fraction is >0.2, while the latter displays a similarly negligible probability that its magnetization fraction is <0.6. Of course these basins are large enough that our probabilistic technique is not necessary; it is obvious by inspection that Hellas has little or no large-scale coherent magnetization and that Daedalia has, but the methodology introduced here allows us to quantify what we mean by magnetized or not.

[46] The Prometheus and Ladon basins (Figures 8 and 9, respectively) were chosen as examples of medium-sized basins (~1000 km diameter). In this case also, while not quite as obvious by inspection, the former is almost certain to be demagnetized and the latter almost certain to be magnetized. Finally, the Antoniadi and Tikhonravov craters (Figures 10 and 11, respectively) were chosen as examples of craters in the size range below where magnetic field intensity is a reliable proxy for magnetization and where the likely magnetization of the crater is not obvious by inspection and hence requires our probabilistic technique. For these cases, the 400 km altitude magnetic field data tells us little or nothing, as evidenced by the flat dashed lines in Figures 10g and 11g. However, the 185 km altitude data tells us that Antoniadi is very likely at least partially demagnetized compared with its surroundings and is quite likely to be nearly or totally demagnetized, while Tikhonravov is very likely to be at least partially magnetized and very unlikely to be completely demagnetized.

[47] For completeness and so the reader can judge, Figure 12 shows magnetization probability curves for each of the 41 craters used in this work, at both 185 km at 400 km altitude, and for Rreset equal to the main topographic rim and transient cavity diameters for each basin.

Figure 12.

(a) Probability distributions of fractional magnetization and magnetic field profiles at both altitudes are plotted for the 33 craters used to constrain the temporal history of Mars' global magnetic field. The first and third columns show the probability distributions, where blue and pink represent probability distributions calculated by assuming a radius of reset magnetization Rreset equal to the main rim and transient cavity diameters, respectively (6th and 7th columns in Table 1). Solid and dashed lines are calculated using Bin/out-185 and Bin/out-400, respectively. The second and fourth columns plot radial profiles of magnetic field magnitude, at 185 km (black) and 400 km (red), averaged azimuthally over the angular ranges listed in Table 1. (b) Same as Figure 12 but for the excluded basins.

4.4 Establishing a New Martian Magnetic Timeline

[48] We may now utilize this probabilistic technique of assigning demagnetization to specific craters, along with crater age estimates, to establish a magnetization timeline. In other words, we may now use the magnetic field signatures of younger and smaller craters to extend our window of Martian magnetic field history to more recent times than previously possible.

[49] There are 33 craters larger than 300 km for which (a) the magnetic field measured outside the crater is high enough above the noise level that a demagnetization signature could be detected and (b) reliable ages have been derived (see Table 1a) and a further four craters (DeVaucoleurs, Schiaparelli, “gamma,” and Newton) for which derived ages are definite minima and the formation age is very likely older. For this reason, we do not include these in the timeline but will comment on them.

[50] As demonstrated in Figures 6-11, the magnetization probability distribution for a given crater depends on our choice of Rreset, which is not always obvious. Nonetheless, in order to establish a magnetic timeline, we must use a standard definition across all craters, despite the large variation in relative demagnetization by excavation, pressure, and temperature effects in impacts leaving the diverse array of large craters we see on Mars. Lillis et al. [2010] found that, for the large demagnetized basins Isidis, Utopia, Hellas, and Argyre (spanning ~1300–3300 km ), demagnetization extends out to 75–85% of the largest topographic ring radius, and to 100–140% of the “middle” or “main” ring radius, as determined by topographic analysis of Frey [2008]. As a best estimate for the sake of uniformity, for all basins we choose Rreset to be the main topographic rim.

[51] The result is the set of Mars magnetic timelines shown in Figure 13, calculated from the 185 km altitude magnetic field data. Specifically, the magnetization probability distribution curves for each crater are shown as colored vertical lines. The horizontal positions of these lines correspond to their measured crater densities above a certain threshold of crater size (left column) and derived absolute model ages (right column), with each row representing a different data set of craters, from Frey [2008], Robbins et al. [2013], and Werner et al. [2008], as discussed in section 2.2.

Figure 13.

Timelines of magnetization probability of large craters formed on early Mars, calculated from the electron reflection map of crustal magnetic field magnitude at 185 km altitude [Lillis et al., 2008b]. The text symbols are contractions of the full crater names listed in Table 1. Magnetization probability distribution curves for each crater are shown as colored vertical lines. The horizontal positions of these lines and error bars correspond to their best estimate ages (see text section 2.2 and Table 1) and uncertainties. The left and right columns show timelines organized by crater densities and absolute model ages, respectively. The top, middle, and bottom rows reflect the crater databases and age estimates of Frey [2008], Robbins et al. [2013], and Werner [2008].

[52] We choose not to make a timeline using the 400 km altitude magnetic field map for two reasons. First, the poorer sensitivity of the map compared to the 185 km ER map precludes any determination of impact demagnetization in regions of weak crustal fields, i.e., the field inside and outside the basin is at or below the noise threshold of the map, as is the case for the “epsilon,” Acidalia, Chryse, Solis, and Amazonis basins. Second, as shown in Figure 12, the magnetization probability curves are generally much wider and are therefore much less useful in constraining whether a given basin is magnetized or demagnetized.

5 Discussion of Probabilistic Martian Dynamo Timeline

[53] Figures 12 and 13 give the full picture of the magnetic signatures of our database of 41 old Martian impact craters/basins, what the likely range of magnetization is for each of them, and hence what they reveal about the history of the Martian dynamo. First we see that the 185 km data is much more useful than the 400 km data in constraining crater magnetizations; the probability distributions are much narrower because the data were collected closer to the source of the magnetic field. Indeed, there are some craters (e.g., SE Elysium, Ladon, CT3-H) where the 185 km and 400 km derived magnetization probability distributions do not overlap very much. This may be attributed to the 400 km magnetic field signal being relatively much weaker and hence less reliable. Another explanation is that our modeling assumption of a single Gaussian distribution of pre-impact magnetization coherence wavelength centered around 1000 km, while the most reasonable value to assume in a global-average sense [Voorhies, 2008; Lillis et al., 2010] may not be a good assumption for individual craters, where geologic processes may have led to other distributions (wider Gaussians, Lorentzian, bimodal, power law, etc.) which may result in quite different magnetic field behavior at 185 km versus 400 km.

5.1 Crater Densities as Proxies for Formation Age

[54] We have chosen to represent the magnetization timeline in this paper not just with absolute model ages but also with measured cratering densities. This is because absolute model ages contain all the systematic uncertainties from the effects of secondary craters and deposition/exhumation, in addition to the conversion of the cratering production function from lunar maria to Martian conditions [Hartmann, 2005]. Further, significant uncertainty in the radiometric ages of the lunar basins Nectaris and Serenitatis casts further doubt on the absolute lunar ages underpinning Martian cratering chronologies. However, it also is important to note that a single value of N(D) provides a less reliable estimate for the relative age of a basin compared to examining the entire crater size frequency distribution (CFSD) and that the optimal choice of D (i.e., that which best represents the age of the basin) depends on how large and how heavily cratered the relevant counting area is. Figure 2 of Robbins et al. [2013] clearly illustrates this issue, comparing the CFSDs measured on the rims of five old basins. Examining Ladon in the bottom panel of that figure, we see that N(50) reflects the “true” age of the terrain far better than N(10), because many overprinted craters in the ~10–25 km range have been eroded away. As a result, isochrons intersecting N(10) and N(50) give disparate model ages for Ladon of 3.84 and 4.17 Ga, respectively. In contrast, the Isidis basin (middle panel of that figure) is substantially younger, and the 10–25 km craters have been eroded to a far lesser degree than Ladon, such that N(10) and N(50) give much closer model ages of 3.86 and 3.95 Ga, respectively. So, why not simply use N(50) for all basins and avoid the effects of erosion of smaller craters? The answer is that younger basins with small pristine crater counting areas, such as Schiaparelli, suffer from poor statistics for large overprinted craters and have large uncertainties, e.g., N(50) = 28 ± 20 gives an almost unusable model age range for Schiaparelli of 3.84 to 4.12 Ga, whereas N(10) = 258 ± 64 gives 3.87 to 3.95 Ga, a narrower and more appropriate range because most of the craters larger than 10 km are preserved, unlike Ladon. Because of these issues and because we wish to compare basins of different cratering densities with a single metric, each basin's CFSD must be examined separately by eye and a judgment made as to which isochron is the best fit to the part of the curve relatively unaffected by erosion.

[55] Thus, despite the unknown systematic error associated with absolute model ages, such ages can be trusted in a relative sense, whereas choosing a single value of D and comparing N(D) can lead to errors even in relative ages, due to poor statistics for larger craters and/or erosion effects for smaller craters. Hence, we choose to interpret the absolute model ages and uncertainties derived from the best isochron fits of Robbins et al. [2013] and Werner [2008] but do not base our interpretation on the specific numbers.

5.2 Possible Dynamo Histories

[56] Figures 13a and 13b show only the basins >1000 km in diameter from Frey [2008]. The basins quite clearly fall into two groups: (1) four basins with essentially zero probability of containing any significant magnetization: Argyre, Hellas, Utopia, and North Polar (Isidis, also with zero magnetization probability, is omitted because it has no QCD/CTAs larger than 300 km overprinting it), all likely formed when no substantial global magnetic field existed, and (2) the remainder of the craters, all with probability distributions implying that they are at least partially magnetized and therefore likely having formed in the presence of a global magnetic field. These two basin populations do not overlap in age by more than a small fraction of the typical age uncertainty. Together they imply that the cessation of the Martian dynamo may have occurred at a cratering density N(300) = ~3 (converted to an absolute model age of ~4.1 Ga), which was also the conclusion of Lillis et al. [2008a]. This should not be surprising given that the magnetic fields measured at 185 km above basins of such size are very reliable proxies for bulk basin subsurface magnetization intensity.

[57] The timelines constructed using the cratering densities and age estimates of Robbins et al. [2013] (Figures 13c and 13d) and Werner [2008] (Figures 13e and 13f) allow us to examine smaller and in many cases younger craters compared to Frey [2008]. If we examine Figure 13d as is, we see a relatively clear pattern emerging from the 13 basins plotted. All six basins with model ages greater than 4.05 Ga (Cassini, “epsilon,” “iota,” Tikhonravov, “eta,” and Ladon) have zero probability of being completely demagnetized, whereas all basins with model ages younger than 4.05 Ga have their probability maxima at zero magnetization (Huygens is an exception with a probability maximum occurring at a magnetization fraction close to zero at 0.1 and still a significant probability of zero magnetization). Antoniadi, Huygens, and Herschel could be somewhat magnetized (their probably distributions are wide due to their small size and do not hit zero until magnetization fractions of 0.4 to 0.5). However, Prometheus, Hellas, Isidis, and Argyre, in the same model age range, have basically zero probability of being magnetized. Considering these 13 basins together, we believe, argues strongly for a single dynamo cessation sometime after the oldest six basins and before the youngest seven. In terms of absolute model age (which, as mentioned earlier, suffers from systematic uncertainties), this dynamo cessation would have occurred between 4.0 and 4.1 Ga. We see a very similar pattern from the smaller set of age estimates (eight basins) from Werner [2008] shown in Figure 13f, similarly arguing for a dynamo cessation before Hellas, Huygens, and Herschel and after Cassini and Tikhonravov.

[58] As mentioned in section 2.2, we believe the isochron ages of Schiaparelli, Newton, DeVaucoleurs, and “gamma” (shown in Table 2) to not be accurate formation ages but younger ages due to resurfacing events subsequent to crater formation (i.e., they show evidence for a substantial amount of postformation modification), and thus we have excluded them from the timelines shown in Figure 13 (Table 3). However, it is prudent to consider these basins more closely, one by one. First, the “gamma” basin is likely somewhat magnetized and has a model age range of 3.98 to 4.11 Ga with a median of 4.05 Ga, according to Robbins et al. [2013]. Even this likely resurfacing age is consistent with the one-time dynamo cessation mentioned above. Newton is very likely magnetized and has a model age of 3.89–4.04 Ga with a median of 3.98 Ga according to Robbins et al. [2013]. However, Werner [2008] gives a model age range of 3.99–4.21 Ga with a median of 4.11 Ga, also consistent with the aforementioned cessation scenario. DeVaucouleurs is likely magnetized, but isochron functions (giving a model age of 3.94) are a poor fit to the CSFD. Taking N(50) alone gives a model age of 4.07–4.16 Ga, and it appears stratigraphically older than Gusev crater (model age 4.15–4.20 Ga), so we believe its isochron model age is not reflective of its formation age. Schiaparelli is very likely magnetized, with an isochron model age of 3.93 Ga. However, its rim, while distinct, has been heavily eroded and reworked, making the isochron age a definite minimum age and the basin likely older.

Table 2. Same as Table 1 but for the Craters Excluded for Constraining the History of the Dynamo
Basic InformationCrater Retention InformationMagnetic Information
[Frey, 2008]Robbins et al. [2013]Werner et al., [2008]Magnetic Field, 185 km alt
NumberSymbolNameEast LongitudeLatitudeDiameter (km)Transient Cavity (km)N(300) (#/106 km2)ΔN(300)Model Age (Ga)N(50) (#/106 km2)ΔN(50)Model Age (Ga)N(10) (#/106 km2)Model Age (Ga)|B|, (r < 0.5R) (nT)|B|, (1.25R < r < 2R) (nT)Ratio Bin/Bout
1IAIn Amazonis192.529.311567583.811.914.15-----1.219.80.06
2NTNorth Tharsis243.617.613478723.511.574.14-----0.01.50.00
3ShSchiaparelli16.8−2.4445315---27.8220.983.933163.9272.949.11.48
4GaGamma2.8−36.7427303---32.1115.214.05--4.814.70.33
5Zezeta283.2−58.8341246---79.4436.463.98--2.45.40.44
6NtNewton201.9−40.4312227---37.2723.663.9810704.11113.180.11.41
7dVdeVaucouleurs171.1−13.2311226---63.3042.113.943833.9534.258.80.58
8CoCopernicus191.2−48.8301219---55.2329.003.995314.00--276.3--
Table 3. The Reasons for Exclusion for the Craters Not Used in Our Preferred Dynamo History Interpretation
  Reason for Exclusion
1Inside AmazonisTwo subsequent overlapping basins formed within, demagnetizing the interior
2North TharsisNegligible to very weak field inside and outside basin due to pervasive Tharsis magmatic demagnetization
3SchiaparelliThe rim is distinct but heavily eroded and reworked. Isochron age is definitely a minimum age for this, and the basin is very likely to be older in reality.
4GammaThe rim is not very distinct. The size frequency distribution is a very poor fit to any isochron function.
5ZetaNegligible to very weak field inside and outside basin precludes judgment on impact demagnetization.
6Newton“Soft” rim has very likely been reworked. Size frequency distribution gives a good isochron fit but can be considered a last resurfacing age.
7deVaucouleursIsochron is a poor fit. N(50) model age is 4.07–4.16 Ga. Stratigraphically appears older than Gusev crater (4.15–4.20 Ga model age).
8CopernicusNo ER magnetic field data within the crater due to permanently closed magnetic topology.

[59] Therefore, while magnetic field data do allow for individual basins to be somewhat magnetized and have model ages younger than 4.0 Ga, we believe the preponderance of evidence implies that the Martian dynamo and global magnetic field ceased sometime before the following impact basins were formed: Antoniadi, Herschel, Argyre, Isidis, Huygens, Utopia, North Polar, Prometheus, and Hellas; and after the formation of the following impact basins: Cassini, “epsilon,” “iota,” Tikhonravov, “eta,” Ladon, and the 18 basins from Frey's database numbered in Table 1 as 4–11, 14–17, and 20–25. Once the dynamo ceased operating, the magnetic field above craters does not indicate that it recommenced.

[60] Our preferred interpretation is based on three primary lines of reasoning. First, the negligible magnetic fields (at or below the typical noise threshold in the ER map) measured over the interiors of the six large basins Prometheus, Hellas, Isidis, Utopia, North Polar, and Argyre is very difficult to reconcile with a global dynamo-driven magnetic field existing at that time. The minimum crustal thickness in these basins is between 7 km and 25 km. Any magnetized solidified melt sheet would have been disrupted by the many subsequent smaller impacts, and the resulting magnetization gradients would result in substantial crustal magnetic fields at 185 km altitude, which are not observed. Second, despite the possibility that craters such as Herschel and Huygens could be young and somewhat magnetized, there is no region of Martian crust, crater, or otherwise, the majority of whose depth is both unambiguously magnetized and unambiguously younger than Hellas. Third, though mechanisms have been proposed whereby large impacts could temporarily cripple a supercritical dynamo, only the very largest impacts like Utopia might have done so [Roberts et al., 2009; Arkani-Hamed and Olson, 2010; Arkani-Hamed and Ghods, 2012]. The impact that produced, say, the Isidis basin, is not expected to have any significant thermal impact on the core-mantle boundary that could potentially temporarily shut down the dynamo and explain the lack of magnetization within the basin. In any other scenario, it is geophysically difficult to restart a dynamo once the core-to-mantle heat flux (and hence the magnetic Rayleigh number in the core) has fallen below a critical value [Kuang et al., 2008]. For these reasons, a permanent dynamo cessation at a time corresponding to a model age range of 4.0–4.1 Ga seems the simplest explanation. This also remains consistent with the magnetization found in meteorite ALH84001 as mentioned in section 1.

[61] Given the close temporal proximity of magnetized and completely demagnetized large impact basins, if the Mars dynamo shut down just once, it may have shut down quite quickly, in less than the typical uncertainty in these giant crater age estimates or ~20 million years of model age that was also noted by Lillis et al. [2008]. Indeed, once dynamo action ceases in the core, the magnetic field at the surface would decay with the magnetic diffusion time constant through the planetary body, or ~10,000 years. In summary, we conclude that the Martian dynamo was already active when the first of these large old impact basins formed (model age of ~4.3 Ga), likely ceased before the formation of the large impact basins Hellas, Isidis, Argyre, and Utopia at a time corresponding to an isochron model age of 4.0–4.1 Ga, and did not thereafter restart.

5.3 Dynamo History in the Context of Mars' Climate Evolution

[62] The history of the Martian dynamo has important consequences for the evolution of the Martian atmosphere and climate. Analysis of data from the OMEGA instrument on the Mars Express spacecraft suggests a transition in the hydration state of crustal minerals early in Martian history, from aqueous alteration, forming phyllosilicates (the “Phyllosian” era), to a drier, more acidic environment, forming sulfates (“Theikian” era) [Bibring et al., 2006]. This transition is believed to have taken place in the late Noachian/early Hesperian stratigraphic epoch in early Mars history, between model ages of 3.7 and 4.0 Ga. Also, a transition in the degradation state of craters shows a transition around a model age of 3.7 Ga, suggesting a global climatic change [Mangold et al., 2012] from a high-erosion environment involving fluvial activity to a low-erosion environment characterized by mostly aeolian processes. This is consistent with Mars having lost ~90% of its original atmosphere, as implied by enhancements in heavier isotopes of O, C, N, Ar, and Ne [Nier and McElroy, 1977; Jakosky et al., 1994]. Further, Manga et al. [2012] use the bomb sag (i.e., depressed and deranged laminae around an included volcanic bomb or block) observed by the Spirit rover at Home Plate to argue that atmospheric pressure in the Noachian epoch was at least 20 times greater than at present.

[63] The time during which the Martian dynamo was active was also characterized by extensive volcanism [e.g., McEwan et al., 1999], outgassing from which would have continually fed the atmosphere, and impacts by large asteroids which contributed to atmospheric erosion [Melosh and Vickery, 1989; Brain and Jakosky, 1998]. When the dynamo-driven global magnetic field disappeared, the early Mars atmosphere was thereafter exposed directly to the solar wind, which was likely substantially stronger than in recent times [Wood et al., 2005]. Thus, the rate of atmospheric erosion likely increased significantly [Chassefiere et al., 2007] from that time onward. It is therefore important to determine whether this occurred in the early Hesperian (model age of ~3.7–3.8 Ga), as suggested by the work of Milbury et al. [2012] or the middle Noachian (model age 4.0–4.1 Ga), as we maintain is the most likely scenario from the present study and earlier work [Lillis et al., 2008a, 2008b].

[64] Regardless, the decrease in atmospheric pressure and associated change in climate and erosional environment were a result of long-term changes in the sources (e.g., volcanism) and sinks (e.g., impacts, escape to space) of the atmosphere, and the history of the dynamo is undoubtedly a key piece of this puzzle. Some compelling questions to ask are the following: (1) Did the climate change rapidly (i.e., 10s of Ma) once the global magnetic field disappeared or more slowly (100 s of Ma)? (2) Were escape rates sufficiently high that the decline in volcanism was the primary driver of the climatic shift? (3) Was impact erosion a significant contributor compared with solar-driven atmospheric escape? Given the multiple interdependent thermal and nonthermal escape channels present in the Martian upper thermosphere and exosphere and how little is known about their dependence on solar activity, the answer is far from clear at present, although data from the NASA MAVEN Mars Scout mission will undoubtedly illuminate the subject, starting in late 2014.

6 Summary and Conclusions

[65] In this paper we have used Monte Carlo Fourier domain magnetic modeling to quantify the detectability of impact demagnetization signatures in orbital magnetic field data because we cannot know the details of the subsurface magnetization patterns either before or after a large impact, due to the inherent nonuniqueness of magnetic inversion techniques. We have calculated probability distributions of such magnetic field signatures as a function of the areal extent and degree (i.e., total, partial, etc.) of impact demagnetization. We have utilized this model framework to calculate the magnetization probability distribution for a number of specific large, old Martian impact craters/basins. Finally, we have compared these probability distributions with the relative ages of these craters/basins, as determined by cratering densities, in order to extend the magnetic history of Mars into the late Hesperian epoch. We conclude that the Martian dynamo was already active when the earliest detectable impact basins formed, likely ceased before the formation of the impact basins Hellas, Isidis, Argyre, and Utopia, at a time corresponding to an isochron model age of 4.0–4.1 Ga, and did not thereafter restart.

[66] We performed this analysis in order to extract the most reliable constraints (with uncertainties) on the history of the Mars dynamo by examining only impact craters with reliable model ages and quantifying the range of magnetic field signatures that can result from a magnetized or demagnetized crater. This technique awaits age estimates of many more Martian craters and lower altitude magnetic field data in order to shed further light on the interconnected magnetic, climatic, and interior histories of early Mars.

Acknowledgments

[67] This work was supported by the NASA Mars Data Analysis program (grants NNX07AN94G and NNX11AI85G).