Reflections On the Anomalous ANITA Events: The Antarctic Subsurface as a Possible Explanation

TL;DR

This paper investigates whether subsurface reflections in Antarctic ice could explain ANITA's anomalous up-going events, suggesting that complex ice layers might mimic signals expected from neutrino interactions.

Contribution

It proposes that subsurface ice layers and density inversions could account for ANITA's anomalous events, challenging the assumption that phase inversion alone distinguishes neutrino signals.

Findings

Subsurface layers may cause signals similar to up-going neutrinos.

Ice fabric layers and wind crusts could influence signal reflections.

Radar surveys can test the subsurface reflection hypothesis.

Abstract

The ANITA balloon experiment was designed to detect radio signals initiated by neutrinos and cosmic ray air showers. These signals are typically discriminated by the polarization and phase inversions of the radio signal. The reflected signal from cosmic rays suffer phase inversion compared to a direct tau neutrino event. In this paper we study sub-surface reflection, which can occur without phase inversion, in the context of the two anomalous up-going events reported by ANITA. We find that subsurface layers and firn density inversions may plausibly account for the events, while ice fabric layers and wind ablation crusts could also play a role. This hypothesis can be tested with radar surveying of the Antarctic region in the vicinity of the anomalous ANITA events. Future experiments should not use phase inversion as a sole criterion to discriminate between downgoing and upgoing events, unless the subsurface reflection properties are well understood.

Equations

$$N$$

$$N_{\mathrm{CR}}\simeq A_{\mathrm{eff}}T\times R_{surf.}\times {\alpha }_{\mathrm{CR}},$$

$$N_{anom.}\simeq \delta A_{\mathrm{eff}}T\times (1-R_{surf.}{)}^2{R}_{sub.}\times {\alpha }_{\mathrm{CR}}$$

$$\left(\frac{\delta A_{\mathrm{eff}}}{A_{\mathrm{eff}}}\right)\simeq \frac{R_{surf.}}{(1-R_{surf.}{)}^2{R}_{sub.}}\left(\frac{N_{anom.}}{N_{\mathrm{CR}}}\right),$$

Full text

††preprint: IPMU19-0070

I Introduction

The Antarctic Impulsive Transient Antenna (ANITA) collaboration reports two unusual steeply pointed up-going air showers with energies near the EeV ($10^{18}$ eV) scale Gorham:2016zah ; Gorham:2018ydl . Additionally ANITA has observed $\sim 30$ events from cosmic rays (CRs) Gorham:2016zah ; Gorham:2018ydl ; 2010PhRvL.105o1101H . Most of the CR events appearing to originate from the Earth display a characteristic phase reversal consistent with the interpretation that the signal originated from a downward-going CR-initiated extensive air shower (EAS) reflected by the Antarctic surface. However, the two anomalous upgoing EASs reported by ANITA Gorham:2016zah ; Gorham:2018ydl lack phase inversion, and they appear to be inconsistent with such surface reflections.

Qualitatively, these events look like air showers initiated by an energetic particle that emerges from the ice. It has been proposed that tau neutrinos interacting in the ice could produce a tau lepton that exits upward to the atmosphere and subsequently decays producing an air shower. Since radio signal from such an event undergoes no reflection, it would be consistent with the observed lack the phase inversion. The problem with this hypothesis, however, is that neutrinos with EeV energies are expected to interact inside Earth with a high probability. For the angles inferred from the observed events, the ice would be well screened from upgoing neutrinos by the underlying layers of Earth. While the neutrino interaction cross sections at high energies are uncertain Kusenko:2001gj , the observed events would require neutrino fluxes well in excess of upper limits from Pierre Auger Observatory and IceCube 2018arXiv181107261R . A number of new physics explanations for the anomaly have been proposed Cherry:2018rxj ; Anchordoqui:2018ucj ; Huang:2018als ; Dudas:2018npp ; Connolly:2018ewv ; Fox:2018syq ; Collins:2018jpg ; Chauhan:2018lnq ; Anchordoqui:2018ssd ; Heurtier:2019git ; Hooper:2019ytr ; Cline:2019snp .

In this Letter, we study the possibility that the mysterious events are explained by the radio signals originating from downward-going CR-initiated EAS reflected by some subsurface features in the Antarctic ice which allow for reflections without a phase inversion. Phase inversion occurs when the radio waves traveling in a medium with a low index of refraction (air) reflect from an interface with a medium that has a high index of refraction (ice). However, if the reflection occurs below the surface, for example from an interface of a high-density layer on top and a low-density layer on the bottom, there is no phase inversion. We will identify the properties of the Antarctic ice that are required for the radio signal from an ordinary CR air shower to undergo a reflection without a phase inversion, and we will also identify the features known to exist in Antarctic ice that can be responsible for such reflections capable to explain the ANITA events.

General Features of Subsurface Reflectors. ANITA reports 33 events with phases consistent with the expectations from cosmic ray induced ultra-high energy cosmic ray (UHECR) EAS events Gorham:2016zah ; Gorham:2018ydl ; 2010PhRvL.105o1101H ; Allison:2018cxu . We compute the number of events above detection threshold $E_{{\rm thr}}$ in an observing time, $T$, reflecting from either surface of subsurface features with area coverage, $A_{{\rm eff}}$, as

[TABLE]

where we take the CR flux to be a power-law, $\Phi(E)\simeq\Phi_{0}(E/E_{0})^{-\gamma}$ with $\gamma\simeq 2.7$. This allows us to estimate the total number of ordinary EAS events from the surface reflection (with phase inversion):

[TABLE]

where we define $\alpha_{{\rm CR}}\equiv\frac{\Phi_{0}}{(\gamma-1)E_{0}}~{}\left(\frac{E_{{\rm thr}}}{E_{0}}\right)^{1-\gamma}$, $R_{{\rm surf.}}$ is the surface reflection coefficient, and $A_{{\rm eff}}$ is the effective area surveyed by ANITA in flight time $T$.

Similarly we estimate the anomalous uninverted radio events from subsurface reflection of EAS. The subsurface reflections may occur only for incidence angles small enough, so that the power transmitted into the ice at the air-ice interface is significant. For the firn index of refraction, the power transmitted downward exceeds 80% if the incidence angle is smaller than $70^{\circ}$. We note that the incident angles of the anomalous ANITA events are well below this upper bound and, in fact, these angles are smaller than the average incidence angle of the cosmic ray events 2016APh….77…32S . Therefore one can estimate the rate of anomalous events as

[TABLE]

where $R_{{\rm sub.}}$ is the subsurface reflection coefficient, and $\delta A_{{\rm eff}}$ is the area of the reflecting subsurface. 111A priori, there is no reason to assume that $\delta A_{{\rm eff}}$ is small. In general, $\delta A_{{\rm eff}}$ could exceed $A_{{\rm eff}}$, especially if several layers at different depths are contributing to the subsurface reflections. However, to explain the ANITA events, only a small fraction of ice needs to host the reflecting features. The estimates in Eqs. (2) and (3) imply that the subsurface features should occupy an area

[TABLE]

where in order to account for ANITA’s observations one needs, $N_{{\rm CR}}=33$ and $N_{{\rm anom.}}=2$. We plot the requisite area estimate from Eq. (4) in Fig. 1 as a function of the subsurface index of refraction assuming that the top layer has $n=1.3$.

In summary, a relevant candidate subsurface feature needs to satisfy the following requirements:

In accordance with the estimate in Fig. 1, $\gtrsim 7\%$ of the area should host a reflector at some depth. 2. 2.

There should not be significant attenuation for the EAS radio pulse above the reflecting feature, since this would render the signal undetectable. Roughly, if the detected anomalous event was attenuated by $\lesssim 0.2$, the resulting field amplitude would drop below the trigger threshold 2018arXiv181107261R . Since the attenuation length for radio waves in ice is (1.2–1.5) km (with some temperature dependence 2012E&PSL.359..173M ) for the frequencies probed by ANITA, this requirement is satisfied by any features not obstructed by an overlying layer of liquid water. (The attenuation length in liquid water is much shorter Ray:72 .) 3. 3.

The reflection must occur without a phase inversion. A subsurface interface with a higher index of refraction above and a lower index of refraction below can reflect a signal without a phase inversion. Likewise, multiple layers of variable index of refraction can reflect a signal without a phase shift Tikhonravov:97 . 4. 4.

Given the wavelengths ANITA is sensitive to, the subsurface layer above the reflecting interface needs to be sufficiently thick, although the layer below the interface can be quite small  siegert_2016 . Similarly, the features should be $>$20 m in diameter doi:10.1029/2004JB003222 . Lastly these surfaces likely need to be tilted with respect to the surface, such that double reflections are rare.

Given these requirements, we now proceed to investigate which glaciological candidates may have the correct distribution and reflective properties.

*Subsurface features * that may have the right properties to account for the anomalous ANITA events include several possibilities.

• (a)

Double Layers: Intriguingly, the work of Ref. arcone_spikes_hamilton_2005 finds direct evidence for reflective surfaces without phase inversions. In particular, they find evidence for “thin double layers of ice over hoar” which have reflection without inversion, and conclude that they are “extensive” throughout West Antarctica. They model the observed reflections as high-permittivity ice sitting above low-permittivity hoar. The modeling done indicates that hoar thickness fluctuations is a major driver of the phase of the wavelet. These results were obtained with 400 MHz short pulse radar (ANITA is in the 200-800 MHz range).

• (b)

**Firn Density Inversions **: In Ref. Kuipers ; Kuipers2 , the authors produced an estimate of snow and firn density (in the top 100 m of depth) on Antarctica for the period 1979-2017 at a horizontal resolution of (27 $\times$ 27) ${\rm km}^{2}$ and a temporal resolution of 10-15 days, using a firn model that includes not only compaction, but also firn hydrology including melt, percolation and refreezing. The model in Kuipers ; Kuipers2 has been evaluated at the two locations of the observed ANITA events. Although there are minor variations in density due of dependence of densification on temperature following the annual cycle, these variations are quite small, and are not large enough to explain the ANITA observations. However, there are additional firn features not accounted for in this model.

For example, ice core samples show substantial density and permittivity variations. We show as an example in the left panel of Fig. 2 the density profile from the East Antarctic Plateau  doi:10.1002/2016JF003919 . These density variations are quite substantial and may constitute a plausible candidate for the ANITA events, and they are rather common in the area sampled in Ref. doi:10.1002/2016JF003919 .

It is well-known that the constructive interference effects from scattering on a medium consisting of multiple thin layers can produce a large reflection coefficient at some wavelengths 1977ApOpt..16…89V (see also Pirozhkov_2015 ; doi:10.1063/1.343131 for generalizations). The ice core sample displayed in Fig. 2 has just this structure, consisting of a number of thin layers with small index of refraction differences. Motivated by this, we display two calculations of the reflection coefficients in Fig. 2. In one case (the red curve) we compute reflection from a medium consisting of regularly spaced layers of 10 cm thickness. This results in a sharp resonance feature, as expected 1977ApOpt..16…89V . In contrast, the blue curve assumes layers whose thickness is randomly chosen between 3-15 cm. In both instances the layers alternating refraction indices, chosen between $n_{1}=1.3$ and $n_{2}=1.6$ for a $60^{\circ}$ incidence angle. We have explicitly computed the phase change in reflections from regular and random layers, and found that the phase shifts are close to zero for the range of wavelengths with maximal reflectivity, in agreement with the results of Ref. Tikhonravov:97 for regular layers. We note that reflections from multiple layers will induce a time delay, impacting the measured time profile of the pulse. This makes a multi-layer reflection interpretation of the event reported in Ref. Gorham:2018ydl unlikely, though it may be a candidate explanation for the event in Ref. Gorham:2016zah .

• (c)

Wind/ablation crusts and Sastrugi: These are abundant in megadune regions, and may create low density regions with large grains above higher density snow. Sastrugi are essentially wind eroded snow, which make irregular ridges on the surface. Given that these regions have a variety of slopes as well, they naturally help explain the lack of double-reflections. By some estimates, as much as 11$\%$ of the East Antarctic Ice Sheet is covered by so-called “wind glaze” 2012JGlac..58..633S , forming a surface with a polished appearance with nearly zero accumulation due to persistent winds. This could produce both the needed reflection phase and range of angles. Since these wind crusts are denser than typical snow, they would naturally have larger indices of refraction than typical surface snow.

• (d)

Ice Fabric Layers: Ice sheet fabrics are formed as a result of rheology and stress, leading to macroscopic ice crystal alignment. Some fabrics appear to have the right dielectric properties to produce a reflection without phase inversion even without index of refraction contrasts doi:10.1029/2003JB002425 . In this case it is the contrasts in crystal orientation fabric that source strong reflections doi:10.1029/2003JB002425 . The spatial distribution of ice-sheet fabric is not very well known since ice cores are restricted in number and distribution across Antarctica Siegert . There is some indication that ice fabric layers are more widespread than originally believed Siegert ; siegert_fujita_2001 ; SIEGERT2000227 , which make it plausible that the distribution is widespread enough to produce the observed reflections.

• (e)

Subglacial Lakes: Most lakes appear to be hydrostatically sealed, and therefore lack an air-water interface which would otherwise provide a useful reflecting surface without phase inversion. The bottom of the lake could in principle work, but only rather shallow and low conductivity subglacial lake regions 2015IGRSL..12..443S would be able to produce a reflection without significant attenuation in water. Exploiting the time delay and amplitude attenuation in water, radio echo surveys provided the first direct evidence for that subglacial lakes were at least several meters deep doi:10.1029/1999JB900271 . Recent model estimates suggest that $(0.6\pm 0.2)\%$ of the Antarctic ice/bed interface is covered by subglacial lakes Lakes . Given that subglacial lakes tend to lack a water-air boundary and that they cover $<1\%$ of the Antarctic area, we do not consider these especially promising candidates for ANITA. We note however the possibility that impurities in the accreted ice above a lake could in principle produce a higher index of refraction layer above a lower index layer, though is likely uncommon. We note that the ice above Lake Vostok has been found to contain ice fabric contrasts, which could source strong reflections MACGREGOR2009222 . If the appearance of ice fabrics is common above subglacial lakes, they may be anomalous reflection candidates. However, such lakes could not be too deep since the signal would be too attenuated otherwise.

• (f)

Snow covered crevasses/hollow caves/ice bridges: An ice-to-air boundary would have the correct properties for reflection without phase inversion. However, fumarolic and volcanic ice caves do not seem to be sufficiently common for the ANITA events. Crevasses are common in regions of fast flow, but not are not common in the middle of the ice sheet where the ANITA events are observed.

• (g)

Englacial Layers: At depths beyond the firn (though still $\lesssim 1$ km), dielectric contrasts in the ice may be sufficiently common to explain the events doi:10.1029/2004JB003222 ; doi:10.1029/2005JD006349 . Moreover, in principle density contrasts in deep englacial layers qualitatively similar to what is displayed in Fig. 2 may also source strong reflection coefficients.

Future probes of subsurface reflections can be designed to definitively test the origin of ANITA events and to learn about the properties of Antarctic ice. This can be done (1) using dedicated survey, and/or (2) digging. Though radio surveying is likely more feasible, we leave a dedicated analysis of these possibilities to future work.

If subsurface features are ultimately responsible for the ANITA events, the distribution and extent of such features will be important for ANITA going forward. Moreover, a dedicated effort to determine if the ANITA events originate from a subsurface reflector may be relevant for glaciology by providing additional information such as the extent, spatial distribution, and reflective properties of these features.

To summarize, we have examined the possibility of the anomalous upward-going ANITA events as originating from ordinary CR initiated air showers. For this to be consistent with the phase information ANITA observes, they must reflect from a subsurface feature without phase inversion. We have surveyed a number of glaciological candidates in order to determine which of these have the correct properties to explain ANITA’s observations. We have found that sunsurface double layers and firn density inversions are a plausible explanation of the anomalous events. In order to conclusively test if surface/subsurface glaciological candidates are responsible for the ANITA events, more information is needed on candidate location, fraction of occurrence in the area sampled by ANITA and a more detailed analysis of the ANITA acceptance. We note that, while firn density contrasts appear to be a plausible candidate, one or more of the other glaciological features discussed here may play a sub-dominant role in sourcing strong un-inverted reflections.

Our results have broad implications for future neutrino and cosmic ray experiments. Given the possibility of reflections without a phase inversion, future experiments should not use the phase inversion in radio signals as a sole criterion for discriminating between downgoing and upgoing events, unless the properties of the subsurface reflection are well understood.

Acknowledgements

We are very grateful to Thomas Laepple for providing the B41 ice core data from Ref. doi:10.1002/2016JF003919 . Furthermore, we warmly acknowledge helpful discussions with Kumiko Azuma, Dmitry Chirkin, Francis Halzen, Stefan Ligtenberg, Henning Loewe, and David Saltzberg. The work of I.M.S. is supported by the U.S. Department of Energy under the award number DE-SC0019163. The work of A.K. was supported by the U.S. Department of Energy Grant No. DE-SC0009937, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan. Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. P.K.M. is supported by the Netherlands Earth System Science Centre (NESSC).