1 Introduction

Meteoroid disintegration mechanisms in the upper atmosphere, and by extension, the composition of these extraterrestrial bodies, have always been a subject of much study and debate in the meteor community. The huge amount of mass flux due to these particles, by some estimates as high a few thousands of kilograms per day (Mathews et al. 2001), and thus the threat they pose to our space infrastructure (Caswell et al. 1995; Close et al. 2010) and the effect they have on E-region aeronomy (Rapp et al. 2007; Malhotra et al. 2008), makes it imperative that we understand the composition of these bodies. Of particular interest has been the role of fragmentation as a meteoroid disintegration mechanism.

Though it was hypothesized by the late 1920s that meteors affect radio transmission (Nagaoka 1929), study of meteor echoes using radars really took off only with the development of radar technologies during World War II. Mathews (2004) provides a good historical overview of radar meteor studies. The generation of radar meteor echoes can be explained as follows. As the meteoroid enters the Earth’s atmosphere, it collides with the air molecules and it heats up due to friction. When the meteoroid surface temperature reaches to the order of ~2,000 K, surface particles start evaporating from the body. These particles quickly ionize and also ionize the air molecules around them. This results in a “ball” of plasma being formed around the meteoroid. With a radar of high sensitivity, it is possible to get scattering from this plasma surrounding and travelling along with the meteoroid. This scattering signature is termed as a “head echo”, and has been used to determine meteoroid velocities (Janches et al. 2000), radiants (Chau et al. 2007), mass flux (Mathews et al. 2001) and disintegration mechanisms (Malhotra and Mathews 2011). As the meteoroid descends down the atmosphere, it also leaves behind a trail of ionization in its path. Strong scattering is obtained when the radar beam is pointed perpendicular to this trail of ionization, and the typical signature hereby obtained is known as a “classical” or “specular” trail echo. These echoes can be observed even with a radar of relatively lesser sensitivity (McKinley 1961) and are used for determining meteoroid velocities, diffusion rates and making background wind measurements (Ceplecha et al. 1997).

The formation of an underdense specular radar meteor trail can be explained with the help of Fig. 1. As the thin, relative to wavelength, meteor trail approaches the t0 point—the point at which the trail is perpendicular to the radar pointing direction—the power received by the radar increases and continues to increase as the trail passes the t0 point due to scattering from trail components lying within one Fresnel zone (length of one Fresnel zone is (Roλ/2)1/2 where Ro is the range and λ is the radar wavelength) on either side of the t0 point adding coherently. As the trail expands beyond one Fresnel zone, the phase-path-difference between the trail components begins to increase, resulting in out-of-phase scattering from these components, thereby reducing the net received power. The ensuing constructive and destructive interference leads to the formation of a power signature, characterized by Fresnel oscillations, shown in Fig. 1. The above discussion does not take into account the effect of diffusion on meteor trails, which is shown in Fig. 2. Cases A, B and C in Fig. 2 show the simulated examples of power profile of underdense meteor trails under conditions of no diffusion, moderate diffusion and extreme diffusion respectively. However, as we discuss later in the Sect. 3, less than 5 % of the specular trail echoes observed by us using the MST Gadanki VHF radar exhibit power profiles similar to what is shown in Figs. 2 and 3. This finding has important implications on the velocity, and hence mass measurements that are made using the post-t0 oscillations.

Fig. 1
figure 1

Viewing geometry for a specular trail echo. The radar is pointed perpendicular to the meteor trail, resulting in generation of a typical Fresnel power signature

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Fig. 2
figure 2

Power profile of a simulated meteor trail under conditions of (a) no diffusion—Case A (b) moderate diffusion—Case B (c) extreme diffusion—Case C

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Fig. 3
figure 3

a Power profile of a specular trail echo exhibiting Fresnel oscillations as expected from the classical ablation theory. Phase and unwrapped phase of the event are shown in b and c respectively

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The classical theory of meteor ablation, presented above, assumes the meteoroid to possess a compact stony structure (Herlofson 1948). However, it was observed that the classical theory of meteor ablation could not account for reduced observed trail durations of fainter optical meteors (Hawkins and Southworth 1958). Jacchia (1955) showed that this anomaly could be accounted for by considering fragmentation of meteoroids and stated, “The concept of pellet-like meteors must be replaced with that of a cluster of breaking fragments in the case of most smaller bodies.” Hawkes and Jones (1975) proposed a quantitative model for the ablation of dustball meteors which assumes that “meteoric bodies are composed of grains that are held together by a lower boiling point glue”, and were able to explain the observed light curves of both fainter and brighter meteors by this model, thus further strengthening the case for fragmentation in optical meteor echoes. The nature and importance of fragmentation of meteoroids is now fairly well understood and appreciated in the optical meteors community.

In contrast to this, fragmentation of radar meteor echoes has become a subject of discussion in the radar meteor community only in the past few years with evidence of fragmentation being found in head echo observations carried out using high power large aperture (HPLA) radars (Kero et al. 2008; Mathews et al. 2008; Malhotra and Mathews 2011). Relatively few studies have been conducted on fragmentation and its effects on radar specular trail echoes. Elford and Campbell (2001) reported that the absence of expected Fresnel oscillations in many observations of specular meteor trails could be explained by “assuming a number of ablating fragments spread out along the trails.” They present an example of one specular trail event (Fig. 2 of Elford and Campbell 2001) exhibiting no Fresnel oscillations, and show via modeling efforts how fragmentation could result in a “washing out” of Fresnel oscillations. Badger (2002) reported observing events exhibiting a sudden dramatic increase in the amplitude of the returned signal. They explained this anomaly by attributing the sudden increase in amplitude of returned signal to catastrophic fragmentation, which increases the surface area to mass ratio of the meteoroid, thus resulting in an increase in the ionization production. We discuss their results further in the next section.

We present results from meteor observations carried out using the MST radar located in Gadanki, India. We present case studies of events that do not exhibit the typical Fresnel power profile and attempt to explain the formation and evolution of these trails. It is hypothesized that most such events can be explained with the aid of fragmentation. The study of fragmentation of specular meteor trails is hampered by lack of radar observation results and our work is an effort to make much-needed amends in this area. This study will form the basis for future modeling efforts and studies on statistical analysis of such events. The observational setup for these observations is explained in Sect. 2. The results and their implications are presented in Sect. 3. A summary of our investigations along with the scope for future studies is presented in Sect. 4.

2 Observational Set Up

The results presented herein all derive from meteor observations carried out using the 53 MHz MST radar facility at Gadanki (13.5°N, 79.2°E, dip angle 13.5), India. These observations were carried out from ~0100 to 0700 hours on 9 May 2012. The main radar parameters of our observations are summarized in Table 1.

Table 1 Radar parameters for MST Gadanki radar
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3 Observational Results

Figure 3 is a representative example of a specular trail exhibiting Fresnel oscillations, as expected from the classical ablation theory, similar to those shown and explained in Fig. 1. Figure 3a shows the power received by the radar whereas Figs. 3b, c show the phase and unwrapped phase respectively of the event in Fig. 3a. Less than 5 % of the events observed by us exhibit Fresnel oscillations and show similarity to the event in Fig. 3. Phase unwrapping takes care of the discontinuities in phase that occur when an extreme value in phase is reached, −π to +π, even though the phase is actually physically continuous. This is done by adding or subtracting multiples of 2 π at the point of extremities, thereby eliminating the phase discontinuities.

Figure 4 shows a specular trail event having its t0 point at ~0.5 s. The power plot shown in Fig. 4a exhibits features resembling that of a “normal” trail echo till about ~0.72 s, shown by the dotted line, followed by sudden increase and later, crests and troughs in the power profile. This instance of sudden increase in power (~0.72 s) is also accompanied by a sudden change in the phase of the received signal, as seen in Fig. 4b, and change in the slope of unwrapped phase, as seen in Fig. 4c. These changes in both the wrapped and unwrapped phase are consistent with sudden shifting of the phase-center of the meteor return due to multiple fragments being produced at this instant. The crests and troughs in amplitude after 0.72 s can be explained by repeated constructive and destructive interference between various fragments of the meteoroid.

Fig. 4
figure 4

a Power profile of a specular trail echo showing sudden rise in power at ~0.72 s. This sudden rise in power is accompanied by a sudden change in b phase and c slope of unwrapped phase at the same instant. An arrow is plotted in the unwrapped phase plot to help observe the change in slope of unwrapped phase. These features are consistent with sudden change in phase center of the meteor event due to fragmentation

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Figure 5 is an example of an event exhibiting catastrophic fragmentation or of a short trail (Mathews 2004). Notice the sudden increase in amplitude at ~0.38 s, followed by a drop and then again a sudden increase at ~0.42 s. As mentioned above, Badger (2002) attributed the sudden increase in amplitude of the received signal to catastrophic fragmentation, which increases the surface area to mass ratio of the meteoroid, thus resulting in an increase in the ionization production. But unlike the event presented in Badger (2002) as an example of such an event, the event presented in Fig. 5 consists of two such peaks in amplitude, thereby further underlining the multiple particle hypotheses. The two successive peaks in amplitude can be explained by occurrence of two fragmentation “flares”, one after another (Mathews et al. 2010). Meteor flares are a commonly observed optical phenomenon characterized by sudden increase in meteor brightness and is attributed to sudden gross fragmentation i.e. an explosion leading to terminal disintegration of the meteoroid into many small pieces (Ceplecha et al. 1997).

Fig. 5
figure 5

a Power profile of an event exhibiting sudden increase in power at ~0.38 and ~0.42 s, consistent with sudden increase in ionization due to catastrophic fragmentation. It is accompanied by a change in slope of the (c) unwrapped phase at the very same instant

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In contrast to the sudden gross fragmentation event reported in Fig. 5, Fig. 6 shows an event undergoing a lot less “violent” fragmentation or continuous fragmentation. A specular trail event is seen to occur between ~0.33 and 0.65 s. During this time frame, the event appears to be a normal specular trail echo. However, there is again an increase in amplitude at ~0.65 s followed by an observation of a beat pattern in amplitude till ~2.4 s. Also, notice the change in the slope of the unwrapped phase at ~0.65 s, at the same instant at which there is an increase in the received power. The change in the slope of the unwrapped phase, while it is still coherent, signifies a change in direction/path of the event. The amplitude again drops to almost noise level at ~1.1 s, followed again by an increase in amplitude. A beat pattern in amplitude is again observed thereafter. Again, notice the change in slope of the unwrapped phase at ~1.2, 1.6, 2.1 and 2.3 s.

Fig. 6
figure 6

a Power profile of a meteor event exhibiting a beat pattern after 0.66 s, consistent with a meteoroid undergoing continuous fragmentation. Notice the change in c slope of the unwrapped phase coinciding with the observed beat pattern after 0.66 s

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These observations may be explained as follows. From ~0.3 to 0.66 ms, the particle behaves pretty much like a “normal” specular echo. At the end of its flight, with the received signal power almost reaching that of noise level, the particle disintegrates into multiple fragments. Progressive constructive and destructive interference between these particles results in formation of the beat pattern that can be seen from ~0.66 to 1.1 s. The production of multiple fragments is accompanied by a change in path of the parent meteoroid, as can be observed from the change in slope of the unwrapped phase from ~0.66 s. The same phenomenon can also be observed at 1.65 and 2.1 s. In contrast with the event shown in Fig. 4 which shows sudden catastrophic fragmentation, this event may be interpreted as exhibiting repeated fragmentation at various instants of time.

Unlike the events shown in Figs. 4 and 6, Fig. 7 shows an event exhibiting the beat pattern in amplitude between 0.3 and 0.37 s, consistent with fragmentation, before the t0 point which occurs at 0.38 s. The disruption in unwrapped phase at 0.3 s is also consistent with interference of multiple particles at this point. Unlike the previous examples, this event does not show any signs of fragmentation after the t0 point. The features noticed in this event are similar to the theoretical diffraction pattern shown in Fig. 6d of Greenhow and Neufeld (1957). They attribute this kind of pattern to irregular ionization caused by fragmentation and comment that “this distortion is most noticeable if the irregularity occurs before the center of the first Fresnel zone”. However, they do not show any observational results to back their theoretical sketches.

Fig. 7
figure 7

a A meteor event exhibiting beat pattern, consistent with multiple body interference pattern, between 0.3 and 0.37 s, before the t0 point for this event. Corresponding changes in the direction of the path of the event can be observed in the unwrapped phase of the event, shown in c

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4 Conclusion and Future Work

As discussed in previous section, the significance and importance of fragmentation as a meteoroid disintegration mechanism is now well known and understood in the optical meteor community. Recent head echo observations using HPLA radars has made the role of fragmentation as a meteoroid disintegration mechanism a topic of much discussion and debate in the radar meteor community, with there being contrasting reports of fragmentation being the dominant meteoroid disintegration mechanism for micrometeoroids observed using the Arecibo UHF radar (Mathews et al. 2010) to differential ablation, and not fragmentation, being the dominant disintegration mechanism for micrometeoroids observed using the same radar (Janches et al. 2009). This distinction is important as it accounts for the form (nature of) the meteoroid mass flux is deposited in the Earth’s upper atmosphere i.e. dust form (on account of fragmentation) or metallic form (on account of differential ablation). Malhotra and Mathews (2011) carried out a statistical analysis on meteor head echo observed using Resolute Bay Incoherent Scatter Radar (RISR), and reported that ~48 % of the RISR head echoes observed by them exhibited signs of fragmentation, ~32 % of the events exhibited signs of simple ablation and ~20 % of the events exhibited signs of differential ablation and also provided example of an event exhibiting features of both fragmentation as well as differential ablation, thus further underling the complex nature of disintegration of radar meteor echoes. The implied evidence of fragmentation being the dominant micrometeoroid disintegration mechanism has serious implications on the aeronomy of E-region as well as formation of PMSEs/Noctilucent clouds (Bellan 2008). Meteoroids are responsible for thousands of kilograms of mass flux into the earth’s upper atmosphere annually (Janches and Chau 2005; Mathews et al. 2001) where, among many effects, their ions form ionospheric sporadic-E and intermediate layers (Mathews 1998; Morton et al. 1993; Raizada et al. 2004; Tong et al. 1988).

In contrast to the extensive research being done and the data set available for study of meteoroid disintegration mechanisms via meteor head echo observations, relatively little work has been done on fragmentation of specular trails and our study aims to fill the void in this area. Elford and Campbell (2001) reported that the absence of Fresnel oscillations in many observations of specular meteor trails could be explained by aid of fragmentation. Less than 5 % of the specular trails observed by us using the MST Gadanki radar exhibit Fresnel patterns “typical” of specular trails, as explained in Sect. 1, further supporting the “dustball” model of structure of meteoroids. Elford and Campbell (2001) present an example of one specular trail event (Fig. 2 of Elford and Campbell 2001) exhibiting no Fresnel oscillations. Badger (2002) took this study further by presenting more examples of specular trail echoes exhibiting signs of fragmentation, and some of these events have been discussed in the previous section. Since then, there has been a long gap in the study of fragmentation of specular trails echoes and the work presented herein, quite probably, is the first major study on fragmentation of specular trail echoes since then.

We present examples of specular meteor trails not exhibiting Fresnel oscillations which are consistent with signs of both gross i.e. sudden and continuous fragmentation and also of trails being associated with flare events. The generation of flares and/or fragmentation at the later end of meteoroid’s flight is consistent with the head echo observations from Jicamarca and Arecibo VHF radars (Mathews et al. 2010). Also presented are examples of fragmentation occurring both before the to point (Fig. 7) and after the to point (Figs. 4, 6) in the viewing geometry of the meteor trail. The wide nature and perhaps almost ubiquitous nature of fragmentation in meteor trails (less than 5 % of the specular trails observed by us exhibit the expected Fresnel pattern) also has important consequences on meteoroid velocities derived from these trails (Baggaley and Grant 2005) and the meteoroid mass flux mass calculations carried out subsequently (McKinley 1961). The varied nature of examples of fragmentation presented herein would form the basis of modeling studies of such trails, which shall be the subject of future papers.