Limit on the ultrahigh-energy neutrino flux from lunar observations with the Parkes radio telescope

We report a limit on the ultrahigh-energy neutrino flux based on a nondetection of radio pulses from neutrino-initiated particle cascades in the Moon, in observations with the Parkes radio telescope undertaken as part of the LUNASKA project. Because of the improved sensitivity of these observations, which had an effective duration of 127 hours and a frequency range of 1.2–1.5 GHz, this limit extends to lower neutrino energies than those from previous lunar radio experiments, with a detection threshold below ${10}^{20}\mathrm{eV}$. The calculation of our limit allows for the possibility of lunar-origin pulses being misidentified as local radio interference, and includes the effect of small-scale lunar surface roughness. The targeting strategy of the observations also allows us to place a directional limit on the neutrino flux from the nearby radio galaxy Centaurus A.

Figure 1

Typical pointings (solid shading) of telescope beams relative to the Moon in our observations, with approximate system temperatures $T_{\text{sys}}$ for each beam. The limb beams are more sensitive than the half-limb beam; the off-Moon beam is even more sensitive, but useful only for identifying RFI. Crosses in each beam indicate the orientation of the orthogonal linear polarizations. The receiver orientation was maintained such that Centaurus A was always in the direction shown. For some of the observing time, the half-limb beam was replaced with an additional off-Moon beam (striped).

Figure 2

Simulation of the offset aperture ratio $A_{\mathrm{R}}(N_{\mathrm{S}}E)/A_{\mathrm{S}}(E)$ in order to determine the parameter $r$, which quantifies the effects of small-scale surface roughness as described in the text [see Eq. (1)]. Points have been slightly offset in energy for clarity. The error bars reflect the statistical uncertainty in the simulation data (inner bars) and with the additional uncertainty from taking $N_{\mathrm{S}}=12\pm 1$ (outer bars). The value $r=0.56$ is a fit to the range $E>{10}^{21}\mathrm{eV}$, for which small-scale surface roughness effects are significant.

Figure 3

Geometric neutrino aperture of this experiment before inclusion of anticoincidence rejection of detected events, after allowing for this effect, and after also including the effects of small-scale lunar surface roughness (see Sec. 4a). Apertures are also shown for other recent lunar radio experiments: a previous LUNASKA experiment with the ATCA [25], NuMoon [32], and RESUN [34]. See text for a discussion of the various models on which these apertures are based.

Figure 4

Model-independent limits to the diffuse neutrino flux from our experiment (solid curve), including the effects of anticoincidence rejection, and (dotted curves) for other experiments shown in Fig. 3, as well as for selected nonlunar neutrino detection experiments, assuming an equal ratio of neutrino flavors: ANITA-2 [37], RICE [38], IceCube [39], FORTE [14] and the Pierre Auger Observatory, combining the exposure to both upgoing [40] and downgoing [41] neutrinos. A range of models is shown for the expected neutrino flux from GZK interactions given by Allard et al. [42] (shaded area), and for top-down UHECR origin models from Lunardini and Sabancilar [18] (dash-dotted curves) and Berezinsky et al. [17] (dot-dash-dotted curves).

Figure 5

Model-independent limits to the diffuse neutrino flux from our experiment (solid curve) and others (dotted curves) compared to models for the expected neutrino flux, as in Fig. 4, but with the limits for lunar radio experiments incorporating the effects of small-scale lunar surface roughness as described in Sec. 4a. The limit for LUNASKA ATCA is as reported [25], and the limit for RESUN is derived from the reported limit [34], which did not include small-scale surface roughness effects, by applying Eq. (2), adopting $N_{\mathrm{S}}=13$ and $r=0.70$ as done by James et al. [25] for LUNASKA ATCA due to the similar detection scheme and radio frequency of these two experiments. For NuMoon, $N_{\mathrm{S}}\sim 1$, and so we make no correction for small-scale surface roughness, displaying the originally reported limit [32].

Figure 6

Directional aperture around the Moon for ${10}^{21}\mathrm{eV}$ neutrinos, for a single limb beam (left) and for three beams as shown in Fig. 1 (right); beams are adjacent to the Moon in the directions indicated by the arrows. The effects of anticoincidence rejection are included, but the effects of scattering due to small-scale lunar surface roughness are not; the roughness on the scale of the radio wavelength has a root-mean-square value of $\sim 9°$ [44], and so the scattering may smooth the directional aperture up to roughly this scale. The closest approach of Centaurus A is 28° from the Moon in the direction shown. Note that the maximum directional aperture is in the overlap between the regions from which a UHE neutrino could be detected by either of the limb beams. The exposure to Centaurus A could have been slightly increased if the limb beams were oriented to place it in the overlap region.

Figure 7

Directional exposure of our experiment, in equatorial coordinates, for ${10}^{21}\mathrm{eV}$ neutrinos. The effects of anticoincidence rejection are included, but the effects of scattering due to small-scale lunar surface roughness are not. Observations were conducted while the Moon was on the section of its orbit marked with the thickened line, to maximize the exposure to Centaurus A. The ANITA experiment has substantially greater sensitivity than our experiment at this energy, but only in the declination range from $-10°$ to $+15°$, as shown.

Figure 8

Model-independent limits to the neutrino flux from Centaurus A from our experiment (solid curves), including the effects of anticoincidence rejection, and (dotted curves) for other experiments from Fig. 4 that have significant sensitivity in this direction, including the LUNASKA ATCA lunar radio experiment [31]. The limits for lunar radio experiments are shown both with (labeled) and without the effects of small-scale lunar surface roughness (see Sec. 4a). The limits for IceCube [48] and the Pierre Auger Observatory [40, 41] are derived from the reported model-dependent limits for Centaurus A, with the energy dependence obtained for the former from the aperture for the appropriate declination range, and for the latter from the exposure to a diffuse flux. For RICE [38] the model-independent diffuse flux limit has been scaled based on the directional dependence of the sensitivity provided by Besson [49], as in James et al. [31] but updated for the increased exposure. Models for the neutrino flux from Centaurus A are shown (dash-dotted curves) based on Cuoco and Hannestad [50] and Kachelrieß et al. [51]; see text for details.