Neutrino Echoes from Multimessenger Transient Sources

TL;DR

This paper proposes using time delay signatures in neutrino signals caused by secret interactions with cosmic backgrounds as a new way to test physics beyond the Standard Model, leveraging future multimessenger observations.

Contribution

It introduces a novel method of probing neutrino interactions beyond the Standard Model through neutrino echoes in multimessenger astrophysics.

Findings

Neutrino echoes can serve as probes of BSM neutrino interactions.

Future experiments like IceCube-Gen2 can detect these signatures.

Constraints from this method complement existing laboratory tests.

Abstract

The detection of the high-energy neutrino event, IceCube-170922A, demonstrated that multimessenger particle astrophysics triggered by neutrino alerts is feasible. We consider time delay signatures caused by secret neutrino interactions with the cosmic neutrino background and dark matter and suggest that these can be used as a novel probe of neutrino interactions beyond the Standard Model (BSM). The tests with BSM-induced neutrino echoes are distinct from existing constraints from the spectral modification and will be enabled by multimessenger observations of bright neutrino transients with future experiments such as IceCube-Gen2, KM3Net, and Hyper-Kamiokande. The constraints are complementary to those from accelerator and laboratory experiments and powerful for testing various particle models that explain tensions prevailing in the cosmological data.

Tables

Table 1. Table 1: List of extragalactic high-energy neutrino sources, where ℰ ~ cr iso superscript subscript ~ ℰ cr iso \tilde{\mathcal{E}}_{\rm cr}^{\rm iso} is the cosmic-ray energy per logarithmic energy, D 𝒩 ν = 1 maxeff superscript subscript 𝐷 subscript 𝒩 𝜈 1 maxeff D_{{\mathcal{N}}_{\nu}=1}^{\rm maxeff} is the critical distance at which the number of neutrinos detected in IceCube-Gen2  Aartsen et al. ( 2014 ) is unity (with the assumption of the maximum neutrino production efficiency), p ​ p / p ​ γ 𝑝 𝑝 𝑝 𝛾 pp/p\gamma is the typical neutrino production channel, Δ ​ T em Δ subscript 𝑇 em {\Delta T}_{\rm em} is the duration of multimessenger emission, and ρ 0 em superscript subscript 𝜌 0 em \rho_{0}^{\rm em} is the local rate density. All values remain as order of magnitude estimates.

Name	${\widetilde{ℰ}}_{\mathrm{cr}}^{\mathrm{iso}}$	$D_{{𝒩}_{\nu }=1}^{\mathrm{maxeff}}$	$pp/p\gamma$	$\Delta T_{\mathrm{em}}$	${\rho }_0^{\mathrm{em}}$
	[erg]	[Mpc]		[s]	[${\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$]
LGRB111Long $\gamma$-ray bursts. See Refs. Waxman and Bahcall (1997); Murase and Nagataki (2006); Murase (2008b); Wang and Dai (2009); Li (2012); He et al. (2012); Hummer et al. (2012).	${10}^{52.5}$	$3000$	$p\gamma$	${10}^{1-2}$	$0.1-1$
SGRB222Short $\gamma$-ray bursts. See Refs. Kimura et al. (2017, 2018); Biehl et al. (2018).	${10}^{50.5}$	$300$	$p\gamma$	$0.1-1$	$10-100$
SN (choked jet)333Supernovae powered by choked jets. See Refs. Mészáros and Waxman (2001); Razzaque et al. (2004); Ando and Beacom (2005); Murase and Ioka (2013).	${10}^{50.5}$	$300$	$p\gamma$	${10}^{1-4}$	${10}^2-{10}^3$
SN (pulsar)444Supernovae powered by pulsar winds. See Refs. Murase et al. (2009a); Fang et al. (2016, 2019).	${10}^{50}$	$200$	$pp$	${10}^{3-6}$	${10}^{3.5}-{10}^{4.5}$
SN (IIn)555Type IIn supernovae powered by shocks. See Refs. Murase et al. (2011); Katz et al. (2011); Petropoulou et al. (2017); Murase et al. (2019).	${10}^{49}$	$50$	$pp$	${10}^{6-7}$	${10}^4$
Jetted TDE666Jetted tidal disruption events. See Refs. Murase (2008a); Wang et al. (2011); Dai and Fang (2017); Senno et al. (2017); Lunardini and Winter (2017).	${10}^{53}$	$5000$	$p\gamma$	${10}^{6-7}$	$0.01-0.1$
Blazar flare777See Refs. Atoyan and Dermer (2001); Halzen and Hooper (2005); Dermer et al. (2012, 2014); Petropoulou et al. (2016); Halzen and Kheirandish (2016); Gao et al. (2017).	${10}^{54}$	$15000$	$p\gamma$	${10}^{5-7}$	$0.1-1$

Equations

$$\sqrt{⟨{\theta }^2⟩}\approx C\frac{\sqrt{s}}{E_{\nu }}\simeq 4.5\times {10}^{-8}C{\left(\frac{m_{\nu }}{0.1\mathrm{eV}}\right)}^{\frac{1}{2}}{\left(\frac{0.1\mathrm{PeV}}{E_{\nu }}\right)}^{\frac{1}{2}},$$

$$⟨(1-\cos \theta )⟩=\frac{1}{\sigma }\int d\Omega (1-\cos \theta )\left(\frac{d\sigma }{d\Omega }\right).$$

$${\tau }_{\nu }=n_{\nu }{\sigma }_{\nu }D\gtrsim 1.$$

$$\Delta t\approx \frac{1}{4}⟨{\phi }^2⟩D$$

$${\sigma }_{\nu }\lesssim \frac{12\Delta T}{D^2{n}_{\nu }⟨{\theta }^2⟩}.$$

$$\Delta t\approx \frac{1}{2}\frac{⟨{\theta }^2⟩}{4}D\simeq 77\mathrm{s}\left(\frac{D}{3\mathrm{Gpc}}\right)C^2\left(\frac{m_{\nu }}{0.1\mathrm{eV}}\right)\left(\frac{0.1\mathrm{PeV}}{E_{\nu }}\right).$$

$${\sigma }_{\nu }\lesssim \frac{2.3}{{\mathcal{N}}_{\nu }{n}_{\nu }D},$$

Full text

The new era of multimessenger astroparticle physics has started thanks to the recent detection of high-energy cosmic neutrinos Aartsen et al. (2013a, b) and gravitational waves Abbott et al. (2016, 2017). The detection of the high-energy neutrino event, IceCube-170922A Aartsen et al. (2018), gave further motivation for “time domain” particle astrophysics. Although the significance of the association with the flaring blazar TXS 0506+056 is only $\sim 3\sigma$, this flaring blazar was observed at various wavelengths Aartsen et al. (2018), including x-rays Keivani et al. (2018) and GeV-TeV $\gamma$ rays Ansoldi et al. (2018), which demonstrated the capability of multimessenger observations initiated by high-energy neutrino observations.

Neutrinos have important clues to particle physics Beyond the Standard Model (BSM), as well as the asymmetry between matter and antimatter. Since the discovery of high-energy cosmic neutrinos in IceCube, not only the properties of neutrinos but also different kinds of BSM physics, including dark matter (DM) and nonstandard interactions, have been discussed (see, e.g., Ahlers et al. (2018); Ackermann et al. (2019a)). In the Standard Model (with a minimal extension for finite neutrino masses), the time delay due to the finite neutrino mass ($m_{\nu}$) is estimated to be $\Delta t\approx m_{\nu}^{2}D/(2E_{\nu}^{2})\simeq 1.5\times{10}^{-13}~{}{\rm s}~{}{(m_{\nu}/0.1~{}\rm eV)}^{2}{(0.1~{}{\rm PeV}/E_{\nu})}^{2}{(D/3~{}{\rm Gpc})}$, which is much shorter than durations of known astrophysical transients. Possible time delay between neutrinos and $\gamma$ rays have been discussed to place constraints on the weak equivalence principle (WEP) and Lorentz invariance violation (LIV) Wang et al. (2016); Ellis et al. (2019); Boran et al. (2019); Laha (2019); Wei et al. (2019). A time delay of a few days was also reported for IceCube-160731 coincident with a possible $\gamma$-ray counterpart, AGL J1418+0008 Lucarelli et al. (2017).

Not only blazar flares but also various transients, such as long and short $\gamma$-ray bursts (GRBs) Paczynski and Xu (1994); Waxman and Bahcall (1997), supernovae (SNe) Murase et al. (2011); Murase (2018), transrelativistic SNe Murase et al. (2006); Gupta and Zhang (2007), and tidal disruption events (TDEs) Murase (2008a); Wang et al. (2011), are promising high-energy neutrino emitters. It is natural that electrons and ions are coaccelerated in these sources, and the temporal and spatial coincidence between neutrinos and $\gamma$ rays is expected. Relevant characteristics of various extragalactic transient sources considered in the literature are summarized in Table 1 (see also Refs. Guépin and Kotera (2017); Murase and Bartos (2019)).

We explore delayed neutrino signatures induced by BSM interactions (see Fig. 1) and suggest that they serve as new probes of secluded interactions with neutrinos themselves and DM particles. Probing the parameter space of new interactions is generally important because they cannot be easily probed by terrestrial experiments (e.g., Scholberg (2006); Denton et al. (2018); Farzan and Shoemaker (2016); Ballett et al. (2019)). While our proposed method is applicable to different BSM interactions, we focus on two highly motivated examples that are of broad interest in cosmology and particle physics. It has been shown that models with a light mediator (1) can address all small-scale structure problems van den Aarssen et al. (2012); Cherry et al. (2014); Loeb and Weiner (2011); Tulin et al. (2013); Kaplinghat et al. (2016); Tulin and Yu (2018), (2) can alleviate Hubble parameter tension Riess et al. (2019); Cyr-Racine and Sigurdson (2014); Escudero (2019); Escudero et al. (2019); Kreisch et al. (2019); Barenboim et al. (2019); Park et al. (2019); Forastieri et al. (2019); Blinov et al. (2019), and (3) may account for the muon anomalous magnetic moment Pospelov (2009); Altmannshofer et al. (2014); Araki et al. (2015, 2016); Altmannshofer et al. (2016); Kamada et al. (2018) and (4) neutrino mass Chikashige et al. (1981); Gelmini and Roncadelli (1981); Blum et al. (2014). Detections of multiple neutrinos from a transient are feasible with next-generation detectors Ackermann et al. (2019b). BSM tests with neutrino echoes are promising in the upcoming era of time domain multimessenger astrophysics.

**Example 1: Neutrino self-interactions. — ** It has been discussed that BSM-induced neutrino self-interactions may occur Bialynicka-Birula (1964); Bardin et al. (1970), and models can generate finite neutrino masses Chikashige et al. (1981); Gelmini and Roncadelli (1981); Blum et al. (2014). We consider such nonstandard, secret neutrino interactions that may lead to effective Lagrangians, e.g., ${\mathcal{L}}\supset g_{ij}\bar{\nu}_{i}\nu_{j}\phi$ (for scalars), ${\mathcal{L}}\supset g_{ij}\bar{\nu}_{i}(i\gamma^{5}\phi)\nu_{j}$ (for pseudoscalars), and ${\mathcal{L}}\supset g_{ij}\bar{\nu}_{i}(\gamma^{\mu}V_{\mu})\nu_{j}$ (for vector bosons), where $g_{ij}$ is the coupling parameter. Note that, although we do not specify whether neutrinos are Dirac or Majorana types, the allowed interactions for scalars and pseudoscalars are, e.g., ${\mathcal{L}}\supset g\nu_{L}\nu_{L}\phi+{\rm c.c.}$ and ${\mathcal{L}}\supset gN_{R}N_{R}\phi+{\rm c.c.}$, where $\nu_{L}$ is the left-handed neutrino and $N_{R}$ is the right-handed neutrino. Remarkably, it has been shown that a $1-100$ MeV scale mediator also enables us to resolve various cosmological issues such as the tension in the Hubble parameter Escudero et al. (2019); Kreisch et al. (2019); Barenboim et al. (2019) and the missing satellite and core-cusp problems van den Aarssen et al. (2012); Cherry et al. (2014). With the mediator mass $m_{\phi}$, the resonance interaction with the cosmic neutrino background (C$\nu$B) happens at $E_{\nu}=m_{\phi}^{2}/(2m_{\nu})\simeq 1.25\times{10}^{14}~{}{\rm eV}~{}{(m_{\phi}/5~{}{\rm MeV})}^{2}{(m_{\nu}/0.1~{}{\rm eV})}^{-1}$, corresponding to the IceCube energy range Ioka and Murase (2014); Ng and Beacom (2014); Ibe and Kaneta (2014); Araki et al. (2015); Blum et al. (2014); Cherry et al. (2014); DiFranzo and Hooper (2015); Araki et al. (2016); Shoemaker and Murase (2016); Kelly and Machado (2018); Barenboim et al. (2019).

Let us consider the neutrino-(anti)neutrino scattering process via $s$ channel, $\nu\nu\rightarrow\phi\rightarrow\nu\nu$. In this case, the angular distribution of the scattered neutrinos is isotopic in the center-of-momentum frame. (In general, details depend on the mediator spin as well as the main scattering channel.) In the C$\nu$B frame, because of the boost $\sim E_{\nu}/\sqrt{s}\sim\sqrt{E_{\nu}/m_{\nu}}$, we may write

[TABLE]

where $\theta$ is the scattering angle and $C\sim 1$ for a scalar or pseudoscalar mediator in the neutrino-neutrino scattering. More generally, for the differential cross section ($d\sigma/d\Omega$), the average scattering angle is evaluated via

[TABLE]

For example, $E_{\nu}=0.1$ PeV and $m_{\nu}=0.1$ eV leads to $\langle\theta\rangle\approx 2.8\times{10}^{-8}$ for a leading neutrino. Resulting angular spreading may be too small to be seen as a “halo” around the source, but can be big enough to make a sizable time delay signal (“neutrino echo”). The geometrical setup is analogous to $\gamma$-ray “pair echoes” proposed as a probe of intergalactic magnetic fields Plaga (1995); Ichiki et al. (2008); Murase et al. (2008); Takahashi et al. (2008); Murase et al. (2009b); Murase (2009), although underlying interaction processes are completely different. Neutrinos scattering during propagation was discussed for SN 1987A Kolb and Turner (1987); Lindner et al. (2002), but detailed methodology to utilize the time delay has not been studied.

Large optical depth (conservative) limit: So far, the expected number of high-energy neutrinos is limited. However, even if statistics are not large, e.g., ${\mathcal{N}}_{\nu}\sim{\rm a~{}few}$, the sizable effect of BSM interactions exists if the optical depth to the neutrino scattering is larger than unity,

[TABLE]

The probability for neutrinos to experience the neutrino scattering is given by $1-\exp(-\tau_{\nu})$. In the large $\tau_{\nu}$ limit, most of the neutrinos are scattered, and the spectral and flux information can be used to probe BSM neutrino interactions Shoemaker and Murase (2016); Argüelles et al. (2017); Kelly and Machado (2018). Large statistics would also be required, and the current constraints are much weaker than the ideal bound placed by $n_{\nu}\sigma_{\nu}H_{0}<1$ (where $H_{0}$ is the Hubble constant). Although the diffuse neutrino limits can be relevant, Ref. Shoemaker and Murase (2016) showed that such an ideal limit [e.g., $g\lesssim 3\times{10}^{-4}~{}(m_{\phi}/10~{}{\rm MeV})$ in the scalar mediator case] can be achieved for $m_{\phi}\sim 20-30$ MeV with ten years of observations by IceCube-Gen2. As we see below, the time delay argument can provide us with a meaningful limit even with limited statistics, without relying much on the spectral information.

In the multiple scattering case, neutrino cascades Ioka and Murase (2014); Ng and Beacom (2014) occur and the arrival angle averaged over scatterings is given by $\langle\varphi^{2}\rangle\approx(\tau_{\nu}/3)\langle\theta^{2}\rangle\propto n_{\nu}\sigma_{\nu}DE_{\nu}^{-1}$. The corresponding characteristic time delay is

[TABLE]

If the neutrinos arrive within a time window of $\Delta T$ that may be the duration of intrinsic multimessenger emission (${\Delta T}_{\rm em}$), possible constraints can be placed by $\Delta t<\Delta T$, which leads to

[TABLE]

This is valid only if $D\langle\theta^{2}\rangle\lesssim 8\Delta T$, otherwise the time delay itself does not give a direct constraint on the cross section because of $\tau_{\nu}\lesssim 1.5$. In the neutrino-neutrino scattering case, this implies $\Delta T\gtrsim 30~{}{\rm s}~{}C^{2}(D/1~{}{\rm Gpc})(m_{\nu}/0.1~{}{\rm eV}){(E_{\nu}/0.1~{}{\rm PeV})}^{-1}$. The detection of neutrinos with $E_{\nu}$ implies that some neutrinos arrive without significant energy losses, for which Eq. (5) is applied 888The flux of survived neutrinos that do not lose significant energies by multiple scatterings is suppressed for $\tau_{\nu}\gtrsim{\mathcal{M}}$. . If one requires the bulk of neutrinos with $E_{\nu}$ survives after $\mathcal{M}$ scatterings, an additional constraint, $\tau_{\nu}\lesssim{\mathcal{M}}$, may be imposed, but the actual limits depend on the unknown primary fluence and spectrum. Eq. (5) typically leads to conservative limits. Note that for $\tau_{\nu}\gg 1$ most neutrinos are cascaded down and appear at sufficiently lower energies. If the optical depth for the cascaded component is less than unity, the bulk of the delayed flux is roughly estimated by $F_{E_{\nu}}^{\rm cas}(t)\sim\int d\tilde{\theta}\,4{[2\pi\langle{\tilde{\varphi}}^{2}(t,\tilde{\theta})\rangle]}^{-1/2}{[{\tilde{\theta}}^{2}+\langle{\tilde{\varphi}}^{2}(t,\tilde{\theta})\rangle]}^{-1}e^{-{\tilde{\theta}}^{2}/[2\langle{\tilde{\varphi}}^{2}(t,\tilde{\theta})\rangle]}$

$F_{E_{\nu}}^{\rm cas0}$, where $F_{E_{\nu}}^{\rm cas0}$ is the flux of cascaded neutrinos in the absence of angular spreading Ichiki et al. (2008). The characteristic time delay of this cascaded component is estimated to be $\Delta t_{\rm cas}\sim(1/12)\langle\theta^{2}\rangle{\mathcal{M}}/(n_{\nu}\sigma_{\nu})$ (cf. Eq. 4). The full radiative transfer calculation is necessary to consistently describe the echo flux for arbitrary $E_{\nu}$ and $\tau_{\nu}$.

Small optical depth (stronger) limit.— The constraints discussed above make sense when the coupling is so large that multiple scattering events occur. However, this may not be possible for several reasons. First, the coupling or the scattering cross section may be bounded by other existing constraints, so that $\sigma_{\nu}$ cannot be large enough. Second, the condition $D\langle\theta^{2}\rangle\lesssim 8\Delta T$ is not satisfied. For example, $\tau_{\nu}\gtrsim 1-2$ is prohibited if the observed time window $\Delta T$ is too short. On the other hand, bright neutrino transients such as choked GRB jets and blazar flares could be detected with a large number of signals (i.e., ${\mathcal{N}}_{\nu}\gg 1$) by future neutrino telescopes such as IceCube-Gen2 and KM3Net, in which we may still obtain useful constraints that can actually be better than those from Eq. (5) and even exceed the mean free path limit Shoemaker and Murase (2016); Kelly and Machado (2018).

In the small $\tau_{\nu}$ limit, most of neutrinos ($\sim{\mathcal{N}}_{\nu}$) are expected to arrive together with photons within $\Delta T={\Delta T}_{\rm em}$. However, in the presence of the BSM neutrino scattering, some neutrinos ($\sim\tau_{\nu}{\mathcal{N}}_{\nu}$) experience the scattering once during the propagation, and the characteristic time delay is given by:

[TABLE]

This expression does not include $\sigma_{\nu}$, and with Eq. (4) the time delay is estimated by $\Delta t\approx{\rm max}[\langle\varphi^{2}\rangle D/4,\langle\theta^{2}\rangle D/8]$. The probability distribution of delayed neutrinos in the small $\tau_{\nu}$ limit is expressed as $P(t,\varphi;D)\approx 1/[t+(D\varphi^{2}/2)](1/\sigma_{\nu})(d\sigma_{\nu}/d\theta)|_{\theta=\varphi+2t/(D\varphi)}$ Alcock and Hatchett (1978). We remark that only one scattering matters and the time delay distribution reflects the differential cross section of the neutrino-neutrino scattering that is generally inelastic.

Given ${\mathcal{N}}_{\nu}\gg 1$, stronger limits can be placed for $\Delta T\lesssim\langle\theta^{2}\rangle D/8$ (implying $\tau_{\nu}\lesssim 1.5$), in which nondetection of time delayed events itself may be used. In the limit that the atmospheric background is negligible, the sizable effect is observable when the number of delayed signals is larger than unity, i.e., $\tau_{\nu}\gtrsim 1/{\mathcal{N}}_{\nu}$. If the background is not negligible, one would need $\tau_{\nu}\gtrsim\sqrt{{\mathcal{N}}_{\nu}^{\rm bkg}}/{\mathcal{N}}_{\nu}$, where ${\mathcal{N}}_{\nu}^{\rm bkg}$ is the number of background events for a given time window. In the background-free regime (that is valid for short duration transients), nondetection of echoes gives:

[TABLE]

where the Poisson probability to observe nonzero time delayed events is set to $<0.9$. One should keep in mind that the neutrino scattering cross section is energy dependent and $D\langle\theta^{2}\rangle\gtrsim 8\Delta T$ should be satisfied. Note that Eq. (5) is applied in the opposite limit.

We show results for a scalar mediator in Fig. 2. Here contributions from $t$ and $u$ channels are also included Ioka and Murase (2014); Blum et al. (2014). In the resonant region ($s\sim m_{\phi}^{2}$), we average the effective cross section by assuming an energy resolution of $\Delta\log(E_{\nu})=0.6$ (which is reasonable for high-energy track events Ackermann et al. (2019b)). At $E_{\nu}=0.1$ PeV, the two cases of $\Delta T=3$ d and $\Delta T=30$ s correspond to the large and small optical depth limits, respectively. We also show another case of $\Delta T=30$ s for $E_{\nu}=1$ PeV, in which the multiple scattering limit is applied.

Other constraints include one from kaon decay, which gives $g\lesssim 0.01$ Blum et al. (2014); Lessa and Peres (2007); Laha et al. (2014). Note that our echo method is especially relevant if only tau neutrinos have BSM interactions. Big Bang Nucleosynthesis (BBN) gives a constraint of $m_{\phi}\gtrsim{\rm a~{}few}$ MeV, although details depend on uncertainty in the extra number of relativistic species (e.g., van den Aarssen et al. (2012); Ahlgren et al. (2013); Blinov et al. (2019)). Astrophysical and laboratory limits are complementary. For example, if neutrinos interact with the C$\nu$B  through sterile neutrinos, the limits can be relaxed, depending on mixing angles Cherry et al. (2014); Shoemaker and Murase (2016).

**Example 2: Neutrino-DM interactions. — ** As a further application of the idea of BSM-induced neutrino echoes, we discuss neutrinophilic DM models in which DM and neutrinos share a new interaction. Very intriguingly, such models give a possible solution to cosmological issues van den Aarssen et al. (2012); Cherry et al. (2014); Tulin and Yu (2018); Escudero (2019); Escudero et al. (2019); Park et al. (2019) and can explain the muon anomalous magnetic moment Araki et al. (2015, 2016); Kamada et al. (2018). For illustration, we consider a simple extension of the vector model mentioned above in which the new gauge boson also couples to a Dirac fermion DM, $\mathcal{L}\supset g_{\nu}V_{\mu}\bar{\nu}\gamma^{\mu}\nu+g_{X}V_{\mu}\bar{X}\gamma^{\mu}X$, where $X$ denotes the DM with a mass $m_{X}$. New gauge bosons appear in many BSM scenarios Langacker (2009), and additional broken U(1) gauge symmetries leading to vector bosons were predicted by grand unification theories London and Rosner (1986); Hewett and Rizzo (1989). While the neutrinos and DM may have different charge assignments, here we take them to be equal and assume $g_{\nu}=g_{X}=g$.

The above model is accompanied by neutrino-DM scatterings, and the resulting constraints are shown in Fig. 3. As in the previous case, if a bright neutrino transient with short duration is observed, we may place strong constraints even in the small optical depth limit, which can be more stringent than previous ones de Salas et al. (2016); Reynoso and Sampayo (2016); Argüelles et al. (2017); Kelly and Machado (2018); Pandey et al. (2019); Choi et al. (2019). Here the coupling should be regarded as an effective parameter. The real coupling to the Standard Model can be made neutrinophilic via coupling the gauge boson to heavy sterile neutrinos. However, their effect is still felt as they effectively endow the active neutrinos with a mixing suppressed coupling to the new mediator. Such models have been explored in Refs. Pospelov (2011); Bertoni et al. (2015); Batell et al. (2018).

For the $t$ channel, we find that the multiple scattering limit may not be applicable to most transients due to large values of $\langle\theta^{2}\rangle$ for relatively heavy DM. The cases for $\Delta T=30$ s are shown in Fig. 3, where the constraint is given for the small optical depth limit (but with the replacement of $n_{\nu}$ with $n_{X}$). As we see, the limits are more stringent for lower-mass mediators. The resulting constraint is comparable to that expected from detailed analyses with spatial and spectral information Argüelles et al. (2017).

We note that the time delay from neutrino-DM scatterings receives contributions from both the Milky Way DM halo and extragalactic DM components. As known for decaying DM signals, the DM located in the line of sight is almost comparable because of $R_{\rm MW}\varrho_{X}^{\rm local}\sim H_{0}^{-1}\varrho_{X}\gtrsim D\varrho_{X}$, where $R_{\rm MW}\sim 10$ kpc is the typical size of the Milky Way. For the Galactic contribution, the condition $\Delta T\gtrsim R_{\rm MW}\langle\theta^{2}\rangle/8$ is more easily satisfied, which may lead to $\sigma_{\nu X}\lesssim 5.4\times{10}^{-24}~{}{\rm cm}^{2}~{}{(\Delta T/1~{}{\rm d})}{(R_{\rm MW}/10~{}\rm kpc)}^{-2}C^{-2}~{}{(E_{\nu}/0.1~{}{\rm PeV})}$. Here $C$ depends on $\sim m_{V}/\sqrt{s}$ for the $t$ channel. For models that lead to sufficiently small scattering angles, the time delay in the large optical depth limit becomes independent of the DM mass, implying $\sigma_{\nu X}\lesssim 10^{-28}~{}{\rm cm}^{2}~{}{(\Delta T/1~{}{\rm d})}{(D/1~{}\rm Gpc)}^{-2}C^{-2}~{}{(E_{\nu}/0.1~{}{\rm PeV})}$. Although such limits would be weaker than the cosmology limits, $\sigma_{\nu X}\lesssim 10^{-33}~{}{\rm cm}^{2}$ Wilkinson et al. (2014), it takes place at much higher center-of-momentum energies.

Finally, we comment on other constraints that can be relevant. If neutrino-DM scatterings are efficient in the early Universe it can inject energy and potentially “heat” the cold DM such that Lyman-$\alpha$ bounds on the small-scale structure are violated Boehm et al. (2001); Hooper et al. (2007); van den Aarssen et al. (2012); Wilkinson et al. (2014). This effect can be used to explain small-scale structure problems of cold DM van den Aarssen et al. (2012), and the region favored by this argument is shown in Fig. 3. Couplings above these regions are excluded. Additionally, note that neutrinophilic DM should not thermalize for DM masses at the MeV scale Boehm et al. (2013), although a narrow window of thermal neutrinophilic DM exists below a MeV Berlin and Blinov (2018, 2019). Finally, in models with direct couplings to active neutrinos laboratory constraints from $Z$ and meson decays can be strong Lessa and Peres (2007); Laha et al. (2014); Araki et al. (2016).

Summary and discussion.— We proposed detailed time delay signatures as a novel probe of BSM neutrino interactions. Notably, BSM-induced neutrino echoes generally predict $\Delta t\propto E_{\nu}^{-1}C^{2}$. This is distinct from predictions of other BSM signatures such as LIV and WEP violation (see a review Ahlers et al. (2018)). For example, LIV shifts the light velocity by ${(E_{\nu}/\zeta_{n}M_{\rm pl})}^{n}$ (where $M_{\rm pl}$ is the Planck mass), leading to $\Delta t=D(E_{\nu}/\zeta_{n}M_{\rm pl})^{n}$ (e.g., Jacob and Piran (2007); Murase (2009)). For neutrino-neutrino scatterings, cosmological time delays are dominant. On the other hand, the Milky Way DM contributes to neutrino-DM scatterings. This implies that DM in the host galaxy may also contribute to the time delay depending on $\Delta T$ and $\langle\theta^{2}\rangle$.

Neutrino echo constraints can be placed without large statistics of neutrino events. If a bright transient occurs, we can even go beyond the mean free path limit without relying on details of neutrino spectra. Nondetection of echoes lead to powerful constraints as long as we only have coincident detections. Possible detections open up a new window for BSM neutrino physics. In the small optical depth limit that is more likely, we could directly measure the differential cross section. In the other limit, the delayed cascaded component accompanied by the strong absorption feature in the neutrino spectrum serves as a testable prediction. The relevant parameter space probed by current and future multimessenger observations of neutrino transients is complementary to those from accelerator and laboratory experiments such as DUNE Farzan and Shoemaker (2016); Ballett et al. (2019) and COHERENT Scholberg (2006); Denton et al. (2018). We demonstrated that our method is particularly powerful for light mediator models, which are extensively discussed in the context of “self-interacting neutrino cosmology” Cyr-Racine and Sigurdson (2014); Escudero (2019); Escudero et al. (2019); Barenboim et al. (2019); Park et al. (2019); Wilkinson et al. (2014) and substructure problems van den Aarssen et al. (2012); Cherry et al. (2014); Tulin and Yu (2018), and has been invoked to explain the muon anomalous magnetic moment Pospelov (2009); Altmannshofer et al. (2014); Araki et al. (2015, 2016); Altmannshofer et al. (2016); Kamada et al. (2018) and neutrino masses Chikashige et al. (1981); Gelmini and Roncadelli (1981); Blum et al. (2014).

We provided intriguing examples for “time domain” multimessenger astroparticle physics, cosmology, and particle physics. BSM tests with neutrino echoes are general and various types of BSM interactions Ackermann et al. (2019a) including the long-range one Bustamante and Agarwalla (2019) could be considered. Neutrino transients (e.g., supernovae) should exist and the proposed method is applicable to lower-energy (e.g., GeV–TeV) neutrino transients including the next Galactic supernova, for which $\sim 100-1000$ events of high-energy neutrinos can be detected in IceCube and KM3Net Murase (2018). Even supernova neutrino bursts in the MeV range will give us useful constraints, because the time delay is $\Delta t\simeq 260~{}{\rm s}~{}{(D/10~{}{\rm kpc})}C^{2}{(m_{\nu}/0.1~{}{\rm eV})}{(E_{\nu}/100~{}{\rm MeV})}^{-1}$. Detections are even more promising for next-generation neutrino detectors such as IceCube-Gen2 Aartsen et al. (2014), KM3Net Adrian-Martinez et al. (2016) and Hyper-Kamiokande Abe et al. (2018). Searches can also be performed for not only a single transient but also “stacked” samples of short duration transients.

Acknowledgements.— We thank Peter Denton, Walter Winter, and an anonymous referee for useful comments. This work is supported by the Alfred P. Sloan Foundation, NSF Grants No. PHY-1620777 and No. AST-1908689 (K.M.), as well as the U.S. Department of Energy under Award No. DE-SC0020250 (I.M.S.). K.M. acknowledges the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe”, and he advanced this project during the workshop in February – March 2018. As the manuscript was being completed, we became aware of a related but independent work Koren (2019).