Could TDE outflows produce the PeV neutrino events?

On 22 September 2017, IceCube reported a neutrino event with energy $\sim 290\ \rm TeV$, which was shown to be associated with the blazar TXS 0506+056 (Telescope et al., 2018). This opened a window of high energy neutrino astrophysics. The origin of high energy neutrinos is not clear yet, and TDEs are the other possible sources.

Recently, Stein et al. (2021) reported a correlation between a neutrino event with energy $\sim$0.2 PeV detected by IceCube on 1 October 2019 (IceCube-191001A) and a TDE (AT2019dsg) discovered by Zwicky Transient Facility (ZTF), and the neutrino event lags the onset of TDE by 6 months. AT2019dsg’s redshift is $z=0.051$, i.e., the luminosity distance is $D=230$ Mpc. The optical luminosity was observed to decrease from $10^{44.5}\rm erg\ s^{-1}$ to $10^{43.5}\rm erg\ s^{-1}$ (van Velzen et al., 2021) on a timescale of a half year. AT2019dsg is among the top 10% of the 40 known optical TDEs in luminosities. The peak radiation is well described by a $10^{14}\rm cm$-sized blackbody photosphere of temperature $10^{4.59}$ K. AT2019dsg is an unusual TDE (Hayasaki, 2021); it belongs to neither the typical soft-X-ray TDEs nor the typical optical/UV TDEs because it emits optical/UV radiations as well as X-ray and radio radiations. Fermi Large Area Telescope (Fermi-LAT) provides an upper limit of flux $1.2\times 10^{-11}\rm erg\ cm^{-2}\ s^{-1}$ in 0.1-800 GeV range. HAWC observatory also set an upper limit for the period from 30 September to 2 October, $E^{2}\Phi=3.51\times 10^{-13}(\frac{E}{\rm TeV})^{-0.3}\rm TeV\ cm^{-2}\ s^{-1}$ for 300 GeV-100 TeV (van Velzen et al., 2021).

In the previous literatures (e.g., Wang & Liu 2016; Liu et al. 2020), a jet from the TDE is assumed to accelerate protons and generate neutrinos via p$\gamma$ interactions, dominating over pp interactions since the density of photons is extremely high. Moreover, in the TDE model by Murase et al. (2020) high-energy neutrinos and soft gamma-rays may be produced via hadronic interactions in the corona, the radiatively inefficient accretion flows and the hidden sub-relativistic wind.

It is known that, in addition to the radiative outburst, TDE is also expected to launch ultra-fast and energetic outflows. First, due to the relativistic apsidal precession, after passing the pericenter, the stream collides with the still falling debris, leading to a collision-induced outflow (Lu & Bonnerot, 2020). Second, after debris settling into an accretion disk, the high accretion mode will launch energetic outflows (Curd & Narayan, 2019). Since the duration of both processes above are of the order of months, the duration of launching energetic TDE outflows is also roughly in months. For AT2019dsg, the physics of the outflow is estimated via radio emission. The velocity inferred in different models are similar: 0.07 c in outflow–circumnuclear medium (CNM) interaction model Cendes et al. (2021), or 0.06–0.1c in outflow–cloud interaction model (Mou et al., 2022)). However, the outflow energy or kinetic luminosity of outflows ranges a lot in different models. Cendes et al. (2021) estimated an energy of $4\times 10^{48}$ erg, which is much smaller than the energy budget of the TDE system ($\sim 10^{53}$ erg). Mou et al. (2022) inferred that the outflow power should be around $10^{44}$ erg s^-1 which is consistent with numerical simulations (Curd & Narayan, 2019), and the total energy should be in the order of $10^{51}$ erg if the outflow continues for months.

When the outflow impacts a cloud, the bow shock (BS) can be produced outside the cloud, and could effectively accelerate particles via diffusive shock acceleration (DSA) processes. The electrons accelerated at BSs give rise to synchrotron emission, which can be detected in $\sim$GHz radio band (Mou et al., 2022). The accelerated high energy protons may be the precursor of the neutrinos, especially considering the high-density cloud near the BS which is favorable for pp collisions (Mou et al., 2021). A basic premise is whether there are clouds around the black hole, especially at the distance of $10^{-2}$ pc as inferred from the delay of the neutrino event and the possible outflow speed. It is well known that for active galactic nuclei (AGN), there exists a so-called broad line region (BLR) around the supper massive black hole (SMBH) (Antonucci, 1993), which is frequently referred to as “clouds”. However, for quiescent SMBH or low-luminosity AGN (the case for AT2019dsg), due to the lack of ionizing radiation irradiating the clouds, the existence of the clouds becomes difficult to verify, and the physics of such clouds remains largely unknown.

To distinguish from the BLR cloud concept in AGN, we hereby call the possibly existing clouds around quiescent or low-luminosity SMBH at similar position of the BLR as “dark clouds”. Transient events may help reveal the physics of dark clouds. For AT2019dsg, in addition to the indirect speculation of the existence of dark clouds via radio emission (Mou et al., 2022), direct evidences arise from the dusty echo, and broad emission line components. First, van Velzen et al. (2021) reported that AT2019dsg was detected with remarkable infrared echo about 30 days after the optical onset, suggesting that clouds should exist at a distance of 0.02 pc to the SMBH (note that there may exist clouds in more inward regions but not surveyed by WISE/neoWISE). Second, it is reported that there exist the broad emission line components (line widths $>$ 70 Å) of H$\alpha$, H$\beta$, and HeII (Cannizzaro et al., 2021), implying the existence of materials of the velocity over several thousand kilometers per second, although their nature is unclear. In our TDE outflow-cloud interaction model, we assume that there exist dark clouds at $\sim 0.01$ pc to the BH, and we simply set up the parameters (covering factor, cloud size and density) of dark clouds similar referring to those of classical BLR clouds.

This paper is organized as follows. We introduce the general physics picture of the model in Sec. 2; The products (GeV-TeV gamma-rays and PeV neutrinos) from hadronic emission are described in Sec. 3; In Sec. 4, we compare the calculations with the present observations; The conclusions and discussion are presented in the last section.

As shown in Fig. 1, consider that there are dark clouds surrounding the SMBH.The TDE outflows released from the SMBH collide with the dark clouds, forming two shock waves (McKee & Cowie, 1975), i.e., a bow shock (BS) outside the cloud and a cloud shock (CS) sweeping through the cloud. Following Celli et al. (2020), protons may be accelerated to very high energy with a power-law distribution. The high-energy protons may partly propagate into the cloud and interact with matter therein.

In the outflow–cloud interaction, the kinetic energy of the outflow will be converted into the BS and CS. The energy ratio between the CS and BS is $\chi^{-0.5}\simeq 0.034$, so the energy dissipation in the CS can be neglected compared to the BS (see appendix A in Mou & Wang 2021).

The covering factor of the clouds is $C_{\rm v}\sim 0.1$, and the shock acceleration efficiency, i.e., the fraction of the shock energy converted to accelerated particles, is $\eta\sim 0.1$. Given the kinetic energy of the outflow, the average luminosity of the accelerated particles is, in the BS,

and in the CS,

Plugging the numbers, $L_{\rm c}\approx 3.4\times 10^{41}\rm erg\ s^{-1}$, and $L_{\rm b}\approx 10^{43}\rm erg\ s^{-1}$ for $\eta=0.1$. The luminosity of CSs is so small, which allow us to neglect their contribution in emission.

We assume the accelerated relativistic particles distribute as a power-law spectrum with spectral index $\Gamma$ and an exponential cut-off at the high energy:

The normalization factor $K_{\rm p}$ can be determined by the normalization of the particle luminosity $L_{\rm p}=\int E_{\rm p}\frac{dn(E_{\rm p})}{dE_{\rm p}}dE_{\rm p}$. Since neglecting contribution from the CS, we have $L_{\rm p}=L_{\rm b}$. We will consider a range of $\Gamma$ value, from 2 to 1.5 (Celli et al., 2020).

The pp collision produce neutral and charged pions,

where $a\approx b$. The pions decay and generate $\gamma$-rays and leptons:

The final product particles produced by pp collisions in the clouds per unit time on average can be given by (e.g. Kamae et al., 2006; Aartsen et al., 2014):

where f$=\gamma,\nu$, etc., represents the type of final particles, $\sigma$ is the inclusive cross section as function of final particles and proton’s energy, and $n_{\rm H}$ is the background number density of protons. The coefficient 1.5 is a correction factor accounting for the contribution of Helium (we assume that the Helium abundance in the BS is similar to Galactic cosmic rays (Mori, 1997)). Here the integration is calculated using the cparamlib package²²2https://github.com/niklask/cparamlib. If the particle escape from the cloud is fast, the calculated spectrum above should be multiplied by a factor $\frac{\tau_{\rm es}(E_{\rm p})}{t_{\rm pp,CS}}$ to take into account the reduction of secondary products by escape.

We summarize in Table 1 the fiducial values for the model parameters used in the calculation. The neutrino luminosity is presented in Fig. 3. According to equation 16, we get the expected event number of 0.1-1PeV neutrinos detected by IceCube. Without considering the partile escape from cloud, the expected number is $7.1\times 10^{-3}$, $2.3\times 10^{-3}$, $7.6\times 10^{-4}$, and $3.8\times 10^{-4}$ for $\Gamma=1.5$, 1.7, 1.9 and 2, respectively. However, if consider particle escape, as described by equation 6, the numbers change to $3.5\times 10^{-3}$, $1.3\times 10^{-3}$, $4\times 10^{-4}$, and $1.9\times 10^{-4}$, respectively. Thus, for the fiducial model parameters, the expected neutrino event number is somewhat lower than the expected neutrino number of $0.008\lesssim N_{\nu}\lesssim 0.76$ for AT2019dsg (Stein et al., 2021).

The interactions produce $\gamma$-rays from GeV to TeV energy bands. Considering the host galaxy distance of 230 Mpc, the photons above $\sim 100$ TeV cannot arrive at the Earth due to the absorptions by CMB and EBL. In addition, the strong absorption by the host galaxy photon field based on the infrared observations (Skrutskie et al., 2006) is moderate. Finally, the $pp$ processes produce the maximum $\gamma$-ray flux up to $\sim 10^{-13}\ \rm erg\ cm^{-2}\ s^{-1}$ for $\Gamma=1.5-2$ in the bands of 0.1 GeV - 1 TeV, which is lower than the present gamma-ray observational limits by Fermi/LAT and HAWC (see Fig. 4).

In this work, we considered the high-speed TDE outflows colliding with the clouds to produce the high-energy neutrinos and gamma-rays, which can explain the sub-PeV neutrino event in AT2019dsg. The assumed outflow velocity is $V_{\rm o}\sim 0.07\rm c$ and the kinetic luminosity is $L_{\rm kin}\sim 10^{45}\rm erg~{}s^{-1}$. The outflow-cloud interactions will produce the BS ahead clouds. Particle acceleration is efficient in the BS and the pp process would contribute to the observational high energy neutrinos and gamma-rays. We assumed an escaping parameter of $F=0.5$, which means half of the accelerated protons escape from the BS region while the rest enter the dense cloud participating in pp collisions. Here we should point out that the escaping parameter of $F$ cannot be constrained well, leading to the $F$ values being quite uncertain, and the factor $F$ may be taken as a much smaller value in the more realistic cosmic-ray escape models.

For the fiducial model parameters, the expected neutrino event number would be relatively low compared to observations. In order to reach the observational neutrino number, one has to invoke some challenging model parameters. For instance, (1) considering a higher cloud density or a larger cloud size, inducing the escaping time $\tau_{\rm es}$ will be much higher than $t_{\rm pp,CS}$ (see equation 6) and the interactions of protons which produce 0.1-1 PeV neutrinos becomes more efficient, the expected number of neutrinos would increase by a factor of $\sim 2$ (see Fig. 3); (2) the converting fraction of energy from the outflow to protons relies on the covering factor of BS $C_{\rm v}$, and shock acceleration efficiency $\eta$, so the expected number of neutrinos could increase by a factor of $\sim 10(C_{\rm v}/0.3)(\eta/0.3)$ by taking a larger $C_{\rm v}$ and a larger $\eta$ than the fiducial values listed in Table. 1. For sure, on the contrary, the expected neutrino number could be reduced if a lower cloud column density, smaller $C_{\rm v}$ and $\eta$, or a softer proton index is adopted. As a result, the predicted neutrino number in our model depends on the uncertainties of model parameters and in order to match the observations, some challenging values of parameters have been involved.

In above calculations, we anchored two parameters of the outflows, the kinetic luminosity $L_{\rm kin}=10^{45}\rm erg~{}s^{-1}$ and the velocity of outflows $V_{\rm o}=0.07\rm c$. Numberical simulations indicate that TDE can launch powerful wind with a kinetic luminosity of $10^{44-45}$ erg s^-1 (Curd & Narayan, 2019), or even higher (Dai et al., 2018). AT2019dsg also exhibits radio flares, arising fifty days post burst and lasting for more than one year (Stein et al., 2021; Cendes et al., 2021). Modeling the radio flare by the outflow-CNM (circumnuclear medium) model suggests that the averaged kinetic luminosity is $10^{43}$ erg s^-1 (Stein et al., 2021) or even lower (Cendes et al., 2021). However, if the radio flare originates from outflow-cloud interaction which is the same scenario as our current model, the inferred kinetic luminosity may be in the order of $10^{44}$ erg s^-1 (Mou et al., 2022). Radio outflow and delayed neutrino may be explained by the same physical process. The detected neutrino number is linearly proportional to the kinetic luminosity. For the case of $L_{\rm kin}=10^{44}\rm erg~{}s^{-1}$, the modeling neutrino luminosity is presented in Fig. 5. The expected neutrino number will be about one order of magnitude lower than the above values in the case of $L_{\rm kin}\sim 10^{45}\rm erg~{}s^{-1}$.

The velocity of the outflow is taken as $V_{\rm o}=0.07\rm c$, but this value is still uncertain, the radio observations suggested the outflow velocity in AT2019dsg is $V_{\rm o}=0.12\rm c$ (Stein et al., 2021), 0.07c (Cendes et al., 2021) or around 0.1c (Mou et al., 2022). If the outflow velocity is higher, the maximum energy of accelerated protons in the BS will be also higher accordingly. Then the peak neutrino luminosity will move to the higher energy ranges. If we integrate the neutrino number from $0.1-1$ PeV, the detected neutrino number would be different. For a comparison, we also plotted the neutrino luminosity versus energy in the case of $L_{\rm kin}=10^{44}~{}\rm{erg~{}s^{-1}}$, $V_{\rm o}=0.12\rm c$ in Fig. 5. Since we only integrate the neutrino number in the range of $0.1-1$ PeV, if $V_{\rm o}$ is about 0.04c, and $E_{\rm p,max}\sim 20$ PeV, the neutrino SED will peak at $0.1-1$ PeV, and the expected number of neutrinos will increase by $50\%$.

After the submission of this work, we notice recent reports on more neutrino events associated with the time-variable emission from accreting SMBHs (van Velzen et al., 2021; Reusch et al., 2021), among which AT2019fdr is a TDE candidate in a Narrow-Line Seyfert 1 AGN in which the BLR clouds should exist. Moreover, the neutrino events lag the optical outbursts by half year to one year (van Velzen et al. 2021), consistent with the assumption that clouds exist at the distance of $\sim 10^{-2}$ pc from the central BH if the outflow velocity is in the order of $10^{9}$ cm s^-1. The outflow–cloud interaction may also contribute to the high energy neutrino background (Abbasi et al., 2021).

We are grateful to the referee for the useful suggestions to improve the manuscript. This work is supported by the National Key Research and Development Program of China (Grants No. 2021YFA0718500, 2021YFA0718503), the NSFC (12133007, U1838103, 11622326, 11773008, 11833007, 11703022, 12003007, 11773003, and U1931201), the Fundamental Research Funds for the Central Universities (No. 2020kfyXJJS039, 2042021kf0224), and the China Manned Space Project (CMS-CSST-2021-B11).

The data used in this paper were collected from the previous literatures. These data X-ray, gamma-ray and neutrino observations are public for all researchers.