# Ultra High Energy Cosmic Rays from Tidal Disruption Events

T. Piran,11footnotetext: Corresponding author. and P. Beniamini

###### Abstract

The tidal disruption event AT2018hyz, was a regular optically detected one
with no special prompt features. However, almost three years after the
disruption it suddenly displayed a fast-rising radio flare. The flare is most
naturally interpreted as arising from an off-axis relativistic jet. We didn’t
see the jet at early times as its emission was relativistically beamed away
from us. However, we could see the radiation once the jet has slowed down due
to interaction with the surrounding matter. Analysis of the radio data enabled
estimates of the jet’s kinetic energy and its opening angle as well as the
conditions (size and magnetic field) within the radio-emitting region. We show
here that such a jet satisfies the Hillas condition for the acceleration of
UHECRs to the highest energies. We also show that the rate and total power of
this event are consistent with the observed luminosity density of UHECRs.
These results strongly support earlier suggestions that TDEs are the sources
of UHECRs.

##  1 Introduction

Ultra-high energy cosmic rays (UHECRs) with energies up to $10^{20}$eV were
first detected more than sixty years ago. Still, their sources of are unknown,
making them one of the most interesting astronomical puzzles. The conditions
for accelerating particles to such high energies, the Hillas criteria [1],
imply that the sources must be very luminous. At the same time photopion
production of UHECRs protons on the CMB or photodissociation of nuclei limit
their propagation distances to about 100 Mpc (for the highest energy UHECRs).
Thus the luminous sources must be local and easily identified. However,
deflection in the intergalactic and our own Galactic magnetic fields divert
UHECRs from their original directions. This of course complicates the
identification of the sources. As there are no specific directions from which
UHECRs accumulate there is no single dominant source. A lack of correlation
with any known population of luminous sources suggests that the sources might
be transients. Indeed two transient sources: flaring Active Galactic Nuclei
(AGNs) [2] and Gamma-ray Bursts (GRBs) [3, 4] have been proposed.

GRBs satisfy the Hillas criteria. However, their total power is small by at
least one order of magnitude compared to the rate of production of UHECRs
(e.g. [5]). Recent upper limit [6] on the neutrino flux from the nearby and
powerful GRB 221009A, put an independent strong limit on UHECR production by
this source and GRBs in general [7]. Tidal disruption events (TDEs) are
natural transients that take place typically around dormant super massive
black holes in galactic centers. A fraction of TDE eject relativistic jets.
Already the first detected jetted TDE (Swift J1644) revealed that the shocks
arising from the interaction of the jet with the surrounding matter, a process
resembling a GRB afterglow, satisfy the Hillas condition for UHECR
acceleration [8].

We explore here the possibility that TDEs are the sources of UHECRs, in view
of recent developments in observations and theory of TDEs. In particular, we
consider the implication of recent observations of some jetted TDEs and we
explore again the question wherther those relativistic jets satisfy the Hillas
criteria and whether the total power of TDEs is sufficient to supply the
observed flux of UHECRs. We begin (in 2) with a very brief summary of
observational features of UHECRs (2.1) and of jetted TDEs (2.2). We continue
(in 3) with a discussion of the Hillas criteria and the conditions within
shocks produced due to the interaction of TDE jets with the surrounding
matter. We discuss (in 4) the rates of jetted TDEs and the implied luminosity
density of these sources. We conclude in 5, summarizing our findings and
possible future confirmation of these ideas.

##  2 Observations

###  2.1 UHECRs

We begin with a brief description of basic properties of UHECRs (see [9] and
references therein for further details). $\bullet$ The UHECR energy extends up
to $\sim 10^{20}$ eV. The spectrum shows an “ankle" at 5 EeV and strong
suppression is observed above 50 EeV. $\bullet$ The UHECRs luminosity density
above 5 EeV is ${\cal L}_{\rm UHECR}=6\times 10^{44}$ erg Mpc-3 yr-1 [10].
$\bullet$ The composition above the ankle is dominated by nuclei. The nuclei
become heavier as the energy increases and they are mostly CNO or heavier
above $40$ EeV [11]. $\bullet$ The only significant departure from isotropy is
the $6.9\sigma$ dipole at energies above 8 EeV [12]. At lower energy the
observations are compatible with isotropy. No clear association with any
population of sources have been identified 222Note, however, that diffusion in
the intergalactic and Galactic magnetic fields may divert significantly UHECRs
trajectories away from the direction of their original source (see e.g. [13,
14, 15, 16, 17, 18]).

###  2.2 Jetted TDEs

Out of about a hundred TDEs, several have been identified as harboring
relativistic jets [19]. The identification was generally made, following the
first TDE with an identified jet, Swift J1644, by a prompt non-thermal prompt
non-thermal X-rays [20, 21]. Likely due to obscuration, optical emission was
not observed in Sw J1644. Radio emission, detected within a few days [22]
provided further support for a relativistic jet. Sw J2058 [23] and Sw J1112
[24] are two other jetted TDEs detected by Swift. Multiwavelength emission,
including non-thermal X-rays was observed from AT2022cmc [25], suggesting that
it also included a jet. Recently, Matsumoto and Piran [26] (see also [27]
proposed a new way to identify off-axis TDE jets. These authors proposed that
the late radio flare observed in AT2018hyz indicated an off-axis jet [26, 27],
opening the venue to identify relativistic jets that are pointing away from
us.

##  3 Hillas limits from late radio observations

###  3.1 The Hillas criterion

Already in 1984, Hillas [1] compared the minimal acceleration time to the
escape time and obtained a necessary condition for the maximal energy, $\cal
E$, to which a source can accelerate a particle. In the simplest version of
this condition, we have

${\cal E}=ZeBR\beta\Gamma\ \ \ {\rm or}\ \ \ \ \frac{\cal E}{\rm eV}\approx
300Z\big{(}\frac{B}{\rm Gauss}\big{)}\big{(}\frac{R}{\rm
cm}\big{)}\beta\Gamma\ ,$ (3.1)

where B is the magnetic field (measured in the rest frame), R is the size of
the source, $\beta$ and $\Gamma$ are the source velocity and its corresponding
Lorentz factor and Z is the charge of the accelerated particle.

Clearly the condition 3.1 should be considered carefully within each model.
For example the factor $\beta$ might not be relevant if the source is static.
When considering jets, it is possible, depending on details of the
acceleration process, that the accelerated particles escape sideways [9]. This
shortens the escape time by a factor $\theta$, the opening angle of the jet.
In this case, we have:

${{\cal\tilde{E}}}=ZeBR\beta\Gamma\theta\ \ \ {\rm or}\ \ \ \
\frac{{\cal\tilde{E}}}{\rm eV}\approx 300Z\big{(}\frac{B}{\rm
Gauss}\big{)}\big{(}\frac{R}{\rm cm}\big{)}\beta\Gamma\theta\ .$ (3.2)

These estimates of the magnetic field and the size of the system imply
associated luminosities of $L>8.4\times
10^{44}Z^{-2}\Gamma^{2}({\cal\tilde{E}})/(10^{20}{\rm eV})^{2}\mbox{erg
s}^{-1}$ (e.g. [9]). The sources are extremely powerful if UHECRs are protons.
Less powerful, but still noticeable within local distances, if UHECRs are
heavier nuclei.

###  3.2 Late radio observations of TDEs

Late radio observations enable us to identify jets whose prompt emission is
not observed. By now about half a dozen TDEs have displayed late ratio flares.
Among those, the rapid rise of the radio emission in AT2018hyz several years
after the event [28, 29] suggests that this TDE harbored a powerful
relativistic jet that was pointing away from us [26, 27].

In this case the late radio emission is generated by relativistic particles
accelerated in shocks between the jet material and the surrounding circum-
nuclear matter. These observations are a calorimetric tool that enables us to
measure the actual energy (not just the isotropic equivalent energy) of these
jets. In some cases, they also enable a determination of the jet’s opening
angle. With detailed modeling of the radio emission, we can also reveal the
conditions within these jets and explore whether they satisfy the Hillas
criteria.

In the following, we focus on the analysis of the radio emission from two of
those jets: Sw J1644, the first discovered and best followed jetted TDE and
AT2018hyz, which is an example of an “off-axis" one in which prompt emission
was not observed. We also consider the implications of the jet observed in
AT2022cmc.

Swift J1644 was the first identified jetted TDE. Its initial unique gamma-rays
signal showed rapid variability, suggesting that it was a white dwarf that was
disrupted [30]. The prompt non-thermal gamma-rays and X-ray from the galactic
nucleus [21, 20] were followed by a strong radio signal [22] confirming the
original suggestion that the event involved a relativistic jet. The radio
light curve was surprising as it increased during the first few hundred days.
Equipartition analysis revealed that the energy of the outflow that produced
this radio signal increased by a factor of ten with time [31, 32, 33]. While
it was suggested that this is due to a structured jet with significant energy
within wings [34, 35], a simpler self-consistent explanation is that Sw J1644
was a slightly off-axis jet [36]. Namely, while the jet width was $\sim
21^{o}$ our viewing angle was $\sim 30^{o}$. The observed radio signal
increased as the relativistic jet’s beam expanded sideways and more radiation
was beamed towards us as the jet slowed down.

The model developed in [36] considers, for simplicity, a relativistic ‘top-
hat’ jet with opening angle $\theta_{0}$ that has a uniform kinetic energy per
unit solid angle. The jet decelerates due to its interaction with the external
medium (assumed to have a radial profile $n\propto r^{-k}$) and its dynamics
can be described analytically in two limiting cases, one in which the jet is
assumed to spread sideways at a velocity of order the speed of sound (maximal
lateral spreading) and the other in which the jet maintains its initial
opening angle until it becomes Newtonian (no lateral spreading).

The forward shock driven by the blast wave into the circum-nuclear matter
amplifies the magnetic field and accelerates electrons to relativistic
velocities, causing them to radiate their energy via synchrotron and
synchrotron self-Compton. The temporal evolution of the flux at a given
frequency band can then be calculated for an observer at an arbitrary viewing
angle relative to the jet using the appropriate Doppler factor corrections.
The model is uniquely described (at all times and frequencies) by a set of 9
parameters, three associated with the jet, $E_{\rm
k,iso},\Gamma_{0},\theta_{0}$ (the jets’ isotropic equivalent kinetic energy,
its initial Lorentz factor and angular width) three describe the microphysics,
$p,\epsilon_{\rm B},\epsilon_{\rm e}$ (the power-law index of the electron’s
distribution, and the magnetic and electronic equipartition parameters), two
characterize the surrounding environment, $k,n(R_{0})$ (the power-law index of
the external density and its normalization) and one identifies the viewing
angle, $\theta_{\rm v}$. The multi-band observations can then be fit with this
model to constrain these model parameters.

Remarkably, the conditions found within these shocks are suitable for
accelerating UHECRs. Namely, these shocks are among the few astronomical
sources that satisfy the Hillas criteria for accelerating particles up to
$10^{20}eV$. In particular, Beniamini et al., [36] modeled the light curve of
Sw J1644 at several radio frequencies and estimated the emitting region’s
magnetic fields and size. This model gives us $B,R,\Gamma$ and $\theta$ as a
function of time. Fig. 1 depicts the factor $B\Gamma R$ for the shocks in Sw
J1644. This result confirms earlier findings [8] that the shock between the
jet and the circum-nucleus gas of the host galaxy satisfies the Hillas
criteria (with $E=10^{20}$ eV even for protons).

Figure 1: The different Hillas criteria with (right) and without (left)
particles being able to escape sideways (Eqs. 3.1 and 3.2) respectively, for
Sw J1644 and for AT2018hyz. For AT 2018hyz two estimates are shown,
corresponding to different assumptions concerning the isotropic equivalent
energy.

As mentioned earlier, it is not clear whether the accelerated particles can
escape sideways from the jet. If they do, the Hillas condition is modified
(see Eq. 3.2). The right panel of Fig. 1 depicts $B\Gamma R\theta$ the Hillas
condition when allowing for sideways escape of accelerated particles. In this
case, the values are lower and the shock cannot accelerate protons to the
highest observed energies, $\sim 10^{20}$ eV. However, it is capable of
accelerating heavier nuclei to this energy. When the jet angle is taken into
account, the factor $BR\Gamma\theta$ increases sharply at around 300 days.
This is because the best-fit model for this event involves a jet that isn’t
spreading significantly during the relativistic phase. The late rise at 300
days, is approximately when the jet becomes Newtonian and starts spreading
sideways quickly.

AT2018hyz was an optically detected TDE located at $z=0.0457$. Its prompt
signature didn’t show non-thermal emission corresponding to a jet and early
radio signal was not detected. A surprising rapidly rising radio flare was
detected from AT 2018hyz 972 days after optical discovery [28, 29]. The
initial interpretation was of a delayed launching of a jet [28]. However,
following an off-axis equipartition analysis [26], Sfaradi et al. [27] have
recently shown that an off-axis jet launched at the time of the optical
discovery was a natural self-consistent interpretation of the radio data. We
didn’t see the prompt emission in AT2018hyz as it is beamed away from us. As
the shock decelerated, it moved into our line of sight. At the same time, it
accumulated more and more emitting electrons. It is for this reason that the
radio signal increased so rapidly. This interpretation implies that the jet in
AT2018hyz was very powerful with $E_{k}\geq 3\times 10^{52}$ erg and an
opening angle of $\sim 7^{o}$. The jet that was launched at the time of the
stellar disruption (or shortly after that) was at $\sim 42^{o}$ to our line of
sight.

The magnetic field in AT2018hyz is uncertain. This arises since, for the best-
fit model for AT2018hyz, most of the data corresponds to a single spectral
band of the synchrotron spectrum - leading to a well-understood degeneracy
between magnetic field, isotropic equivalent energy and external density (see
[27] for details). Still, the magnetic field can be bounded from below. A
lower magnetic field (a lower $\epsilon_{B}$) requires a larger total energy.
Considering two possible values of the total energy $6\times 10^{52}$ erg and
$6\times 10^{53}$ erg (the latter can be regarded as a safe upper limit), we
present in Fig. 1 the two possible estimates for the Hillas conditions Eq. 3.1
and 3.2. Like in Sw J1644, if sideways escape of the accelerated particles is
negligible, the shocks in AT2018hyz can accelerate even protons to
$10^{20}$eV. If sideways escape is significant, the shocks can still
accelerate nuclei (with $Z\geq 10$) to this energy, even when considering the
lower values for the magnetic field.

Fig. 1 shows that for off-axis jets, the optimal conditions for UHECR
acceleration are obtained when the jet comes into view of the observer
($\Gamma\approx 1/\theta_{\rm v}$ for far off-axis jets). As such, there could
be a delay of several hundred days between the optical TDE and the peak of
UHECR production from such sources. This delay is irrelevant as UHECR
diffusion between the source and Earth results in much longer delays. However,
it is important when considering the association with possible secondary
neutrinos.

AT2022cmc was a third jetted TDE [25]. It was a rather distant event, located
at $z=1.19$. Its implied isotropic equivalent energy was $10^{53}-10^{54}$
erg. If viewed on-axis, there is no clear estimate of the opening angle.
However, the 15 GHz radio light curve during the first 100 days (in the rest
frame) resembles the one of Sw J1644 [37]. Lacking further data, we note the
possibility that this is also a slightly off-axis jet but adopt in the rest of
the text, the original interpretation [25], that it was viewed on-axis.

##  4 Rates and total emitted power density

###  4.1 Rates

The overall rate of optical TDEs is estimated as $\mathcal{R}\approx
10^{-6}\mbox{ Mpc}^{-3}\mbox{ yr}^{-1}$ [38]. However, the question what is
the rate of jetted TDEs is much more subtle as those are fewer and detection
selection effects are more dubious.

For a given jetted TDE event, we can use its distance (corresponding to a
cosmological redshift $z_{\rm ob}$ and volume $V_{\rm ob}$ within which there
is at least one event), the observation time during which similar events could
have been detected ($T_{\rm ob}$) and the sky coverage fraction ($f_{\rm
sky}$) of the relevant telescope/s to estimate the intrinsic rate of such
events. Since events generally get dimmer with increasing viewing angle, this
estimate can be considered as an approximate estimate of similar events with
$\theta<\theta_{\rm v}$, (where $\theta_{\rm v}$ is the viewing angle to the
event considered). Therefore, we can write

$\mathcal{R}_{j}\approx 0.7\frac{(1+z_{\rm ob})}{f_{\rm sky}V_{\rm ob}T_{\rm
ob}(1-\cos\theta_{\rm v})}$ (4.1)

where we have assumed that intrinsically the events are double-sided jets
(such that $\theta_{\rm v}<\pi/2$) and that the intrinsic rate of events does
not strongly evolve with redshift (TDEs are observed from relatively low
redshifts). For clarity, we have also approximated
$\int^{z^{\prime}}(dV/dz)(1+z)^{-1}dz\approx V(z^{\prime})/(1+z^{\prime})$
which is a good approximation for the range of redshifts from which TDEs are
observed.

Applying the estimate given by Eq. 4.1 to Sw J1644 (with $z_{\rm ob}=0.35$,
$T_{\rm ob}\approx T_{Swift}\approx 20\mbox{ yr}$, $f_{\rm sky}=f_{\it
Swift}\approx 0.1$, $\theta_{\rm v}\approx 0.5$), we find
$\mathcal{R}_{1644}\approx 3\times 10^{-10}\mbox{ Mpc}^{-3}\mbox{ yr}^{-1}$.
During this time Swift-BAT detected two other TDE jet candidates, Sw J2058 and
Sw J1112 [23, 24]. However, since the distance to those events was
significantly larger than that of Sw J1644, they are sub-dominant in their
contribution to the estimated rate.

The estimate given by Eq. 4.1 can also be applied to radio-monitored
optically-discovered TDE jet candidates such as AT2018hyz. Taking $z_{\rm
ob}=0.045$, $T_{\rm ob}\approx T_{\rm ZTF}\approx 5\mbox{ yr}$, $f_{\rm
sky}=f_{\rm ZTF}\approx 0.6$, $\theta_{\rm v}\approx 0.85$ we get
$\mathcal{R}_{hyz}\gtrsim 2\times 10^{-8}\mbox{ Mpc}^{-3}\mbox{ yr}^{-1}$.
This is very likely a lower limit, considering that it requires an optical TDE
candidate to have long-duration radio follow-up observations.

AT2022cmc provides another constraint on the rate of jetted TDEs. The
estimated observed rate of AT2022cmc-like events with ZTF is
$\mathcal{R}_{cmc}\approx 2\times 10^{-11}(1-\cos\theta_{\rm v})^{-1}\mbox{
Mpc}^{-3}\mbox{ yr}^{-1}$ [25]. AT2022cmc’s 100GHz light curve is
monotonically declining in time from the earliest observations at $t\gtrsim
10$ days after its onset. This motivated modeling it as being viewed on-axis
[25] (see also [39]). More recently, observations at 5-30 GHz [37] show a
slowly rising light curve between 5-100 days after onset. Such a rise could,
in principle, be attributed to an observed band being below the synchrotron
injection frequency at the time of observations (see Fig. 7 of [36]).
Comparison of their results to the lightcurve of Sw 1644, suggests that
AT2022cmc is consistent with being viewed slightly off-axis. Considering an
opening angle $\theta_{\rm j}\approx 0.1$ and an on-axis viewing angle, we
find that $\mathcal{R}_{cmc}\approx 4\times 10^{-9}\theta_{\rm
j,-1}^{-2}\mbox{ Mpc}^{-3}\mbox{ yr}^{-1}$. This estimate would increase if
the event were observed slightly off-axis, as the radio afterglow suggests.
Further radio data is required for a detailed analysis.

We find three different estimates of the rate, ranging from $3\times
10^{-10}$Mpc-3 yr-1 to $2\times 10^{-8}$Mpc-3 yr-1. Namely, a fraction of
$10^{-4}$ to $10^{-2}$ of jetted out of total TDEs. The large range is
surprising, even given the small number statistics involved. It may indicate a
somewhat different nature of the three TDEs. The least certain of these is the
rate associated with AT2022cmc, which depends on an unknown beaming factor and
could end up being comparable to either of the other two rates. Furthermore,
it is possible that AT2018hyz-like events are indeed much more common than Sw
J1644-like events. This is because we have no detections of early X-ray and
$\gamma$-ray emission from AT2018hyz. If similar jets, as viewed by far off-
axis observers, are initially extremely dim in these bands, this would explain
why they could be lacking from the Swift sample despite being intrinsically
common. Finally, it is worth considering that if AT2018hyz was an on-axis
event, as suggested by [28], the rate implied from Eq. 4.1 (and hence the
apparent discrepancy with Sw J1644) would have been even greater, by perhaps
two orders of magnitude.

###  4.2 Power density estimates

Using the rates above, we can estimate the energy input per unit volume and
time from a population of jets for which these events are representative. The
best fit model for Sw J1644 and AT2018hyz, suggest collimated-corrected
kinetic energy of $E_{\rm k,1644}=7\times 10^{52}\mbox{ erg}$ [36], $E_{\rm
k,hyz}=6.5\times 10^{52}\mbox{ erg}$ [27] 333Cendes et al. [28] suggested that
AT2018hyz was an on-axis outflow with late time energy injection. The minimal
electron and magnetic energy they estimate, using equipartition analysis, is
$\sim 6\times 10^{49}$ erg. The true kinetic energy of the outflow in an
energy injection scenario is typically significantly larger considering: (i) A
factor of $\sim 10$ conversion from electron and magnetic energy to kinetic
energy; (ii) The equipartition analysis does not account for a self-consistent
evolution of the spectral frequencies and peak flux (see [36] and [27] for
details) and as such it under-predicts the required energy (for example by not
accounting for the fact that the synchrotron spectrum is likely deep in the
slow cooling regime, and the radiated energy is therefore much smaller than
the energy stored in the electrons). Since in both the late energy injection
and the off-axis interpretation, the peak of AT2018hyz is obtained at a mildly
relativistic stage, the energy required for the two scenarios should be
similar. This means that the volumetric energy injection rate would be larger
by one over the beaming factor for the late energy injection scenario, which
could correspond to an overall estimate of the energy injection rate greater
by up to two orders of magnitude.. For AT2022cmc, we use the kinetic energy
estimate of [25], $E_{\rm k,cmc}\approx 1.5\times 10^{51}\theta_{\rm
j,-1}^{2}\mbox{ erg}$. Putting this together we have:

$\displaystyle E_{\rm k}\mathcal{R}\approx\left\\{\begin{array}[]{ll}2.2\times
10^{43}\mbox{erg Mpc}^{-3}\mbox{ yr}^{-1}&\mbox{Sw J1644}\ ,\\\ 1.4\times
10^{45}\mbox{erg Mpc}^{-3}\mbox{ yr}^{-1}&\mbox{AT2018hyz}\ ,\\\ 6\times
10^{42}\mbox{erg Mpc}^{-3}\mbox{ yr}^{-1}&\mbox{AT2022cmc}.\end{array}\right.$
(4.5)

The results are summarized in table 1.

Table 1: A comparison of rates and energy input rate of the three different
TDEs

TDE | Sw J1644a | AT2018hyzb | AT2022cmcc
---|---|---|---
Red Shift | 0.35 | 0.0457 | 1.19
Kinetic energy (erg) | $7\times 10^{52}$ | $6.5\times 10^{52}$ |  $1.5\times 10^{51}$ d,e
Rate (Mpc-3yr-1) | $3\times 10^{-10}$ | $2\times 10^{-8}$ |  $4\times 10^{-9}$ d
Energy input rate (erg Mpc-3yr-1) | $2.2\times 10^{43}$ |  $1.4\times 10^{45}$ f |  $6\times 10^{42}$ d,e

a. From [36]. b. From [27]. c. From [25], (see also [39]). d. The rate and the
kinetic energy depend on the assumed jet opening angle. However, the energy
input rate doesn’t depend on it, if the jet was viewed on-axis. e. The energy
and energy input rate will be slightly larger if the event was observed
slightly off-axis. f. The rate and the overall energy injection rate will be
larger by up to two orders of magnitude if interpreted within the late jet
scenario of [28].

##  5 Conclusions

Detailed modeling of TDEs radio emission have shown that jetted TDEs are
capable of accelerating UHECRs nuclei to the highest observed energies.
Depending on the nature of the acceleration process, these jets may even be
able to accelerate protons (if there is no sideways escape from the jet).
These recent results confirm the earlier findings [8] on this question.

The situation is more complicated concerning the luminosity density. Here, the
estimates based on Sw J1644 are about an order of magnitude below ${\cal
L}_{\rm UHECR}$, and an even lower estimate is obtained from AT2022cmc.
However, At2018hyz sheds a different light on this issue. While the lower
limit estimate for its kinetic energy is comparable to the kinetic energy
estimate of Sw J1644, because of its small redshift its implied event rate
hundred times larger. With these parameters the estimated luminosity density,
$1.4\times 10^{45}$ erg Mpc-3yr-1 is sufficient to produce the observed UHECR
flux, making jetted TDEs a viable candidate for UHECR sources candidate.

It is interesting to compare jetted TDEs and GRBs as potential UHECR sources.
Remarkably in both cases, the acceleration model is rather similar. The shocks
produced in the interaction of the jetted TDEs with the surrounding matter are
similar to GRBs afterglows’ shocks444Within GRBs UHECR acceleration can also
take place within the internal shocks. (note that the GRB jets have a higher
Lorentz factor). Both events have a comparable rate. However, it seems that
the jetted TDEs are more energetic, making their total energy input comparable
to the required ${\cal L}_{\rm UHECR}$.

As TDEs are transient and as diffusion of UHECRs prolongs their travel from
sources to Earth and also diverts them from their original directions, we
cannot expect a direct identification of an excess of UHECRs with a TDE.
However, indirect evidence could arise from the detection of a secondary high-
energy neutrino that could be produced by an interaction of a UHECR with the
ambient matter of radiation field. Interestingly, some evidence for an
association of high-energy neutrinos with TDEs has already been found [40,
41].

To conclude, we have shown here that TDE jets satisfy the Hillas criteria.
Evidence from an off-axis jet observed in AT2018hyz suggest that these jets
are also carry sufficient power to produce the whole flux of UHECRs above 5
EeV. As new data on TDEs are accumulating rapidly now and with the realization
that we can identify jetted once via their late radio flares we can expect to
rule out or support this model by further observations of other TDEs that will
improve the current poor statistics.

## Acknowledgments

We acknowledge support from an Advanced ERC grant MultiJets (TP) and grant no.
2020747 from the United States-Israel Binational Science Foundation (PB).

## Data Availability

No new data was generated in this research. Details about modeling the light
curve of off-axis TDE are given in [36] and [27].

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