In many models, the sources of ultra-high-energy cosmic rays (UHECRs) are assumed to accelerate particles to the same maximum energy. Motivated by the fact that candidate astrophysical accelerators exhibit a vast diversity in terms of their relevant properties such as luminosity, Lorentz factor, and magnetic field strength, we study the compatibility of a population of sources with non-identical maximum cosmic-ray energies with the observed energy spectrum and composition of UHECRs at Earth. For this purpose, we compute the UHECR spectrum emerging from a population of sources with a power-law, or broken-power-law, distribution of maximum energies, applicable to a broad range of astrophysical scenarios. We find that the allowed source-to-source variance of the maximum energy must be small to describe the data if a power-law distribution is considered. Even in the most extreme scenario, with a very sharp cutoff of individual source spectra and negative redshift evolution of the accelerators, the maximum energies of 90\% of sources must be identical within a factor of three -- in contrast to the variance expected for astrophysical sources. Substantial variance of the maximum energy in the source population is only possible if the maximum energies follow a broken power-law distribution with a very steep spectrum above the break. However, in this scenario, the individual source energy spectra are required to be unusually hard with increasing energy output as a function of energy. 

/pdf/curious-case-of-the-maximum-rigidity-distribution-of-cosmic-2q61oh6l.pdf

Curious case of the maximum rigidity distribution of cosmic-ray accelerators


 The equipartition analysis yields estimates of the radius and energy of synchrotron self-absorbed radio sources. Here we generalize this method to relativistic off-axis viewed emitters. We find that the Lorentz factor Γ and the viewing angle θ cannot be determined independently but become degenerate along a trajectory of minimal energy solutions. The solutions are divided into on-axis and off-axis branches, with the former reproducing the classical analysis. A relativistic source viewed off-axis can be disguised as an apparent Newtonian one. Applying this method to radio observations of several tidal disruption events (TDEs), we find that the radio flare of AT 2018hyz, which was observed a few years after the optical discovery, could have been produced by a relativistic off-axis jet with a kinetic energy of $\sim 10^{53}\, \rm erg$ that was launched around the time of discovery.

/pdf/generalized-equipartition-method-from-an-arbitrary-viewing-1yzum9yp.pdf

Generalized equipartition method from an arbitrary viewing angle

In many models, the sources of ultra-high-energy cosmic rays (UHECRs) are assumed to accelerate particles to the same maximum energy. Motivated by the fact that candidate astrophysical accelerators exhibit a vast diversity in terms of their relevant properties such as luminosity, Lorentz factor, and magnetic field strength, we study the compatibility of a population of sources with non-identical maximum cosmic-ray energies with the observed energy spectrum and composition of UHECRs at Earth. For this purpose, we compute the UHECR spectrum emerging from a population of sources with a power-law, or broken-power-law, distribution of maximum energies, applicable to a broad range of astrophysical scenarios. We find that the allowed source-to-source variance of the maximum energy must be small to describe the data if a power-law distribution is considered. Even in the most extreme scenario, with a very sharp cutoff of individual source spectra and negative redshift evolution of the accelerators, the maximum energies of 90\% of sources must be identical within a factor of three -- in contrast to the variance expected for astrophysical sources. Substantial variance of the maximum energy in the source population is only possible if the maximum energies follow a broken power-law distribution with a very steep spectrum above the break. However, in this scenario, the individual source energy spectra are required to be unusually hard with increasing energy output as a function of energy.

We present an analysis of the optical and UV properties of AT 2020wey, a faint and fast tidal disruption event (TDE) at 124.3 Mpc. The light curve of the object peaked at an absolute magnitude of $M_{g} = -17.45$ mag and a maximum bolometric luminosity of $L_{\rm peak}=(8.74\pm0.69)\times10^{42}$ erg s$^{-1}$, making it comparably faint with iPTF16fnl, the faintest TDE to date. The time from the last non-detection to the $g$-band peak is 22.94 $\pm$ 2.03 days and the rise is well described by $L\propto t^{1.8}$. The decline of the bolometric light curve is described by a sharp exponential decay steeper than the canonical $t^{-5/3}$ power law, making AT 2020wey the fastest declining TDE to date. Multi-wavelength fits to the light curve indicate a complete disruption of a star of $M_*=0.11M_{\odot}$ by a black hole of $M_{\rm BH}=10^{6.46}M_{\odot}$. Our spectroscopic dataset reveals broad ($\sim10^{4}$ km s$^{-1}$) Balmer and He II $\lambda$4686 lines, with H$\alpha$ reaching its peak with a lag of $\sim8.2$ days compared to the continuum. In contrast to previous faint and fast TDEs, there are no obvious Bowen fluorescence lines in the spectra of AT 2020wey. There is a strong correlation between the MOSFIT-derived black hole masses of TDEs and their decline rate. However, AT 2020wey is an outlier in this correlation, which could indicate that its fast early decline may be dictated by a different physical mechanism than fallback. After performing a volumetric correction to a sample of 30 TDEs observed between 2018 and 2020, we conclude that faint TDEs are not rare by nature and that they should constitute up to $\sim$ 50 - 60 % of the entire population and their numbers could alleviate some of the tension between the observed and theoretical TDE rate estimates. We calculate the optical TDE luminosity function and we find a steep power-law relation $dN/dL_{g} \propto {L_{g}}^{-2.36}$.

AT 2020wey and the class of faint and fast tidal disruption events

Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function, dṄTDE/dL , which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L −2.5 for high luminosities, provided that the SMBH mass function dN•/dM• —the number of SMBHs (N •) per SMBH mass (M •)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. If dN•/dM• is flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, if dN•/dlogM• is flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension.

https://iopscience.iop.org/article/10.3847/2041-8213/acd0b2/pdf

The Luminosity Function of Tidal Disruption Events from Fallback-powered Emission: Implications for the Black Hole Mass Function

The high-cadence survey of the Zwicky Transient Facility (ZTF) has completely dominated the discovery of tidal disruption events (TDEs) in the past few years and resulted in the largest sample of TDEs with optical/UV light curves well sampled around their peaks, providing us an excellent opportunity to construct a peak luminosity function (LF) of tidal disruption flares (TDFs). The new construction is necessary particularly considering that the most updated LF reported in literature has been inferred from only 13 sources from five different surveys. Here we present the optical and blackbody LFs calculated by 33 TDFs discovered in the ZTF-I survey. The optical LF can be described by both a power-law profile dN/dLg∝Lg−2.3±0.2 , and a Schechter-like function. The blackbody LF can be described by a power-law profile dN/dLbb∝Lbb−2.2±0.2 , shallower than the LF made of the previous van Velzen (2018) sample. A possible low-luminosity turnover in the optical LF supports an Eddington-limited emission scenario. The drop of the volumetric rate at high luminosity suggests a rate suppression due to direct captures of the black hole. The total volumetric rate is 1 order of magnitude lower than the previous estimation, which is probably not simply caused by the high fraction postpeak sources (7/13) in the previous sample. Instead, the normalization step during the previous LF construction to reconcile various surveys might adversely amplify the influence of serendipitous discoveries. Therefore, TDFs selected from ongoing and upcoming uniform surveys like ZTF, Vera Rubin Observatory, and the Wide-Field Survey Telescope should yield more accurate LFs.

The Luminosity Function of Tidal Disruption Flares for the ZTF-I Survey

We report the discovery of a faint optical tidal disruption event (TDE) in the nearby star-forming galaxy NGC 3799. Identification of the TDE is based on its position at the galaxy nucleus, a light curve declining as t^-5/3, a blue continuum with an almost constant blackbody temperature of ~12,000K, and broad (~15,000kms^-1) Balmer lines and characteristic He~II 4686A emission. The light curve of AT 2023clx peaked at an absolute magnitude of -17.16mag in the g-band and a maximum blackbody bolometric luminosity of 4.56*10^42 ergs^-1, making it the faintest TDE discovered to date. With a redshift of 0.01107 and a corresponding luminosity distance of 47.8Mpc, it is also the closest optical TDE ever discovered to our best knowledge. Furthermore, our analysis of Swift/XRT observations of AT 2023clx yields a very tight 3 sigma upper limit of 9.53*10^39 ergs^-1 in the range 0.3--10keV. AT 2023clx, together with very few other faint TDEs such as AT 2020wey, prove that there are probably a large number of faint TDEs yet to be discovered at higher redshifts, which is consistent with the prediction of luminosity functions (LFs). The upcoming deeper optical time-domain surveys, such as the Legacy Survey of Space and Time (LSST) and the Wide-Field Survey Telescope (WFST) will discover more TDEs at even lower luminosities, allowing for a more precise constraint of the low-end of the LF.

AT 2023clx: the Faintest and Closest Optical Tidal Disruption Event Discovered in Nearby Star-forming Galaxy NGC 3799


 Research into OJ 287 has been ongoing for many years. In 2020 April–June, this source underwent the second highest X-ray outburst (second only to the 2016–2017 outburst) and the mechanism of this outburst is still under debate. In this paper, we discuss two scenarios to explore the origin of the outburst: an after-effect of a black hole–disc impact and a tidal disruption event (TDE). We present the weak correlations of the spectral index versus X-ray flux and the hardness ratio (HR) versus the soft X-ray flux during the outburst, and these features are different from the case in the quiescent state. The correlations are compared with those of the 2016–2017 outburst with the highest X-ray flux in monitoring history. Analysis of the outbursts in 2016–2017 and 2020 shows that the expected time of the X-ray outburst, based on the theory of the after-effect of the black hole–disc impact and the estimation of available data, is inconsistent with historical observations. The soft X-ray spectra, the barely temporal evolution of colour, and the evolution of the HR mean that the 2020 outburst shares similar features with the 2016–2017 outburst, which was considered as a possible candidate for a TDE. Additionally, we find that the predictions of full TDEs (t−5/3) and partial TDEs (t−9/4) for the soft X-ray decay light curve are well fitted. Our analysis suggests that the 2020 outburst in OJ 287 is probably related to the TDE candidate.

/pdf/exploration-of-the-origin-of-the-2020-x-ray-outburst-in-oj-3eji75x0.pdf

Shifeng Huang

Papers

The Luminosity Function of Tidal Disruption Flares for the ZTF-I Survey

AT 2023clx: the Faintest and Closest Optical Tidal Disruption Event Discovered in Nearby Star-forming Galaxy NGC 3799

Exploration of the origin of the 2020 X-ray outburst in OJ 287