The On-axis Jetted Tidal Disruption Event AT2022cmc: X-Ray Observations and Broadband Spectral Modeling

AT2022cmc was recently reported as the first on-axis jetted tidal disruption event (TDE) discovered in the last decade, and the fourth on-axis jetted TDE candidate known so far. In this work, we present NuSTAR hard X-ray (3–30 keV) observations of AT2022cmc, as well as soft X-ray (0.3–6 keV) observations obtained by NICER, Swift, and XMM-Newton. Our analysis reveals that the broadband X-ray spectra can be well described by a broken power law with f ν ∝ ν −0.5 (f ν ∝ ν −1) below (above) the rest-frame break energy of E bk ∼ 10 keV at the observer frame t obs = 7.8 and 17.6 days since discovery. At t obs = 36.2 days, the X-ray spectrum is consistent with either a single power law or a broken power law. By modeling the spectral energy distribution from radio to hard X-ray across the three NuSTAR observing epochs, we find that the submillimeter/radio emission originates from external shocks at large distances ≳1017 cm from the black hole, the UV/optical light comes from a thermal envelope with radius ∼1015 cm, and the X-ray emission is consistent with synchrotron radiation powered by energy dissipation at intermediate radii within the (likely magnetically dominated) jet. We constrain the bulk Lorentz factor of the jet to be of the order 10–100. Our interpretation differs from the model proposed by Pasham et al. where both the radio and X-rays come from the same emitting zone in a matter-dominated jet. Our model for the jet X-ray emission has broad implications on the nature of relativistic jets in other sources such as gamma-ray bursts.


INTRODUCTION
An unlucky star coming too close to a massive black hole (BH) gets disrupted by the tidal forces and the subsequent accretion gives rise to a luminous transient.A fraction of such tidal disruption events (TDEs) launch collimated relativistic jets (hereafter jetted TDEs; see De Colle & Lu 2020 for a review).So far, only four jetyuhanyao@berkeley.edu ted TDE candidates with on-axis jets have been found, including three objects discovered by the hard X-ray burst alert telescope (BAT) on board Swift more than a decade ago, Sw J1644+57 (Bloom et al. 2011;Burrows et al. 2011;Levan et al. 2011;Zauderer et al. 2011), Sw J2058+05 (Cenko et al. 2012;Pasham et al. 2015), Sw J1112-82 (Brown et al. 2015(Brown et al. , 2017)).In contrast to the first three events, AT2022cmc was recently discovered by the Zwicky Transient Facility (ZTF) in the optical band (Andreoni et al. 2022;Pasham et al. 2023).
Jetted TDEs form a rare class of transients with limited observational data.They are similar to blazarsactive galactic nuclei with powerful jets beamed towards the observer.However, the broadband spectral energy distribution (SED) of jetted TDEs do not follow the ensemble properties of blazars in the sense that the ratio of X-ray to radio luminosity is extremely high (Cenko et al. 2012).In addition, jetted TDEs might be similar to gamma-ray bursts (GRBs, see Kumar & Zhang 2015 for a review), as both are triggered by super/hyper-Eddington accretion onto BHs that produce jets.In the standard GRB fireball model, the long-lasting afterglow emission comes from external shocks propagating into the ambient medium, whereas the seconds-long prompt γ-ray emission comes from energy dissipation (by e.g., internal shocks or magnetic reconnection) in a region closer to the BH (Zhang 2018).
Among the Swift jetted TDEs, Sw J1644+57 is the most well observed event.Evolution of its millimeter (mm) and radio SED over a decade can be well described by synchrotron emission from an outgoing forward shock (Zauderer et al. 2011;Berger et al. 2012;Zauderer et al. 2013;Mimica et al. 2015;Generozov et al. 2017;Eftekhari et al. 2018;Cendes et al. 2021), indeed similar to GRB afterglows.As the blast wave travels through the circumnuclear medium (CNM), the shock is decelerated and the CNM density decreases, resulting in the peak of the radio SED moving to lower frequencies over time.
Unlike the better-understood radio emission, the site and radiation mechanism(s) of the bright X-ray emission in jetted TDEs remain actively debated.Burrows et al. (2011) showed that the X-ray spectrum of Sw J1644+57 is consistent with synchrotron emission of a particle-starved magnetically-dominated jet, whereas Bloom et al. (2011) found acceptable fits with synchrotron self-Compton (SSC) and external inverse Compton (EIC) models.Reis et al. (2012) detected a 5 mHz quasi-periodic oscillation in X-ray observations of Sw J1644+57, suggesting that the jet production is modulated by accretion variability near the event horizon.Crumley et al. (2016) studied a wide range of emission mechanisms and concluded that the X-ray emission can be produced by either synchrotron emission or EIC scattering off optical photons from the thermal envelope.Kara et al. (2016) found a blueshifted (∼0.1-0.2c)Fe Kα line and the associated reverberation lags in the XMM-Newton data.Different interpretations for the re-flector have been proposed, including a radiation pressure driven sub-relativistic outflow close to the black hole (∼ 30R g where R g is the gravitational radius; Kara et al. 2016;Thomsen et al. 2022a), and a gas layer accelerated by the interaction between the jet X-rays and a thermal envelope (∼ 300R g ; Lu et al. 2017).
AT2022cmc (ZTF22aaajecp) was discovered as a fast optical transient on 2022 February 11 10:42:40 (Andreoni 2022).Shortly afterwards, it was detected by follow up observations in the radio (Perley 2022) and X-ray (Pasham et al. 2022) bands.An optical spectrum obtained by ESO's Very Large Telescope reveals host galaxy lines at the redshift of z = 1.193 (Tanvir et al. 2022).At the cosmological distance, its X-ray and radio luminosities are comparable to Sw J1644+47 at similar phases (Yao et al. 2022a).Further multi-wavelength follow-up observations revealed the remarkable similarities between AT2022cmc and Sw J1644+57, suggesting that AT2022cmc was indeed a jetted TDE (Andreoni et al. 2022;Pasham et al. 2023;Rhodes et al. 2023).In this paper, we adopt this interpretation.
As the only jetted TDE discovered in the last decade, AT2022cmc offers a great opportunity to address several key questions related to the X-ray emission of jetted TDEs, such as the jet composition, the particle acceleration and energy dissipation processes, and the emission mechanisms.By computing the X-ray power density spectrum, Pasham et al. (2023) demonstrated that the rest-frame systematic X-ray variability timescale is t var ≲ 10 3 /(1 + 1.193) s.By requiring that t var exceed the light-crossing time of the Schwarzschild radius of the BH, an upper limit of the BH mass can be derived as Pasham et al. (2023) fitted the radio and soft Xray SEDs of AT2022cmc with SSC/EIC models, concluding that the relativistic jet exhibits a high ratio of electron-to-magnetic-field energy densities.In this work, we present NuSTAR hard X-ray observations, independently analyze the soft X-ray and UV data, and reexamine the broadband SED evolution across nine orders of magnitude in frequency.We follow the physical picture outlined in Andreoni et al. (2022) and propose that the observed broken power-law X-ray spectrum can be explained with a synchrotron origin.
The paper is organized as follows.We describe the observations and data reduction in §2.In §3, we first outline the rationales of treating the broadband radiation with three separate emission components ( §3.1), and then perform model fitting on the sub-mm/radio ( §3.2), UV/optical ( §3.3), and X-ray ( §3.4) SEDs.A discussion is given in §4.
Hereafter we use t obs (t rest ) to denote observer-frame (rest-frame) time relative to the first ZTF detection.We adopt a redshift of z = 1.1933 (Andreoni et al. 2022), a standard ΛCDM cosmology with Ω M = 0.3, Ω Λ = 0.7, and H 0 = 70 km s −1 Mpc −1 .The luminosity distance d L = 8.22 Gpc.We use UT time and the usual notation Q n = Q/10 n , where Q is in CGS units.Uncertainties are reported at the 68% confidence intervals unless otherwise noted, and upper limits are reported at 3σ.

OBSERVATION AND DATA ANALYSIS
All X-ray observations were processed using HEASoft version 6.31.1.X-ray spectral fitting was performed with xspec (v12.13,Arnaud 1996).We used the vern cross sections (Verner et al. 1996) and the Anders & Grevesse (1989) abundances for the X-ray absorption by the neutral hydrogen column along the line of sight.

NuSTAR
We obtained Nuclear Spectroscopic Telescope ARray (NuSTAR; Harrison et al. 2013)  To generate the first epoch's spectra for the two photon counting detector modules (FPMA and FPMB), source photons were extracted from a circular region with a radius of r src = 45 ′′ centered on the apparent position of the source in both FPMA and FPMB.The background was extracted from a r bkg = 80 ′′ region located on the same detector.For the second and third epochs, since the source became fainter, we used r src = 40 ′′ and r src = 35 ′′ , respectively.
All spectra were binned with ftgrouppha using the optimal binning scheme developed by Kaastra & Bleeker (2016).For the first two NuSTAR epochs, we further binned the spectra to have at least 20 counts per bin.First, we ran nicerl2 to obtain the cleaned and screened event files, and ran nicerl3-lc to obtain light )

NICER
Figure 1.X-ray light curve of AT2022cmc in the observerframe 0.3-10 keV.The vertical bands mark epochs of the three NuSTAR observations.For comparison, we also show the 0.3-10 keV X-ray light curve of Sw J1544+57 (Mangano et al. 2016).
curves in the 0.3-1 keV, 1-5 keV, 0.3-5 keV and 13-15 keV bands with a time bin of 30 s. nicerl3-lc estimates the background using a space weather model.For good time intervals (GTIs) where more than four focal plane modules (FPMs) were turned off, we scaled the count rate up to an effective area with 52 FPMs.We removed four obsIDs where the background count rate is NaN, and removed time bins where the 13-15 keV count rate is above 0.1 count s −1 .AT2022cmc was detected above 3σ in both 0.3-1 keV and 1-5 keV in 39 obsIDs.
For the remaining 30 obsIDs, we computed the 3σ upper limits.
For each of the 39 obsIDs with significant detections, we ran nicerl3-spec to extract one spectrum using the default parameters.Using C-statistics (Cash 1979), we fitted each spectrum in the 0.22-15 keV energy range with a combination of source and background models.The source model is an absorbed power-law (i.e., tbabs*ztbabs*zashift*(cglumin*powerlaw) in xspec).The background model includes both X-ray and non-X-ray components 1 .We fixed the Galactic hydrogen-equivalent column density to be N H = 8.88 × 10 19 cm −2 (HI4PI Collaboration et al. 2016), and the host absorption to be N H,host = 10 21 cm −2 , which is the best-fit value found in the first joint spectral analysis (see §2.5.1).When t rest > 10 d, the source flux was too faint to provide stringent constraints on both the powerlaw index and the normalization.Therefore, we further fixed the power-law index Γ = 1.6.Using the best-fit spectral models, we obtained the conversion factors to convert 0.3-5 keV count rate to 0.3-10 keV flux (in both observer frame and the rest frame).Figure 1 shows the resulting NICER light curve.
Using observations contemporaneously obtained with the first two NuSTAR observations (see §2.1), we also produced two NICER spectra to be jointly analyzed with the NuSTAR spectra (see §2.5.1 and §2.5.2).The obsIDs of the NICER data used in this step are shown in Table 1.The source and background spectra were created with nibackgen3C50.Following the screening criteria suggested by Remillard et al. (2022), we removed GTIs with hbgcut=0.05and s0cut=2.0, and added systematic errors of 1.5% with grppha.

Swift/XRT
AT2022cmc was observed by the X-Ray Telescope (XRT; Burrows et al. 2005) on board Swift following a series of ToO requests (submitted by Y. Yao and D. R. Pasham).All XRT observations were obtained under the photon counting (PC) mode.
We generated the XRT light curve using an automated online tool 2 (Evans et al. 2007(Evans et al. , 2009)).For data at t rest < 19 d, we binned the light curve by obsID.For data at t rest > 19 d, we used dynamic binning to ensure a minimum of five counts per bin.Using the same tool, 2 https://www.swift.ac.uk/user objects we also created three stacked XRT spectra for data at t rest < 9 d, 9 < t rest < 19 d, and t rest > 19 d.We then fitted the three spectra using the same absorbed powerlaw model as described in §2.2.From the best-fit models, we obtained conversion factors to convert 0.3-10 keV net count rate to 0.3-10 keV flux (in both observer frame and the rest frame).The XRT light curve is shown in Figure 1.
To generate an XRT spectrum for obsID 15023014 (to be jointly analyzed with the third NuSTAR epoch), we processed the data using xrtproducts.We extracted source photons from a circular region with a radius of r src = 30 ′′ , and background photons from eight background regions with r bkg = 25 ′′ evenly spaced at 80 ′′ from AT2022cmc.The spectrum was first binned with ftgrouppha using the optimal binning scheme (Kaastra & Bleeker 2016), and then further binned to have at least one count per bin.

XMM-Newton
AT2022cmc was observed twice by XMM-Newton as part of our GO program (PI: S. Gezari, obsIDs 0882591301, 0882592101).The first observation took place on 2022 June 6 and lasted ∼ 18 ks, while the second observation occurred on 2022 December 9 and lasted ∼ 21 ks.Since the pn instrument of the EPIC camera has a larger effective area than MOS1 and MOS2, we only analyzed the pn data.The raw data files were processed using the epproc task.Following the XMM-Newton data analysis guide, to check for background activity and generate GTIs, we manually inspected the background light curves in the 10-12 keV band.The source was detected in the first epoch, but not in the second one.
For the first epoch, source photons were extracted from a circular region with r src = 33 ′′ centered on the position of the source.The background was extracted from a r bkg = 45 ′′ region on the same detector.The observation data files were reduced using the XMM-Newton Standard Analysis Software (SAS; Gabriel et al. 2004).The ARFs and RMF files were created using the arfgen and rmfgen tasks, respectively.The resulting EPIC-pn spectrum has ∼ 200 background subtracted counts, at a rate of ∼ 0.023 count s −1 .The spectrum was binned using the optimal binning criteria (Kaastra & Bleeker 2016), ensuring that each bin had at least one count.
For the second epoch, we ran the eregionanalyse task using the same apertures as in the first epoch, and obtained a background-subtracted 3σ upper limit of ∼ 0.006 count s −1 .
For the first epoch XMM-Newton EPIC-pn data, we selected the energy range of 0.35-4.5 keV, where the source spectrum dominates over the background.The data was modeled with an absorbed power-law using Cstatistics.The best-fit model parameters are N H,host = 0.22 +0.31  −0.14 × 10 22 cm −2 , Γ = 1.65 ± 0.14, and cstat/dof = 11/8.Figure 2 displays the spectrum along with the best-fitting model.The X-ray luminosity at this first epoch is L X = 2.08 +0.35  −0.25 × 10 45 erg s −1 .Assuming the same spectrum we estimate the 3σ upper-limit luminosity of the second epoch to be L X < 5.45 × 10 44 erg s −1 .

Joint X-ray Spectral Analysis
Here performed joint spectral analysis between NuS-TAR and soft X-ray observations (NICER or XRT).Data were fitted with χ 2 -statistics for the first two epochs, and with C-statistics for the third epoch.Uncertainties of X-ray model parameters are reported at the 90% confidence level.For all models described below, we included a calibration coefficient (constant; Madsen et al. 2017) between FPMA, FPMB, and NICER (or XRT), with C FPMA fixed at one.

Epoch 1
We chose energy ranges where the source spectrum dominates over the background.For NICER we used 0.3-5.0keV; For NuSTAR FPMA and FPMB we used 3-27 keV.Fitting the data with a single power-law results in a poor fit with a χ 2 over degrees of freedom (dof ) of 302/206 = 1.47.Replacing the single power-law with a broken power-law (bknpower) gives a good fit.This model assumes that the photon energy distribution takes the form n(E)dE ∝ E −Γ1 below a break energy E bk , and that n(E)dE ∝ E −Γ2 where E > E bk .

Epoch 2
We chose energy ranges where the source spectrum dominates over the background.For NICER we used 0.3-4.0keV; For NuSTAR FPMA and FPMB we used 3-24 keV.Similar to what was found in §2.5.1, a single power-law leaves an unacceptable χ 2 /dof of 204/150 = 1.36, whereas a broken power-law describes the data much better (see the middle panel of Figure 3).

Epoch 3
We chose energy ranges where the source spectrum dominates over the background.For XRT we used 0.3-10.0keV.For NuSTAR FPMA and FPMB we used 3-15 keV.Compared with the previous two NuSTAR epochs, AT2022cmc has become much fainter at this observing epoch.Both a single power-law and a double power-law give acceptable fits.First, we model the X-ray spectrum with a double power-law with Γ 1 = 1.5 and Γ 2 = 2.0 (similar to the previous two epochs).The best-fit model parameters are: C FPMB = 0.92 +0.15  −0.13 , C XRT = 0.81 +0.19 −0.25 , N H,host = 0.26 +0.37  −0.25 × 10 21 cm −2 , E bk = 11.7 +3.6 −6.5 keV, and cstat/dof = 140/98.Next, we model the X-ray spectrum with a single power-law.The best-fit model parameters are: C FPMB = 0.92 +0.15  −0.13 , C XRT = 0.68 +0.22 −0.17 , N H,host = 0.56 +0.54  −0.36 × 10 21 cm −2 , Γ = 1.79 +0.18 −0.17 keV, and cstat/dof = 129/98.The bottom panel of Figure 3 shows the single power-law fit, which is favored by the fit statistics.The X-ray luminosity at this epoch is L X = (0.12 ± 0.01) × 10 47 erg s −1 .The top panel of Figure 4 shows the optical data reported in Andreoni et al. (2022, Supplementary table 1).For UV data taken by the Ultra-Violet/Optical Telescope (UVOT; Roming et al. 2005) on board Swift, we stacked a few adjacent obsIDs with uvotimsum to improve the sensitivity, and performed photometry on the stacked images with uvotsource.The bottom panel of Figure 4 shows the results.
We note that the UV and optical photometry exhibits short-timescale (∼ hr-day) wiggles (either due to intrinsic stochastic variability or underestimated systematic uncertainties across multiple instruments).Therefore, to capture the general trend of the photometric evolution, we fit the UV and optical data in each filter with Gaussian process models, following the same procedures described in Yao et al. (2022b).We then infer the photometry at the NuSTAR observing epochs using the best-fit models (shown as the transparent lines in Figure 4).In this work, we analyze radio and sub-mm observations of AT2022cmc reported in Andreoni et al. (2022).Figure 1 shows the time and frequency of the observations.We prepare eight epochs (indicated by the vertical colored bands) of SEDs with good frequency sampling to be analyzed in §3.Since the sub-mm observations were much sparser, we fitted the light curves at five frequencies (indicated by the horizontal grey bands) with Gaussian process models to infer the high-frequency flux densities.The resulting SED at the eight epochs are shown in Figure 6.2023) consider the scenario where the X-ray and radio photons are emitted from the same region at the jet front, whereas the UV/optical emission originates from a quasi-spherical thermal envelope (modeled with a blackbody).In their model 1 (syn-chrotron+SSC), the jet radio synchrotron photons are inverse Compton scattered by relativistic electrons to produce the X-ray emission; in their model 2 (syn-chrotron+EIC), seed photons from a thermal envelope outside the jet are inverse Compton scattered to produce the X-rays.SED fitting was performed at three epochs with good multi-wavelength coverage (t obs = 15-16 d, 25-27 d, and 41-46 d) using the BHjet code developed by Lucchini et al. (2022).Pasham et al. (2023) find that model 1 was favored over model 2.
Figure 7 displays the best-fit synchrotron+blackbody +SSC models from Pasham et al. (2023).Although the 15-16 d model is fitted to data obtained close in time to the second NuSTAR epoch (t obs = 17.6 d), it fails to match the observed optical spectral slope or reproduce the broken power-law shape in the X-ray band.Moreover, both the 25-27 d model and the 41-46 d model significantly under-predict the 30-300 GHz flux, which likely results from the fact that sub-mm data was not included in the SED fitting.Notably, the models are in conflict with the observed 100 GHz light curve of AT2022cmc, which exhibits a slight monotonic decline   3).We show the Galactic and host galaxy absorption corrected X-ray spectra (see §2.5), the Galactic extinction corrected UV/optical data at the NuSTAR observing epochs (solid squares, see §2.6), and the observed radio/sub-mm data at eight epochs from t obs = 5.1 d to 47.7 d (circles, see §2.7 and Figure 6).The dashed grey lines show the blazar sequence from Ghisellini et al. (2017, their Tab. 1).
A novel result from our joint NICER and NuSTAR observations is that the X-ray spectrum exhibits a relatively sharp break (at least in the first two epochs, see Figure 3), whereas the spectra produced by the SSC process are quite smooth (Ghisellini 2013;Zhang 2018).
Given the aforementioned issues of the syn-chrotron+SSC models, hereafter we consider an alternative scenario where the X-ray and radio photons arise from two separate regions, akin to the prompt and afterglow emitting sites observed in GRBs.This physical picture is motivated by the following two arguments.First, the external shock model developed for GRB afterglows has been successfully applied to the radio/mm observations of Sw J1644+57 (Zauderer et al. 2011;Berger et al. 2012;Zauderer et al. 2013;Mimica et al. 2015;Eftekhari et al. 2018;Cendes et al. 2021).Second, the observed host-frame X-ray variability timescale places an upper limit on the size of the X-ray emitting region, R X ≲ cΓ 2 j t var = 1.2 × 10 16 (Γ j /30) 2 cm; and the external shock modeling of the radio SEDs places a lower limit on the size of the radio emitting region, R radio ≳ 10 17 cm (see details in §3.2).The fact that R X and R radio are not consistent indicates that X-ray and radio photons are coming from different regions.
A similar interpretation has also been adopted by several previous works to explain Sw J1644+57 (Crumley et al. 2016;Lu et al. 2017) and AT2022cmc (Andreoni et al. 2022;Matsumoto & Metzger 2023).For the X-ray emission of AT2022cmc, we explore the possibility of a pure synchrotron origin, which is the leading emission mechanism for the GRB prompt emission (Oganesyan et al. 2019; Zhang 2020).

Sub-mm/Radio: External Shock
We use the standard external shock afterglow model (Sari et al. 1998;Granot & Sari 2002) to fit the submm and radio SEDs.Here Γ = 1/ 1 − β 2 is the bulk Lorentz factor of the emitting region.The electrons in the shock are accelerated into a power-law distribution, N (γ e ) ∝ γ −p e for γ e ≥ γ m , where γ m is the minimum Lorentz factor of the relativistic electrons.A fraction ϵ e of the shock energy goes into electrons and a fraction ϵ B of shock energy goes into magnetic energy density.The critical electron Lorentz factor at which syn-chrotron cooling time equals to the dynamical time is γ c .The characteristic synchrotron frequencies for electrons with γ e = γ m and γ e = γ c are denoted as ν m and ν c , respectively.The self-absorption frequency is denoted as ν a , below which the system is optically thick to its own synchrotron emission.
From the observed radio spectra, we infer that the system is in the slow cooling regime, i.e., ν m < ν c .In this regime, one can use spectrum 1 and spectrum 2 of Granot & Sari (2002).At sufficiently early times, ν a ≪ ν m , the synchrotron spectrum is given by (1) where s 1 and s 2 are smoothing parameters, β 1 = 2, β 2 = 1/3, β 3 = (1 − p)/2 are the power-law indices of each segment.At late times, ν m ≪ ν a , and we have where s 4 and s 5 are smoothing parameters, β 2 = 5/2, and β 3 = (1 − p)/2.To smoothly connect the evolution in the two phases, we follow Berger et al. (2012) and use a weighted average where w 1 = (ν m /ν a ) 2 and w 2 = (ν a /ν m ) 2 .As the optically thin part of the spectrum is not well sampled at early times, hereafter we assume p = 3, which is the typical value found in Sw J1644+57 (Cendes et al. 2021).We perform the fit using the Markov chain Monte Carlo (MCMC) approach with emcee (Foreman-Mackey et al. 2013).The best-fit models are shown in Figure 6.For all radio epochs analyzed in this work, w 1 ≫ 1, F ν (ν) ≈ F ν,1 , the observed peak frequency ν p = ν m , and the observed peak specific flux Using equipartition analysis in the relativistic regime (Barniol Duran et al. 2013) Here f V and f A are geometry factors, and η = ν m /ν a .We consider a narrow jet with a half-opening angle of Following Barniol Duran & Piran (2013); Barniol Duran et al. ( 2013) and Eftekhari et al. (2018), we assume ϵ e = 0.1, ϵ B = 10 −3 , and that the kinetic energy of hot protons is 10 times more than the electrons.Defining ξ ≡ 1 + ϵ e = 11, the equipartition radius will be increased by a factor of ξ 1/17 = 1.15 and the total minimal energy will be increased by a factor of ξ 11/17 = 4.72.Defining ϵ ≡ (ϵ B /ϵ e )/(6/11), the actual radius R corresponding to the minimum energy is different from R eq by a multiplicative factor of ϵ 1/17 = 0.79 and the total energy E T is greater than E eq by a multiplicative factor of (11/17)ϵ −6/17 + (6/17)ϵ 11/17 = 2.68.
The magnetic field in the source frame is Γ is related to the emitting radius R by Figure 8 shows the evolution of Γ, R, E T , and B. Similar values have also been obtained with afterglow model fitting performed by Matsumoto & Metzger (2023).The cooling frequency ν c lie in the infrared band.The bestfit afterglow models at the three NuSTAR observing epochs are shown as the dashed lines in Figure 9.

UV/optical: Thermal Envelope
We analyze the Galactic extinction corrected UV and optical photometry, take E B−V,MW = 0.0095 (Schlafly & Finkbeiner 2011), assume R V = 3.1, and adopt the reddening law from (Cardelli et al. 1989).
First, we assume negligible host extinction.The optical (griz) spectral slopes α (for f ν ∝ ν α ) at t obs = 7.8, 17.6, and 36.2 d are 0.06 ± 0.15, 0.40 ± 0.143, and 0.22 ± 0.26, respectively.The optical emission is therefore not an extension of the radio/mm synchrotron SED.In the UV bands, the spectral slope at the second and third NuSTAR epochs are −1.35±0.31and −1.68±0.54.Following Andreoni et al. (2022) and Pasham et al. (2023), we fit the UV/optical SED of AT2022cmc with a blackbody function.The best-fit blackbody radius, temperature, and luminosity are presented in Table 2.The derived parameters can be compared with Sw J2058+05, which is the only previously known on-axis jetted TDE with early-time multi-band optical photometry and negligible/small host extinction.AT2022cmc has blackbody temperatures that are similar to Sw J2058+05 and blackbody radii that are a factor of ∼ 3 greater than that obsevred in Sw J2058+05 (see Figure 10).Next, we assume that the line-of-sight absorption from X-ray and UV/optical are correlated, using the calibra-tion of N H,host = 5.55 × 10 21 × E B−V,host (Predehl & Schmitt 1995).The joint X-ray spectral analysis ( §2.5) shows that N H,host ≈ 10 21 cm −2 at t obs = 7.8 d and decreases by a factor of 2-4 in the next two epochs.This implies an extinction from E B−V,host ≈ 0.18 to 0.05 ≲ E B−V,host ≲ 0.1.The best-fit blackbody models are plotted in Figure 10.As is shown in Table 2, taking host extinction into consideration renders R bb lower by a multiplicative factor of ∼ 1.1, and T bb and L bb greater by multiplicative factors of ∼ 1.3 and ∼ 2.2, respectively.
By fitting the UV/optical SED as a blackbody, we are agnostic of the nature of this thermal component, which might be generated either by energy dissipation in stellar debris self-crossing shocks3 (Piran et al. 2015;Jiang et al. 2016;Huang et al. 2023) or by reprocessing in an optically thick wind (Miller 2015;Metzger & Stone 2016;Dai et al. 2018;Lu & Bonnerot 2020;Thomsen et al. 2022b).A peak blackbody luminosity of L bb ≈ 1045 erg s −1 is on the high end of the bolometric luminosity function of ZTF-selected non-jetted TDEs (see Fig. 14 of Yao et al. 2023).The majority of such UV/optically overluminous TDEs do not exhibit broad emission lines of hydrogen, helium, and nitrogen that are commonly observed in TDEs (van Velzen et al. 2020).Instead, many of them belong to the "TDE-featureless" subclass (Hammerstein et al. 2023;Yao et al. 2023), characterized by blue and featureless continuum emission in rest-frame UV and optical bands.

A Jet Synchrotron Model
We consider an emitting plasma that is moving towards the observer at a bulk Lorentz factor Γ j .The emitting plasma is at a characteristic distance r from the center of ejection, where r is measured in the lab frame.In the comoving frame of the plasma, the size of the causally connected region is r/Γ j .Therefore, we will only consider the emission from a roughly-spherical comoving volume of ∼ (r/Γ j ) 3 -what is beyond this volume cannot be correctly captured by the one-zone model considered here.The transverse size of the emitting region is r/Γ j , defining the area of emission as πr 2 /Γ 2 j , which is the same in the lab and comoving frames.The longitudinal size of the emitting region is r/Γ j in the comoving frame, and r/Γ 2 j in the lab frame due to length contraction.
Hereafter, all primed quantities are measured in the comoving frame of the emitting plasma.We omit the  (Hz) Figure 9. Broadband SEDs of AT2022cmc, as compared to our 3-component best-fit models at the NuSTAR observing epochs.The models include the sub-mm/radio synchrotron component (dashed lines, see §3.2), the UV/optical blackbody component (solid lines, see §3.3), and an example of the X-ray synchrotron component (dotted lines, §3.4).The minimum cooling frequency νc,min and the break frequency ν b are marked by the plus sign and cross sign, respectively.Data are the same as shown in Figure 7.
prime for the electron Lorentz factors (γ and those with subscripts).We assume that the plasma consists of electrons characterized by a broken-power-law distribution of Lorentz factors: where γ b is the break Lorentz factor, n ′ b denotes the comoving number density of electrons with γ ∼ γ b , and p 1 , p 2 are two power-law indices (p 2 > p 1 ).The power-law indices are directly given by the photon indices below and above the break: Γ i = (p i + 1)/2 for i = 1, 2. In the NuSTAR observing epochs, Γ 1 ∼ 1.5 and Γ 2 ∼ 2, indicating that p 1 ∼ 2 and p 2 ∼ 3.
The dynamical timescale t ′ dyn = r/(Γ j c) can be described by the light-crossing time of the causally connected region.We denote the cooling timescale for particles with Lorentz factor γ as t ′ c (γ).If particles are accelerated to a power-law distribution with injection index p above a minimum Lorentz factor γ m on a dynamical timescale and at the same time they undergo (synchrotron+inverse-Compton) cooling, then depending on whether t ′ c (γ m ) is longer or shorter than t ′ dyn , we may have two possible cases (Sari et al. 1998) Case 1: In the "slow-cooling" case, t ′ c (γ m ) > t ′ dyn , p 1 = p, p 2 = p + 1, and γ b = γ c .
Here the cooling Lorentz factor γ c is defined such that t ′ c (γ c ) ≡ t ′ dyn .The observed X-ray spectral shape of AT2022cmc may be consistent with either of the two cases as long as the injection index is p ≈ 2.
The magnetic field strength in the plasma is denoted as B ′ .An electron with a Lorentz factor γ has a characteristic synchrotron frequency of and the peak specific power is given by (see, e.g., Ghisellini 2013) Consequently, the synchrotron emissivity at the break frequency ν ′ b is given by  The intensity at the surface of the emitting plasma is given by , and the lab-frame intensity is . The observed flux density at a distance of d (without considering cosmological effects) is: Therefore, the isotropic equivalent spectral luminosity at the break frequency The radiation energy density at a radius r from the center is and the magnetic energy density is U ′ B = B ′2 /(8π).The break frequency is (cf.Eq. 9) To take into account cosmological effects, we use ν b = ν b,obs (1 + z) and L b,iso = 4πd 2 L ν b,obs F b,obs , where ν b,obs is the observed break frequency, and F b,obs is the measured flux density at the observed break frequency.Suppose a certain mechanism puts a fraction ϵ e of the local energy into non-thermal electrons and another fraction ϵ B of the energy into magnetic fields, we see that ϵ e /ϵ B ≃ U ′ X /U ′ B , because an order unity fraction of the electrons' energy must be radiated in the X-ray band in either Case 1 or 2. For the same energy dissipation mechanism, we may expect the ratio ϵ e /ϵ B to be constant in different epochs, which motivates us to define a single variable If we treat ξ eB as a known, then we have three equations (13, 15, and 16) for five unknowns (Γ j , r, n ′ b , B ′ , γ b ).We can then express three of the unknowns (r, n ′ b , B ′ ) as functions of two independent variables (Γ j , γ b ): Ignoring inverse-Compton cooling which is strongly Klein-Nishina suppressed (to be justified later), we consider the synchrotron cooling timescale The cooling frequency is ν c = Γ j ν ′ (γ c ).

Solutions under Additional Constraints
The system of equations is subjected to some additional constraints.First, we have an upper limit for the X-ray variability timescale t var = t ′ dyn /Γ j .Second, there is a lower limit to the cooling frequency (ν c > ν c,min ) so as to avoid the low-frequency tail of the synchrotron emission overproducing the thermal optical emission (see the dotted lines in Figure 9).Third, in either the slow-or fast-cooling cases, the cooling frequency must not exceed ν b .Next, the X-ray emitting radius must not exceed the emitting radius of the radio afterglow, which is constrained to be of the order 10 17 cm from §3.2, so we require r < 10 17 cm.Finally, the X-ray emitting radius should be outside of the photosphere of the UV/optical thermal envelope (to be justified later).
A consequence of the high bulk Lorentz factor is that, if the X-ray emission occurs below the optical photospheric radius r opt ∼ 10 15 cm ( §3.3), the external radiation field will contribute a rather high energy density in the jet's comoving frame where τ opt is the Rosseland-mean optical depth of the gas that is responsible for the thermal optical emission and L opt ∼ 10 45 erg s −1 is the optical luminosity.Notably, the ratio U ′ opt /U ′ X = τ opt Γ 4 j L opt /L b,iso ≫ 1.Such a high radiation energy density would lead to a very short cooling timescale: where the Klein-Nishina effects have been included here via the correction factor Y KN ≤ 1, and E ′ opt = Γ j E opt ≃ 10Γ j eV is the average photon energy in the comoving frame.By comparing the cooling time to the dynamical time t ′ dyn = r/(Γ j c) = 667 s r 15 (Γ j /50) −1 , it becomes evident that at small radii r ≲ r opt ∼ 10 15 cm, the intense radiation field of optical photons will rapidly cool relativistic electrons in the jet down to γ ≈ 1.Thus, these low-Lorentz-factor electrons on their cooling track to γ ≈ 1 will unavoidably overproduce the optical emission because ν c,min will be below the optical band (cf. Figure 9).
Alternatively, if the X-ray emission is generated above the optical photosphere, the optical photons will move nearly parallel to the jet's motion.According to Lorentz transformation, this leads to a considerable reduction in the energy density U ′ opt in the jet's comoving frame.As a result, a highly relativistic broken power-law electron population can exist.Therefore, a requirement of r > r opt is necessary for the synchrotron model to remain viable.As can be seen in in Figure 11, this constraint eliminates a substantial portion of the parameter space.
Finally, we return to the question of the physical identification of the X-ray break frequency ν b .
In the slow-cooling case, we have ν c = ν b > ν m and the solutions lie on the upper right edge of the surviving parameter space shown as red solid lines in Figure 11.In different epochs, we find Γ j ∼ 100 and γ c = γ b ∼ 10 5 .In this case, we require ν m > ν c,min so as to avoid overproducing the UV/optical emission.We also require ν m < 10 17.2 Hz which corresponds to observer-frame 0.3 keV, otherwise we should have observed two energy breaks in the X-ray band.This means that 0.1 ≲ γ m /γ b ≲ 0.2 or γ m ∼ 10 4 .The exact constraints on Γ j and γ m are presented in Table 3.
If the electrons are accelerated by internal shocks within a baryonic jet, γ m ∼ m p /m e Γ rel ϵ e , where Γ rel is the relative Lorentz factor between two colliding shells.When Γ rel ≳ 10, acceleration by internal shocks is possible.A magnetically dominated jet with high magnetization is also plausible, as long as the magnetic en-ergy in the average volume per electron is as high as γ m m e c 2 .For instance, if the jet is made of protonelectron plasma and particles are initially cold in the comoving frame, then the magnetization is given by σ ≃ B ′2 /(8π)/(n ′ m p c 2 ), and as long as σ ∼ γ m m e /m p ≳ 10, our solution is plausible.
In the fast-cooling case, we have ν m = ν b > ν c .Since only one energy break was observed in the X-ray band, we have ν c,min < ν c < 10 17.2 Hz, and the solutions lie within the regions marked by the dashed blue lines in Figure 11.In different epochs, we find the bulk Lorentz factor to be smaller than in the slow-cooling case, 20 ≲ Γ j ≲ 90, and the minimum Lorentz factor for particle acceleration to be greater, γ m = γ b ∼ 10 5 .Such a high γ m disfavors internal shocks within a baryonic jet.
A magnetically dominated jet with high magnetization σ ∼ 100 is a plausible solution.
Now that we have reasonable solutions for the Lorentz factor of the electrons radiating near the break frequency γ b ∼ 10 5 , we go back to the question whether their cooling is dominated by synchrotron (as assumed in Eq. 20) or synchrotron-self-Compton.The typical energy of the X-ray photons in the electron's rest frame is This leads to a large Klein-Nishina suppression factor of Y KN ∼ (m e c 2 /E ′ X ) 2 ∼ 10 −3 (for fiducial parameters in the above expression) for the inverse-Compton scattering power as compared to the case of Thomson scattering.This means that synchrotron-self-Compton cooling rate is a factor of Y KN ξ eB ≪ 1 smaller than synchrotron cooling rate, so Eq. ( 20) is justified.
Unfortunately, current observations cannot break the degeneracy between the two cases.Additional knowledge about the particle number density (or magnetization) in the jet is needed -this piece of information may be obtained if the source is at a closer distance such that we detect the synchrotron self-Compton emission in the high-energy gamma-ray band.

DISCUSSION
Using NICER, Swift, and XMM-Newton, we constructed the 0.3-10 keV X-ray light curve of the onaxis jetted TDE AT2022cmc, which roughly follows L X ∝ t −2 (Figure 1) in the first ∼ 10 months of evolution.At late time during the X-ray evolution of other on-axis jetted TDEs, a sudden flux drop has been observed in both Sw J1644+57 (at rest-frame days since discovery t rest ≈ 370 days; Zauderer et al. 2013) and Sw J2058+05 (t rest ≈ 200 days; Pasham et al. 2015), which has been explained by a jet shut-off as the accretion flow transitions from a supercritical thick disk to a geometrically thin disk state (Tchekhovskoy et al. 2014).Such a disk instability triggered state transition is naturally predicted as a result of the decreasing mass accretion rate (Shen & Matzner 2014;Lu 2022), and has recently also been observed in the non-jetted TDE AT2021ehb (Yao et al. 2022b).Future Chandra X-ray monitoring observations of AT2022cmc will reveal if the luminosity continues to follow the power-law decay and verify the existence of such a disk state transition.
AT2022cmc is the first on-axis jetted TDE ever observed with NuSTAR.Joint X-ray spectral analysis between NuSTAR and NICER reveals a broken powerlaw spectral shape.We interpret the X-rays as synchrotron emission generated by internal dissipation within the jet.The inferred jet Lorentz factor Γ j ∼ 50, which is higher than the Γ j ≈ 10 estimated in Sw J1644+57 (Bloom et al. 2011).Unfortunately, our current model does not constrain the physical opening angle of the jet, which may be wider than 1/Γ j ≃ 1 • (Γ j /50).For instance, the jet opening angles of GRBs are typically much wider than 1/Γ j for their high Lorentz factors Γ j ≳ 100 (Frail et al. 2001).However, jets in jetted TDEs must be strongly beamed because of their low rates.
The rate of on-axis jetted TDEs with prompt Xray luminosity above 10 48 erg s −1 has been estimated to be 0.03 +0.04  −0.02 Gpc −3 yr −1 from Swift/BAT (Sun et al. 2015).The volumetric rates of TDEs with soft X-ray and UV/optical thermal emission above 10 43 erg s −1 is ∼ 230 Gpc −3 yr −1 and ∼ 310 Gpc −3 yr −1 , respectively (Sazonov et al. 2021;Yao et al. 2023).Given the recent infrared discovery of a sample of mid-IR TDE candidates in nearby galaxies (Jiang et al. 2021) and another nearby heavily dust-extincted TDE (Panagiotou et al. 2023), we assume that a comparable fraction of TDEs are missed by soft X-ray/optical time domain surveys, implying a total TDE rate of the order ∼ 10 3 Gpc −3 yr −1 .This means that only a very small fraction, ∼ 3 × 10 −5 , of TDEs have bright, on-axis jet X-ray emission.Part of the reason for this small fraction is the beaming factor of jets f b > πΓ −2 j /2 = 6 × 10 −4 (Γ j /50) −2 , but we see that beaming alone does not account for the low detection rate of jetted TDEs.In fact, less than a few percent of TDEs are intrinsically jetted -possibly due to the lack of a strong magnetic flux (Tchekhovskoy et al. 2014;Kelley et al. 2014) or slow black hole spins (Andreoni et al. 2022) in most cases, or a large fraction of jets are hydrodynamically choked by the surrounding gas (De Colle et al. 2012).

Figure 3 .
Figure 3. From top to bottom: the X-ray spectrum at three epochs.NuSTAR/FPMB, NICER, and XRT data have been divided by CFPMB, CNICER, and CXRT respectively.The data have been rebinned for visual clarity.

Figure 4 .
Figure 4.Optical and UV photometry of AT2022cmc.The transparent lines are simple Gaussian process fits in each filter, where the width of the lines represent 1σ model uncertainties.The vertical bands mark periods of the three NuSTAR observations.

Figure 5 .
Figure 5. Radio/mm observing time and frequency reported in Andreoni et al. (2022).Detections are shown in solid circles and upper limits are shown as hollow circles.We fitted the light curves in five frequencies (33.5, 86, 102, 225, and 347 GHz) over the time range indicated by the vertical grey bands to infer the flux densities at the epochs with dense low-frequency coverage (marked by the vertical colored bands).

3.
BROADBAND SED MODELING 3.1.Preliminary Considerations Since Pasham et al. (2023) is the only previous work that have modeled the radio-to-X-ray SED of AT2022cmc, we briefly summarize their results here.

Figure 6 .
Figure6.Radio SED of AT2022cmc, overplotted with the best-fit afterglow models (see §3.2).Solid circles (with the black edge color) are measurements; Hollow circles are inferred from Gaussian process fitting of radio light curves in the corresponding frequencies.

Figure 7 .
Figure7.Broadband SEDs of AT2022cmc, as compared to the best-fit synchrotron+blackbody+SSC models (solid lines) fromPasham et al. (2023, their Fig. 3).We show the Galactic and host galaxy absorption corrected X-ray spectra (see §2.5), the Galactic extinction corrected UV/optical data at the NuSTAR observing epochs (solid squares, see §2.6), and the observed radio/sub-mm data at eight epochs from t obs = 5.1 d to 47.7 d (circles, see §2.7 and Figure6).The dashed grey lines show the blazar sequence fromGhisellini et al. (2017, their Tab.1).

Figure 8 .
Figure 8. Evolution of physical properties inferred by fitting the sub-mm/radio SEDs.

Figure 10 .
Figure10.UV/optical SEDs of AT2022cmc at three epochs, overplotted with the best-fit blackbody models assuming various values of host extinction E B−V,host .The lower right panel shows best-fit blackbody models of Sw J2058+05(Pasham et al. 2015, their Tab.5).

Figure 11 .
Figure 11.The colormaps show the parameter space for three epochs of NuSTAR observations that satisfy νc,min < νc ≤ ν b , r < 10 17 cm, r > ropt, and the limits on tvar.ξeB = 1 is assumed.The orange lines show constant values of log(tvar/s), and the olive lines show constant values of log(r/cm).The solid red lines along the upper right edge of the colormaps mark the parameter space in the slow cooling solution, where νc = ν b .The dashed blue lines mark the parameter space in the fast cooling solution, where νm = ν b .
observations under a pre-approved Target of Opportunity (ToO) program (PI: Y. Yao; obsID 80701510002) and Director's Discretionary Time (DDT) programs (PI: Y. Yao; obsIDs 90801501002, 90802306004).The three epochs of observations are summarized in Table 1.The first two NuS-TAR observations were conducted jointly with NICER, and the last NuSTAR observation was conducted jointly with Swift/XRT.

Table 1 .
Log of X-ray Observations Used in Joint Spectral Analysis.Note-The last column is the mean net count rate within the energy range where the source is above background.For NuSTAR observations we show the total count rate in the two optical modules (FPMA and FPMB).

Table 2 .
Best-fit Parameters of the Thermal Envelope.